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2008-12-10T13:46:28+08:00
TeX output 2008.12.03:1051
2011-07-07T12:15:09+08:00
2011-07-07T12:15:09+08:00
dvipdfm 0.13.2c, Copyright © 1998, by Mark A. Wicks
application/pdf
Group key management for wireless networks.
Teo, Joseph Chee Ming.
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[(supp)-27(ort)-334(regarding)-333(m)27(y)-332(studies.)]TJ
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[(I)-302(w)26(ould)-302(also)-302(lik)26(e)-301(to)-303(thank)-303(Prof.)-434(Lo)26(w)-302(Chor)-302(Ping,)-309(Head,)-309(Division)-303(of)-303(Information)-303(Comm)27(unication)]TJ
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T*
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T*
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[(2.1.3)-1144(Bilinear)-334(Maps)-333(from)-333(Elliptic)-334(Curv)27(e)-332(P)27(airings)-852(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-928(19)]TJ
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T*
[(2.2.2)-1144(RSA)-334(Problem)-413(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-928(20)]TJ
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[(2.2.3)-1144(Discrete)-334(Logarithm)-333(Problem)-1000(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-929(20)]TJ
188.1 -27.65 Td
(vi)Tj
ET
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endstream
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[(Computational)-334(Di\261e-Hellman)]TJ
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(CDH)Tj
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[(2.2.5)-1144(Decisional)-334(Di\261e-Hellman)]TJ
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25.08 -13.55 Td
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[(2.4.2)-1144(Infrastructureless)-334(Wireless)-333(Net)27(w)28(orks)-618(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-929(32)]TJ
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[(2.4.3)-1144(Hybrid)-334(Net)27(w)28(orks)-571(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-928(35)]TJ
T*
[(2.4.4)-1144(Inheren)27(t)-333(Characteristics)-333(of)-333(Wireless)-334(Net)27(w)28(orks)-429(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-929(36)]TJ
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[(2.5)-1022(Key)-333(Establishmen)27(t)-333(Concept)-535(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-928(39)]TJ
25.08 -13.54 Td
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25.08 -13.54 Td
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[(2.7)-1022(Examples)-333(of)-333(Group)-334(Key)-333(Managemen)27(t)-333(Proto)-27(col)-793(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-928(46)]TJ
25.08 -13.55 Td
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T*
[(2.7.2)-1144(Hyp)-28(ercub)-28(e)-333(and)-333(Octopus)-334(Proto)-28(cols)-746(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-929(46)]TJ
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[(2.7.11)-644(Kim-Lee-Lee)-334(Group)-333(Key)-333(Agreemen)27(t)-333(Proto)-28(cols)-964(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-929(58)]TJ
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T*
[(2.7.13)-644(Other)-334(GKA)-333(proto)-28(cols)-333(in)-333(Curren)26(t)-332(Literature)-512(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-928(64)]TJ
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25.08 -13.54 Td
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25.08 -13.55 Td
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0 -13.55 TD
[(2.9.3)-1144(Ring)-334(T)83(op)-27(ology)-819(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-928(75)]TJ
T*
[(2.9.4)-1144(Star)-334(T)83(op)-27(ology)-275(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-929(75)]TJ
-25.08 -13.54 Td
[(2.10)-522(A)27(ttac)28(ks)-332(on)-334(Group)-333(Key)-333(Managemen)26(t)-332(Proto)-28(cols)-1023(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-928(75)]TJ
T*
[(2.11)-522(Denial-of-Service)-333(A)27(ttac)28(ks)-333(and)-333(Coun)27(termeasures)-521(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-928(77)]TJ
211.67 -33.92 Td
(vii)Tj
ET
q
1 0 0 1 -62.5 824 cm
/GS0 gs
/Fm0 Do
Q
endstream
endobj
345 0 obj
<<
/XObject <<
/Fm0 975 0 R
>>
/Font 988 0 R
/ProcSet [/PDF /Text]
/ExtGState 989 0 R
>>
endobj
346 0 obj
<<
/Length 12411
>>
stream
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 88.3646 758.8569 Tm
(2.12)Tj
1.0003 0 0 1.0003 72 769.82 Tm
41.453 -10.96 Td
[(Summary)-333(of)-333(Hierarc)26(hical)-332(Group)-333(Mo)-28(del)-333(T)82(op)-27(ologies)-870(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-928(79)]TJ
-0.013 -13.54 Td
[(2.12.1)-644(Generalized)-334(Circular)-333(Hierarc)27(hical)-332(\(C-H\))-334(Group)-333(Mo)-28(del)-691(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-928(79)]TJ
0 -13.55 TD
[(2.12.2)-644(Con)27(tributory)-333(Ring-Cen)27(tralized)-332(Group)-334(Mo)-27(del)-857(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-928(82)]TJ
0 -13.54 TD
[(2.12.3)-644(Cen)27(tralized-Con)27(tributory)-332(Ring)-333(Group)-334(Mo)-27(del)-857(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-928(84)]TJ
0 -13.55 TD
[(2.12.4)-644(Cen)27(tralized-Cen)27(tralized)-332(Group)-333(Mo)-28(del)-901(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-928(85)]TJ
/T1_1 10.91 Tf
-41.44 -24.45 Td
[(Chapter)-383(3)-1150(Energy)-383(Analysis)-596(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-1029(87)]TJ
/T1_0 10.91 Tf
16.36 -13.54 Td
[(3.1)-1022(In)27(tro)-27(duction)-308(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-929(87)]TJ
T*
[(3.2)-1022(Curren)27(t)-332(W)82(ork)-332(in)-334(Literature)-755(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-928(88)]TJ
T*
[(3.3)-1022(Computational)-333(Energy)-333(Cost)-334(Analysis)-333(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-929(90)]TJ
25.08 -13.54 Td
[(3.3.1)-1144(133MHz)-334(SA-1110)-333(\\StrongARM")-333(Micropro)-28(cessor)-908(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-928(90)]TJ
T*
[(3.3.2)-1144(206)-334(MHz)-333(SA-1110)-333(\\StrongARM")-334(Micropro)-27(cessor)-575(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-928(94)]TJ
-25.08 -13.54 Td
[(3.4)-1022(Comm)27(unication)-332(Energy)-334(Cost)-333(Analysis)-750(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-929(95)]TJ
25.08 -13.55 Td
[(3.4.1)-1144(100kbps)-380(transceiv)27(er)-379(mo)-28(dule)-380(and)-380(IEEE)-379(802.11)-380(Sp)-28(ectrum24)-380(LA-4121)-380(WLAN)]TJ
34.9 -13.54 Td
[(card)-691(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-928(96)]TJ
-34.9 -13.55 Td
[(3.4.2)-1144(Lucen)27(t)-333(IEEE)-333(802.11)-333(11Mbps)-334(W)83(a)27(v)28(eLAN)-332(card)-839(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-928(98)]TJ
0 -13.54 TD
[(3.4.3)-1144(Certi\257cate)-334(Size)-635(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-928(99)]TJ
-25.08 -13.55 Td
[(3.5)-1022(Summary)-808(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-429(101)]TJ
/T1_1 10.91 Tf
-16.36 -24.45 Td
[(Chapter)-383(4)-1150(Authen)31(ticated)-382(Group)-384(Key)-383(Agreemen)31(t)-382(for)-384(Wireless)-383(Net)31(w)32(orks)-1050(.)-500(.)-500(.)-500(.)-454(102)]TJ
/T1_0 10.91 Tf
16.36 -13.55 Td
[(4.1)-1022(In)27(tro)-27(duction)-308(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-429(102)]TJ
T*
[(4.2)-1022(Characteristic)-333(of)-333(Burmester-Desmedt)-334(proto)-27(col)-334(\(BD\))-863(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-428(103)]TJ
0 -13.55 TD
[(4.3)-1022(Authen)27(tication)-332(T)82(ec)28(hniques)-332(for)-334(Burmester-Desmedt)-333(\(BD\))-369(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-428(104)]TJ
25.08 -13.54 Td
[(4.3.1)-1144(Authen)27(ticated)-333(BD)-333(using)-333(digital)-334(signatures)-424(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-429(104)]TJ
T*
[(4.3.2)-1144(Authen)27(ticated)-333(BD)-333(using)-333(an)-334(extra)-333(round)-628(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-429(105)]TJ
-25.08 -13.54 Td
[(4.4)-1022(Prop)-27(osed)-334(Authen)27(ticated)-332(Group)-334(Key)-333(Agreemen)27(t)-333(Proto)-27(col)-315(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-428(106)]TJ
25.08 -13.55 Td
[(4.4.1)-1144(Securit)27(y)-333(Analysis)-458(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-428(108)]TJ
-25.08 -13.54 Td
[(4.5)-1022(Comparison)-333(of)-333(Computational)-334(Complexit)27(y)-385(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-429(111)]TJ
T*
[(4.6)-1022(Summary)-808(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-429(112)]TJ
/T1_1 10.91 Tf
-16.36 -24.45 Td
[(Chapter)-288(5)-1150(Authen)31(ticated)-288(Dynamic)-288(Group)-289(Key)-288(Agreemen)31(t)-288(for)-288(Auto)-32(con\257gurable)]TJ
16.36 -13.55 Td
[(MANETs)-435(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-454(113)]TJ
/T1_0 10.91 Tf
0 -13.54 TD
[(5.1)-1022(In)27(tro)-27(duction)-308(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-429(113)]TJ
0 -13.55 TD
[(5.2)-1022(Cryptanalysis)-333(of)-333(Steiner)-334(et)-333(al.)-444(Join)-334(Proto)-28(col)-333(for)-333(BD)-900(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-428(115)]TJ
0 -13.54 TD
[(5.3)-1022(Cryptanalysis)-333(of)-333(Dutta)-334(and)-333(Barua's)-333(Lea)26(v)28(e)-332(Proto)-28(col)-341(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-428(117)]TJ
25.08 -13.55 Td
[(5.3.1)-1144(A)27(ttac)27(k)-332(on)-333(the)-334(Dutta)-333(and)-333(Barua's)-334(Lea)27(v)28(e)-332(Proto)-28(col)-572(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-428(117)]TJ
T*
[(5.3.2)-1144(Fla)27(w)-333(in)-333(Dutta)-333(and)-334(Barua's)-333(securit)27(y)-333(pro)-27(of)-745(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-429(118)]TJ
-25.08 -13.55 Td
[(5.4)-1022(Authen)27(ticated)-332(Dynamic)-334(GKA)-333(for)-333(Auto)-28(con\257gurable)-333(MANETs)-543(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-428(119)]TJ
25.08 -13.54 Td
[(5.4.1)-1144(IP)-334(Address)-333(Auto)-28(con\257guration)-333(Classes)-758(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-428(119)]TJ
0 -13.55 TD
[(5.4.2)-1144(Requiremen)27(ts)-505(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-429(119)]TJ
-25.08 -13.55 Td
[(5.5)-1022(The)-333(Prop)-28(osed)-333(Proto)-28(cols)-683(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-428(120)]TJ
25.08 -13.54 Td
[(5.5.1)-1144(Initial)-334(Key)-333(Agreemen)27(t)-332(\(Group)-334(F)83(ormation\))-333(Proto)-28(col)-1009(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-428(121)]TJ
T*
[(5.5.2)-1144(Join)-334(Proto)-27(col)-581(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-429(122)]TJ
0 -13.54 TD
[(5.5.3)-1144(Merge)-334(Proto)-27(col)-508(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-428(124)]TJ
0 -13.55 TD
[(5.5.4)-1144(Lea)27(v)27(e)-332(Proto)-28(col)-719(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-428(127)]TJ
-25.08 -13.54 Td
[(5.6)-1022(Securit)27(y)-332(Analysis)-547(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-428(129)]TJ
25.08 -13.55 Td
[(5.6.1)-1144(Securit)27(y)-333(Analysis)-333(of)-333(IKA)-334(Proto)-28(col)-830(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-428(129)]TJ
0 -13.54 TD
[(5.6.2)-1144(Securit)27(y)-333(Analysis)-333(of)-333(Join)-334(Proto)-28(col)-871(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-429(130)]TJ
185.07 -28.3 Td
(viii)Tj
ET
q
1 0 0 1 -62.5 824 cm
/GS0 gs
/Fm0 Do
Q
endstream
endobj
347 0 obj
<<
/XObject <<
/Fm0 975 0 R
>>
/Font 990 0 R
/ProcSet [/PDF /Text]
/ExtGState 991 0 R
>>
endobj
348 0 obj
<<
/Length 13171
>>
stream
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 113.4516 758.8569 Tm
(5.6.3)Tj
1.0003 0 0 1.0003 72 769.82 Tm
76.352 -10.96 Td
[(Securit)27(y)-333(Analysis)-333(of)-333(Merge)-334(Proto)-28(col)-799(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-428(132)]TJ
-34.912 -13.54 Td
[(5.6.4)-1144(Securit)27(y)-333(Analysis)-333(of)-333(Lea)26(v)28(e)-332(Proto)-28(col)-1011(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-428(134)]TJ
-25.08 -13.55 Td
[(5.7)-1022(Complexit)27(y)-332(Analysis)-633(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-428(136)]TJ
0 -13.54 TD
[(5.8)-1022(Discussion)-447(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-429(138)]TJ
0 -13.55 TD
[(5.9)-1022(Summary)-808(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-429(140)]TJ
/T1_1 10.91 Tf
-16.36 -24.45 Td
[(Chapter)-260(6)-1150(Energy-E\261cien)31(t)-260(ID-based)-261(Group)-261(Key)-261(Agreemen)31(t)-260(Proto)-32(cols)-260(for)-261(Wire-)]TJ
16.36 -13.54 Td
[(less)-383(Net)31(w)32(orks)-875(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-453(141)]TJ
/T1_0 10.91 Tf
T*
[(6.1)-1022(In)27(tro)-27(duction)-308(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-429(141)]TJ
T*
[(6.2)-1022(Prop)-27(osed)-334(ID-based)-333(Authen)27(ticated)-333(GKA)-333(Proto)-28(col)-579(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-429(142)]TJ
25.08 -13.54 Td
[(6.2.1)-1144(Initial)-334(Group)-333(Key)-333(Agreemen)27(t)-333(\(IKA\))-333(Proto)-28(col)-526(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-428(142)]TJ
T*
[(6.2.2)-1144(Join)-334(Proto)-27(col)-581(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-429(144)]TJ
0 -13.54 TD
[(6.2.3)-1144(Merge)-334(Proto)-27(col)-508(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-428(145)]TJ
0 -13.55 TD
[(6.2.4)-1144(Lea)27(v)27(e)-332(Proto)-28(col)-719(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-428(147)]TJ
-25.08 -13.54 Td
[(6.3)-1022(Securit)27(y)-332(Analysis)-547(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-428(148)]TJ
25.08 -13.55 Td
[(6.3.1)-1144(Securit)27(y)-333(Analysis)-333(of)-333(IKA)-334(Proto)-28(col)-830(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-428(148)]TJ
0 -13.54 TD
[(6.3.2)-1144(Securit)27(y)-333(Analysis)-333(of)-333(Join)-334(Proto)-28(col)-871(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-429(150)]TJ
0 -13.55 TD
[(6.3.3)-1144(Securit)27(y)-333(Analysis)-333(of)-333(Merge)-334(Proto)-28(col)-799(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-428(151)]TJ
0 -13.54 TD
[(6.3.4)-1144(Securit)27(y)-333(Analysis)-333(of)-333(Lea)26(v)28(e)-332(Proto)-28(col)-1011(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-428(153)]TJ
-25.08 -13.55 Td
[(6.4)-1022(Complexit)27(y)-332(Analysis)-633(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-428(154)]TJ
0 -13.55 TD
[(6.5)-1022(Energy)-333(Analysis)-1005(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-428(156)]TJ
0 -13.54 TD
[(6.6)-1022(Summary)-808(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-429(159)]TJ
/T1_1 10.91 Tf
-16.36 -24.45 Td
[(Chapter)-444(7)-1150(Energy-E\261cien)31(t)-444(and)-444(Scalable)-445(Group)-445(Key)-444(Agreemen)31(t)-444(for)-445(Large)-444(Ad)]TJ
16.36 -13.55 Td
[(Ho)-31(c)-384(Net)31(w)32(orks)-611(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-453(160)]TJ
/T1_0 10.91 Tf
T*
[(7.1)-1022(In)27(tro)-27(duction)-308(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-429(160)]TJ
0 -13.55 TD
[(7.2)-1022(Group)-333(Key)-333(Agreemen)26(t)-332(Proto)-28(col)-333(for)-333(Circular)-334(Hierarc)27(hical)-332(\(C-H\))-334(Group)-333(Mo)-28(del)-507(.)-500(.)-500(.)-500(.)-429(161)]TJ
25.08 -13.54 Td
[(7.2.1)-1144(Securit)27(y)-333(Analysis)-458(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-428(163)]TJ
-25.08 -13.55 Td
[(7.3)-1022(Complexit)27(y)-332(Analysis)-633(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-428(164)]TJ
0 -13.54 TD
[(7.4)-1022(Energy)-333(Analysis)-1005(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-428(166)]TJ
0 -13.55 TD
[(7.5)-1022(Summary)-808(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-429(170)]TJ
/T1_1 10.91 Tf
-16.36 -24.45 Td
[(Chapter)-360(8)-1150(Lo)31(w-P)32(o)32(w)32(er)-359(Group)-360(Key)-360(Agreemen)31(t)-359(for)-361(Heterogeneous)-360(Wireless)-360(Net-)]TJ
16.36 -13.55 Td
[(w)32(orks)-758(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-453(171)]TJ
/T1_0 10.91 Tf
0 -13.54 TD
[(8.1)-1022(In)27(tro)-27(duction)-308(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-429(171)]TJ
0 -13.55 TD
[(8.2)-1022(GKA)-333(Proto)-28(col)-333(for)-333(Con)26(tRi-Cen)28(tral)-332(Group)-334(Mo)-27(del)-980(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-429(172)]TJ
0 -13.54 TD
[(8.3)-1022(Securit)27(y)-332(Analysis)-547(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-428(175)]TJ
0 -13.55 TD
[(8.4)-1022(Complexit)27(y)-332(Analysis)-633(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-428(178)]TJ
0 -13.54 TD
[(8.5)-1022(Energy)-333(Analysis)-1005(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-428(181)]TJ
25.08 -13.55 Td
[(8.5.1)-1144(Energy)-334(Consumption)-333(Cost)-333(Results)-669(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-428(182)]TJ
0 -13.55 TD
[(8.5.2)-1144(Discussion)-358(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-428(187)]TJ
-25.08 -13.54 Td
[(8.6)-1022(Summary)-808(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-429(188)]TJ
/T1_1 10.91 Tf
-16.36 -24.45 Td
[(Chapter)-332(9)-1150(Denial-of-Service)-333(A)31(ttac)31(k)-331(Resilience)-333(Dynamic)-333(Group)-333(Key)-333(Agreemen)31(t)]TJ
16.36 -13.55 Td
[(for)-383(Heterogeneous)-383(Net)31(w)32(orks)-836(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-454(189)]TJ
/T1_0 10.91 Tf
0 -13.54 TD
[(9.1)-1022(In)27(tro)-27(duction)-308(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-429(189)]TJ
25.08 -13.55 Td
[(9.1.1)-1144(Certi\257cation)-334(Authorit)27(y)-271(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-429(190)]TJ
T*
[(9.1.2)-1144(Heterogeneous)-334(Net)27(w)28(ork)-332(no)-28(des)-344(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-428(190)]TJ
188.1 -30.94 Td
(ix)Tj
ET
q
1 0 0 1 -62.5 824 cm
/GS0 gs
/Fm0 Do
Q
endstream
endobj
349 0 obj
<<
/XObject <<
/Fm0 975 0 R
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/Font 992 0 R
/ProcSet [/PDF /Text]
/ExtGState 993 0 R
>>
endobj
350 0 obj
<<
/Length 9028
>>
stream
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 88.3646 758.8569 Tm
(9.2)Tj
1.0003 0 0 1.0003 72 769.82 Tm
41.453 -10.96 Td
[(Prop)-27(osed)-334(Group)-333(Key)-333(Agreemen)26(t)-332(Proto)-28(cols)-333(for)-333(the)-334(Cen)27(tral-Con)28(tRi)-333(Group)-333(Mo)-28(del)-863(.)-500(.)-428(191)]TJ
-0.013 -13.54 Td
[(9.2.1)-1144(Initial)-334(Group)-333(Key)-333(Agreemen)27(t)-570(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-428(192)]TJ
0 -13.55 TD
[(9.2.2)-1144(Join)-334(Proto)-27(col)-581(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-429(196)]TJ
0 -13.54 TD
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T*
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[(adv)55(an)28(tages)-237(of)-237(di\256eren)27(t)-237(t)27(yp)-27(es)-237(of)-237(wireless)-238(net)27(w)28(orks)-237(suc)27(h)-236(as)-238(wireless)-237(ad)-238(ho)-27(c)-238(net)27(w)28(orks)-237(and)-237(wireless)-237(mesh)]TJ
T*
[(net)27(w)28(orks)-419(\(WMNs\))-419(are)-420(b)-28(eing)-420(en)27(visioned.)-703(Group)-419(comm)26(unication)-418(in)-420(wireless)-420(net)27(w)28(ork)-419(has)-420(b)-28(ecome)]TJ
0 -21.91 TD
[(imp)-27(ortan)27(t)-295(due)-295(to)-295(the)-296(gro)27(wing)-294(p)-28(opularit)27(y)-295(of)-295(group)-295(orien)27(ted)-295(applications)-295(suc)27(h)-294(as)-296(video)-295(conferencing,)]TJ
0 -21.92 TD
[(pa)27(y-p)-26(er-view)-349(media)-349(distribution,)-352(real-time)-348(information)-349(services)-348(and)-349(collab)-28(orativ)27(e)-347(w)26(ork)-347(in)-349(wireless)]TJ
T*
[(net)27(w)28(orks.)-762(Besides)-439(civilian)-440(applications,)-466(group-orien)27(ted)-438(applications)-440(and)-439(proto)-28(cols)-439(are)-440(also)-439(used)]TJ
0 -21.91 TD
[(widely)-346(in)-347(military)-347(op)-28(erations.)-485(F)83(or)-346(example)-347(in)-347(a)-347(military)-347(net)27(w)28(ork,)-349(a)-347(battalion)-347(could)-347(b)-28(e)-346(considered)]TJ
0 -21.92 TD
[(as)-268(a)-269(large)-268(group)-269(and)-268(soldiers)-269(in)-268(the)-269(battalion)-268(are)-269(required)-268(to)-269(comm)27(unicate)-268(with)-268(one)-269(another.)-423(In)-268(this)]TJ
T*
[(case,)-395(a)-383(wireless)-383(net)27(w)27(ork)-382(\(e.g.)-593(ad)-384(ho)-27(c)-383(net)26(w)28(ork\))-382(could)-383(b)-28(e)-383(set)-383(up)-383(for)-383(group)-383(comm)27(unications)-383(within)]TJ
0 -21.91 TD
[(the)-333(battalion.)]TJ
16.93 -21.92 Td
[(Ho)27(w)28(ev)28(er,)-313(messages)-308(broadcast)-308(in)-308(wireless)-308(net)27(w)27(orks)-307(are)-308(transmitted)-308(in)-308(plain)-308(radio)-309(w)27(a)28(v)28(es.)-435(There-)]TJ
-16.93 -21.91 Td
[(fore,)-533(an)27(y)28(one)-492(can)-493(easily)-494(listen)-493(to)-493(the)-493(messages)-493(b)-28(eing)-493(broadcast)-494([BGW01].)-924(F)83(urthermore,)-533(man)27(y)]TJ
0 -21.92 TD
[(of)-417(these)-417(group)-418(comm)27(unication)-417(applications)-417(in)-418(wireless)-417(net)27(w)27(orks)-416(distribute)-418(sensitiv)27(e)-416(information.)]TJ
T*
[(Hence,)-453(there)-430(is)-430(a)-429(need)-430(to)-430(main)27(tain)-429(the)-429(con\257den)26(tialit)28(y)-428(and)-430(in)27(tegrit)27(y)-428(of)-430(the)-430(data)-429(exc)26(hanged)-428(dur-)]TJ
231.21 -43.34 Td
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[(the)-292(energy)-293(requiremen)27(ts)-291(of)-293(PK)27(C)-292(are)-292(orders)-293(of)-292(magnitude)]TJ
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T*
[(for)-409(secure)-409(group)-409(comm)27(unication)-408(in)-409(wireless)-409(net)27(w)27(orks.)-670(This)-409(is)-409(esp)-28(ecially)-409(desirable)-409(and)-409(useful)-409(for)]TJ
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[(wireless)-458(net)27(w)28(orks)-457(since)-458(most)-458(user)-458(devices)-458(are)-459(battery-op)-27(erated,)-490(and)-458(there)-458(is)-458(a)-458(need)-458(to)-458(prolong)]TJ
T*
[(their)-417(battery)-418(lifespan.)-697(One)-417(widespread)-418(solution)-417(of)-418(using)-417(symmetric-k)27(ey)-417(cryptograph)27(y)-417(for)-417(secure)]TJ
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[(comm)27(unication)-283(is)-283(to)-284(\257rst)-284(emplo)27(y)-283(a)-284(t)27(w)28(o-part)27(y)-283(k)27(ey)-283(exc)27(hange)-283(proto)-27(col)-284(suc)26(h)-282(as)-284(IPSec)-284([DH03,)-86(FKL)]TJ
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[(to)-387(establish)-388(a)-388(k)27(ey)-387(b)-28(et)27(w)28(een)-387(t)27(w)28(o)-387(comm)27(unicating)-387(parties)-388(so)-388(as)-387(to)-388(create)-388(a)-388(Virtual)-387(Priv)54(ate)-387(Net)27(w)28(ork)]TJ
0 -21.92 TD
[(\(VPN\))-368(in)-369(a)-369(tunnel)-369(for)-369(secure)-369(comm)27(unications)-368(b)-27(et)26(w)28(een)-368(the)-369(t)27(w)28(o)-368(comm)27(unicating)-368(parties.)-551(Ho)27(w)28(ev)27(er,)]TJ
0 -21.91 TD
[(this)-286(solution)-287(requires)-286(eac)26(h)-285(no)-28(de)-287(to)-286(ha)26(v)28(e)-286(di\256eren)27(t)-285(secret)-287(k)27(eys)-286(to)-287(comm)27(unicate)-286(with)-286(ev)27(ery)-286(other)-287(no)-28(de)]TJ
0 -21.92 TD
[(in)-338(the)-339(wireless)-338(net)26(w)28(ork.)-459(F)82(urthermore,)-339(VPN)-339(solutions)-338(can)-339(only)-339(handle)-338(unicast)-339(tra\261c.)-460(A)-339(b)-28(etter)-338(so-)]TJ
T*
[(lution)-300(is)-301(the)-301(use)-301(of)-301(a)-301(shared)-301(secret)-301(group)-301(k)27(ey)-300(for)-301(secure)-301(wireless)-300(group)-301(comm)26(unications.)-432(T)82(o)-300(ac)27(hiev)28(e)]TJ
0 -21.91 TD
[(this,)-318(the)-315(no)-27(des)-315(in)-315(the)-314(wireless)-315(net)27(w)27(ork)-313(will)-315(\257rst)-315(run)-314(a)-315(group)-315(k)27(ey)-314(managemen)27(t)-314(proto)-27(col)-315(to)-315(establish)]TJ
0 -21.92 TD
[(a)-288(common)-289(group)-289(k)27(ey)83(.)-428(This)-289(k)27(ey)-288(will)-289(then)-289(b)-27(e)-289(used)-289(as)-289(a)-288(secret)-289(k)27(ey)-288(for)-289(symmetric-k)27(ey)-288(cryptograph)27(y)-288(to)]TJ
T*
[(encrypt)-284(messages)-285(that)-284(they)-285(wish)-284(to)-285(broadcast)-285(to)-284(the)-285(wireless)-284(net)26(w)28(ork.)-427(En)27(tities)-284(outside)-284(the)-285(net)27(w)28(ork)]TJ
0 -21.91 TD
[(w)27(ould)-332(not)-333(b)-28(e)-333(able)-334(to)-333(deco)-28(de)-333(these)-334(messages.)]TJ
/T1_4 14.34 Tf
0 -45.44 TD
[(1.1)-1124(Wireless)-375(Net)30(w)31(orks)]TJ
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0 -21.92 TD
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0 -37.17 TD
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148.76 0 Td
[(These)-445(net)27(w)28(orks)-445(consist)-445(of)-445(mobile)-446(devices)-445(that)-445(comm)27(unicate)-445(with)]TJ
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0 -21.92 TD
[(Examples)-271(of)-272(this)-271(t)26(yp)-26(e)-272(of)-272(net)27(w)28(orks)-271(include)-271(the)-272(cellular)-272(telephone)-271(net)27(w)27(ork)-270(where)-272(eac)27(h)-271(phone)-271(comm)26(u-)]TJ
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231.21 -37.6 Td
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[(with)-361(other)-361(devices)-361(that)-361(are)-361(within)-361(its)-361(comm)27(unication)-361(range.)-527(Infra-structureless)-361(wireless)-362(net)27(w)28(orks)]TJ
T*
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[(situations)-374(\(e.g.)-568(\260o)-28(o)-28(ding,)-385(earthquak)27(e,)-384(rescue)-374(op)-28(erations)-375(etc\).)-568(Dep)-28(ending)-374(on)-375(the)-374(scenario)-375(that)-375(the)]TJ
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T*
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0 -21.91 TD
[(net)27(w)28(ork)-372(for)-373(an)-373(electronic)-373(meeting.)-564(The)-373(devices)-373(in)-373(this)-373(t)26(yp)-26(e)-374(of)-373(ad)-373(ho)-28(c)-373(net)27(w)28(ork)-372(setting)-373(can)-373(b)-28(e)-373(as-)]TJ
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T*
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0 -21.91 TD
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0 -21.92 TD
[(least)-354(one)-354(c)26(hain)-353(of)-354(devices)-355(that)-354(is)-355(reac)27(hable)-353(b)26(y)-353(b)-28(oth.)-508(These)-354(c)27(hain)-354(of)-354(devices)-355(will)-354(help)-355(to)-354(route)-354(the)]TJ
T*
[(pac)27(k)28(ets)-354(through)-355(m)27(ultiple)-354(hops)-355(to)-355(its)-355(destination.)-509(Wireless)-355(sensor)-355(net)27(w)27(orks)-354(\(WSNs\))-355([ASSC02])-354(are)]TJ
0 -21.91 TD
[(another)-381(example)-381(of)-381(infra-structureless)-381(net)27(w)27(orks.)-586(In)-382(WSN,)-381(h)27(undreds)-380(or)-381(thousands)-381(of)-382(no)-27(des)-381(could)]TJ
0 -21.92 TD
[(b)-27(e)-327(deplo)27(y)27(ed)-325(to)-327(collect)-327(data)-327(on)-327(the)-327(en)27(vironmen)28(t)-326(\(e.g.)-442(enem)26(y)-326(mo)27(v)28(emen)28(t)-326(in)-327(military)-327(op)-28(erations)-326(etc\).)]TJ
/T1_0 10.91 Tf
0 -37.18 TD
[(Hybrid)-413(net)31(w)32(ork)]TJ
/T1_1 10.91 Tf
98.44 0 Td
[(Hybrid)-359(net)27(w)27(orks)-358(consist)-359(of)-360(elemen)27(ts)-358(from)-360(b)-28(oth)-359(infrastructure)-359(and)-360(infrastruc-)]TJ
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0 -21.92 TD
[(net)27(w)28(ork)-392(whic)27(h)-392(consists)-393(of)-392(serv)26(ers,)-406(APs)-393(and)-393(BSs)-393(while)-392(the)-393(user)-393(domains)-393(are)-392(either)-393(infrastructure)]TJ
T*
[(or)-320(infra-structureless)-321(net)27(w)27(orks.)-439(In)-321(general,)-323(the)-321(serv)27(er/con)28(troller)-320(no)-28(des)-321(that)-321(form)-321(the)-320(bac)26(kb)-26(one)-321(are)]TJ
0 -21.91 TD
[(t)27(ypically)-350(high)-352(p)-28(o)27(w)28(er)-351(no)-27(des)-352(while)-352(the)-351(user)-352(devices)-351(in)-352(the)-351(user)-352(domains)-351(are)-352(lo)27(w)-351(p)-28(o)27(w)28(er)-351(devices)-351(suc)27(h)]TJ
0 -21.92 TD
[(as)-333(P)27(ersonal)-332(Digital)-334(Assistan)27(ts)-332(\(PD)27(As\))-333(and)-333(laptop)-333(computers.)]TJ
16.93 -21.92 Td
[(One)-409(t)27(ypical)-409(example)-409(of)-409(a)-410(h)27(ybrid)-408(net)27(w)27(ork)-408(is)-409(the)-410(Wireless)-409(Mesh)-409(Net)26(w)28(ork)-408(\(WMN\))-409([A)110(WW05])-409(.)]TJ
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[(WMNs)-287(are)-288(t)27(ypically)-287(large-scale)-287(net)27(w)27(orks)-286(where)-288(the)-287(bac)26(kb)-26(one)-288(comprises)-288(of)-287(mesh)-288(routers)-287(\(serv)26(ers)-286(or)]TJ
T*
[(con)27(trollers\))-359(and)-360(the)-360(user)-361(domains)-360(ma)27(y)-359(con)26(tain)-359(infrastructured)-360(net)27(w)27(orks)-359(suc)27(h)-359(as)-361(Wi-Fi)-360(or)-360(cellular)]TJ
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[(net)27(w)28(orks)-448(or)-450(infra-structureless)-450(net)27(w)28(orks)-449(suc)27(h)-448(as)-450(ad)-449(ho)-28(c)-450(net)27(w)28(orks)-449(or)-449(sensor)-450(net)27(w)28(orks)-449(connected)]TJ
0 -21.92 TD
[(to)-415(the)-416(bac)27(kb)-27(one)-416(domain)-415(via)-416(a)-416(mesh)-415(router.)-692(Another)-415(example)-416(of)-416(h)27(ybrid)-415(net)27(w)28(ork)-415(is)-416(the)-415(military)]TJ
T*
[(net)27(w)28(ork)-308(kno)26(wn)-308(as)-309(Unmanned)-310(Aerial)-309(V)82(ehicle-Mobile)-308(Bac)26(kb)-26(one)-310(No)-28(de)-309(\(UA)110(V-MBN\))-308(net)26(w)28(ork)-308([CL06].)]TJ
231.21 -28.09 Td
(3)Tj
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[(UA)110(V-MBN)-301(net)27(w)28(orks,)-307(the)-302(Mobile)-302(Bac)27(kb)-27(one)-302(No)-27(des)-302(\(MBNs\))-302(are)-301(high)-302(p)-28(o)27(w)28(er)-301(devices)-302(suc)27(h)-301(as)-302(arm)27(y)]TJ
-13.288 -21.91 Td
[(tanks)-391(or)-392(jeeps)-391(that)-392(form)-392(the)-391(infrastructured)-392(part)-392(of)-391(the)-392(net)27(w)27(ork)-390(while)-392(the)-392(lo)27(w-p)-27(o)27(w)28(er)-391(user)-391(no)-28(des)]TJ
0 -21.92 TD
[(are)-383(t)27(ypically)-382(soldiers)-384(carrying)-383(handheld)-383(devices)-384(suc)27(h)-382(as)-384(PD)27(As)-382(and)-383(laptop)-384(computers)-383(p)-28(o)27(w)28(ered)-383(b)27(y)]TJ
T*
[(batteries.)-524(These)-360(lo)27(w-p)-27(o)27(w)27(er)-359(user)-360(no)-28(des)-360(\(soldiers\))-360(are)-360(split)-360(up)-360(in)27(to)-359(small)-360(groups)-360(or)-360(subgroups)-360(\(e.g.)]TJ
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[(plato)-27(ons)-334(or)-333(section)-333(in)-334(the)-333(arm)27(y\))-332(and)-334(form)-333(the)-334(infra-structureless)-333(part)-333(of)-334(the)-333(UA)110(V-MBN)-332(net)27(w)28(ork.)]TJ
/T1_1 10.91 Tf
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[(Characteristics)-384(of)-385(Wireless)-384(Net)31(w)32(orks)]TJ
/T1_0 10.91 Tf
213.95 0 Td
[(User)-334(no)-28(des)-334(of)-334(wireless)-335(net)27(w)28(orks)-333(\(e.g.)-448(PD)27(As\))-334(are)-334(usu-)]TJ
-213.95 -21.92 Td
[(ally)-491(bandwidth-constrained)-492(and)-491(energy-constrained.)-920(Therefore,)-531(computations)-491(m)26(ust)-490(b)-28(e)-492(k)27(ept)-490(at)]TJ
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[(minim)27(um)-381(and)-383(transmission)-382(range)-382(ma)26(y)-381(b)-28(e)-382(lo)27(w)-382(due)-382(to)-383(lac)27(k)-381(of)-383(p)-27(o)26(w)28(er.)-591(No)-27(des)-383(in)-382(an)-383(mobile)-382(wireless)]TJ
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[(net)27(w)28(ork)-294(ma)27(y)-294(also)-295(tend)-295(to)-295(mo)27(v)28(e)-294(in)-295(and)-295(out)-294(of)-295(range)-295(of)-295(other)-295(no)-28(des)-295(frequen)27(tly)84(.)-431(This)-295(ma)27(y)-294(cause)-295(links)]TJ
0 -21.91 TD
[(to)-257(break)-258(and)-258(the)-258(net)27(w)27(ork)-257(top)-27(ology)-258(to)-258(c)26(hange)-256(at)-258(an)26(y)-257(time.)-419(Infrastructured)-258(or)-258(h)27(ybrid)-257(net)27(w)28(orks)-257(where)]TJ
0 -21.92 TD
[(there)-359(are)-359(user)-359(no)-28(des)-359(with)-359(limited)-359(computing)-360(capabilities)-359(and)-359(p)-28(o)27(w)28(erful)-358(no)-28(des)-359(without)-359(energy)-360(con-)]TJ
T*
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125.58 0 Td
(asymmetric)Tj
/T1_0 10.91 Tf
66.72 0 Td
[(wireless)-303(net)27(w)28(orks)-302(while)-303(infra-structureless)-303(net)27(w)28(orks)-302(where)]TJ
-192.3 -21.91 Td
[(all)-333(no)-28(des)-333(ha)27(v)28(e)-333(equal)-333(limited)-333(computing)-334(capabilities)-333(are)-333(kno)26(wn)-332(as)]TJ
/T1_1 10.91 Tf
313.76 0 Td
(symmetric)Tj
/T1_0 10.91 Tf
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-374.72 -45.45 Td
[(1.2)-1124(Group)-375(Key)-375(Managemen)30(t)]TJ
/T1_0 10.91 Tf
0 -32.71 TD
[(Group)-317(Key)-318(Managemen)27(t)-317(refers)-318(to)-317(a)-318(set)-318(of)-318(tec)27(hniques)-317(and)-317(pro)-28(cedures)-318(to)-318(supp)-28(ort)-317(the)-318(establishmen)27(t)]TJ
0 -21.92 TD
[(and)-464(main)26(tenance)-464(of)-465(group)-465(k)27(eys)-464(b)-28(et)27(w)28(een)-464(authorized)-465(parties)-465(in)-465(a)-465(group.)-840(The)-465(established)-465(group)]TJ
T*
[(k)27(ey)-432(can)-433(b)-28(e)-433(used)-433(for)-433(symmetric)-433(k)26(ey)-432(encryption)-433(to)-433(pro)27(vide)-432(secure)-434(group)-433(comm)27(unications.)-743(There)]TJ
0 -21.91 TD
[(are)-377(three)-377(di\256eren)27(t)-377(approac)27(hes)-376(to)-377(Group)-378(Key)-377(Managemen)27(t)-377(\(GKM\),)-377(namely)-377(cen)27(tralized)-377(group)-377(k)27(ey)]TJ
0 -21.92 TD
[(distribution,)-333(decen)27(tralized)-332(group)-334(k)27(ey)-332(distribution)-334(and)-333(con)27(tributory)-332(group)-334(k)27(ey)-332(agreemen)26(t.)]TJ
/T1_1 10.91 Tf
0 -37.18 TD
[(Cen)31(tralized)-473(group)-475(k)31(ey)-474(distribution)]TJ
/T1_0 10.91 Tf
204.01 0 Td
[(This)-412(approac)27(h)-412(relies)-413(on)-413(a)-413(single)-413(en)27(tit)27(y)-411(\(also)-413(kno)26(wn)-412(as)]TJ
-204.01 -21.91 Td
[(the)-457(k)27(ey)-456(serv)26(er\))-456(whic)27(h)-456(could)-458(b)-27(e)-458(one)-457(of)-457(the)-458(group)-457(mem)27(b)-27(ers)-457(or)-457(an)-458(external)-457(T)82(rusted)-456(Third)-457(P)27(art)27(y)]TJ
0 -21.92 TD
[(\(TTP\))-320(to)-321(generate)-321(and)-321(distribute)-321(the)-320(group)-321(k)26(eys.)-439(The)-321(k)27(ey)-320(serv)27(er)-320(main)27(tains)-320(long-term)-321(shared)-320(k)26(eys)]TJ
T*
[(with)-424(eac)27(h)-423(group)-425(mem)27(b)-27(er)-424(and)-424(uses)-425(these)-424(shared)-424(k)27(eys)-424(to)-424(distribute)-424(the)-425(group)-424(k)27(ey)-423(securely)-425(to)-424(all)]TJ
0 -21.91 TD
[(group)-331(mem)27(b)-27(ers.)-444(Although)-331(this)-332(t)27(yp)-27(e)-331(of)-332(k)27(ey)-331(distribution)-331(minimizes)-332(the)-331(computational)-332(p)-28(o)27(w)28(er)-331(of)-331(the)]TJ
0 -21.92 TD
[(users)-378(and)-379(pro)27(vides)-378(bandwidth)-379(utilization,)-390(it)-379(has)-378(t)27(w)27(o)-377(ma)-56(jor)-379(dra)27(wbac)28(ks.)-580(The)-379(\257rst)-378(is)-379(that)-379(the)-379(user)]TJ
0 -21.91 TD
[(designated)-368(to)-369(b)-28(e)-368(the)-369(k)27(ey)-368(serv)27(er)-368(w)27(ould)-367(require)-369(greater)-369(computational)-368(p)-28(o)27(w)27(er)-367(in)-369(order)-369(to)-368(distribute)]TJ
231.21 -44.26 Td
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[(group)-352(k)27(ey)-351(to)-351(all)-352(group)-352(mem)27(b)-27(ers.)-499(On)-351(the)-352(other)-352(hand,)-356(if)-352(the)-351(k)27(ey)-351(serv)27(er)-351(is)-352(not)-351(a)-352(group)-351(mem)26(b)-26(er)]TJ
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[(but)-368(a)-368(TTP)82(,)-368(then)-368(this)-369(TTP)-368(w)27(ould)-368(ha)27(v)28(e)-368(to)-368(b)-28(e)-368(trusted)-369(b)27(y)-367(the)-369(group.)-550(The)-368(second)-369(dra)27(wbac)28(k)-368(is)-368(that)]TJ
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[(the)-333(k)27(ey)-332(serv)26(er)-332(ma)27(y)-332(generate)-334(w)27(eak)-332(k)26(eys)-332(that)-333(lessen)-334(the)-333(securit)27(y)-332(of)-334(the)-333(group)-333(comm)26(unication.)]TJ
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[(Decen)31(tralized)-535(group)-536(k)31(ey)-536(distribution)]TJ
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[(In)-466(this)-466(arc)26(hitecture,)-498(the)-467(managemen)27(t)-465(of)-467(the)-466(whole)]TJ
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[(group)-294(\(the)-294(role)-294(of)-294(the)-294(k)27(ey)-294(serv)27(er\))-293(is)-294(distributed)-294(to)-294(a)-295(n)27(um)28(b)-27(er)-294(of)-294(group)-294(mem)27(b)-27(ers,)-302(kno)27(wn)-294(as)-294(subgroup)]TJ
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[(con)27(trollers.)-609(The)-388(en)26(tire)-387(group)-389(is)-388(split)-389(in)27(to)-387(smaller)-389(subgroups)-389(and)-388(di\256eren)27(t)-388(con)27(trollers)-388(are)-388(used)-389(to)]TJ
T*
[(manage)-338(eac)27(h)-338(subgroup.)-459(This)-339(reduces)-338(the)-338(c)26(hances)-337(of)-338(the)-339(k)27(ey)-337(serv)26(er)-337(creating)-338(w)26(eak)-337(k)27(eys)-338(and)-338(lessens)]TJ
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[(the)-353(computational)-353(w)27(eigh)27(t)-352(on)-353(the)-354(k)27(ey)-352(serv)27(er.)-504(F)83(urthermore,)-358(more)-353(en)27(tities)-353(are)-353(allo)27(w)28(ed)-353(to)-353(fail)-353(b)-28(efore)]TJ
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[(the)-333(whole)-333(group)-333(is)-334(a\256ected.)]TJ
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0 -37.18 TD
[(Con)31(tributory)-510(group)-511(k)31(ey)-510(agreemen)31(t)]TJ
/T1_0 10.91 Tf
206.98 0 Td
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0 -21.92 TD
[(of)-368(cen)26(tralized)-367(trust)-369(and)-369(single)-369(p)-28(oin)27(t)-368(of)-369(failure.)-551(It)-369(also)-369(reduces)-369(the)-369(risk)-368(of)-369(malicious)-369(b)-28(eha)27(vior.)-550(All)]TJ
T*
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[(require)-302(eac)27(h)-302(user)-303(to)-302(b)-28(e)-303(a)27(w)28(are)-302(of)-302(the)-303(group)-302(mem)26(b)-26(ership)-303(list)-303(to)-302(ensure)-303(that)-303(the)-302(proto)-28(cols)-303(are)-302(robust.)]TJ
16.93 -21.92 Td
[(Due)-339(to)-338(ab)-28(o)27(v)27(e-men)28(tioned)-338(adv)55(an)27(tages)-337(of)-339(con)26(tributory)-337(group)-339(k)26(ey)-337(agreemen)26(t)-338(o)27(v)28(er)-338(cen)27(tralized)-338(and)]TJ
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0 -21.92 TD
[(this)-305(thesis,)-312(w)27(e)-305(shall)-306(use)-306(the)-306(terms)-306(group)-306(k)27(ey)-305(agreemen)27(t)-305(and)-306(group)-306(k)27(ey)-305(managemen)26(t)-304(synon)26(ymously)84(.)]TJ
/T1_2 14.34 Tf
0 -45.44 TD
[(1.3)-1124(Challenges)-375(for)-375(Group)-375(Key)-375(Agreemen)30(t)-374(in)-375(Wireless)-375(Net)30(w)31(orks)]TJ
/T1_0 10.91 Tf
0 -32.72 TD
[(Con)27(tributory)-493(group)-495(k)27(ey)-494(agreemen)27(t)-494(\(GKA\))-495(for)-495(wireless)-494(net)26(w)28(orks)-494(not)-494(only)-495(ha)27(v)27(e)-493(to)-495(ensure)-495(that)]TJ
0 -21.92 TD
[(the)-399(basic)-400(securit)27(y)-399(requiremen)27(ts)-399(for)-400(traditional)-399(GKA)-400(are)-400(met,)-416(but)-400(they)-399(also)-400(ha)27(v)27(e)-398(to)-400(consider)-400(the)]TJ
0 -21.91 TD
[(c)27(haracteristics)-359(of)-360(the)-360(wireless)-360(net)26(w)28(ork)-359(when)-360(designing)-360(an)-360(e\256ectiv)26(e)-359(and)-360(e\261cien)27(t)-359(GKA)-360(proto)-28(col)-360(for)]TJ
0 -21.92 TD
[(wireless)-419(net)27(w)27(orks.)-702(F)82(or)-418(example,)-442(user)-419(no)-28(des)-420(in)-419(wireless)-420(net)27(w)27(orks)-418(are)-420(t)27(ypically)-419(lo)27(w)-419(p)-27(o)26(w)28(er)-419(energy)]TJ
T*
[(constrained)-499(devices)-500(suc)27(h)-499(as)-500(PD)27(As)-499(that)-500(ha)27(v)28(e)-499(lo)27(w)28(er)-499(computational)-500(capabilities)-499(compared)-500(to)-500(an)]TJ
0 -21.91 TD
[(a)27(v)28(erage)-232(desktop)-233(system)-232(in)-233(wired)-233(net)27(w)27(ork.)-409(F)82(urthermore,)-252(user)-233(devices)-233(in)-233(wireless)-232(net)26(w)28(orks)-232(are)-232(usually)]TJ
0 -21.92 TD
[(p)-27(o)27(w)27(ered)-351(b)26(y)-351(batteries)-353(whic)27(h)-352(are)-353(limited)-353(resource.)-503(Mo)-27(ore's)-353(La)27(w)-352([Mo)-28(o98])-353(states)-352(that)-353(the)-353(n)27(um)28(b)-27(er)-353(of)]TJ
0 -21.91 TD
[(transistors)-493(in)-493(a)-493(micropro)-28(cessor)-494(will)-493(double)-493(appro)27(ximately)-493(ev)27(ery)-492(18)-494(mon)27(ths)-492(\(i.e.)-925(the)-493(p)-28(o)27(w)28(er)-493(of)]TJ
231.21 -44.26 Td
(5)Tj
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[(a)-309(result,)-314(there)-309(is)-310(a)-309(di\256erence)-309(\(\\p)-28(o)27(w)28(er)-309(gap"\))-309(b)-28(et)27(w)28(een)-309(the)-309(p)-28(o)27(w)28(er)-308(required)-310(b)27(y)-308(computing)-309(and)-310(battery)]TJ
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[(capacit)27(y)-410([LRDP02].)-677(Hence,)-430(battery)-411(p)-28(o)27(w)28(er)-410(is)-411(a)-411(v)27(ery)-410(limited)-411(resource)-411(for)-411(user)-411(devices)-411(in)-411(wireless)]TJ
T*
[(net)27(w)28(orks)-324(and)-324(in)-325(fact,)-326(there)-325(ha)27(v)28(e)-324(b)-28(een)-325(sev)27(eral)-323(w)26(orks)-323(in)-325(curren)27(t)-324(literature)-325([HSW)27(C00,)-121(LH01,)-122(SCI)]TJ
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T*
[(for)-239(wireless)-240(net)26(w)28(orks)-239(should)-240(use)-240(as)-240(little)-240(energy)-240(as)-240(p)-27(ossible)-240(in)-240(order)-240(to)-240(prolong)-240(the)-240(battery)-240(life)-240(in)-240(user)]TJ
0 -21.91 TD
[(devices.)-435(The)-306(GKA)-306(proto)-28(cols)-305(designed)-306(for)-306(wireless)-306(net)26(w)28(orks)-305(also)-306(has)-306(to)-306(ensure)-306(that)-306(comm)27(unication)]TJ
0 -21.92 TD
[(\(transmission)-330(and)-330(reception)-330(of)-330(messages\))-330(costs)-330(are)-330(k)26(ept)-329(as)-330(lo)27(w)-329(as)-330(p)-28(ossible)-330(b)-28(ecause)-330(comm)27(unication)]TJ
T*
[(bandwidth)-426(in)-426(wireless)-427(net)27(w)28(orks)-426(is)-426(a)-426(limited)-427(resource)-426(and)-426(a)-427(GKA)-426(proto)-28(col)-426(that)-427(sends)-426(to)-28(o)-426(man)26(y)]TJ
0 -21.91 TD
[(messages)-350(w)26(ould)-349(result)-351(in)-351(a)-351(big)-351(drain)-351(of)-350(user)-351(devices')-351(batteries.)-497(In)-351(the)-351(follo)27(wing,)-354(w)27(e)-350(highligh)27(t)-350(four)]TJ
0 -21.92 TD
[(c)27(hallenges)-332(for)-333(GKA)-334(in)-333(wireless)-333(net)26(w)28(orks.)]TJ
/T1_2 11.95 Tf
0 -37.82 TD
[(1.3.1)-1125(Authen)31(tication)]TJ
/T1_0 10.91 Tf
0 -28.96 TD
[(Authen)27(tication)-337(is)-339(a)-338(v)26(ery)-337(imp)-28(ortan)27(t)-338(requiremen)27(t)-338(for)-338(GKA)-339(in)-338(wireless)-339(net)27(w)28(orks.)-460(Without)-338(authen)26(ti-)]TJ
0 -21.92 TD
[(cation,)-378(a)-369(malicious)-369(adv)27(ersary)-368(can)-369(simply)-370(pretend)-369(to)-369(b)-28(e)-369(a)-369(legitimate)-369(user)-369(no)-28(de)-369(and)-369(join)-369(the)-370(GKA)]TJ
T*
[(to)-417(obtain)-418(the)-418(shared)-418(group)-417(k)26(ey)84(.)-697(The)-418(adv)27(ersary)-417(can)-418(then)-417(use)-418(the)-418(group)-418(k)27(ey)-417(to)-417(listen)-418(in)-418(or)-418(send)]TJ
0 -21.91 TD
[(in)27(v)56(alid)-371(messages)-372(to)-372(the)-371(group,)-382(th)27(us)-371(resulting)-372(in)-371(the)-372(failure)-372(of)-372(secure)-372(group)-371(comm)26(unications.)-558(The)]TJ
0 -21.92 TD
[(curren)27(t)-406(approac)26(h)-406([BCEP04,)-175(BC04,)-175(BCP07])-408(to)-407(pro)26(vide)-406(authen)26(tication)-406(in)-408(GKA)-408(proto)-28(cols)-407(is)-408(to)-408(use)]TJ
0 -21.91 TD
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0 -21.92 TD
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T*
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T*
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T*
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T*
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T*
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0 -21.92 TD
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T*
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T*
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T*
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T*
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T*
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T*
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T*
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T*
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T*
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T*
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T*
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T*
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T*
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[(the)-333(design)-333(of)-333(GKA)-334(proto)-28(cols)-333(for)-333(wireless)-334(net)27(w)28(orks)-332(are)-334(de\257ned:)]TJ
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[(design)-332(more)-334(e\261cien)27(t)-332(dynamic)-334(GKA)-333(proto)-28(cols)-333(for)-333(wireless)-334(net)27(w)28(orks.)]TJ
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T*
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T*
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T*
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T*
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T*
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T*
[(cards)-436(and)-437(access)-437(p)-28(oin)27(ts.)-754(Subsequen)26(t)-436(amendmen)27(ts)-436(to)-437(802.11)-436(de\257ne)-437(sp)-28(eci\257c)-437(ph)27(ysical)-436(\(PHY\))-437(la)27(y-)]TJ
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T*
[(authen)27(tication,)-411(including)-396(op)-28(en)-396(system)-396(and)-397(shared)-396(k)27(ey)-396(authen)27(tication)-395(and)-396(Wired)-397(Equiv)55(alen)28(t)-396(Pri-)]TJ
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[(v)55(acy)-265(\(WEP\))-266(ha)27(v)28(e)-265(b)-28(een)-266(sho)27(wn)-265(to)-266(b)-28(e)-266(vulnerable)-266([CJL05].)-422(T)82(o)-265(enhance)-266(securit)27(y)-265(of)-266(IEEE)-266(802.11,)-279(a)-266(new)]TJ
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T*
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[(802.11i)-355(sp)-27(eci\257es)-356(enhanced)-355(encryption)-355(to)-355(pro)27(vide)-354(stronger)-355(priv)54(acy)84(.)-509(802.11i)-355(also)-356(incorp)-27(orates)-355(IEEE)]TJ
0 -21.92 TD
[(802.1X)-394([IEEb])-395(as)-395(its)-395(authen)26(tication)-394(enhancemen)27(t.)-628(802.1X)-395(is)-395(widely)-395(deplo)26(y)28(ed)-394(in)-395(man)27(y)-394(IEEE)-395(802)]TJ
T*
[(series)-292(standards)-292(with)-292(the)-293(Remote)-292(Authen)27(tication)-292(Dial)-292(In)-292(User)-292(Service)-293(\(RADIUS\))-292([R)110(WRS00])-291(as)-293(the)]TJ
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[(authen)27(tication)-361(serv)27(er.)-530(But)-362(it)-362(w)27(as)-361(men)27(tioned)-362(in)-362([CJL05])-362(that)-362(802.1X)-362(is)-362(still)-362(unlik)27(ely)-361(to)-362(resolv)26(e)-361(all)]TJ
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[(securit)27(y)-324(threats)-325(in)-325(wireless)-326(net)27(w)28(orks.)-441(The)-325(802.11i)-325(also)-325(de\257nes)-326(a)-325(group)-325(k)27(ey)-324(handshak)26(e)-324(that)-325(enables)]TJ
T*
[(the)-373(authen)26(ticator)-372(\(Access)-374(P)27(oin)27(t\))-372(to)-374(deliv)27(er)-373(the)-374(group)-374(transien)27(t)-373(k)27(ey)-373(to)-374(the)-374(supplican)27(t)-373(\(user)-373(no)-28(de\))]TJ
228.48 -46.39 Td
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T*
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[(net)27(w)28(ork)-304(is)-305(a)-305(net)27(w)28(ork)-304(formed)-305(without)-305(an)27(y)-304(cen)27(tral)-304(administration)-305([FJL00].)-435(Wireless)-305(ad)-305(ho)-28(c)-305(net)27(w)28(ork)]TJ
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T*
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[(forw)27(ard)-309(pac)27(k)28(ets)-309(on)-310(b)-28(ehalf)-309(of)-310(other)-310(no)-28(des)-310(and)-310(run)-310(user)-310(applications.)-436(Wireless)-310(ad)-310(ho)-28(c)-310(net)27(w)28(orks)-309(uses)]TJ
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T*
[(\(PRnet\))-380(and)-380(IEEE)-380(802.11)-380(ad)-380(ho)-28(c)-380(mo)-28(de)-380(to)-381(create)-380(di\256eren)27(t)-379(t)26(yp)-26(es)-381(of)-380(ad)-380(ho)-28(c)-380(net)27(w)28(orks)-380(for)-380(di\256eren)27(t)]TJ
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[(sensor)-333(net)27(w)28(orks)-333(\(WSNs\))-333(and)-333(p)-28(ersonal)-333(area)-334(net)27(w)28(orks)-332(\(P)82(ANs\).)]TJ
16.93 -21.91 Td
[(W)83(e)-333(discuss)-333(some)-333(of)-334(the)-333(c)27(haracteristics)-333(of)-333(wireless)-333(ad)-334(ho)-27(c)-334(net)27(w)28(orks)-332(b)-28(elo)27(w)-333(tak)27(en)-332(from)-334([FJL00]:)]TJ
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T*
[(ground)-328(to)-330(supp)-28(ort)-329(securit)27(y)-328(and)-330(routing)-329(functions.)-443(Instead,)-330(these)-330(functions)-329(m)27(ust)-329(b)-27(e)-330(designed)]TJ
T*
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[(they)-305(desire,)-312(whic)27(h)-305(also)-306(c)26(hanges)-305(the)-306(net)27(w)28(ork)-305(top)-28(ology)82(.)-434(Therefore,)-312(connectivit)27(y)-305(in)-306(the)-306(net)26(w)28(ork)]TJ
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[(this)-332(c)26(haracteristic)-332(will)-333(in\260uence)-334(the)-333(design)-333(of)-334(routing)-333(proto)-28(cols.)]TJ
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[(m)28(ultihop)-234(ad)-235(ho)-27(c)-235(net)27(w)27(orks,)-253(since)-235(the)-234(aggregate)-235(of)-235(all)-235(link)-234(errors)-235(is)-235(what)-234(a\256ects)-235(a)-235(m)27(ultihop)-234(path.)]TJ
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T*
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T*
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T*
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T*
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[(large)-274(n)27(um)27(b)-26(ers)-275(of)-275(ph)27(ysical)-273(sensors)-275(\(e.g.,)-287(acoustic,)-286(seismic,)-286(visual\))-275(comm)27(unicating)-274(via)-274(ad)-275(ho)-28(c)-274(wireless)]TJ
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T*
[(re-programmable)-378(in)-379(the)-379(battle\257eld,)-390(self-lo)-28(calizing,)-390(and)-379(to)-378(supp)-28(ort)-379(lo)27(w-energy)83(,)-389(wireless,)-390(m)27(ulti-hop)]TJ
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14.859 -10.96 Td
[(w)28(orking,)-332(while)-334(requiring)-333(only)-333(minimal)-334(pre-con\257guration)-333([CKM00].)]TJ
2.071 -21.91 Td
[(One)-253(primary)-254(application)-254(of)-254(WSNs)-254(in)-253(military)-254(op)-28(erations)-254(is)-254(to)-253(detect)-254(and)-254(rep)-28(ort)-253(ev)26(en)28(ts)-253(o)-27(ccurring)]TJ
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[(within)-395(range)-396(of)-396(the)-396(WSN.)-396(Once)-396(an)-396(ev)26(en)28(t)-395(suc)27(h)-395(as)-396(mo)27(v)27(emen)28(t)-395(of)-396(dismoun)27(ted)-395(tro)-28(ops,)-411(mo)26(v)28(emen)28(t)-395(of)]TJ
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[(armored)-299(v)27(ehicles,)-305(detection)-300(of)-300(c)27(hemical)-298(o)-28(ccurrences,)-306(etc)-300(is)-299(detected,)-307(the)-299(detecting)-300(sensor)-299(no)-28(de)-299(ma)26(y)]TJ
0 -21.91 TD
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0 -21.92 TD
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0 -21.91 TD
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0 -21.92 TD
[(mand)-356(and)-357(con)26(trol)-355(application)-357(or)-357(when)-357(accepting)-357(legitimate)-357(queries,)-363(commands)-357(and)-357(ev)27(en)-356(soft)27(w)28(are)]TJ
T*
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0 -21.91 TD
[(messages/data)-392(transmissions)-392(in)-392(WSNs)-393(are)-392(sen)27(t)-392(through)-392(radio)-392(w)27(a)27(v)28(es)-391(that)-392(enable)-393(an)-392(adv)27(ersary)-392(to)]TJ
0 -21.92 TD
[(ea)27(v)28(esdrop)-275(on)-275(the)-276(comm)27(unication,)-286(inject)-276(false)-276(messages)-275(and)-276(repla)27(y)-275(or)-275(c)26(hange)-274(old)-276(messages.)-425(F)82(urther-)]TJ
T*
[(more,)-296(sensor)-288(no)-28(des)-288(are)-288(usually)-288(deplo)27(y)28(ed)-287(in)-288(hostile)-288(en)27(vironmen)28(ts)-287(where)-288(they)-287(can)-288(b)-28(e)-288(easily)-288(captured,)]TJ
0 -21.91 TD
[(compromised)-287(or)-287(manipulated)-287(b)27(y)-286(an)-288(adv)27(ersary)84(.)-429(Hence,)-296(k)27(ey)-286(managemen)26(t)-286(and)-287(authen)27(tication)-286(are)-287(t)26(w)28(o)]TJ
0 -21.92 TD
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T*
[(based)-316(on)-316(pre-deplo)27(y)28(ed)-315(k)27(eying)-315(\(i.e.)-439(the)-316(k)27(ey)-316(is)-316(issued)-316(b)-28(efore)-316(deplo)27(ymen)28(t\))-315(are)-316(easy)-316(to)-316(implemen)26(t)-315(and)]TJ
0 -21.91 TD
[(ha)27(v)28(e)-425(little)-426(o)27(v)28(erheads.)-721(Ho)27(w)27(ev)28(er,)-448(most)-426(of)-426(these)-425(proto)-28(cols)-426(based)-426(on)-426(pre-deplo)27(y)28(ed)-425(k)27(eying)-425(ha)27(v)27(e)-424(dis-)]TJ
0 -21.92 TD
[(adv)55(an)28(tages)-361(regarding)-361(scalabilit)27(y)-361(and)-362(vulnerabilit)27(y)-360(to)-362(no)-28(de)-361(capture.)-529(As)-362(compared)-361(to)-362(pre-deplo)27(y)28(ed)]TJ
T*
[(k)27(eying,)-337(a)-338(b)-28(etter)-337(k)26(ey)-336(establishmen)27(t)-337(tec)27(hnique)-337(for)-337(WSNs)-338(is)-338(the)-337(use)-338(of)-337(group)-338(k)27(ey)-337(transp)-28(ort)-337(or)-338(group)]TJ
0 -21.91 TD
[(k)27(ey)-422(agreemen)26(t)-422(proto)-28(cols)-424(where)-424(the)-423(no)-28(des)-424(set)-423(up)-424(a)-424(shared)-424(secret)-423(k)26(ey)-422(after)-424(deplo)27(ymen)28(t)-423([GST07].)]TJ
0 -21.92 TD
[(Group)-316(k)27(ey)-315(agreemen)26(t)-315(proto)-28(cols)-316(are)-316(b)-28(etter)-317(solutions)-316(than)-316(group)-317(k)27(ey)-315(transp)-28(ort)-316(proto)-28(cols)-316(b)-28(ecause)-317(in)]TJ
T*
[(group)-346(k)27(ey)-345(agreemen)27(t)-345(proto)-28(cols,)-349(no)-346(en)26(tit)28(y)-345(can)-346(predetermine)-346(the)-346(resulting)-346(k)27(ey)-345(as)-347(it)-346(dep)-27(ends)-346(on)-347(the)]TJ
0 -21.91 TD
[(input)-333(of)-333(all)-333(participan)26(ts.)]TJ
16.93 -21.92 Td
[(Sensor)-486(no)-28(des)-486(are)-487(the)-486(basic)-487(comp)-28(onen)27(ts)-485(of)-487(a)-486(WSN.)-487(Once)-486(the)-487(sensor)-486(no)-28(des)-487(are)-486(deplo)27(y)27(ed)-485(in)]TJ
-16.93 -21.91 Td
[(battle\257elds,)-254(they)-235(usually)-235(ha)27(v)28(e)-234(no)-235(mobilit)27(y)84(.)-411(Sensor)-235(no)-28(des)-234(suc)26(h)-233(as)-235(the)-235(Ro)-28(c)27(kw)28(ell)-234(Scien)27(ti\257c)-234(WINS)-235(no)-27(des)]TJ
0 -21.92 TD
[([A)27(CPR99])-326(are)-326(usually)-327(small,)-328(ligh)26(t)28(w)28(eigh)28(t,)-328(inexp)-27(ensiv)26(e,)-327(lo)27(w-p)-27(o)27(w)28(er)-326(and)-327(battery-op)-28(erated.)-442(Therefore,)]TJ
T*
[(proto)-27(cols)-441(designed)-441(for)-441(WSNs)-441(should)-441(consume)-441(as)-440(little)-441(energy)-441(as)-441(p)-28(ossible)-441(to)-441(extend)-440(the)-441(battery)]TJ
0 -21.91 TD
[(lifespan.)-603(Moreo)26(v)28(er,)-399(sensor)-386(no)-28(des)-386(are)-387(usually)-386(placed)-387(in)-386(hostile)-387(en)27(vironmen)28(ts)-386(and)-386(it)-387(is)-386(usually)-387(not)]TJ
0 -21.92 TD
[(p)-27(ossible)-334(to)-333(replace)-333(the)-334(batteries)-333(of)-333(sensor)-334(no)-27(des)-334(when)-333(the)-333(batteries)-334(are)-333(depleted.)]TJ
16.93 -21.92 Td
[(F)83(or)-271(more)-272(information)-271(ab)-28(out)-272(WSNs)-271(and)-272(sensor)-271(no)-28(des,)-284(w)27(e)-271(refer)-271(readers)-272(to)-272(Chapter)-271(2)-272(of)-271([CKM00].)]TJ
211.55 -43.35 Td
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[(as)-350(a)-351(router)-351(or)-351(host)-351(for)-351(other)-350(no)-28(des)-351(in)-351(the)-351(net)27(w)28(ork.)-496(Ho)27(w)27(ev)28(er,)-354(unlik)27(e)-350(wireless)-351(ad)-351(ho)-28(c)-351(net)27(w)28(orks,)-354(the)]TJ
0 -21.92 TD
[(no)-27(des)-380(in)-379(WMNs)-380(can)-379(b)-28(e)-380(\257xed)-379(pieces)-380(of)-379(the)-380(net)27(w)28(ork)-379(\(infrastructure)-379(suc)27(h)-379(as)-379(access)-380(p)-28(oin)27(ts)-378(\(AP\))-380(or)]TJ
T*
[(base)-303(station)-303(\(BS\)\))-303(or)-303(mobile)-303(or)-304(stationary)-303(user)-303(no)-28(des)-303(\(infrastructureless)-303(suc)26(h)-302(as)-303(laptop)-303(computers,)]TJ
0 -21.91 TD
[(PD)27(As)-388(and)-390(mobile)-389(phones\).)-613(Hence,)-403(WMNs)-389(are)-390(h)27(ybrid)-388(net)26(w)28(orks)-388(where)-390(there)-389(can)-389(b)-28(e)-390(devices)-389(from)]TJ
0 -21.92 TD
[(b)-27(oth)-334(infrastructured)-333(and)-333(infrastructureless)-334(net)27(w)28(orks.)]TJ
16.93 -21.91 Td
[(It)-246(should)-246(b)-28(e)-246(noted)-246(that)-246(wireless)-246(mesh)-246(net)27(w)27(orks)-245(is)-246(a)-246(t)27(yp)-27(e)-246(of)-246(net)27(w)28(ork)-246(arc)27(hitecture)-245(and)-246(is)-246(not)-246(ab)-28(out)]TJ
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[(whic)27(h)-415(particular)-416(radio)-416(tec)27(hnology)-415(is)-416(used)-416([Mot05].)-693(Radio)-416(mo)-28(dulation)-416(determines)-416(ho)27(w)-415(a)-416(sp)-28(eci\257c)]TJ
T*
[(radio)-297(will)-298(transmit)-298(and)-297(receiv)27(e)-297(information)-298(o)27(v)28(er)-297(the)-298(wireless)-297(medium)-298(whereas)-298(net)27(w)28(ork)-297(arc)27(hitecture)]TJ
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[(de\257nes)-350(the)-350(o)27(v)28(erall)-349(structure,)-355(comp)-27(onen)26(ts)-349(and)-350(in)27(terrelationships)-349(of)-350(devices)-350(in)-350(the)-350(net)26(w)28(ork.)-494(Hence,)]TJ
0 -21.92 TD
[(WMNs)-393(can)-394(b)-28(e)-394(applied)-394(to)-394(practically)-394(an)27(y)-393(radio)-394(sc)26(hemes,)-408(e\256ectiv)27(ely)-393(allo)27(wing)-393(the)-394(b)-28(est)-394(radio)-394(to)-394(\257t)]TJ
T*
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16.93 -21.91 Td
[(There)-437(are)-438(t)27(w)27(o)-436(t)27(yp)-27(es)-438(of)-438(no)-27(des)-438(in)-438(WMNs)-438([A)110(WW05],)-462(namely)-438(the)-438(mesh)-438(routers)-437(suc)27(h)-437(as)-438(access)]TJ
-16.93 -21.92 Td
[(p)-27(oin)27(ts)-297(\(AP\))-297(or)-297(base)-297(station)-297(\(BS\))-297(and)-297(the)-297(mesh)-298(clien)27(ts)-296(suc)27(h)-296(as)-297(laptop)-297(computers,)-305(PD)27(As)-296(and)-297(mobile)]TJ
T*
[(phones.)-444(W)82(e)-332(describ)-28(e)-333(these)-333(t)26(w)28(o)-332(t)27(yp)-27(es)-333(of)-334(no)-28(des)-333(in)-333(WMNs)-334(b)-27(elo)26(w:)]TJ
/T1_3 10.91 Tf
16.36 -33.86 Td
(\262)Tj
/T1_2 10.91 Tf
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[(Mesh)-319(Routers:)-437(The)-320(mesh)-319(routers)-320(are)-319(\257xed)-320(pieces)-319(of)-320(the)-319(net)26(w)28(ork)-318(and)-320(do)-319(not)-320(ha)27(v)28(e)-319(an)27(y)-319(energy)]TJ
T*
[(constrain)28(ts)-269(as)-270(they)-270(are)-270(usually)-270(connected)-271(to)-270(a)-270(\257xed)-270(p)-27(o)26(w)28(er)-269(supply)82(.)-422(Besides)-270(routing)-270(capabilities)]TJ
T*
[(for)-405(gatew)27(a)27(y/rep)-26(eater)-407(functions)-406(as)-406(in)-406(a)-406(con)27(v)28(en)27(tional)-405(wireless)-406(router,)-424(a)-406(wireless)-406(mesh)-407(router)]TJ
0 -21.91 TD
[(con)28(tains)-343(additional)-344(routing)-344(functions)-344(to)-344(supp)-28(ort)-344(mesh)-344(net)27(w)27(orking.)-475(T)82(o)-343(further)-344(impro)27(v)28(e)-343(\260exi-)]TJ
0 -21.92 TD
[(bilit)28(y)-333(of)-334(mesh)-334(net)26(w)28(orking,)-333(mesh)-334(routers)-334(is)-334(usually)-334(equipp)-28(ed)-334(with)-334(m)27(ultiple)-333(wireless)-334(in)27(terfaces)]TJ
T*
[(built)-482(on)-483(either)-483(the)-484(same)-483(or)-483(di\256eren)27(t)-482(wireless)-483(access)-484(tec)27(hnology)84(.)-893(Compared)-484(to)-483(a)-483(con)27(v)28(en-)]TJ
0 -21.91 TD
[(tional)-313(wireless)-314(router,)-318(a)-314(wireless)-314(mesh)-314(router)-314(can)-314(ac)27(hiev)28(e)-313(the)-314(same)-314(co)26(v)28(erage)-313(with)-314(m)27(uc)28(h)-313(lo)26(w)28(er)]TJ
0 -21.92 TD
[(transmission)-352(p)-28(o)27(w)28(er)-352(through)-353(m)26(ulti-hop)-352(comm)27(unications.)-502(The)-353(medium)-353(access)-353(con)26(trol)-352(\(MA)27(C\))]TJ
T*
[(proto)-27(col)-369(in)-369(a)-368(mesh)-369(router)-369(can)-369(also)-369(b)-28(e)-369(enhanced)-369(with)-368(b)-28(etter)-369(scalabilit)27(y)-368(in)-369(a)-369(m)27(ulti-hop)-368(mesh)]TJ
0 -21.91 TD
[(en)28(vironmen)27(t.)-719(Despite)-426(all)-425(these)-425(di\256erences,)-449(mesh)-425(routers)-426(and)-425(con)27(v)28(en)27(tional)-424(wireless)-425(routers)]TJ
0 -21.92 TD
[(are)-351(usually)-352(built)-352(based)-353(on)-352(a)-352(similar)-352(hardw)27(are)-351(platform.)-501(Mesh)-352(routers)-352(can)-352(b)-28(e)-352(built)-352(based)-353(on)]TJ
201.21 -39.23 Td
(35)Tj
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[(based)-330(on)-331(general-purp)-28(ose)-331(computer)-331(systems)-331(suc)27(h)-330(as)-331(laptop)-332(or)-331(desktop)-331(computers)-331([A)110(WW05].)]TJ
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[(energy-constrain)28(ts.)-690(Mesh)-416(clien)27(ts)-415(usually)-415(ha)27(v)27(e)-414(only)-416(one)-415(wireless)-416(in)27(terface.)-690(As)-416(a)-415(result,)-436(the)]TJ
T*
[(hardw)28(are)-319(platform)-320(and)-319(soft)27(w)27(are)-318(for)-320(mesh)-320(clien)27(ts)-318(can)-320(b)-28(e)-319(simpler)-320(than)-320(those)-319(for)-320(mesh)-320(routers.)]TJ
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[(As)-499(compared)-501(to)-500(mesh)-500(routers,)-543(mesh)-500(clien)27(ts)-499(ha)26(v)28(e)-499(a)-501(higher)-500(v)55(ariet)27(y)-499(of)-500(devices.)-946(They)-500(can)]TJ
0 -21.92 TD
[(b)-27(e)-397(laptop/desktop)-397(computers,)-414(p)-27(o)-28(c)27(k)27(et)-396(PC,)-397(PD)27(As,)-412(IP)-398(phone,)-413(RFID)-397(reader,)-413(and)-397(man)26(y)-396(other)]TJ
T*
[(devices)-381([A)110(WW05].)-591(Ho)27(w)27(ev)28(er,)-394(similar)-382(to)-382(the)-383(no)-28(des)-382(in)-382(wireless)-383(ad)-382(ho)-28(c)-383(net)27(w)28(orks,)-394(mesh)-382(clien)27(ts)]TJ
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[(ma)28(y)-401(require)-402(energy-e\261cien)27(t)-401(proto)-28(cols)-401(in)-402(order)-402(to)-402(prolong)-402(its)-401(battery)-402(lifespan.)-650(Hence)-402(CPU)]TJ
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[(computations)-391(for)-392(net)26(w)28(ork)-391(applications)-392(in)-392(mesh)-392(clien)27(ts)-392(should)-392(k)27(ept)-391(as)-392(minim)27(um)-392(as)-392(p)-27(ossible)]TJ
T*
[(and)-267(the)-269(comm)27(unications)-267(proto)-28(cols)-269(should)-268(b)-28(e)-268(optimized)-268(to)-269(consume)-268(as)-269(little)-268(energy)-268(as)-269(p)-27(ossible)]TJ
0 -21.91 TD
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[(In)-440(a)-439(t)26(ypical)-438(infrastructured)-440(wireless)-440(net)27(w)27(orks)-438(suc)26(h)-438(as)-440(WLAN,)-440(Radio)-440(F)82(requency)-438(\(RF\))-440(signal)]TJ
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[(atten)27(uation)-425(can)-426(imp)-28(ose)-426(unacceptable)-426(tradeo\256s)-426(b)-27(et)26(w)28(een)-425(p)-28(o)27(w)28(er)-425(distance)-426(and)-426(throughput,)-449(disrupt)]TJ
0 -21.92 TD
[(data)-245(streams)-246(as)-245(users)-246(cross)-246(roaming)-245(b)-28(oundaries)-246(and)-245(ev)26(en)-244(lead)-246(to)-245(dropp)-28(ed)-246(connections)-245(when)-246(ph)27(ysical)]TJ
0 -21.91 TD
[(barriers)-394(\(e.g.)-630(ob)-55(jects)-395(that)-395(absorb)-395(or)-395(re\260ect)-395(signal)-395(strength\))-394(are)-395(presen)26(t.)-628(All)-395(of)-395(these)-394(limitations)]TJ
0 -21.92 TD
[(result)-247(from)-247(the)-247(w)27(a)27(y)-246(signal)-247(strength)-247(drops)-247(exp)-28(onen)27(tially)-247(as)-247(a)-247(function)-247(of)-248(distance)-247(b)-28(et)27(w)28(een)-246(sender)-247(and)]TJ
0 -21.91 TD
[(receiv)27(er.)-424(WMNs)-275(solv)27(e)-274(this)-276(problem)-275(with)-275(the)-275(use)-276(of)-275(m)27(ulti-hopping)-274([K)26(CY)]TJ
/T1_2 7.97 Tf
338.87 3.95 Td
(+)Tj
/T1_0 10.91 Tf
7.08 -3.95 Td
[(02],)-287(whic)27(h)-274(ac)27(hiev)28(es)-275(higher)]TJ
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[(throughput)-475(without)-475(sacri\257cing)-475(e\256ectiv)27(e)-474(radio)-475(range)-475(via)-475(shorter)-475(link)-475(distances,)-511(less)-475(in)27(terference)]TJ
0 -21.92 TD
[(b)-27(et)27(w)27(een)-356(the)-358(no)-28(des)-358(and)-358(more)-357(e\261cien)26(t)-356(frequency)-358(re-use.)-518(Multi-hopping)-358(mak)27(es)-357(routing)-357(in)-358(WMNs)-358(a)]TJ
0 -21.91 TD
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0 -21.92 TD
[(secure)-331(as)-332(adv)26(ersaries)-331(ma)27(y)-331(b)-27(e)-332(tempted)-332(to)-332(attac)27(k)-331(it.)-444(W)82(e)-331(refer)-332(readers)-332(to)-332([A)110(WW05,)-127(SH06,)-129(Mot05])-332(for)]TJ
T*
[(more)-333(detail)-333(discussions)-333(of)-334(WMNs.)]TJ
/T1_3 11.95 Tf
0 -37.19 TD
[(2.4.4)-1125(Inheren)31(t)-374(Characteristics)-375(of)-375(Wireless)-375(Net)30(w)31(orks)]TJ
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0 -21.92 TD
[(pla)27(y)-379(an)-380(imp)-28(ortan)27(t)-379(in\260uence)-380(in)-381(the)-380(design)-380(of)-380(e\261cien)27(t,)-391(scalable)-381(and)-380(authen)27(ticated)-379(GKM)-380(proto)-28(cols)]TJ
T*
[(for)-396(wireless)-396(net)27(w)28(orks.)-632(These)-396(inheren)27(t)-396(c)27(haracteristics)-395(that)-396(p)-28(ose)-396(c)27(hallenges)-395(to)-396(GKM)-396(proto)-28(cols)-396(the)]TJ
0 -21.91 TD
[(v)55(arious)-332(t)27(yp)-27(es)-334(of)-333(wireless)-333(net)27(w)27(orks)-332(include:)]TJ
228.48 -27.35 Td
(36)Tj
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[(it)-308(is)-308(fairly)-309(easy)-308(for)-309(an)27(y)28(one)-308(with)-308(the)-309(righ)27(t)-308(kind)-308(of)-309(radio)-308(to)-309(ea)27(v)28(esdrop)-308(on)-308(the)-309(wireless)-308(comm)27(unication)]TJ
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[(unless)-312(in)-313(a)-313(wired)-313(net)27(w)28(ork)-312(where)-313(the)-313(ea)27(v)28(esdropp)-27(er)-313(needs)-313(to)-313(do)-313(some)-312(w)26(ork)-312(\(e.g.)-437(wire-tapping\))-313(to)-313(b)-28(e)]TJ
T*
[(able)-333(to)-333(ea)27(v)27(esdrop)-332(in)-333(the)-334(comm)27(unication.)]TJ
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[(Most)-298(user)-298(devices)-298(in)-299(wireless)-298(net)27(w)28(orks)-298(are)-298(t)27(ypically)-297(lo)26(w)-297(p)-28(o)27(w)28(er)]TJ
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[(Wireless)-267(devices)-268(suc)27(h)-267(as)-268(PD)26(As)-267(and)-268(laptop)-268(computers)-268(are)]TJ
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[(the)-302(wireless)-303(device)-303(runs)-302(out,)-309(the)-303(user)-303(w)27(ould)-302(ha)27(v)28(e)-302(to)-303(man)27(ually)-302(replace)-302(or)-303(rec)27(harge)-302(the)-303(batteries)-303(and)]TJ
0 -21.91 TD
[(comm)27(unications)-381(ma)27(y)-381(b)-28(e)-382(in)27(terrupted)-381(esp)-28(ecially)-382(when)-382(replacing)-382(batteries.)-591(F)82(urthermore,)-393(in)-382(certain)]TJ
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[(wireless)-412(sensor)-412(net)27(w)27(orks,)-431(it)-412(ma)27(y)-412(not)-412(ev)27(en)-412(b)-28(e)-412(p)-28(ossible)-412(to)-412(replace)-413(batteries.)-681(Therefore,)-433(there)-412(is)-412(a)]TJ
T*
[(need)-291(to)-291(design)-291(energy-e\261cien)27(t)-290(GKM)-291(proto)-28(cols)-291(for)-291(wireless)-292(net)27(w)28(orks)-290(to)-291(prolong)-291(the)-291(battery)-292(lifespan)]TJ
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/T1_1 10.91 Tf
160.09 0 Td
[(Comm)27(unication)-221(in)-223(wireless)-222(net)27(w)28(orks)-221(consume)-223(quite)-222(a)-222(large)-222(amoun)26(t)]TJ
-160.09 -21.92 Td
[(of)-333(battery)-333(p)-28(o)27(w)28(er)-333(and)-333(furthermore,)-333(wireless)-334(comm)27(unications)-332(ha)27(v)27(e)-332(limited)-333(transmission)-334(range.)]TJ
/T1_0 10.91 Tf
0 -37.17 TD
[(Lac)31(k)-339(of)-341(cen)31(tral)-340(infrastructures)]TJ
/T1_1 10.91 Tf
175.99 0 Td
[(In)-296(certain)-296(t)27(yp)-27(es)-297(of)-296(wireless)-296(net)27(w)27(orks)-295(suc)27(h)-295(as)-297(ad)-296(ho)-28(c)-296(net)27(w)28(orks,)]TJ
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[(there)-333(is)-333(v)27(ery)-333(little)-333(or)-333(no)-334(cen)27(tral)-332(infrastructure)-334(to)-333(mak)27(e)-332(use)-334(of.)]TJ
/T1_0 10.91 Tf
0 -37.18 TD
[(Scalabilit)31(y)]TJ
/T1_1 10.91 Tf
67.69 0 Td
[(In)-476(some)-476(large)-476(scale)-476(wireless)-476(net)27(w)28(orks)-475(suc)26(h)-475(as)-476(wireless)-476(mesh)-476(net)27(w)28(orks)-475(or)-476(wireless)]TJ
-67.69 -21.91 Td
[(sensor)-390(net)27(w)28(orks,)-403(there)-390(migh)26(t)-389(b)-27(e)-390(h)26(undreds)-389(or)-390(thousands)-390(of)-390(no)-28(des.)-614(Therefore,)-404(GKM)-390(proto)-28(cols)-390(for)]TJ
0 -21.92 TD
[(wireless)-427(net)27(w)28(orks)-427(m)27(ust)-426(b)-28(e)-427(scalable)-428(to)-427(ensure)-428(no)-27(des)-428(in)-427(suc)27(h)-427(large-scale)-427(wireless)-427(net)26(w)28(orks)-426(do)-428(not)]TJ
T*
[(deplete)-333(a)-333(large)-333(amoun)26(t)-332(of)-333(energy)-334(when)-333(running)-333(GKM)-334(proto)-27(cols.)]TJ
/T1_0 10.91 Tf
0 -37.17 TD
[(Highly)-342(dynamic)-343(top)-32(ology)]TJ
/T1_1 10.91 Tf
148.56 0 Td
[(Wireless)-298(net)27(w)28(orks)-297(ha)27(v)28(e)-297(net)26(w)28(ork)-297(top)-28(ologies)-298(that)-297(are)-298(highly)-298(dynamic)]TJ
-148.56 -21.92 Td
[(as)-333(user)-333(no)-28(des)-333(whic)27(h)-333(can)-333(b)-28(e)-333(mobile)-334(can)-333(join)-333(and)-334(lea)27(v)28(e)-332(the)-334(wireless)-333(net)27(w)28(ork)-333(at)-333(an)27(y)-333(time.)]TJ
228.48 -61.37 Td
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T*
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[(con)27(troller)-380(no)-28(des)-382(\(e.g.NLKW)-381([NLKW05],)-394(NLKKW)-381([NLK)]TJ
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T*
[(to)-348(constan)27(tly)-348(p)-28(erform)-348(computations,)-352(th)26(us)-347(depleting)-349(the)-348(con)27(troller)-348(no)-28(des')-348(computational)-349(resources)]TJ
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[(and)-355(prev)27(en)28(ting)-354(legitimate)-355(group)-355(mem)27(b)-27(ers)-355(from)-355(sending)-355(legitimate)-355(Start)-355(GKA)-355(or)-355(Join)-355(requests)-355(to)]TJ
T*
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-16.93 -21.92 Td
[(wired)-379(net)27(w)28(orks)-378(\(e.g.)-582(In)27(ternet\))-378(ha)27(v)27(e)-378(resulted)-379(in)-379(some)-379(curren)27(t)-378(GKM)-379(proto)-28(cols)-379(to)-379(b)-28(e)-379(unsuitable)-379(or)]TJ
T*
[(ine\261cien)27(t)-415(for)-416(use)-416(in)-417(wireless)-416(net)27(w)28(orks.)-693(Therefore,)-436(there)-417(is)-416(a)-416(need)-416(to)-417(design)-416(energy-e\261cien)27(t)-415(and)]TJ
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[(suitable)-333(GKM)-333(proto)-28(cols)-333(that)-334(address)-333(the)-333(ab)-28(o)27(v)28(e-men)27(tioned)-332(c)27(hallenges)-333(in)-333(wireless)-333(net)27(w)27(orks.)]TJ
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0 -37.82 TD
[(2.4.5)-1125(Heterogeneous)-375(and)-375(homogeneous)-375(Wireless)-375(Net)31(w)31(orks)]TJ
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0 -21.92 TD
[(dep)-27(ending)-354(on)-353(the)-353(t)27(yp)-27(e)-353(of)-353(no)-28(des)-353(in)-354(the)-353(net)27(w)28(ork.)-504(W)83(e)-352(explain)-354(these)-353(t)27(yp)-27(e)-353(t)27(yp)-27(es)-353(of)-354(wireless)-353(net)27(w)28(orks)]TJ
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198.47 0 Td
[(refer)-347(to)-348(wireless)-348(net)27(w)28(orks)-347(that)-348(consist)-347(of)-348(no)-28(des)-348(with)-347(dif-)]TJ
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[(\(WMNs\),)-291(whic)27(h)-280(is)-282(a)-281(t)27(yp)-27(e)-281(of)-281(h)27(ybrid)-280(net)26(w)28(ork,)-291(the)-281(mesh)-281(routers)-281(are)-281(high)-281(p)-28(o)27(w)27(er)-280(no)-27(des)-282(without)-281(energy)]TJ
T*
[(constrain)27(ts)-262(while)-263(the)-262(mesh)-263(clien)26(ts)-261(are)-263(lo)26(w)-261(p)-28(o)27(w)27(er)-262(energy)-262(constrained)-263(devices.)-421(A)]TJ
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372.01 0 Td
(static)Tj
/T1_1 10.91 Tf
29.12 0 Td
(heterogeneous)Tj
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[(wireless)-386(net)27(w)27(ork)-385(consists)-387(of)-387(stationary)-387(net)27(w)28(ork)-386(no)-27(des)-387(that)-387(do)-387(not)-386(mo)26(v)28(e)-385(while)-387(a)]TJ
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[(geneous)-340(wireless)-340(net)26(w)28(ork)-339(consists)-341(of)-340(b)-28(oth)-340(mobile)-341(no)-28(des)-340(\(e.g.)-466(PD)27(As\))-340(and)-340(stationary)-340(no)-28(des)-341(that)-340(do)]TJ
T*
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228.48 -70.89 Td
(38)Tj
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[(w)27(orks)-416(are)-417(examples)-416(of)-417(homogeneous)-417(wireless)-417(net)27(w)27(orks.)-694(F)82(or)-415(example,)-438(in)-417(certain)-417(t)27(yp)-27(es)-417(of)-417(ad)-417(ho)-28(c)]TJ
T*
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[(Ro)-27(c)27(kw)27(ell)-450(Scien)27(ti\257c)-450(Wireless)-451(In)27(tegrated)-450(Net)27(w)27(ork)-450(Sensor)-451(\(WINS\))-451(no)-27(des\).)-798(A)]TJ
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(static)Tj
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T*
[(wireless)-333(sensor)-333(net)27(w)28(orks\))-332(while)-333(a)]TJ
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[(2.5)-1124(Key)-375(Establishmen)30(t)-374(Concept)]TJ
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[(In)-281(most)-282(cryptographic)-281(op)-28(erations,)-292(it)-282(can)-281(b)-28(e)-282(seen)-282(that)-281(the)-282(k)27(ey)-281(is)-281(an)-282(essen)27(tial)-281(comp)-28(onen)27(t.)-426(Therefore,)]TJ
0 -21.91 TD
[(Key)-322(Managemen)27(t,)-324(whic)27(h)-322(is)-323(the)-322(set)-323(of)-323(tec)27(hniques)-322(and)-322(pro)-28(cedures)-323(to)-322(supp)-28(ort)-323(the)-322(establishmen)26(t)-321(and)]TJ
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[(main)27(tenance)-461(of)-463(k)27(eys)-462(b)-28(et)27(w)28(een)-462(authorized)-462(parties,)-495(is)-463(a)-462(v)26(ery)-461(imp)-28(ortan)27(t)-462(task.)-832(In)-463(this)-463(section,)-494(w)26(e)]TJ
T*
[(shall)-340(giv)26(e)-339(an)-341(o)27(v)27(erview)-339(of)-341(k)27(ey)-340(establishmen)27(t)-340(and)-341(also)-341(discuss)-341(on)-340(the)-341(di\256eren)27(t)-340(t)27(yp)-27(es)-341(of)-341(attac)27(ks)-340(from)]TJ
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[(di\256eren)27(t)-272(adv)27(ersaries.)-423(Key)-273(Establishmen)27(t)-272(is)-273(de\257ned)-273(as)-273(a)-273(pro)-28(cess)-273(or)-272(proto)-28(col)-273(whereb)27(y)-272(a)-273(shared)-273(secret)]TJ
0 -21.92 TD
[(k)27(ey)-306(b)-28(ecomes)-307(a)27(v)55(ailable)-306(to)-307(t)27(w)28(o)-307(or)-307(more)-307(parties)-307(for)-307(subsequen)26(t)-306(cryptographic)-307(use.)-436(Key)-307(establishmen)27(t)]TJ
0 -21.91 TD
[(can)-333(b)-28(e)-333(divided)-333(in)27(to)-333(t)27(w)28(o)-333(categories)-333(:)-444(Key)-334(transp)-27(ort)-334(and)-333(k)27(ey)-333(agreemen)27(t.)]TJ
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[(Key)-571(T)95(ransp)-31(ort)]TJ
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93.82 0 Td
[(proto)-28(cols)-496(or)-497(mec)26(hanisms)-495(are)-497(k)26(ey)-496(establishmen)27(t)-496(tec)27(hniques)-496(where)-497(one)-497(part)27(y)]TJ
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[(creates)-443(or)-444(otherwise)-444(obtains)-444(a)-444(secret)-444(v)55(alue)-443(and)-444(securely)-444(transfers)-444(this)-444(secret)-444(v)55(alue)-443(to)-444(the)-444(other)]TJ
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[(de\257ned)-294(for)-295(EAP)-295(suc)27(h)-294(as)-295(EAP-MD5,)-302(EAP-TLS)-295(\(T)82(ransp)-27(ort)-294(La)26(y)28(er)-294(Securit)27(y\),)-301(EAP-TTLS)-295(\(T)82(unnelled)]TJ
T*
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/T1_0 10.91 Tf
12.58 4.37 Td
[(is)-414(called)-414(a)-413(quadratic)-414(residue)-414(mo)-28(dulo)]TJ
184.32 2.76 Td
(\271)Tj
/T1_3 10.91 Tf
-3.15 -2.76 Td
(N)Tj
/T1_0 10.91 Tf
14.46 0 Td
[(if)-414(there)-413(exist)-414(an)]TJ
/T1_3 10.91 Tf
82.37 0 Td
(x)Tj
/T1_6 10.91 Tf
10.73 0 Td
(2)Tj
/T1_3 10.91 Tf
11.76 0 Td
(Z)Tj
/T1_4 7.97 Tf
8.23 3.96 Td
(\244)Tj
/T1_1 7.97 Tf
1.59 -6.32 Td
(\271)Tj
/T1_5 7.97 Tf
-2.37 -2.01 Td
(N)Tj
/T1_0 10.91 Tf
12.58 4.37 Td
[(suc)27(h)-412(that)]TJ
/T1_3 10.91 Tf
-422.4 -21.91 Td
(x)Tj
/T1_1 7.97 Tf
6.23 3.95 Td
(2)Tj
/T1_6 10.91 Tf
8.54 -3.95 Td
(\264)Tj
/T1_3 10.91 Tf
12.3 0 Td
(v)Tj
/T1_0 10.91 Tf
8.7 0 Td
[(mo)-28(d)]TJ
27.09 2.75 Td
(\271)Tj
/T1_3 10.91 Tf
-3.15 -2.75 Td
(N)Tj
/T1_0 10.91 Tf
9.95 0 Td
[(.)-572(If)-377(no)-376(suc)27(h)]TJ
/T1_3 10.91 Tf
61.34 0 Td
(x)Tj
/T1_0 10.91 Tf
10.33 0 Td
[(exists,)-387(then)]TJ
/T1_3 10.91 Tf
59.04 0 Td
(v)Tj
/T1_0 10.91 Tf
9.78 0 Td
[(is)-376(called)-376(a)-376(quadratic)-377(non-residue)-376(mo)-28(dulo)]TJ
203.06 2.75 Td
(\271)Tj
/T1_3 10.91 Tf
-3.15 -2.75 Td
(N)Tj
/T1_0 10.91 Tf
9.95 0 Td
(.)Tj
/T1_3 10.91 Tf
9.28 0 Td
(g)Tj
/T1_6 10.91 Tf
9.4 0 Td
(6)Tj
/T1_0 10.91 Tf
[(=)-349(1)-376(is)]TJ
-438.69 -21.92 Td
[(denoted)-255(as)-256(a)-255(quadratic)-256(residue)-255(that)-256(is)-255(c)26(hosen)-254(uniformly)-256(at)-255(random)-256(in)-255(the)-256(set)-255(of)-256(quadratic)-256(residues)-255(in)]TJ
/T1_3 10.91 Tf
T*
(Z)Tj
/T1_4 7.97 Tf
8.22 3.96 Td
(\244)Tj
/T1_1 7.97 Tf
1.6 -6.31 Td
(\271)Tj
/T1_5 7.97 Tf
-2.38 -2.02 Td
(N)Tj
/T1_0 10.91 Tf
8.07 4.37 Td
[(.)-415(Using)-245(this)-245(quadratic)-245(residue)]TJ
/T1_3 10.91 Tf
141.49 0 Td
(g)Tj
/T1_0 10.91 Tf
5.6 0 Td
[(,)-262(a)-245(\257nite)-245(group)]TJ
/T1_3 10.91 Tf
70.9 0 Td
(G)Tj
/T1_0 10.91 Tf
11.6 0 Td
(=)Tj
/T1_6 10.91 Tf
11.51 0 Td
(h)Tj
/T1_3 10.91 Tf
4.25 0 Td
(g)Tj
/T1_6 10.91 Tf
5.59 0 Td
(i)Tj
/T1_0 10.91 Tf
6.91 0 Td
[(is)-245(de\257ned)-245(where)]TJ
/T1_6 10.91 Tf
77.19 0 Td
(h)Tj
/T1_3 10.91 Tf
(g)Tj
/T1_6 10.91 Tf
9.83 0 Td
(i)Tj
/T1_0 10.91 Tf
6.92 0 Td
[(is)-245(the)-245(cyclic)-245(subgroup)]TJ
-367.3 -21.91 Td
(of)Tj
/T1_3 10.91 Tf
11.83 0 Td
(Z)Tj
/T1_4 7.97 Tf
8.23 3.95 Td
(\244)Tj
/T1_1 7.97 Tf
1.59 -6.31 Td
(\271)Tj
/T1_5 7.97 Tf
-2.37 -2.02 Td
(N)Tj
/T1_0 10.91 Tf
11.11 4.38 Td
[(generated)-278(b)26(y)]TJ
/T1_3 10.91 Tf
63.68 0 Td
(g)Tj
/T1_0 10.91 Tf
5.59 0 Td
[(.)-426(Let)]TJ
/T1_2 10.91 Tf
26.63 0 Td
(H)Tj
/T1_0 10.91 Tf
10.77 0 Td
[(b)-27(e)-280(a)-279(one)-279(w)27(a)28(y)-279(cryptographic)-279(hash)-279(function)-279(where)]TJ
/T1_2 10.91 Tf
230.52 0 Td
(H)Tj
/T1_0 10.91 Tf
10.75 0 Td
(:)Tj
/T1_6 10.91 Tf
6.06 0 Td
(f)Tj
/T1_0 10.91 Tf
(0)Tj
/T1_3 10.91 Tf
(;)Tj
/T1_0 10.91 Tf
15.75 0 Td
(1)Tj
/T1_6 10.91 Tf
(g)Tj
/T1_4 7.97 Tf
10.91 3.95 Td
(\244)Tj
/T1_6 10.91 Tf
7.76 -3.95 Td
[(!)-277(f)]TJ
/T1_0 10.91 Tf
(0)Tj
/T1_3 10.91 Tf
(;)Tj
/T1_0 10.91 Tf
29.69 0 Td
(1)Tj
/T1_6 10.91 Tf
(g)Tj
/T1_5 7.97 Tf
10.9 3.95 Td
(\270)Tj
/T1_0 10.91 Tf
5.44 -3.95 Td
(,)Tj
-464.84 -21.92 Td
(where)Tj
/T1_3 10.91 Tf
31.45 0 Td
(\270)Tj
/T1_0 10.91 Tf
9.91 0 Td
[(is)-324(an)-326(in)27(teger.)-441(In)-325(the)-325(NLKKW)-325(proto)-28(col,)-327(all)-325(messages)-325(sen)26(t)-324(are)-325(signed)-325(b)26(y)-324(the)-325(sender)-325(and)-325(all)]TJ
-41.36 -21.92 Td
[(messages)-333(receiv)27(ed)-332(are)-334(v)27(eri\257ed)-332(to)-334(ensure)-333(that)-333(the)-334(group)-333(k)27(ey)-332(agreemen)26(t)-332(is)-333(authen)26(ticated.)]TJ
/T1_7 10.91 Tf
0 -37.17 TD
[(Initial)-538(GKA)-539(Proto)-32(col)]TJ
/T1_0 10.91 Tf
131.81 0 Td
[(Assume)-468(w)27(e)-468(ha)27(v)28(e)-468(a)-468(group)-469(of)]TJ
/T1_3 10.91 Tf
142.9 0 Td
(n)Tj
/T1_0 10.91 Tf
11.65 0 Td
(users,)Tj
/T1_6 10.91 Tf
32.29 0 Td
(G)Tj
/T1_0 10.91 Tf
12.62 0 Td
(=)Tj
/T1_6 10.91 Tf
13.97 0 Td
(f)Tj
/T1_8 10.91 Tf
(U)Tj
/T1_1 7.97 Tf
11.17 -1.64 Td
(1)Tj
/T1_3 10.91 Tf
4.74 1.64 Td
[(;)-166(:)-166(:)-167(:)-167(;)]TJ
/T1_8 10.91 Tf
24.23 0 Td
(U)Tj
/T1_5 7.97 Tf
5.73 -1.64 Td
(n)Tj
/T1_6 10.91 Tf
5.63 1.64 Td
(g)Tj
/T1_0 10.91 Tf
10.56 0 Td
[(who)-468(wish)-469(to)]TJ
-407.3 -21.92 Td
[(establish)-279(a)-279(group)-279(k)27(ey)-279(b)27(y)-278(running)-279(the)-280(Initial)-279(GKA)-279(Proto)-28(col)-279(proto)-28(col)-279(where)]TJ
/T1_8 10.91 Tf
351.8 0 Td
(U)Tj
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5.73 -1.64 Td
(1)Tj
/T1_0 10.91 Tf
7.78 1.64 Td
[(is)-278(the)-280(con)27(troller)-278(no)-28(de.)]TJ
-365.31 -21.92 Td
[(The)-333(Initial)-333(GKA)-333(Proto)-28(col)-334(proto)-27(col)-334(runs)-333(in)-333(t)26(w)28(o)-332(rounds)-334(and)-333(is)-333(describ)-28(ed)-333(as)-334(follo)27(ws:)]TJ
0 -21.91 TD
[(During)-430(Round)-430(1,)-455(all)-430(users)]TJ
/T1_8 10.91 Tf
132.37 0 Td
(U)Tj
/T1_5 7.97 Tf
5.72 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
8.08 1.64 Td
[(for)-429(2)]TJ
/T1_6 10.91 Tf
27.99 0 Td
(\267)Tj
/T1_3 10.91 Tf
13.28 0 Td
(i)Tj
/T1_6 10.91 Tf
8.55 0 Td
(\267)Tj
/T1_3 10.91 Tf
13.27 0 Td
(n)Tj
/T1_0 10.91 Tf
11.24 0 Td
[(selects)-430(random)]TJ
/T1_3 10.91 Tf
76.18 0 Td
(r)Tj
/T1_5 7.97 Tf
4.93 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
8.17 1.64 Td
(=)Tj
/T1_6 10.91 Tf
13.27 0 Td
(f)Tj
/T1_0 10.91 Tf
(1)Tj
/T1_3 10.91 Tf
(;)Tj
/T1_0 10.91 Tf
15.76 0 Td
(2)Tj
/T1_3 10.91 Tf
(;)Tj
/T1_0 10.91 Tf
10.3 0 Td
(3)Tj
/T1_3 10.91 Tf
(;)Tj
/T1_6 10.91 Tf
10.3 0 Td
[(\242)-166(\242)-166(\242)]TJ
/T1_3 10.91 Tf
16.36 0 Td
(;)Tj
/T1_0 10.91 Tf
8 2.75 Td
(\271)Tj
/T1_3 10.91 Tf
-3.16 -2.75 Td
(N)Tj
/T1_6 10.91 Tf
9.95 0 Td
(g)Tj
/T1_0 10.91 Tf
10.15 0 Td
[(and)-430(computes)]TJ
/T1_3 10.91 Tf
-400.71 -21.92 Td
(z)Tj
/T1_5 7.97 Tf
5.07 -1.64 Td
(i)Tj
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7.25 1.64 Td
(=)Tj
/T1_3 10.91 Tf
12.36 0 Td
(g)Tj
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5.59 3.96 Td
(r)Tj
/T1_9 5.98 Tf
3.82 -1.22 Td
(i)Tj
/T1_0 10.91 Tf
6.69 -2.74 Td
[(mo)-27(d)]TJ
27.09 2.76 Td
(\271)Tj
/T1_3 10.91 Tf
-3.16 -2.76 Td
(N)Tj
/T1_0 10.91 Tf
9.96 0 Td
[(.)-583(Next)]TJ
/T1_8 10.91 Tf
36.55 0 Td
(U)Tj
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5.73 -1.64 Td
(i)Tj
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7.52 1.64 Td
(sends)Tj
/T1_3 10.91 Tf
29.71 0 Td
(z)Tj
/T1_5 7.97 Tf
5.07 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
7.52 1.64 Td
[(with)-380(signature)]TJ
/T1_3 10.91 Tf
73.21 0 Td
(\276)Tj
/T1_5 7.97 Tf
6.23 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
7.52 1.64 Td
[(to)-379(con)27(troller)]TJ
/T1_8 10.91 Tf
63.18 0 Td
(U)Tj
/T1_1 7.97 Tf
5.72 -1.64 Td
(1)Tj
/T1_0 10.91 Tf
4.73 1.64 Td
[(.)-583(In)-380(Round)-380(2,)-391(after)-380(receiving)]TJ
-327.36 -21.92 Td
[(and)-353(v)27(erifying)-352(all)-353(receiv)27(ed)-352(messages,)]TJ
/T1_8 10.91 Tf
173.44 0 Td
(U)Tj
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5.73 -1.63 Td
(1)Tj
/T1_0 10.91 Tf
8.58 1.63 Td
[(\257rst)-353(selects)]TJ
/T1_3 10.91 Tf
56.99 0 Td
(r)Tj
/T1_1 7.97 Tf
4.92 -1.63 Td
(1)Tj
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8.58 1.63 Td
[(and)-353(compute)]TJ
/T1_3 10.91 Tf
65.87 0 Td
(z)Tj
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5.07 -1.63 Td
(1)Tj
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8.12 1.63 Td
(=)Tj
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11.87 0 Td
(g)Tj
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5.59 3.96 Td
(r)Tj
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3.82 -1.1 Td
(1)Tj
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7.68 -2.86 Td
[(mo)-27(d)]TJ
27.09 2.76 Td
(\271)Tj
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-3.16 -2.76 Td
(N)Tj
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9.96 0 Td
(.)Tj
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8.52 0 Td
(U)Tj
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5.72 -1.63 Td
(1)Tj
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8.58 1.63 Td
(computes)Tj
/T1_3 10.91 Tf
-422.97 -21.91 Td
(y)Tj
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5.35 -1.64 Td
(i)Tj
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6.41 1.64 Td
(=)Tj
/T1_3 10.91 Tf
11.51 0 Td
(z)Tj
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5.55 4.86 Td
(r)Tj
/T1_10 5.98 Tf
3.82 -1.11 Td
(1)Tj
/T1_5 7.97 Tf
-4.3 -7.01 Td
(i)Tj
/T1_0 10.91 Tf
11.98 3.26 Td
[(mo)-27(d)]TJ
27.09 2.75 Td
(\271)Tj
/T1_3 10.91 Tf
-3.16 -2.75 Td
(N)Tj
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9.95 0 Td
(.)Tj
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7.76 0 Td
(U)Tj
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5.73 -1.64 Td
(1)Tj
/T1_0 10.91 Tf
8.01 1.64 Td
[(then)-301(computes)]TJ
/T1_3 10.91 Tf
72.67 0 Td
(Y)Tj
/T1_0 10.91 Tf
12.04 0 Td
(as)Tj
/T1_3 10.91 Tf
13.04 0 Td
(Y)Tj
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11.79 0 Td
(=)Tj
/T1_11 10.91 Tf
11.51 8.18 Td
(Q)Tj
/T1_5 7.97 Tf
10.3 -3.16 Td
(n)Tj
0 -8.25 TD
(i)Tj
/T1_1 7.97 Tf
2.88 0 Td
(=2)Tj
/T1_3 10.91 Tf
13.13 3.23 Td
(y)Tj
/T1_5 7.97 Tf
5.35 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
6.41 1.64 Td
[(mo)-27(d)]TJ
27.09 2.75 Td
(\271)Tj
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-3.16 -2.75 Td
(N)Tj
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13.24 0 Td
(if)Tj
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9.64 0 Td
(n)Tj
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9.83 0 Td
[(is)-301(ev)27(en)-300(or)-301(as)]TJ
/T1_3 10.91 Tf
61.16 0 Td
(Y)Tj
/T1_0 10.91 Tf
11.78 0 Td
(=)Tj
/T1_11 10.91 Tf
11.51 8.18 Td
(Q)Tj
/T1_5 7.97 Tf
10.3 -3.16 Td
(n)Tj
T*
(i)Tj
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2.89 0 Td
(=1)Tj
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13.13 3.23 Td
(y)Tj
/T1_5 7.97 Tf
5.35 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
6.41 1.64 Td
[(mo)-27(d)]TJ
27.09 2.75 Td
(\271)Tj
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-3.16 -2.75 Td
(N)Tj
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-457.92 -21.92 Td
(if)Tj
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10.04 0 Td
(n)Tj
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10.22 0 Td
[(is)-336(o)-28(dd.)]TJ
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36.88 0 Td
(U)Tj
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5.72 -1.63 Td
(1)Tj
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8.41 1.63 Td
[(also)-336(computes)-337(the)-337(set)]TJ
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106.37 0 Td
(T)Tj
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10.98 0 Td
(=)Tj
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11.58 0 Td
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(T)Tj
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11.83 -1.63 Td
(i)Tj
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3.38 1.63 Td
(j)Tj
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(2)Tj
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11.58 0 Td
(\267)Tj
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11.58 0 Td
(i)Tj
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6.85 0 Td
(\267)Tj
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11.58 0 Td
(n)Tj
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6.54 0 Td
(g)Tj
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9.13 0 Td
(where)Tj
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31.58 0 Td
(T)Tj
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6.37 -1.63 Td
(i)Tj
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6.48 1.63 Td
(=)Tj
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11.58 0 Td
(Y)Tj
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11.2 0 Td
(\242)Tj
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5.48 0 Td
(y)Tj
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5.74 4.59 Td
(\241)Tj
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(1)Tj
/T1_5 7.97 Tf
-0.39 -7.84 Td
(i)Tj
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14.73 3.25 Td
[(mo)-28(d)]TJ
27.1 2.76 Td
(\271)Tj
/T1_3 10.91 Tf
-3.16 -2.76 Td
(N)Tj
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13.62 0 Td
[(for)-337(2)]TJ
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25.29 0 Td
(\267)Tj
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11.57 0 Td
(i)Tj
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6.86 0 Td
(\267)Tj
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11.58 0 Td
(n)Tj
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6.54 0 Td
(.)Tj
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(Let)Tj
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19.85 0 Td
(Z)Tj
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11.78 0 Td
(=)Tj
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12.04 0 Td
(f)Tj
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(z)Tj
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10.52 -1.63 Td
(i)Tj
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3.38 1.63 Td
(j)Tj
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(1)Tj
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12.04 0 Td
(\267)Tj
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12.03 0 Td
(i)Tj
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7.31 0 Td
(\267)Tj
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12.03 0 Td
(n)Tj
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(g)Tj
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[(.)-530(Next,)]TJ
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50.9 0 Td
(U)Tj
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5.73 -1.63 Td
(1)Tj
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8.68 1.63 Td
(broadcast)Tj
/T1_3 10.91 Tf
50.08 0 Td
(Z)Tj
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8.23 0 Td
(,)Tj
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7.06 0 Td
(T)Tj
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11.83 0 Td
(and)Tj
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21.52 0 Td
(\276)Tj
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6.23 -1.63 Td
(1)Tj
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8.68 1.63 Td
[(to)-362(the)-362(group,)-369(where)]TJ
/T1_3 10.91 Tf
98.95 0 Td
(\276)Tj
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6.23 -1.63 Td
(1)Tj
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8.68 1.63 Td
[(is)-361(the)-363(signature)]TJ
-393.78 -21.91 Td
[(of)-409(the)-409(broadcast)-410(message.)-673(During)-409(the)-410(k)27(ey)-408(computation)-410(round,)-428(up)-28(on)-410(receiving)-409(and)-410(v)27(erifying)-408(the)]TJ
0 -21.92 TD
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/T1_4 10.91 Tf
44.29 0 Td
(U)Tj
/T1_8 7.97 Tf
5.72 -1.64 Td
(1)Tj
/T1_1 10.91 Tf
8.66 1.64 Td
(broadcast)Tj
/T1_2 10.91 Tf
50.08 0 Td
(z)Tj
/T1_8 7.97 Tf
5.07 -1.64 Td
(1)Tj
/T1_1 10.91 Tf
4.73 1.64 Td
(,)Tj
/T1_2 10.91 Tf
7.04 0 Td
(z)Tj
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5.55 3.95 Td
(0)Tj
/T1_8 7.97 Tf
-0.48 -6.88 Td
(1)Tj
/T1_1 10.91 Tf
4.73 2.93 Td
(,)Tj
/T1_2 10.91 Tf
7.03 0 Td
(T)Tj
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7.89 3.95 Td
(0)Tj
/T1_1 10.91 Tf
6.73 -3.95 Td
(and)Tj
/T1_2 10.91 Tf
21.5 0 Td
(\276)Tj
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6.63 3.95 Td
(0)Tj
/T1_8 7.97 Tf
-0.39 -6.88 Td
(1)Tj
/T1_1 10.91 Tf
8.66 2.93 Td
[(to)-360(the)-361(group,)]TJ
-404.84 -21.92 Td
(where)Tj
/T1_2 10.91 Tf
31.54 0 Td
(\276)Tj
/T1_9 7.97 Tf
6.62 3.96 Td
(0)Tj
/T1_8 7.97 Tf
-0.39 -6.88 Td
(1)Tj
/T1_1 10.91 Tf
8.37 2.92 Td
[(is)-332(the)-334(signature)-333(of)-333(the)-334(broadcast)-333(message.)]TJ
-46.14 -21.92 Td
[(Up)-27(on)-487(receiving)-486(and)-487(v)27(erifying)-486(the)-486(broadcast)-487(message)-487(from)]TJ
/T1_4 10.91 Tf
291.17 0 Td
(U)Tj
/T1_8 7.97 Tf
5.73 -1.63 Td
(1)Tj
/T1_1 10.91 Tf
4.73 1.63 Td
[(,)-524(eac)26(h)-485(remaining)-487(user)]TJ
/T1_4 10.91 Tf
112.35 0 Td
(U)Tj
/T1_5 7.97 Tf
5.72 -1.63 Td
(i)Tj
/T1_2 10.91 Tf
10.41 1.63 Td
(=)Tj
/T1_3 10.91 Tf
-1.21 0 Td
[(2)-533(L)]TJ
/T1_1 10.91 Tf
25.91 0 Td
(for)Tj
-454.81 -21.91 Td
(2)Tj
/T1_3 10.91 Tf
9.55 0 Td
(\267)Tj
/T1_2 10.91 Tf
12.58 0 Td
(i)Tj
/T1_3 10.91 Tf
7.85 0 Td
(6)Tj
/T1_1 10.91 Tf
(=)Tj
/T1_2 10.91 Tf
12.58 0 Td
(l)Tj
/T1_5 7.97 Tf
3.25 -1.78 Td
(k)Tj
/T1_3 10.91 Tf
9.21 1.78 Td
(\267)Tj
/T1_2 10.91 Tf
12.58 0 Td
(n)Tj
/T1_1 10.91 Tf
10.82 0 Td
[(c)27(hec)28(ks)-391(if)-392(the)-392(receiv)27(ed)]TJ
/T1_2 10.91 Tf
106.87 0 Td
(z)Tj
/T1_8 7.97 Tf
5.07 -1.64 Td
(1)Tj
/T1_1 10.91 Tf
9 1.64 Td
[(is)-392(equal)-392(to)-392(the)-392(one)-392(receiv)27(ed)-391(in)-392(the)-392(previous)-392(session)-392(and)]TJ
-199.36 -21.92 Td
(computes)Tj
/T1_2 10.91 Tf
48.39 0 Td
(Y)Tj
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8.76 3.96 Td
(0)Tj
/T1_1 10.91 Tf
5.82 -3.96 Td
[(=)-278(\()]TJ
/T1_2 10.91 Tf
(z)Tj
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21.31 3.96 Td
(0)Tj
/T1_8 7.97 Tf
-0.48 -6.88 Td
(1)Tj
/T1_1 10.91 Tf
4.73 2.92 Td
(\))Tj
/T1_5 7.97 Tf
4.24 3.96 Td
(r)Tj
/T1_7 5.98 Tf
3.82 -1.22 Td
(i)Tj
/T1_3 10.91 Tf
5.81 -2.74 Td
(\242)Tj
/T1_2 10.91 Tf
5.18 0 Td
(T)Tj
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7.88 3.96 Td
(0)Tj
/T1_5 7.97 Tf
-1.51 -7.01 Td
(i)Tj
/T1_1 10.91 Tf
7.34 3.05 Td
[(mo)-27(d)]TJ
27.09 2.76 Td
(\271)Tj
/T1_2 10.91 Tf
-3.16 -2.76 Td
(N)Tj
/T1_1 10.91 Tf
9.95 0 Td
[(.)-440(All)]TJ
/T1_4 10.91 Tf
25.57 0 Td
(U)Tj
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5.72 -1.64 Td
(i)Tj
/T1_2 10.91 Tf
7.63 1.64 Td
(=)Tj
/T1_3 10.91 Tf
-1.22 0 Td
[(2)-278(L)]TJ
/T1_1 10.91 Tf
21.32 0 Td
[(for)-321(1)]TJ
/T1_3 10.91 Tf
25.04 0 Td
(\267)Tj
/T1_2 10.91 Tf
11.51 0 Td
(i)Tj
/T1_3 10.91 Tf
6.79 0 Td
(6)Tj
/T1_1 10.91 Tf
(=)Tj
/T1_2 10.91 Tf
11.51 0 Td
(l)Tj
/T1_5 7.97 Tf
3.26 -1.78 Td
(k)Tj
/T1_3 10.91 Tf
8.14 1.78 Td
(\267)Tj
/T1_2 10.91 Tf
11.52 0 Td
(n)Tj
/T1_1 10.91 Tf
10.04 0 Td
[(then)-320(computes)-321(the)-321(new)-320(session)-321(k)27(ey)]TJ
/T1_2 10.91 Tf
-302 -21.92 Td
(K)Tj
/T1_9 7.97 Tf
10.04 3.96 Td
(0)Tj
/T1_1 10.91 Tf
5.83 -3.96 Td
(=)Tj
/T1_12 10.91 Tf
11.51 0 Td
(H)Tj
/T1_1 10.91 Tf
(\()Tj
/T1_2 10.91 Tf
(T)Tj
/T1_9 7.97 Tf
19.85 3.96 Td
(0)Tj
/T1_3 10.91 Tf
2.8 -3.96 Td
(jj)Tj
/T1_2 10.91 Tf
6.06 0 Td
(Y)Tj
/T1_9 7.97 Tf
8.75 3.96 Td
(0)Tj
/T1_1 10.91 Tf
2.8 -3.96 Td
[(\))-332(and)-334(up)-28(dates)]TJ
/T1_2 10.91 Tf
70.04 0 Td
(Z)Tj
/T1_9 7.97 Tf
8.22 3.96 Td
(0)Tj
/T1_1 10.91 Tf
5.83 -3.96 Td
(=)Tj
/T1_3 10.91 Tf
11.51 0 Td
(f)Tj
/T1_2 10.91 Tf
(z)Tj
/T1_5 7.97 Tf
10.52 -1.63 Td
(i)Tj
/T1_3 10.91 Tf
3.38 1.63 Td
(j)Tj
/T1_1 10.91 Tf
(1)Tj
/T1_3 10.91 Tf
11.51 0 Td
(\267)Tj
/T1_2 10.91 Tf
11.52 0 Td
(i)Tj
/T1_3 10.91 Tf
6.78 0 Td
(6)Tj
/T1_1 10.91 Tf
(=)Tj
/T1_2 10.91 Tf
11.52 0 Td
(l)Tj
/T1_5 7.97 Tf
3.25 -1.77 Td
(k)Tj
/T1_3 10.91 Tf
8.15 1.77 Td
(\267)Tj
/T1_2 10.91 Tf
11.51 0 Td
(n)Tj
/T1_3 10.91 Tf
(g)Tj
/T1_1 10.91 Tf
(.)Tj
/T1_0 10.91 Tf
-241.38 -37.17 Td
[(Join)-502(Proto)-32(col)]TJ
/T1_1 10.91 Tf
86.43 0 Td
[(The)-437(Join)-437(Proto)-28(col)-437(is)-438(executed)-437(when)-437(a)-437(set)-438(of)]TJ
/T1_2 10.91 Tf
223.63 0 Td
(m)Tj
/T1_1 10.91 Tf
14.35 0 Td
[(new)-436(users)]TJ
/T1_3 10.91 Tf
52.1 0 Td
(J)Tj
/T1_1 10.91 Tf
14.17 0 Td
[(joins)-437(the)-438(group.)]TJ
-390.68 -21.92 Td
[(The)-319(Join)-320(proto)-27(col)-320(will)-320(c)27(hange)-318(the)-320(curren)27(t)-319(group)-319(k)26(ey)-318(to)-320(a)-320(new)-319(group)-320(k)27(ey)-319(to)-319(ensure)-320(that)-319(the)-320(joining)]TJ
0 -21.92 TD
[(users)-317(are)-318(not)-317(able)-318(to)-317(compute)-318(the)-317(previous)-318(group)-317(k)26(eys)-316(that)-318(w)27(ere)-317(used.)-439(It)-317(is)-318(assumed)-317(that)]TJ
/T1_4 10.91 Tf
428.01 0 Td
(U)Tj
/T1_8 7.97 Tf
5.72 -1.63 Td
(1)Tj
/T1_1 10.91 Tf
8.2 1.63 Td
[(is)-317(the)]TJ
-441.93 -21.91 Td
[(con)27(troller)-332(no)-28(de.)-444(The)-334(Join)-333(proto)-28(col)-333(tak)27(es)-333(t)27(w)28(o)-332(comm)26(unication)-332(rounds)-333(and)-334(is)-333(describ)-28(ed)-333(as)-333(follo)26(ws:)]TJ
T*
[(During)-318(Round)-318(1,)-321(eac)27(h)-317(new)-319(user)]TJ
/T1_4 10.91 Tf
153.36 0 Td
(U)Tj
/T1_5 7.97 Tf
5.73 -1.64 Td
(j)Tj
/T1_3 10.91 Tf
7.41 1.64 Td
[(2)-277(J)]TJ
/T1_1 10.91 Tf
23.17 0 Td
(for)Tj
/T1_2 10.91 Tf
16.53 0 Td
(n)Tj
/T1_1 10.91 Tf
8.64 0 Td
[(+)-191(1)]TJ
/T1_3 10.91 Tf
19.06 0 Td
(\267)Tj
/T1_2 10.91 Tf
11.51 0 Td
(j)Tj
/T1_3 10.91 Tf
8.14 0 Td
(\267)Tj
/T1_2 10.91 Tf
11.52 0 Td
(n)Tj
/T1_1 10.91 Tf
8.63 0 Td
(+)Tj
/T1_2 10.91 Tf
10.58 0 Td
(m)Tj
/T1_1 10.91 Tf
13.04 0 Td
[(selects)-318(random)]TJ
/T1_2 10.91 Tf
73.74 0 Td
(r)Tj
/T1_5 7.97 Tf
4.92 -1.64 Td
(j)Tj
/T1_1 10.91 Tf
7.41 1.64 Td
(=)Tj
/T1_3 10.91 Tf
11.52 0 Td
(f)Tj
/T1_1 10.91 Tf
(1)Tj
/T1_2 10.91 Tf
(;)Tj
/T1_1 10.91 Tf
15.75 0 Td
(2)Tj
/T1_2 10.91 Tf
(;)Tj
/T1_1 10.91 Tf
10.3 0 Td
(3)Tj
/T1_2 10.91 Tf
(;)Tj
/T1_3 10.91 Tf
10.3 0 Td
[(\242)-166(\242)-167(\242)]TJ
/T1_2 10.91 Tf
16.36 0 Td
(;)Tj
/T1_1 10.91 Tf
8 2.76 Td
(\271)Tj
/T1_2 10.91 Tf
-3.15 -2.76 Td
(N)Tj
/T1_3 10.91 Tf
9.95 0 Td
(g)Tj
/T1_1 10.91 Tf
-462.42 -21.92 Td
[(and)-353(computes)]TJ
/T1_2 10.91 Tf
70.19 0 Td
(z)Tj
/T1_5 7.97 Tf
5.07 -1.63 Td
(j)Tj
/T1_1 10.91 Tf
7.79 1.63 Td
(=)Tj
/T1_2 10.91 Tf
11.88 0 Td
(g)Tj
/T1_5 7.97 Tf
5.6 3.96 Td
(r)Tj
/T1_7 5.98 Tf
3.82 -1.21 Td
(j)Tj
/T1_1 10.91 Tf
7.42 -2.75 Td
[(mo)-28(d)]TJ
27.1 2.76 Td
(\271)Tj
/T1_2 10.91 Tf
-3.16 -2.76 Td
(N)Tj
/T1_1 10.91 Tf
9.95 0 Td
(.)Tj
/T1_4 10.91 Tf
8.55 0 Td
(U)Tj
/T1_5 7.97 Tf
5.73 -1.63 Td
(j)Tj
/T1_3 10.91 Tf
7.78 1.63 Td
[(2)-312(J)]TJ
/T1_1 10.91 Tf
23.94 0 Td
(broadcast)Tj
/T1_2 10.91 Tf
50 0 Td
(z)Tj
/T1_5 7.97 Tf
5.07 -1.63 Td
(j)Tj
/T1_1 10.91 Tf
8.25 1.63 Td
[(with)-353(signature)]TJ
/T1_2 10.91 Tf
72.64 0 Td
(\276)Tj
/T1_5 7.97 Tf
6.23 -1.63 Td
(j)Tj
/T1_1 10.91 Tf
8.24 1.63 Td
[(to)-354(con)27(troller)]TJ
/T1_4 10.91 Tf
62.62 0 Td
(U)Tj
/T1_8 7.97 Tf
5.72 -1.63 Td
(1)Tj
/T1_1 10.91 Tf
8.59 1.63 Td
[(and)-354(stores)]TJ
-419.02 -21.91 Td
[(its)-466(random)]TJ
/T1_2 10.91 Tf
58.13 0 Td
(r)Tj
/T1_5 7.97 Tf
4.93 -1.64 Td
(j)Tj
/T1_1 10.91 Tf
4.38 1.64 Td
[(.)-843(In)-467(Round)-467(2,)-500(after)-466(receiving)-467(and)-467(v)27(erifying)-465(all)-467(messages,)]TJ
/T1_4 10.91 Tf
289.12 0 Td
(U)Tj
/T1_8 7.97 Tf
5.73 -1.64 Td
(1)Tj
/T1_1 10.91 Tf
9.82 1.64 Td
[(selects)-466(new)-467(random)]TJ
/T1_2 10.91 Tf
-372.11 -21.92 Td
(r)Tj
/T1_9 7.97 Tf
5.22 3.96 Td
(0)Tj
/T1_8 7.97 Tf
-0.3 -6.88 Td
(1)Tj
/T1_1 10.91 Tf
7.82 2.92 Td
(=)Tj
/T1_3 10.91 Tf
11.58 0 Td
(f)Tj
/T1_1 10.91 Tf
(1)Tj
/T1_2 10.91 Tf
(;)Tj
/T1_1 10.91 Tf
15.75 0 Td
(2)Tj
/T1_2 10.91 Tf
(;)Tj
/T1_1 10.91 Tf
10.3 0 Td
(3)Tj
/T1_2 10.91 Tf
(;)Tj
/T1_3 10.91 Tf
10.3 0 Td
[(\242)-166(\242)-167(\242)]TJ
/T1_2 10.91 Tf
16.36 0 Td
(;)Tj
/T1_1 10.91 Tf
8 2.76 Td
(\271)Tj
/T1_2 10.91 Tf
-3.15 -2.76 Td
(N)Tj
/T1_3 10.91 Tf
9.95 0 Td
(g)Tj
/T1_1 10.91 Tf
[(,)-337(computes)]TJ
/T1_2 10.91 Tf
60.73 0 Td
(z)Tj
/T1_9 7.97 Tf
5.55 3.96 Td
(0)Tj
/T1_8 7.97 Tf
-0.48 -6.88 Td
(1)Tj
/T1_1 10.91 Tf
7.83 2.92 Td
(=)Tj
/T1_2 10.91 Tf
11.57 0 Td
(g)Tj
/T1_5 7.97 Tf
5.59 3.96 Td
(r)Tj
/T1_10 5.98 Tf
4.06 2.81 Td
(0)Tj
/T1_6 5.98 Tf
-0.24 -5.28 Td
(1)Tj
/T1_1 10.91 Tf
7.68 -1.49 Td
[(mo)-27(d)]TJ
27.09 2.76 Td
(\271)Tj
/T1_2 10.91 Tf
-3.16 -2.76 Td
(N)Tj
/T1_1 10.91 Tf
13.63 0 Td
(and)Tj
/T1_2 10.91 Tf
21.24 0 Td
(y)Tj
/T1_9 7.97 Tf
5.74 3.96 Td
(0)Tj
/T1_5 7.97 Tf
-0.39 -7.28 Td
(k)Tj
/T1_1 10.91 Tf
8.21 3.32 Td
(=)Tj
/T1_2 10.91 Tf
11.57 0 Td
(z)Tj
/T1_5 7.97 Tf
5.55 6.23 Td
(r)Tj
/T1_10 5.98 Tf
4.06 2.81 Td
(0)Tj
/T1_6 5.98 Tf
-0.24 -5.28 Td
(1)Tj
/T1_5 7.97 Tf
-4.3 -7.28 Td
(k)Tj
/T1_1 10.91 Tf
11.98 3.52 Td
[(mo)-27(d)]TJ
27.09 2.76 Td
(\271)Tj
/T1_2 10.91 Tf
-3.16 -2.76 Td
(N)Tj
/T1_1 10.91 Tf
13.63 0 Td
[(for)-336(1)]TJ
/T1_3 10.91 Tf
25.27 0 Td
(\267)Tj
/T1_2 10.91 Tf
11.57 0 Td
(k)Tj
/T1_3 10.91 Tf
9.12 0 Td
(\267)Tj
/T1_2 10.91 Tf
11.57 0 Td
(n)Tj
/T1_1 10.91 Tf
8.99 0 Td
(+)Tj
/T1_2 10.91 Tf
10.94 0 Td
(m)Tj
/T1_1 10.91 Tf
9.57 0 Td
[(.)-454(Next,)]TJ
/T1_4 10.91 Tf
37.72 0 Td
(U)Tj
/T1_8 7.97 Tf
5.73 -1.63 Td
(1)Tj
/T1_1 10.91 Tf
-463.14 -20.29 Td
(computes)Tj
/T1_2 10.91 Tf
48.57 0 Td
(Y)Tj
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8.76 3.96 Td
(0)Tj
/T1_1 10.91 Tf
6.46 -3.96 Td
(as)Tj
/T1_2 10.91 Tf
13.43 0 Td
(Y)Tj
/T1_9 7.97 Tf
8.76 3.96 Td
(0)Tj
/T1_1 10.91 Tf
5.88 -3.96 Td
(=)Tj
/T1_11 10.91 Tf
11.58 8.18 Td
(Q)Tj
/T1_5 7.97 Tf
10.3 -3.15 Td
(n)Tj
/T1_8 7.97 Tf
(+)Tj
/T1_5 7.97 Tf
(m)Tj
0 -8.25 TD
(k)Tj
/T1_8 7.97 Tf
4.62 0 Td
(=2)Tj
/T1_2 10.91 Tf
16.9 3.22 Td
(y)Tj
/T1_9 7.97 Tf
5.74 3.96 Td
(0)Tj
/T1_5 7.97 Tf
-0.39 -7.28 Td
(k)Tj
/T1_1 10.91 Tf
8.15 3.32 Td
[(mo)-27(d)]TJ
27.09 2.76 Td
(\271)Tj
/T1_2 10.91 Tf
-3.16 -2.76 Td
(N)Tj
/T1_1 10.91 Tf
13.63 0 Td
(if)Tj
/T1_2 10.91 Tf
10.03 0 Td
(n)Tj
/T1_1 10.91 Tf
10.22 0 Td
[(is)-337(ev)27(en)-336(or)-336(as)]TJ
/T1_2 10.91 Tf
62.71 0 Td
(Y)Tj
/T1_9 7.97 Tf
8.76 3.96 Td
(0)Tj
/T1_1 10.91 Tf
5.89 -3.96 Td
(=)Tj
/T1_11 10.91 Tf
11.57 8.18 Td
(Q)Tj
/T1_5 7.97 Tf
10.3 -3.15 Td
(n)Tj
/T1_8 7.97 Tf
(+)Tj
/T1_5 7.97 Tf
(m)Tj
T*
(k)Tj
/T1_8 7.97 Tf
4.62 0 Td
(=1)Tj
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16.91 3.22 Td
(y)Tj
/T1_9 7.97 Tf
5.73 3.96 Td
(0)Tj
/T1_5 7.97 Tf
-0.39 -7.28 Td
(k)Tj
/T1_1 10.91 Tf
8.15 3.32 Td
[(mo)-27(d)]TJ
27.09 2.76 Td
(\271)Tj
/T1_2 10.91 Tf
-3.16 -2.76 Td
(N)Tj
/T1_1 10.91 Tf
13.63 0 Td
(if)Tj
/T1_2 10.91 Tf
10.03 0 Td
(n)Tj
/T1_1 10.91 Tf
10.22 0 Td
[(is)-337(o)-27(dd.)]TJ
/T1_4 10.91 Tf
36.87 0 Td
(U)Tj
/T1_8 7.97 Tf
5.73 -1.63 Td
(1)Tj
/T1_1 10.91 Tf
8.4 1.63 Td
(also)Tj
-449.63 -21.91 Td
[(computes)-335(the)-336(set)]TJ
/T1_2 10.91 Tf
84.42 0 Td
(T)Tj
/T1_9 7.97 Tf
7.89 3.96 Td
(0)Tj
/T1_1 10.91 Tf
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/T1_0 10.91 Tf
(j)Tj
/T1_5 10.91 Tf
11.17 0 Td
(2)Tj
/T1_2 10.91 Tf
10.3 0 Td
([2)Tj
/T1_0 10.91 Tf
8.48 0 Td
[(;)-166(m)]TJ
/T1_2 10.91 Tf
16.3 0 Td
[(+)-171(1])]TJ
/T1_5 10.91 Tf
18.83 0 Td
(g)Tj
/T1_2 10.91 Tf
[(,)-312(where)-377(^)]TJ
/T1_0 10.91 Tf
43.16 0 Td
(y)Tj
/T1_1 7.97 Tf
5.35 -1.64 Td
(j)Tj
/T1_2 10.91 Tf
7.41 1.64 Td
(=)Tj
/T1_0 10.91 Tf
11.51 0 Td
(X)Tj
/T1_6 7.97 Tf
9.04 -1.64 Td
(1)Tj
/T1_5 10.91 Tf
6.6 1.64 Td
(\242)Tj
/T1_2 10.91 Tf
5.59 0 Td
(^)Tj
/T1_0 10.91 Tf
-0.69 0 Td
(x)Tj
/T1_8 7.97 Tf
6.23 4.58 Td
(\241)Tj
/T1_6 7.97 Tf
6.59 0 Td
(1)Tj
/T1_1 7.97 Tf
-6.59 -7.84 Td
(j)Tj
/T1_2 10.91 Tf
11.32 3.26 Td
(,)Tj
/T1_4 10.91 Tf
6.44 0 Td
(U)Tj
/T1_6 7.97 Tf
5.73 -1.64 Td
(1)Tj
/T1_2 10.91 Tf
8.09 1.64 Td
(broadcasts)Tj
/T1_0 10.91 Tf
53.8 0 Td
(!)Tj
/T1_6 7.97 Tf
6.79 -1.64 Td
(1)Tj
/T1_5 10.91 Tf
4.73 1.64 Td
(jj)Tj
/T1_0 10.91 Tf
6.06 0 Td
(Y)Tj
/T1_6 7.97 Tf
6.33 -1.64 Td
(1)Tj
/T1_2 10.91 Tf
4.73 1.64 Td
(.)Tj
-464.84 -21.92 Td
[(In)-410(the)-410(Key)-410(Computation)-410(round,)-429(all)-411(users)]TJ
/T1_4 10.91 Tf
204.99 0 Td
(U)Tj
/T1_1 7.97 Tf
5.72 -1.63 Td
(i)Tj
/T1_2 10.91 Tf
3.38 1.63 Td
[(,)-429(subgroup)-410(con)26(trollers)]TJ
/T1_4 10.91 Tf
109.88 0 Td
(U)Tj
/T1_1 7.97 Tf
5.73 -1.63 Td
(j)Tj
/T1_2 10.91 Tf
8.85 1.63 Td
[(and)-410(main)-410(con)27(troller)]TJ
/T1_4 10.91 Tf
99.82 0 Td
(U)Tj
/T1_6 7.97 Tf
5.73 -1.63 Td
(1)Tj
/T1_2 10.91 Tf
9.2 1.63 Td
(are)Tj
-453.3 -21.91 Td
[(able)-342(to)-343(generate)-343(the)-342(session)-343(k)27(ey)]TJ
/T1_0 10.91 Tf
155.02 0 Td
(K)Tj
/T1_2 10.91 Tf
13.79 0 Td
[(b)28(y)-342(\257rst)-343(calculating)]TJ
/T1_0 10.91 Tf
93.09 0 Td
(k)Tj
/T1_1 7.97 Tf
5.68 -1.64 Td
(j)Tj
/T1_2 10.91 Tf
7.58 1.64 Td
(=)Tj
/T1_9 10.91 Tf
11.68 0 Td
(H)Tj
/T1_2 10.91 Tf
7.73 0 Td
(\()Tj
/T1_0 10.91 Tf
(Y)Tj
/T1_1 7.97 Tf
10.57 -1.64 Td
(j)Tj
/T1_5 10.91 Tf
4.38 1.64 Td
(jj)Tj
/T1_0 10.91 Tf
6.06 0 Td
(X)Tj
/T1_1 7.97 Tf
9.04 -1.64 Td
(j)Tj
/T1_2 10.91 Tf
4.38 1.64 Td
[(\))-342(with)]TJ
/T1_0 10.91 Tf
32.92 0 Td
(X)Tj
/T1_1 7.97 Tf
9.04 -1.64 Td
(j)Tj
/T1_2 10.91 Tf
7.58 1.64 Td
(=)Tj
/T1_0 10.91 Tf
11.68 0 Td
(y)Tj
/T1_1 7.97 Tf
5.35 -1.64 Td
(i)Tj
/T1_5 10.91 Tf
5.87 1.64 Td
(\242)Tj
/T1_0 10.91 Tf
5.52 0 Td
(!)Tj
/T1_1 7.97 Tf
7.18 4.97 Td
(r)Tj
/T1_3 5.98 Tf
3.82 -1.22 Td
(i)Tj
/T1_1 7.97 Tf
-4.21 -7.01 Td
(j)Tj
/T1_2 10.91 Tf
11.61 3.26 Td
[(and)-342(then)]TJ
/T1_0 10.91 Tf
-425.36 -21.92 Td
(K)Tj
/T1_2 10.91 Tf
13.07 0 Td
(=)Tj
/T1_9 10.91 Tf
11.51 0 Td
(H)Tj
/T1_2 10.91 Tf
7.73 0 Td
(\()Tj
/T1_0 10.91 Tf
(Y)Tj
/T1_6 7.97 Tf
10.57 -1.64 Td
(1)Tj
/T1_5 10.91 Tf
4.73 1.64 Td
(jj)Tj
/T1_0 10.91 Tf
6.06 0 Td
(X)Tj
/T1_6 7.97 Tf
9.04 -1.64 Td
(1)Tj
/T1_2 10.91 Tf
4.73 1.64 Td
[(\))-333(with)]TJ
/T1_0 10.91 Tf
32.72 0 Td
(X)Tj
/T1_6 7.97 Tf
9.03 -1.64 Td
(1)Tj
/T1_2 10.91 Tf
7.76 1.64 Td
[(=)-346(^)]TJ
/T1_0 10.91 Tf
11.51 0 Td
(y)Tj
/T1_1 7.97 Tf
5.35 -1.64 Td
(j)Tj
/T1_5 10.91 Tf
6.81 1.64 Td
(\242)Tj
/T1_0 10.91 Tf
5.45 0 Td
(!)Tj
/T1_1 7.97 Tf
7.18 6.13 Td
(k)Tj
/T1_3 5.98 Tf
4.41 -1.21 Td
(j)Tj
/T1_6 7.97 Tf
-4.8 -8.04 Td
(1)Tj
/T1_2 10.91 Tf
9.2 3.12 Td
(.)Tj
/T1_11 11.95 Tf
-162.06 -37.82 Td
[(2.7.10)-1125(Saeednia)-375(and)-375(Safa)31(vi-Naini)-374(sc)30(heme)]TJ
/T1_2 10.91 Tf
0 -28.96 TD
[(Saeednia)-236(and)-237(Safa)26(vi-Naini)-236([SSN98])-236(prop)-28(osed)-237(an)-237(iden)27(tit)27(y-based)-235(GKA)-237(proto)-28(col)-237(called)-237(the)-237(SSN)-237(sc)27(heme)]TJ
0 -21.92 TD
[(that)-317(is)-317(based)-317(on)-317(the)-317(BD)-317(GKA)-317(proto)-28(col)-317(describ)-28(ed)-317(in)-317(Section)-317(2.7.6.)-439(Their)-317(idea)-317(is)-317(to)-317(use)-317(the)-317(iden)27(tit)27(y)]TJ
T*
[(information)-267(of)-268(adjacen)26(t)-266(principals)-268(to)-268(gain)-268(authen)27(tication)-267(of)-268(k)27(eying)-267(materials.)-423(A)-268(comp)-27(osite)-268(mo)-28(dulus)]TJ
3.16 -19.16 Td
(\271)Tj
/T1_0 10.91 Tf
-3.16 -2.75 Td
(N)Tj
/T1_2 10.91 Tf
12.98 0 Td
[(=)-362(\271)]TJ
/T1_0 10.91 Tf
11.51 0 Td
(p)Tj
/T1_2 10.91 Tf
6.3 0 Td
(\271)Tj
/T1_0 10.91 Tf
-0.81 0 Td
(q)Tj
/T1_2 10.91 Tf
8.81 0 Td
[(is)-325(selected,)-327(where)-411(\271)]TJ
/T1_0 10.91 Tf
85.95 0 Td
(p)Tj
/T1_2 10.91 Tf
9.04 0 Td
[(and)-399(\271)]TJ
/T1_0 10.91 Tf
21.12 0 Td
(q)Tj
/T1_2 10.91 Tf
8.81 0 Td
[(are)-325(large)-325(primes)-326(suc)27(h)-325(that)-410(\271)]TJ
/T1_0 10.91 Tf
127.93 0 Td
(p)Tj
/T1_5 10.91 Tf
7.74 0 Td
(\241)Tj
/T1_2 10.91 Tf
10.74 0 Td
[(1)-277(=)-278(2)-85(\271)]TJ
/T1_0 10.91 Tf
25.44 0 Td
(p)Tj
/T1_8 7.97 Tf
5.49 3.96 Td
(0)Tj
/T1_2 10.91 Tf
2.8 -3.96 Td
[(,)-401(\271)]TJ
/T1_0 10.91 Tf
6.59 0 Td
(q)Tj
/T1_5 10.91 Tf
7.52 0 Td
(\241)Tj
/T1_2 10.91 Tf
10.73 0 Td
[(1)-277(=)-278(2)-75(\271)]TJ
/T1_0 10.91 Tf
25.45 0 Td
(q)Tj
/T1_8 7.97 Tf
5.26 3.96 Td
(0)Tj
/T1_2 10.91 Tf
6.34 -3.96 Td
[(and)-410(\271)]TJ
/T1_0 10.91 Tf
21.12 0 Td
(p)Tj
/T1_8 7.97 Tf
5.49 3.96 Td
(0)Tj
/T1_2 10.91 Tf
6.35 -3.96 Td
[(and)-399(\271)]TJ
/T1_0 10.91 Tf
21.12 0 Td
(q)Tj
/T1_8 7.97 Tf
5.26 3.96 Td
(0)Tj
/T1_2 10.91 Tf
-465.08 -25.88 Td
[(are)-348(also)-349(primes.)-492(Next,)-352(t)26(w)28(o)-348(bases)]TJ
/T1_0 10.91 Tf
159.84 0 Td
(g)Tj
/T1_2 10.91 Tf
9.4 0 Td
(and)Tj
/T1_0 10.91 Tf
21.38 0 Td
(h)Tj
/T1_2 10.91 Tf
10.09 0 Td
[(of)-348(order)-434(\271)]TJ
/T1_0 10.91 Tf
41.3 0 Td
(p)Tj
/T1_8 7.97 Tf
5.48 3.96 Td
(0)Tj
/T1_2 10.91 Tf
3.61 -3.96 Td
(\271)Tj
/T1_0 10.91 Tf
-0.81 0 Td
(q)Tj
/T1_8 7.97 Tf
5.26 3.96 Td
(0)Tj
/T1_2 10.91 Tf
6.6 -3.96 Td
[(are)-348(c)26(hosen)-347(b)26(y)-348(the)-349(T)83(rusted)-348(Authorit)27(y)-348(\(T)82(A\).)]TJ
-262.15 -21.92 Td
[(A)-358(large)-358(in)27(teger)]TJ
/T1_0 10.91 Tf
75.4 0 Td
[(u)-318(<)]TJ
/T1_2 10.91 Tf
22.61 0 Td
(\271)Tj
/T1_0 10.91 Tf
-0.93 0 Td
(p)Tj
/T1_8 7.97 Tf
5.49 3.96 Td
(0)Tj
/T1_2 10.91 Tf
3.61 -3.96 Td
(\271)Tj
/T1_0 10.91 Tf
-0.81 0 Td
(q)Tj
/T1_8 7.97 Tf
5.26 3.96 Td
(0)Tj
/T1_2 10.91 Tf
6.7 -3.96 Td
[(and)-357(one)-358(w)26(a)28(y)-357(cryptographic)-358(hash)-358(function)]TJ
/T1_9 10.91 Tf
202.6 0 Td
(H)Tj
/T1_2 10.91 Tf
11.63 0 Td
[(are)-357(also)-358(selected.)-519(The)-359(group)]TJ
-331.56 -21.91 Td
[(size)-387(is)-387(denoted)-388(as)]TJ
/T1_0 10.91 Tf
88.58 0 Td
(n)Tj
/T1_2 10.91 Tf
10.77 0 Td
(while)Tj
/T1_5 10.91 Tf
29.07 0 Td
(jj)Tj
/T1_2 10.91 Tf
10.28 0 Td
[(denotes)-387(concatenation.)-607(During)-387(the)-388(initialization)-387(phase,)-401(all)-387(users)-388(are)]TJ
-138.7 -21.92 Td
[(issued)-357(t)27(w)28(o)-356(secrets)-357(b)26(y)-356(the)-357(T)82(A,)-356(namely)]TJ
/T1_0 10.91 Tf
183.56 0 Td
(S)Tj
/T1_1 7.97 Tf
6.68 -1.63 Td
(i)Tj
/T1_2 10.91 Tf
6.85 1.63 Td
(=)Tj
/T1_0 10.91 Tf
11.94 0 Td
(g)Tj
/T1_1 7.97 Tf
5.59 3.96 Td
[(I)-78(D)]TJ
/T1_12 5.98 Tf
11.48 3.57 Td
(\241)Tj
/T1_10 5.98 Tf
5.75 0 Td
(1)Tj
/T1_3 5.98 Tf
-5.99 -6.22 Td
(i)Tj
/T1_6 7.97 Tf
12.49 2.65 Td
[(mo)-29(d)-386(\271)]TJ
/T1_1 7.97 Tf
18.58 0 Td
(p)Tj
/T1_12 5.98 Tf
4.26 2.81 Td
(0)Tj
/T1_6 7.97 Tf
3.31 -2.81 Td
(\271)Tj
/T1_1 7.97 Tf
-0.62 0 Td
(q)Tj
/T1_12 5.98 Tf
4.06 2.81 Td
(0)Tj
/T1_2 10.91 Tf
6.21 -6.77 Td
[(mo)-28(d)]TJ
27.09 2.76 Td
(\271)Tj
/T1_0 10.91 Tf
-3.15 -2.76 Td
(N)Tj
/T1_2 10.91 Tf
13.84 0 Td
(and)Tj
/T1_0 10.91 Tf
21.47 0 Td
(T)Tj
/T1_1 7.97 Tf
6.37 -1.63 Td
(i)Tj
/T1_2 10.91 Tf
6.84 1.63 Td
(=)Tj
/T1_0 10.91 Tf
11.95 0 Td
(h)Tj
/T1_8 7.97 Tf
6.28 3.96 Td
(\241)Tj
/T1_1 7.97 Tf
6.59 0 Td
[(I)-77(D)]TJ
/T1_12 5.98 Tf
11.47 3.57 Td
(\241)Tj
/T1_10 5.98 Tf
(1)Tj
/T1_3 5.98 Tf
-0.23 -6.22 Td
(i)Tj
/T1_6 7.97 Tf
12.49 2.65 Td
[(mo)-29(d)-385(\271)]TJ
/T1_1 7.97 Tf
18.57 0 Td
(p)Tj
/T1_12 5.98 Tf
4.27 2.81 Td
(0)Tj
/T1_6 7.97 Tf
3.3 -2.81 Td
(\271)Tj
/T1_1 7.97 Tf
-0.62 0 Td
(q)Tj
/T1_12 5.98 Tf
4.07 2.81 Td
(0)Tj
/T1_2 10.91 Tf
6.21 -6.77 Td
[(mo)-27(d)]TJ
27.09 2.76 Td
(\271)Tj
/T1_0 10.91 Tf
-3.16 -2.76 Td
(N)Tj
/T1_2 10.91 Tf
9.95 0 Td
(,)Tj
-464.84 -21.91 Td
(where)Tj
/T1_0 10.91 Tf
31.95 0 Td
[(I)-78(D)]TJ
/T1_1 7.97 Tf
14.68 -1.64 Td
(i)Tj
/T1_2 10.91 Tf
7.43 1.64 Td
[(corresp)-27(onds)-372(to)-371(the)-371(iden)27(tit)27(y)-370(of)-371(user)]TJ
/T1_4 10.91 Tf
170.29 0 Td
(U)Tj
/T1_1 7.97 Tf
5.72 -1.64 Td
(i)Tj
/T1_2 10.91 Tf
7.43 1.64 Td
[(for)-371(1)]TJ
/T1_5 10.91 Tf
26.28 0 Td
(\267)Tj
/T1_0 10.91 Tf
12.2 0 Td
(i)Tj
/T1_5 10.91 Tf
7.48 0 Td
(\267)Tj
/T1_0 10.91 Tf
12.2 0 Td
(n)Tj
/T1_2 10.91 Tf
[(.)-558(A)-371(form)-371(of)-372(signature)-371(is)-371(broadcast)]TJ
-295.66 -21.92 Td
[(b)27(y)-311(all)-312(users,)-316(thereb)26(y)-311(allo)27(wing)-311(stronger)-312(authen)26(tication.)-436(Their)-312(proto)-28(col)-312(consists)-312(of)-313(t)27(w)28(o)-311(phases)-312(and)-313(is)]TJ
T*
[(describ)-27(ed)-334(as)-333(follo)27(ws:)]TJ
16.93 -21.91 Td
[(In)-498(Phase)-498(1,)-539(eac)27(h)-498(user)]TJ
/T1_4 10.91 Tf
114.56 0 Td
(U)Tj
/T1_1 7.97 Tf
5.72 -1.64 Td
(i)Tj
/T1_2 10.91 Tf
8.82 1.64 Td
[(for)-497(1)]TJ
/T1_5 10.91 Tf
29.96 0 Td
(\267)Tj
/T1_0 10.91 Tf
14.51 0 Td
(i)Tj
/T1_5 10.91 Tf
9.78 0 Td
(\267)Tj
/T1_0 10.91 Tf
14.51 0 Td
(n)Tj
/T1_2 10.91 Tf
11.98 0 Td
[(c)27(ho)-26(oses)]TJ
/T1_0 10.91 Tf
40.69 0 Td
(r)Tj
/T1_1 7.97 Tf
4.92 -1.64 Td
(i)Tj
/T1_5 10.91 Tf
9.41 1.64 Td
(2)Tj
/T1_0 10.91 Tf
13.29 0 Td
(Z)Tj
/T1_1 7.97 Tf
7.45 -1.64 Td
(u)Tj
/T1_2 10.91 Tf
5.4 1.64 Td
[(,)-539(computes)-498(and)-498(broadcasts)]TJ
/T1_0 10.91 Tf
138.12 0 Td
(t)Tj
/T1_1 7.97 Tf
3.93 -1.64 Td
(i)Tj
/T1_2 10.91 Tf
9.41 1.64 Td
(=)Tj
/T1_0 10.91 Tf
-459.39 -21.92 Td
(g)Tj
/T1_1 7.97 Tf
5.59 3.96 Td
(r)Tj
/T1_3 5.98 Tf
3.82 -1.22 Td
(i)Tj
/T1_2 10.91 Tf
6.69 -2.74 Td
[(mo)-27(d)]TJ
27.09 2.76 Td
(\271)Tj
/T1_0 10.91 Tf
-3.16 -2.76 Td
(N)Tj
/T1_2 10.91 Tf
9.96 0 Td
[(.)-807(Up)-28(on)-455(receiving)-454(all)]TJ
/T1_0 10.91 Tf
106.42 0 Td
(t)Tj
/T1_1 7.97 Tf
3.94 -1.64 Td
(j)Tj
/T1_2 10.91 Tf
9.34 1.64 Td
[(for)-454(1)]TJ
/T1_5 10.91 Tf
28.7 0 Td
(\267)Tj
/T1_0 10.91 Tf
13.71 0 Td
(j)Tj
/T1_5 10.91 Tf
10.35 0 Td
(6)Tj
/T1_2 10.91 Tf
(=)Tj
/T1_0 10.91 Tf
13.72 0 Td
(i)Tj
/T1_5 10.91 Tf
8.99 0 Td
(\267)Tj
/T1_0 10.91 Tf
13.71 0 Td
(n)Tj
/T1_2 10.91 Tf
[(,)-484(eac)26(h)]TJ
/T1_4 10.91 Tf
40.73 0 Td
(U)Tj
/T1_1 7.97 Tf
5.72 -1.64 Td
(i)Tj
/T1_2 10.91 Tf
8.34 1.64 Td
(computes)Tj
/T1_0 10.91 Tf
49.86 0 Td
(c)Tj
/T1_2 10.91 Tf
9.95 0 Td
(=)Tj
/T1_9 10.91 Tf
13.72 0 Td
(H)Tj
/T1_2 10.91 Tf
(\()Tj
/T1_0 10.91 Tf
(t)Tj
/T1_6 7.97 Tf
15.9 -1.64 Td
(1)Tj
/T1_5 10.91 Tf
4.73 1.64 Td
(jj)Tj
/T1_0 10.91 Tf
6.06 0 Td
(t)Tj
/T1_6 7.97 Tf
3.94 -1.64 Td
(2)Tj
/T1_5 10.91 Tf
4.73 1.64 Td
(jj)Tj
/T1_0 10.91 Tf
7.88 0 Td
[(:)-166(:)-167(:)]TJ
/T1_5 10.91 Tf
14.54 0 Td
(jj)Tj
/T1_0 10.91 Tf
6.06 0 Td
(t)Tj
/T1_1 7.97 Tf
3.94 -1.64 Td
(n)Tj
/T1_2 10.91 Tf
5.63 1.64 Td
(\),)Tj
/T1_0 10.91 Tf
-460.6 -21.92 Td
(X)Tj
/T1_1 7.97 Tf
9.04 -1.63 Td
(i)Tj
/T1_2 10.91 Tf
6.41 1.63 Td
[(=)-277(\()]TJ
/T1_0 10.91 Tf
(t)Tj
/T1_1 7.97 Tf
19.69 -1.63 Td
(i)Tj
/T1_6 7.97 Tf
2.88 0 Td
(+1)Tj
/T1_0 10.91 Tf
11.31 1.63 Td
(=t)Tj
/T1_1 7.97 Tf
9.4 -1.63 Td
(i)Tj
/T1_8 7.97 Tf
2.88 0 Td
(\241)Tj
/T1_6 7.97 Tf
(1)Tj
/T1_2 10.91 Tf
11.31 1.63 Td
(\))Tj
/T1_1 7.97 Tf
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(n)Tj
/T1_2 10.91 Tf
5.64 1.64 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
[(0\).)-646(Eac)27(h)-400(mem)27(b)-27(er)]TJ
/T1_8 10.91 Tf
90.19 0 Td
(U)Tj
/T1_4 7.97 Tf
5.73 -1.64 Td
(i)Tj
/T1_1 10.91 Tf
-464.49 -20.28 Td
[(for)-426(1)]TJ
/T1_2 10.91 Tf
27.89 0 Td
(\267)Tj
/T1_3 10.91 Tf
13.21 0 Td
(i)Tj
/T1_2 10.91 Tf
8.49 0 Td
(\267)Tj
/T1_3 10.91 Tf
13.21 0 Td
(n)Tj
/T1_2 10.91 Tf
9.65 0 Td
(\241)Tj
/T1_1 10.91 Tf
11.59 0 Td
[(1)-426(broadcasts)]TJ
/T1_2 10.91 Tf
65.2 0 Td
(f)Tj
/T1_3 10.91 Tf
(z)Tj
/T1_4 7.97 Tf
10.52 -1.64 Td
(i)Tj
/T1_2 10.91 Tf
3.38 1.64 Td
(jj)Tj
/T1_3 10.91 Tf
6.06 0 Td
(\276)Tj
/T1_4 7.97 Tf
6.23 -1.64 Td
(i)Tj
/T1_2 10.91 Tf
3.38 1.64 Td
(g)Tj
/T1_1 10.91 Tf
10.11 0 Td
[(and)-427(last)-426(mem)26(b)-26(er)]TJ
/T1_8 10.91 Tf
86.76 0 Td
(U)Tj
/T1_4 7.97 Tf
5.73 -1.64 Td
(n)Tj
/T1_1 10.91 Tf
10.29 1.64 Td
(broadcasts)Tj
/T1_2 10.91 Tf
55.1 0 Td
(f)Tj
/T1_5 10.91 Tf
(H)Tj
/T1_1 10.91 Tf
(\()Tj
/T1_3 10.91 Tf
(\267)Tj
/T1_4 7.97 Tf
23.7 -1.64 Td
(n)Tj
/T1_2 10.91 Tf
5.63 1.64 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(0\))Tj
/T1_2 10.91 Tf
(jj)Tj
/T1_3 10.91 Tf
15.76 0 Td
(z)Tj
/T1_4 7.97 Tf
5.07 -1.64 Td
(n)Tj
/T1_2 10.91 Tf
5.63 1.64 Td
(jj)Tj
/T1_3 10.91 Tf
6.06 0 Td
(\276)Tj
/T1_4 7.97 Tf
6.23 -1.64 Td
(n)Tj
/T1_2 10.91 Tf
5.64 1.64 Td
(g)Tj
/T1_1 10.91 Tf
[(,)-450(where)]TJ
-426.58 -21.92 Td
(signature)Tj
/T1_3 10.91 Tf
47.35 0 Td
(\276)Tj
/T1_4 7.97 Tf
6.23 -1.63 Td
(i)Tj
/T1_1 10.91 Tf
6.41 1.63 Td
(=)Tj
/T1_2 10.91 Tf
11.51 0 Td
(S)Tj
/T1_1 10.91 Tf
7.43 0 Td
(\()Tj
/T1_3 10.91 Tf
(z)Tj
/T1_4 7.97 Tf
9.31 -1.63 Td
(i)Tj
/T1_2 10.91 Tf
3.38 1.63 Td
(jj)Tj
/T1_3 10.91 Tf
6.06 0 Td
(I)Tj
/T1_9 7.97 Tf
4.79 -1.63 Td
(0)Tj
/T1_2 10.91 Tf
4.73 1.63 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
[(0\))-333(and)]TJ
/T1_3 10.91 Tf
34.54 0 Td
(\276)Tj
/T1_4 7.97 Tf
6.23 -1.63 Td
(n)Tj
/T1_1 10.91 Tf
8.66 1.63 Td
(=)Tj
/T1_2 10.91 Tf
11.52 0 Td
(S)Tj
/T1_1 10.91 Tf
7.42 0 Td
(\()Tj
/T1_5 10.91 Tf
(H)Tj
/T1_1 10.91 Tf
11.97 0 Td
(\()Tj
/T1_3 10.91 Tf
(\267)Tj
/T1_4 7.97 Tf
10.52 -1.63 Td
(n)Tj
/T1_2 10.91 Tf
5.64 1.63 Td
(jj)Tj
/T1_1 10.91 Tf
6.05 0 Td
(0\))Tj
/T1_2 10.91 Tf
(jj)Tj
/T1_3 10.91 Tf
15.76 0 Td
(z)Tj
/T1_4 7.97 Tf
5.07 -1.63 Td
(n)Tj
/T1_2 10.91 Tf
5.63 1.63 Td
(jj)Tj
/T1_3 10.91 Tf
6.06 0 Td
(I)Tj
/T1_9 7.97 Tf
4.8 -1.63 Td
(0)Tj
/T1_2 10.91 Tf
4.73 1.63 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(0\).)Tj
-263.92 -21.91 Td
[(Round)-333(2)]TJ
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 0 -414.41 cm
0 0 m
40.75 0 l
S
Q
Q
BT
/T1_1 10.91 Tf
1.0003 0 0 1.0003 112.7614 356.8244 Tm
(:)Tj
1.0003 0 0 1.0003 72 769.82 Tm
49.773 -412.88 Td
[(Eac)26(h)-385(mem)27(b)-27(er)]TJ
/T1_8 10.91 Tf
70.107 0 Td
(U)Tj
/T1_4 7.97 Tf
5.73 -1.64 Td
(i)Tj
/T1_1 10.91 Tf
7.59 1.64 Td
[(for)-386(1)]TJ
/T1_2 10.91 Tf
26.72 0 Td
(\267)Tj
/T1_3 10.91 Tf
12.47 0 Td
(i)Tj
/T1_2 10.91 Tf
7.75 0 Td
(\267)Tj
/T1_3 10.91 Tf
12.47 0 Td
(n)Tj
/T1_1 10.91 Tf
10.76 0 Td
[(v)27(eri\257es)-385(the)-386(signature)]TJ
/T1_3 10.91 Tf
104.31 0 Td
(\276)Tj
/T1_4 7.97 Tf
6.23 -1.64 Td
(j)Tj
/T1_1 10.91 Tf
8.6 1.64 Td
[(for)-386(1)]TJ
/T1_2 10.91 Tf
26.71 0 Td
(\267)Tj
/T1_3 10.91 Tf
12.48 0 Td
(j)Tj
/T1_2 10.91 Tf
9.1 0 Td
(6)Tj
/T1_1 10.91 Tf
(=)Tj
/T1_3 10.91 Tf
12.48 0 Td
(i)Tj
/T1_2 10.91 Tf
7.75 0 Td
(\267)Tj
/T1_3 10.91 Tf
12.47 0 Td
(n)Tj
/T1_1 10.91 Tf
[(.)-602(The)-387(GKA)]TJ
-403.5 -21.92 Td
[(proto)-27(col)-336(fails)-335(and)-336(halts)-336(if)-335(there)-336(are)-335(in)26(v)56(alid)-335(signatures.)-451(Otherwise,)]TJ
/T1_8 10.91 Tf
315.52 0 Td
(U)Tj
/T1_4 7.97 Tf
5.72 -1.64 Td
(i)Tj
/T1_1 10.91 Tf
7.04 1.64 Td
(computes)Tj
/T1_3 10.91 Tf
48.56 0 Td
(L)Tj
/T1_4 7.97 Tf
7.42 -1.64 Td
(i)Tj
/T1_1 10.91 Tf
6.45 1.64 Td
(=)Tj
/T1_5 10.91 Tf
11.56 0 Td
(H)Tj
/T1_1 10.91 Tf
(\()Tj
/T1_3 10.91 Tf
(z)Tj
/T1_4 7.97 Tf
17.52 4.97 Td
(r)Tj
/T1_10 5.98 Tf
3.82 -1.21 Td
(i)Tj
/T1_4 7.97 Tf
-4.3 -7.02 Td
(i)Tj
/T1_6 7.97 Tf
2.88 0 Td
(\241)Tj
/T1_9 7.97 Tf
(1)Tj
/T1_2 10.91 Tf
11.31 3.26 Td
(jj)Tj
/T1_3 10.91 Tf
6.06 0 Td
(I)Tj
/T1_9 7.97 Tf
4.8 -1.64 Td
(0)Tj
/T1_2 10.91 Tf
4.73 1.64 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(0\),)Tj
/T1_3 10.91 Tf
-455.15 -21.92 Td
(R)Tj
/T1_4 7.97 Tf
8.28 -1.63 Td
(i)Tj
/T1_1 10.91 Tf
6.41 1.63 Td
(=)Tj
/T1_5 10.91 Tf
11.51 0 Td
(H)Tj
/T1_1 10.91 Tf
7.73 0 Td
(\()Tj
/T1_3 10.91 Tf
(z)Tj
/T1_4 7.97 Tf
9.79 4.97 Td
(r)Tj
/T1_10 5.98 Tf
3.82 -1.21 Td
(i)Tj
/T1_4 7.97 Tf
-4.3 -7.01 Td
(i)Tj
/T1_9 7.97 Tf
2.88 0 Td
(+1)Tj
/T1_2 10.91 Tf
11.32 3.25 Td
(jj)Tj
/T1_3 10.91 Tf
6.06 0 Td
(I)Tj
/T1_9 7.97 Tf
4.79 -1.63 Td
(0)Tj
/T1_2 10.91 Tf
4.73 1.63 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
[(0\))-223(and)]TJ
/T1_3 10.91 Tf
32.13 0 Td
(X)Tj
/T1_4 7.97 Tf
9.04 -1.63 Td
(i)Tj
/T1_1 10.91 Tf
6.41 1.63 Td
(=)Tj
/T1_3 10.91 Tf
11.51 0 Td
(L)Tj
/T1_4 7.97 Tf
7.42 -1.63 Td
(i)Tj
/T1_2 10.91 Tf
3.4 1.63 Td
(\251)Tj
/T1_3 10.91 Tf
8.5 0 Td
(R)Tj
/T1_4 7.97 Tf
8.28 -1.63 Td
(i)Tj
/T1_1 10.91 Tf
3.38 1.63 Td
[(.)-407(The)-223(last)-223(mem)27(b)-27(er)]TJ
/T1_8 10.91 Tf
88.78 0 Td
(U)Tj
/T1_4 7.97 Tf
5.73 -1.63 Td
(n)Tj
/T1_1 10.91 Tf
8.06 1.63 Td
[(additionally)-223(computes)]TJ
/T1_11 10.91 Tf
109.24 2.76 Td
(b)Tj
/T1_3 10.91 Tf
-2.83 -2.76 Td
(X)Tj
/T1_1 10.91 Tf
12.92 0 Td
(=)Tj
/T1_3 10.91 Tf
11.52 0 Td
(\267)Tj
/T1_4 7.97 Tf
6.28 -1.63 Td
(n)Tj
/T1_2 10.91 Tf
5.65 1.63 Td
(\251)Tj
/T1_3 10.91 Tf
8.5 0 Td
(R)Tj
/T1_4 7.97 Tf
8.28 -1.63 Td
(n)Tj
/T1_1 10.91 Tf
5.64 1.63 Td
[(.)-407(Eac)27(h)]TJ
-436.92 -21.91 Td
[(mem)27(b)-26(er)]TJ
/T1_8 10.91 Tf
41.92 0 Td
(U)Tj
/T1_4 7.97 Tf
5.73 -1.64 Td
(i)Tj
/T1_1 10.91 Tf
7.1 1.64 Td
[(for)-341(1)]TJ
/T1_2 10.91 Tf
25.41 0 Td
(\267)Tj
/T1_3 10.91 Tf
11.66 0 Td
(i)Tj
/T1_2 10.91 Tf
6.93 0 Td
(\267)Tj
/T1_3 10.91 Tf
11.66 0 Td
(n)Tj
/T1_2 10.91 Tf
9.03 0 Td
(\241)Tj
/T1_1 10.91 Tf
10.96 0 Td
[(1)-341(broadcasts)]TJ
/T1_2 10.91 Tf
63.34 0 Td
(f)Tj
/T1_3 10.91 Tf
(\267)Tj
/T1_4 7.97 Tf
11.74 -1.64 Td
(i)Tj
/T1_2 10.91 Tf
3.38 1.64 Td
(jj)Tj
/T1_3 10.91 Tf
6.05 0 Td
(X)Tj
/T1_4 7.97 Tf
9.04 -1.64 Td
(i)Tj
/T1_2 10.91 Tf
3.38 1.64 Td
(jj)Tj
/T1_3 10.91 Tf
6.06 0 Td
(\276)Tj
/T1_6 7.97 Tf
6.62 3.95 Td
(0)Tj
/T1_4 7.97 Tf
-0.39 -7.01 Td
(i)Tj
/T1_2 10.91 Tf
3.38 3.06 Td
(g)Tj
/T1_1 10.91 Tf
9.18 0 Td
[(and)-341(last)-341(mem)27(b)-27(er)]TJ
/T1_8 10.91 Tf
83.96 0 Td
(U)Tj
/T1_4 7.97 Tf
5.73 -1.64 Td
(n)Tj
/T1_1 10.91 Tf
9.36 1.64 Td
(broadcasts)Tj
/T1_2 10.91 Tf
54.16 0 Td
(f)Tj
/T1_11 10.91 Tf
8.28 2.75 Td
(b)Tj
/T1_3 10.91 Tf
-2.83 -2.75 Td
(X)Tj
/T1_2 10.91 Tf
9.89 0 Td
(jj)Tj
/T1_3 10.91 Tf
6.06 0 Td
(X)Tj
/T1_4 7.97 Tf
9.04 -1.64 Td
(n)Tj
/T1_2 10.91 Tf
5.63 1.64 Td
(jj)Tj
/T1_3 10.91 Tf
6.06 0 Td
(\276)Tj
/T1_6 7.97 Tf
6.62 3.95 Td
(0)Tj
/T1_4 7.97 Tf
-0.39 -6.65 Td
(n)Tj
/T1_2 10.91 Tf
5.64 2.7 Td
(g)Tj
/T1_1 10.91 Tf
(,)Tj
-459.39 -21.92 Td
[(where)-333(signature)]TJ
/T1_3 10.91 Tf
78.89 0 Td
(\276)Tj
/T1_6 7.97 Tf
6.62 3.96 Td
(0)Tj
/T1_4 7.97 Tf
-0.39 -7.01 Td
(i)Tj
/T1_1 10.91 Tf
6.41 3.05 Td
(=)Tj
/T1_2 10.91 Tf
11.51 0 Td
(S)Tj
/T1_1 10.91 Tf
7.42 0 Td
(\()Tj
/T1_3 10.91 Tf
(\267)Tj
/T1_4 7.97 Tf
10.53 -1.64 Td
(i)Tj
/T1_2 10.91 Tf
3.38 1.64 Td
(jj)Tj
/T1_3 10.91 Tf
6.06 0 Td
(X)Tj
/T1_4 7.97 Tf
9.03 -1.64 Td
(i)Tj
/T1_2 10.91 Tf
3.38 1.64 Td
(jj)Tj
/T1_3 10.91 Tf
6.06 0 Td
(I)Tj
/T1_9 7.97 Tf
4.8 -1.64 Td
(0)Tj
/T1_2 10.91 Tf
4.73 1.64 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
[(0\))-332(and)]TJ
/T1_3 10.91 Tf
34.53 0 Td
(\276)Tj
/T1_6 7.97 Tf
6.63 3.96 Td
(0)Tj
/T1_4 7.97 Tf
-0.4 -6.66 Td
(n)Tj
/T1_1 10.91 Tf
8.67 2.7 Td
(=)Tj
/T1_2 10.91 Tf
11.51 0 Td
(S)Tj
/T1_1 10.91 Tf
7.42 0 Td
(\()Tj
/T1_11 10.91 Tf
7.07 2.76 Td
(b)Tj
/T1_3 10.91 Tf
-2.83 -2.76 Td
(X)Tj
/T1_2 10.91 Tf
9.89 0 Td
(jj)Tj
/T1_3 10.91 Tf
6.06 0 Td
(X)Tj
/T1_4 7.97 Tf
9.04 -1.64 Td
(n)Tj
/T1_2 10.91 Tf
5.63 1.64 Td
(jj)Tj
/T1_3 10.91 Tf
6.06 0 Td
(I)Tj
/T1_9 7.97 Tf
4.8 -1.64 Td
(0)Tj
/T1_2 10.91 Tf
4.73 1.64 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(0\).)Tj
-289.36 -21.92 Td
[(Key)-333(Computation)]TJ
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 0 -526.11 cm
0 0 m
85.73 0 l
S
Q
Q
BT
/T1_1 10.91 Tf
1.0003 0 0 1.0003 157.754 247.2037 Tm
(:)Tj
1.0003 0 0 1.0003 72 769.82 Tm
93.432 -522.47 Td
[(Eac)27(h)-301(mem)27(b)-27(er)]TJ
/T1_8 10.91 Tf
68.248 0 Td
(U)Tj
/T1_4 7.97 Tf
5.73 -1.63 Td
(i)Tj
/T1_1 10.91 Tf
6.66 1.63 Td
[(for)-301(1)]TJ
/T1_2 10.91 Tf
24.83 0 Td
(\267)Tj
/T1_3 10.91 Tf
11.51 0 Td
(i)Tj
/T1_2 10.91 Tf
6.79 0 Td
(\267)Tj
/T1_3 10.91 Tf
11.51 0 Td
(n)Tj
/T1_2 10.91 Tf
8.26 0 Td
(\241)Tj
/T1_1 10.91 Tf
10.21 0 Td
[(1)-300(v)26(eri\257es)]TJ
/T1_3 10.91 Tf
44.83 0 Td
(\276)Tj
/T1_6 7.97 Tf
6.62 3.96 Td
(0)Tj
/T1_4 7.97 Tf
-0.39 -7.01 Td
(j)Tj
/T1_1 10.91 Tf
7.67 3.05 Td
[(for)-300(1)]TJ
/T1_2 10.91 Tf
24.82 0 Td
(\267)Tj
/T1_3 10.91 Tf
11.51 0 Td
(j)Tj
/T1_2 10.91 Tf
8.15 0 Td
(6)Tj
/T1_1 10.91 Tf
(=)Tj
/T1_3 10.91 Tf
11.51 0 Td
(i)Tj
/T1_2 10.91 Tf
6.78 0 Td
(\267)Tj
/T1_3 10.91 Tf
11.52 0 Td
(n)Tj
/T1_1 10.91 Tf
6.54 0 Td
[(.)-433(If)-302(all)-301(signatures)]TJ
-386.74 -21.91 Td
[(are)-333(v)55(alid,)]TJ
/T1_8 10.91 Tf
47.59 0 Td
(U)Tj
/T1_4 7.97 Tf
5.73 -1.64 Td
(i)Tj
/T1_1 10.91 Tf
7.01 1.64 Td
(computes)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 66.84 -575.05 cm
0 0 m
8.36 0 l
S
Q
Q
BT
/T1_3 10.91 Tf
1.0003 0 0 1.0003 138.8587 185.6265 Tm
(R)Tj
/T1_4 7.97 Tf
8.36 -1.63 Td
(i)Tj
/T1_9 7.97 Tf
2.89 0 Td
(+1)Tj
/T1_1 10.91 Tf
14.34 1.63 Td
(=)Tj
/T1_3 10.91 Tf
11.51 0 Td
(X)Tj
/T1_4 7.97 Tf
9.04 -1.63 Td
(i)Tj
/T1_9 7.97 Tf
2.88 0 Td
(+1)Tj
/T1_2 10.91 Tf
13.74 1.63 Td
(\251)Tj
/T1_3 10.91 Tf
10.91 0 Td
(R)Tj
/T1_4 7.97 Tf
8.28 -1.63 Td
(i)Tj
/T1_3 10.91 Tf
3.38 1.63 Td
(;)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 165.52 -575.05 cm
0 0 m
8.36 0 l
S
Q
Q
BT
/T1_3 10.91 Tf
1.0003 0 0 1.0003 237.5663 185.6265 Tm
(R)Tj
/T1_4 7.97 Tf
8.36 -1.63 Td
(i)Tj
/T1_9 7.97 Tf
2.88 0 Td
(+2)Tj
/T1_1 10.91 Tf
14.35 1.63 Td
(=)Tj
/T1_3 10.91 Tf
11.51 0 Td
(X)Tj
/T1_4 7.97 Tf
9.03 -1.63 Td
(i)Tj
/T1_9 7.97 Tf
2.89 0 Td
(+2)Tj
/T1_2 10.91 Tf
13.74 1.63 Td
(\251)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 239.18 -575.05 cm
0 0 m
8.37 0 l
S
Q
Q
BT
/T1_3 10.91 Tf
1.0003 0 0 1.0003 311.247 185.6265 Tm
(R)Tj
/T1_4 7.97 Tf
8.37 -1.63 Td
(i)Tj
/T1_9 7.97 Tf
2.88 0 Td
(+1)Tj
/T1_3 10.91 Tf
11.32 1.63 Td
(;)Tj
/T1_2 10.91 Tf
13.34 0 Td
(\242)Tj
1.0003 0 0 1.0003 72 769.82 Tm
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24.24 0 Td
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5.72 -1.64 Td
(n)Tj
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(m)Tj
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7.48 0 Td
(+3)Tj
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(g)Tj
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9.51 0 Td
(and)Tj
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21.62 0 Td
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(0)Tj
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6.52 -3.96 Td
(=)Tj
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12.21 0 Td
[(I)-78(D)]TJ
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14.68 -1.64 Td
(1)Tj
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4.73 1.64 Td
[(jj)-167(\242)-166(\242)-167(\242)-167(jj)]TJ
/T1_4 10.91 Tf
28.48 0 Td
[(I)-78(D)]TJ
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14.68 -1.64 Td
(n)Tj
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(+)Tj
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(m)Tj
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19.71 1.64 Td
[(.)-559(A)-372(so-called)-371(ring)-372(structure)]TJ
-335.79 -21.92 Td
[(is)-333(considered)-333(among)-333(the)-334(mem)27(b)-27(ers)-333(in)]TJ
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177.16 0 Td
(G)Tj
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7.14 3.96 Td
(0)Tj
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2.79 -3.96 Td
[(.)-444(Their)-333(Join)-334(Proto)-28(col)-333(is)-333(describ)-28(ed)-333(as)-334(follo)27(ws:)]TJ
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[(Round)-333(1)]TJ
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 0 -311.32 cm
0 0 m
40.75 0 l
S
Q
Q
BT
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1.0003 0 0 1.0003 112.7614 459.9433 Tm
(:)Tj
1.0003 0 0 1.0003 72 769.82 Tm
52.249 -309.79 Td
[(Eac)27(h)-498(mem)26(b)-26(er)]TJ
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72.571 0 Td
(U)Tj
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5.72 -1.64 Td
(j)Tj
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9.83 1.64 Td
(for)Tj
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18.5 0 Td
(n)Tj
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10.18 0 Td
[(+)-333(1)]TJ
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23.62 0 Td
(\267)Tj
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14.53 0 Td
(j)Tj
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11.16 0 Td
(\267)Tj
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14.53 0 Td
(n)Tj
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10.18 0 Td
(+)Tj
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12.11 0 Td
(m)Tj
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13.21 0 Td
[(+)-332(3)-500(randomly)-499(c)27(ho)-27(oses)]TJ
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114.34 0 Td
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6.28 -1.64 Td
(j)Tj
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10.43 1.64 Td
[(2)-554(f)]TJ
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18.77 0 Td
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(\270)Tj
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(and)Tj
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(2)Tj
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(\244)Tj
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-0.78 -6.66 Td
(p)Tj
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5.51 2.7 Td
[(,)-544(computes)]TJ
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59.33 0 Td
(z)Tj
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(j)Tj
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10.48 1.64 Td
(=)Tj
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14.57 0 Td
(g)Tj
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(r)Tj
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3.82 -1.22 Td
(j)Tj
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7.43 -2.74 Td
[(mo)-28(d)]TJ
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23.94 0 Td
(p)Tj
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10.96 0 Td
[(and)-501(k)27(eeps)]TJ
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54.02 0 Td
(\267)Tj
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6.28 -1.64 Td
(j)Tj
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9.86 1.64 Td
[(secretly)83(.)-949(The)-502(mem)27(b)-27(er)]TJ
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116.55 0 Td
(U)Tj
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5.73 -1.64 Td
(n)Tj
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5.13 0 Td
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6.59 0 Td
(m)Tj
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7.48 0 Td
(+2)Tj
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11.32 1.64 Td
(\(=)Tj
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18.82 0 Td
(U)Tj
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5.72 -1.64 Td
(2)Tj
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4.73 1.64 Td
[(\))-502(com-)]TJ
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30.9 0 Td
(z)Tj
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5.13 0 Td
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(m)Tj
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(+2)Tj
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24.77 1.63 Td
(=)Tj
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14.44 0 Td
(g)Tj
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5.59 3.96 Td
(\261)Tj
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7.58 -3.96 Td
[(mo)-27(d)]TJ
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23.93 0 Td
(p)Tj
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10.88 0 Td
[(and)-495(the)-494(mem)26(b)-26(er)]TJ
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87.11 0 Td
(U)Tj
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5.73 -1.63 Td
(n)Tj
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5.13 0 Td
(+)Tj
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6.59 0 Td
(m)Tj
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(+3)Tj
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18.8 1.63 Td
(\(=)Tj
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18.69 0 Td
(U)Tj
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5.73 -1.63 Td
(n)Tj
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5.63 1.63 Td
[(\))-494(computes)]TJ
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59.93 0 Td
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(\267)Tj
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(n)Tj
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(m)Tj
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(+3)Tj
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30.53 1.63 Td
(jj)Tj
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[(\),)-535(where)-495(in-)]TJ
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[(,)-410(whic)27(h)-395(starts)-395(from)-395(0)-395(in)-395(the)-396(Initial)-395(GKA)-395(Proto)-28(col,)-410(will)-396(increase)-395(b)27(y)-394(1)-396(whenev)27(er)-394(the)-395(Join)-395(or)]TJ
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[(Lea)27(v)28(e)-457(Proto)-28(col)-457(is)-458(executed.)-818(Eac)27(h)-457(mem)27(b)-27(er)]TJ
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215.02 0 Td
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(j)Tj
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9.38 1.64 Td
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18.05 0 Td
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[(+)-305(1)]TJ
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22.56 0 Td
(\267)Tj
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13.78 0 Td
(j)Tj
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(\267)Tj
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13.78 0 Td
(n)Tj
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9.87 0 Td
(+)Tj
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11.81 0 Td
(m)Tj
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[(+)-305(2)-457(broadcasts)]TJ
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4.38 1.64 Td
(jj)Tj
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6.05 0 Td
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(g)Tj
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34.9 1.63 Td
(broadcasts)Tj
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54.81 0 Td
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13.18 0 Td
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(\267)Tj
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10.52 -1.63 Td
(n)Tj
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(m)Tj
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7.48 0 Td
(+3)Tj
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11.32 1.63 Td
(jj)Tj
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6.06 0 Td
(v)Tj
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5.68 0 Td
(\))Tj
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(jj)Tj
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10.3 0 Td
(z)Tj
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5.07 -1.63 Td
(n)Tj
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(+)Tj
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(m)Tj
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(+3)Tj
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30.52 1.63 Td
(jj)Tj
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6.06 0 Td
(\276)Tj
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6.23 -1.63 Td
(n)Tj
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11.32 1.63 Td
(g)Tj
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[(,)-418(where)-401(signature)]TJ
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93.4 0 Td
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(z)Tj
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9.31 -1.63 Td
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4.38 1.63 Td
(jj)Tj
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6.06 0 Td
(I)Tj
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4.79 -1.63 Td
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4.91 1.63 Td
(jj)Tj
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6.06 0 Td
(v)Tj
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5.68 0 Td
[(\))-400(and)]TJ
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-441.69 -21.91 Td
(\276)Tj
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(n)Tj
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(m)Tj
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(+3)Tj
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33.56 1.64 Td
(=)Tj
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11.51 0 Td
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7.42 0 Td
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(H)Tj
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11.97 0 Td
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(\267)Tj
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(n)Tj
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(m)Tj
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(+3)Tj
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30.53 1.64 Td
(jj)Tj
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6.06 0 Td
(v)Tj
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5.67 0 Td
(\))Tj
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4.25 0 Td
(jj)Tj
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6.05 0 Td
(z)Tj
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5.08 -1.64 Td
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6.59 0 Td
(m)Tj
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(+3)Tj
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18.8 1.64 Td
(jj)Tj
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6.06 0 Td
(I)Tj
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4.8 -1.64 Td
(v)Tj
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4.9 1.64 Td
(jj)Tj
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6.06 0 Td
(v)Tj
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5.68 0 Td
(\).)Tj
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[(Round)-333(2)]TJ
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 0 -464.74 cm
0 0 m
40.75 0 l
S
Q
Q
BT
/T1_2 10.91 Tf
1.0003 0 0 1.0003 112.7614 306.4803 Tm
(:)Tj
1.0003 0 0 1.0003 72 769.82 Tm
48.049 -463.21 Td
[(Eac)27(h)-228(mem)27(b)-27(er)]TJ
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66.661 0 Td
(U)Tj
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5.73 -1.64 Td
(j)Tj
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6.87 1.64 Td
(for)Tj
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15.55 0 Td
(n)Tj
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6.67 0 Td
[(+)-12(1)]TJ
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17.1 0 Td
(\267)Tj
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11.52 0 Td
(j)Tj
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8.14 0 Td
(\267)Tj
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11.51 0 Td
(n)Tj
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6.68 0 Td
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8.62 0 Td
(m)Tj
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9.71 0 Td
[(+)-11(3)-229(v)27(eri\257es)-227(signature)]TJ
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6.23 -1.78 Td
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7.61 1.78 Td
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15.55 0 Td
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[(+)-12(1)]TJ
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17.1 0 Td
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(m)Tj
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[(+)-12(3.)]TJ
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(\()Tj
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(z)Tj
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(1)Tj
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(jj)Tj
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6.06 0 Td
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(j)Tj
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9.06 1.64 Td
(=)Tj
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13.17 0 Td
(H)Tj
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7.73 0 Td
(\()Tj
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(z)Tj
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(r)Tj
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(j)Tj
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(j)Tj
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3.88 0 Td
(+1)Tj
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11.32 3.26 Td
(jj)Tj
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6.06 0 Td
(I)Tj
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4.79 -1.64 Td
(v)Tj
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4.91 1.64 Td
(jj)Tj
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6.06 0 Td
(v)Tj
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5.67 0 Td
[(\))-424(and)]TJ
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31.07 0 Td
(X)Tj
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9.04 -1.64 Td
(j)Tj
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9.06 1.64 Td
(=)Tj
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13.17 0 Td
(L)Tj
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7.42 -1.64 Td
(j)Tj
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7.47 1.64 Td
(\251)Tj
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11.57 0 Td
(R)Tj
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8.28 -1.64 Td
(j)Tj
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4.38 1.64 Td
[(.)-717(The)-425(mem)27(b)-27(er)]TJ
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/T1_0 10.91 Tf
-0.89 -2.88 Td
(X)Tj
/T1_6 7.97 Tf
9.89 3.15 Td
(0)Tj
/T1_2 10.91 Tf
6.48 -3.15 Td
[(and)-338(compute)-338(new)]TJ
-383.54 -21.91 Td
[(group)-333(k)27(ey)]TJ
/T1_0 10.91 Tf
50.62 0 Td
(K)Tj
/T1_6 7.97 Tf
10.05 3.95 Td
(0)Tj
/T1_2 10.91 Tf
6.42 -3.95 Td
[(as)-333(follo)27(ws:)]TJ
/T1_0 10.91 Tf
73.84 -39.65 Td
(K)Tj
/T1_6 7.97 Tf
10.05 4.51 Td
(0)Tj
/T1_2 10.91 Tf
12.75 -4.51 Td
(=)Tj
/T1_8 10.91 Tf
18.44 0 Td
(H)Tj
/T1_2 10.91 Tf
7.73 0 Td
(\()Tj
/T1_0 10.91 Tf
(\267)Tj
/T1_4 7.97 Tf
10.52 -1.63 Td
(n)Tj
/T1_5 7.97 Tf
(+1)Tj
/T1_1 10.91 Tf
16.46 1.63 Td
(jj)Tj
/T1_0 10.91 Tf
6.06 0 Td
(\267)Tj
/T1_4 7.97 Tf
6.28 -1.63 Td
(n)Tj
/T1_5 7.97 Tf
(+2)Tj
/T1_1 10.91 Tf
16.45 1.63 Td
[(jj)-166(\242)-167(\242)-167(\242)-166(jj)]TJ
/T1_0 10.91 Tf
28.48 0 Td
(\267)Tj
/T1_4 7.97 Tf
6.28 -1.63 Td
(n)Tj
/T1_5 7.97 Tf
(+)Tj
/T1_4 7.97 Tf
(m)Tj
/T1_5 7.97 Tf
(+3)Tj
/T1_1 10.91 Tf
30.53 1.63 Td
(jj)Tj
/T1_0 10.91 Tf
6.06 0 Td
(v)Tj
/T1_2 10.91 Tf
5.67 0 Td
(\))Tj
122.803 0 Td
(\(2.5\))Tj
-445.493 -39.64 Td
[(P)27(ost)-332(Computation)]TJ
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 0 -217.01 cm
0 0 m
87.76 0 l
S
Q
Q
BT
/T1_2 10.91 Tf
1.0003 0 0 1.0003 159.7846 556.4003 Tm
(:)Tj
1.0003 0 0 1.0003 72 769.82 Tm
95.386 -213.36 Td
[(Eac)26(h)-286(mem)26(b)-26(er)]TJ
/T1_3 10.91 Tf
67.964 0 Td
(U)Tj
/T1_4 7.97 Tf
5.72 -1.64 Td
(j)Tj
/T1_2 10.91 Tf
7.52 1.64 Td
(for)Tj
/T1_0 10.91 Tf
16.2 0 Td
(n)Tj
/T1_2 10.91 Tf
7.97 0 Td
[(+)-130(1)]TJ
/T1_1 10.91 Tf
18.39 0 Td
(\267)Tj
/T1_0 10.91 Tf
11.51 0 Td
(j)Tj
/T1_1 10.91 Tf
8.15 0 Td
(\267)Tj
/T1_0 10.91 Tf
11.51 0 Td
(n)Tj
/T1_2 10.91 Tf
7.98 0 Td
(+)Tj
/T1_0 10.91 Tf
9.91 0 Td
(m)Tj
/T1_2 10.91 Tf
12.71 0 Td
(computes)Tj
/T1_0 10.91 Tf
48.03 0 Td
(\256)Tj
/T1_4 7.97 Tf
6.98 -1.64 Td
(j)Tj
/T1_2 10.91 Tf
7.41 1.64 Td
(=)Tj
/T1_8 10.91 Tf
11.51 0 Td
(H)Tj
/T1_2 10.91 Tf
7.73 0 Td
(\()Tj
/T1_0 10.91 Tf
(z)Tj
/T1_4 7.97 Tf
9.79 6.13 Td
(r)Tj
/T1_9 5.98 Tf
3.82 -1.21 Td
(j)Tj
/T1_4 7.97 Tf
-4.3 -8.18 Td
(j)Tj
/T1_6 7.97 Tf
3.88 0 Td
(\241)Tj
/T1_5 7.97 Tf
6.59 0 Td
(1)Tj
/T1_1 10.91 Tf
4.73 3.26 Td
(jj)Tj
/T1_0 10.91 Tf
6.06 0 Td
(K)Tj
/T1_6 7.97 Tf
10.04 3.96 Td
(0)Tj
/T1_1 10.91 Tf
2.79 -3.96 Td
(jj)Tj
/T1_0 10.91 Tf
6.06 0 Td
(v)Tj
/T1_2 10.91 Tf
5.68 0 Td
[(\))-287(and)]TJ
/T1_0 10.91 Tf
28.09 0 Td
(\257)Tj
/T1_4 7.97 Tf
6.17 -1.64 Td
(j)Tj
/T1_2 10.91 Tf
7.41 1.64 Td
(=)Tj
/T1_8 10.91 Tf
-459.39 -21.92 Td
(H)Tj
/T1_2 10.91 Tf
7.73 0 Td
(\()Tj
/T1_0 10.91 Tf
(z)Tj
/T1_4 7.97 Tf
9.79 6.14 Td
(r)Tj
/T1_9 5.98 Tf
3.82 -1.22 Td
(j)Tj
/T1_4 7.97 Tf
-4.3 -8.17 Td
(j)Tj
/T1_5 7.97 Tf
3.88 0 Td
(+1)Tj
/T1_1 10.91 Tf
11.32 3.25 Td
(jj)Tj
/T1_0 10.91 Tf
6.06 0 Td
(K)Tj
/T1_6 7.97 Tf
10.04 3.96 Td
(0)Tj
/T1_1 10.91 Tf
2.79 -3.96 Td
(jj)Tj
/T1_0 10.91 Tf
6.06 0 Td
(v)Tj
/T1_2 10.91 Tf
5.68 0 Td
(\).)Tj
/T1_3 10.91 Tf
11.94 0 Td
(U)Tj
/T1_5 7.97 Tf
5.73 -1.63 Td
(1)Tj
/T1_2 10.91 Tf
7.84 1.63 Td
(and)Tj
/T1_3 10.91 Tf
20.68 0 Td
(U)Tj
/T1_4 7.97 Tf
5.72 -1.63 Td
(n)Tj
/T1_2 10.91 Tf
8.75 1.63 Td
(computes)Tj
/T1_0 10.91 Tf
48 0 Td
(\256)Tj
/T1_6 7.97 Tf
7.02 3.96 Td
(0)Tj
/T1_5 7.97 Tf
-0.04 -6.88 Td
(1)Tj
/T1_2 10.91 Tf
7.76 2.92 Td
(=)Tj
/T1_8 10.91 Tf
11.51 0 Td
(H)Tj
/T1_2 10.91 Tf
7.73 0 Td
(\()Tj
/T1_0 10.91 Tf
(z)Tj
/T1_4 7.97 Tf
9.79 4.87 Td
(r)Tj
/T1_10 5.98 Tf
3.82 -1.11 Td
(1)Tj
/T1_4 7.97 Tf
-4.3 -6.56 Td
(n)Tj
/T1_5 7.97 Tf
(+)Tj
/T1_4 7.97 Tf
(m)Tj
/T1_1 10.91 Tf
19.71 2.8 Td
(jj)Tj
/T1_0 10.91 Tf
6.06 0 Td
(K)Tj
/T1_6 7.97 Tf
10.04 3.96 Td
(0)Tj
/T1_1 10.91 Tf
2.79 -3.96 Td
(jj)Tj
/T1_0 10.91 Tf
6.06 0 Td
(v)Tj
/T1_2 10.91 Tf
5.68 0 Td
[(\))-284(and)]TJ
/T1_0 10.91 Tf
28.03 0 Td
(\257)Tj
/T1_6 7.97 Tf
6.74 3.96 Td
(0)Tj
/T1_4 7.97 Tf
-0.57 -6.65 Td
(n)Tj
/T1_2 10.91 Tf
8.66 2.69 Td
(=)Tj
/T1_8 10.91 Tf
11.51 0 Td
(H)Tj
/T1_2 10.91 Tf
7.73 0 Td
(\()Tj
/T1_0 10.91 Tf
(z)Tj
/T1_4 7.97 Tf
9.79 4.76 Td
(r)Tj
/T1_9 5.98 Tf
3.82 -1 Td
(n)Tj
/T1_4 7.97 Tf
-4.3 -6.88 Td
(n)Tj
/T1_5 7.97 Tf
(+1)Tj
/T1_1 10.91 Tf
16.45 3.12 Td
(jj)Tj
/T1_0 10.91 Tf
6.06 0 Td
(K)Tj
/T1_6 7.97 Tf
10.05 3.96 Td
(0)Tj
/T1_1 10.91 Tf
2.79 -3.96 Td
(jj)Tj
/T1_0 10.91 Tf
6.06 0 Td
(v)Tj
/T1_2 10.91 Tf
5.68 0 Td
[(\))-284(resp)-28(ectiv)27(ely)83(.)-427(All)]TJ
-383.66 -21.91 Td
[(mem)27(b)-26(ers)]TJ
/T1_3 10.91 Tf
45.82 0 Td
(U)Tj
/T1_4 7.97 Tf
5.73 -1.64 Td
(i)Tj
/T1_2 10.91 Tf
6.7 1.64 Td
[(for)-303(1)]TJ
/T1_1 10.91 Tf
24.85 0 Td
(\267)Tj
/T1_0 10.91 Tf
11.51 0 Td
(i)Tj
/T1_1 10.91 Tf
6.79 0 Td
(\267)Tj
/T1_0 10.91 Tf
11.51 0 Td
(n)Tj
/T1_2 10.91 Tf
8.34 0 Td
(+)Tj
/T1_0 10.91 Tf
10.27 0 Td
(m)Tj
/T1_2 10.91 Tf
12.89 0 Td
[(then)-304(compute)]TJ
/T1_0 10.91 Tf
68.44 0 Td
(\261)Tj
/T1_6 7.97 Tf
5.26 3.95 Td
(0)Tj
/T1_2 10.91 Tf
5.82 -3.95 Td
(=)Tj
/T1_8 10.91 Tf
11.51 0 Td
(H)Tj
/T1_2 10.91 Tf
7.73 0 Td
(\()Tj
/T1_0 10.91 Tf
(\267)Tj
/T1_6 7.97 Tf
10.52 3.95 Td
(0)Tj
/T1_4 7.97 Tf
0 -6.65 TD
(n)Tj
/T1_1 10.91 Tf
5.64 2.7 Td
(jj)Tj
/T1_0 10.91 Tf
6.06 0 Td
(K)Tj
/T1_6 7.97 Tf
10.04 3.95 Td
(0)Tj
/T1_1 10.91 Tf
2.8 -3.95 Td
(jj)Tj
/T1_0 10.91 Tf
6.05 0 Td
(v)Tj
/T1_2 10.91 Tf
5.68 0 Td
[(\),)-310(where)]TJ
/T1_0 10.91 Tf
41.87 0 Td
(\267)Tj
/T1_6 7.97 Tf
6.29 3.95 Td
(0)Tj
/T1_4 7.97 Tf
T*
(n)Tj
/T1_2 10.91 Tf
8.66 2.7 Td
(=)Tj
/T1_0 10.91 Tf
11.51 0 Td
(\267)Tj
/T1_4 7.97 Tf
6.29 -1.64 Td
(n)Tj
/T1_5 7.97 Tf
5.13 0 Td
(+)Tj
/T1_4 7.97 Tf
6.59 0 Td
(m)Tj
/T1_5 7.97 Tf
(+3)Tj
/T1_2 10.91 Tf
18.8 1.64 Td
[(.)-434(Eac)26(h)-303(mem)27(b)-27(er)]TJ
/T1_3 10.91 Tf
-395.1 -21.92 Td
(U)Tj
/T1_4 7.97 Tf
5.73 -1.64 Td
(j)Tj
/T1_2 10.91 Tf
7.71 1.64 Td
(for)Tj
/T1_0 10.91 Tf
16.38 0 Td
(n)Tj
/T1_2 10.91 Tf
8.36 0 Td
[(+)-165(1)]TJ
/T1_1 10.91 Tf
18.77 0 Td
(\267)Tj
/T1_0 10.91 Tf
11.51 0 Td
(j)Tj
/T1_1 10.91 Tf
8.15 0 Td
(\267)Tj
/T1_0 10.91 Tf
11.51 0 Td
(n)Tj
/T1_2 10.91 Tf
8.36 0 Td
(+)Tj
/T1_0 10.91 Tf
10.29 0 Td
(m)Tj
/T1_2 10.91 Tf
12.9 0 Td
[(sa)27(v)28(es)-305(\()]TJ
/T1_0 10.91 Tf
31.63 0 Td
(\256)Tj
/T1_4 7.97 Tf
6.97 -1.64 Td
(j)Tj
/T1_0 10.91 Tf
4.39 1.64 Td
[(;)-166(\257)]TJ
/T1_4 7.97 Tf
11.01 -1.64 Td
(j)Tj
/T1_0 10.91 Tf
4.38 1.64 Td
[(;)-166(\261)]TJ
/T1_6 7.97 Tf
10.11 3.96 Td
(0)Tj
/T1_0 10.91 Tf
2.79 -3.96 Td
[(;)-167(K)]TJ
/T1_6 7.97 Tf
14.89 3.96 Td
(0)Tj
/T1_2 10.91 Tf
2.8 -3.96 Td
[(\))-305(secretly)83(,)-310(mem)27(b)-27(ers)]TJ
/T1_3 10.91 Tf
95.05 0 Td
(U)Tj
/T1_5 7.97 Tf
5.73 -1.64 Td
(1)Tj
/T1_2 10.91 Tf
8.06 1.64 Td
(and)Tj
/T1_3 10.91 Tf
20.9 0 Td
(U)Tj
/T1_4 7.97 Tf
5.72 -1.64 Td
(n)Tj
/T1_2 10.91 Tf
8.97 1.64 Td
[(sa)28(v)27(es)-304(\()]TJ
/T1_0 10.91 Tf
31.62 0 Td
(\256)Tj
/T1_6 7.97 Tf
7.02 3.96 Td
(0)Tj
/T1_5 7.97 Tf
-0.04 -6.88 Td
(1)Tj
/T1_0 10.91 Tf
4.73 2.92 Td
[(;)-166(\257)]TJ
/T1_5 7.97 Tf
11.01 -1.64 Td
(1)Tj
/T1_0 10.91 Tf
4.73 1.64 Td
[(;)-167(\261)]TJ
/T1_6 7.97 Tf
10.11 3.96 Td
(0)Tj
/T1_0 10.91 Tf
2.8 -3.96 Td
[(;)-166(K)]TJ
/T1_6 7.97 Tf
14.89 3.96 Td
(0)Tj
/T1_2 10.91 Tf
2.79 -3.96 Td
[(\))-305(and)]TJ
-442.73 -21.92 Td
(\()Tj
/T1_0 10.91 Tf
(\256)Tj
/T1_4 7.97 Tf
11.22 -1.63 Td
(n)Tj
/T1_0 10.91 Tf
5.63 1.63 Td
[(;)-166(\257)]TJ
/T1_6 7.97 Tf
11.59 3.96 Td
(0)Tj
/T1_4 7.97 Tf
-0.57 -6.65 Td
(n)Tj
/T1_0 10.91 Tf
5.63 2.69 Td
[(;)-166(\261)]TJ
/T1_6 7.97 Tf
10.11 3.96 Td
(0)Tj
/T1_0 10.91 Tf
2.79 -3.96 Td
[(;)-167(K)]TJ
/T1_6 7.97 Tf
14.89 3.96 Td
(0)Tj
/T1_2 10.91 Tf
2.8 -3.96 Td
[(\))-297(secretly)-297(resp)-28(ectiv)27(ely)-296(and)-297(all)-298(other)-297(mem)27(b)-27(ers)]TJ
/T1_3 10.91 Tf
215.37 0 Td
(U)Tj
/T1_4 7.97 Tf
5.72 -1.63 Td
(i)Tj
/T1_2 10.91 Tf
6.62 1.63 Td
[(for)-297(2)]TJ
/T1_1 10.91 Tf
24.78 0 Td
(\267)Tj
/T1_0 10.91 Tf
11.52 0 Td
(i)Tj
/T1_1 10.91 Tf
6.78 0 Td
(\267)Tj
/T1_0 10.91 Tf
11.51 0 Td
(n)Tj
/T1_1 10.91 Tf
8.19 0 Td
(\241)Tj
/T1_2 10.91 Tf
10.12 0 Td
[(1)-296(stores)-298(\()]TJ
/T1_0 10.91 Tf
43.59 0 Td
(\256)Tj
/T1_4 7.97 Tf
6.98 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
3.38 1.63 Td
[(;)-166(\257)]TJ
/T1_4 7.97 Tf
11.01 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
3.38 1.63 Td
[(;)-167(\261)]TJ
/T1_6 7.97 Tf
10.11 3.96 Td
(0)Tj
/T1_0 10.91 Tf
2.8 -3.96 Td
[(;)-166(K)]TJ
/T1_6 7.97 Tf
14.89 3.96 Td
(0)Tj
/T1_2 10.91 Tf
2.79 -3.96 Td
(\))Tj
-463.63 -21.91 Td
[(in)-333(secure)-333(storage.)]TJ
/T1_11 10.91 Tf
0 -37.18 TD
[(Lea)31(v)32(e)-382(Proto)-32(col)]TJ
/T1_2 10.91 Tf
0 -28.96 TD
[(Supp)-27(ose)-368(a)-368(set)-367(of)]TJ
/T1_0 10.91 Tf
82.81 0 Td
(`)Tj
/T1_2 10.91 Tf
8.55 0 Td
(users)Tj
/T1_1 10.91 Tf
27.79 0 Td
(L)Tj
/T1_2 10.91 Tf
11.18 0 Td
(=)Tj
/T1_1 10.91 Tf
12.13 0 Td
(f)Tj
/T1_3 10.91 Tf
(U)Tj
/T1_4 7.97 Tf
11.18 -1.78 Td
(l)Tj
/T1_10 5.98 Tf
2.53 -1.1 Td
(1)Tj
/T1_0 10.91 Tf
4.65 2.88 Td
(;)Tj
/T1_1 10.91 Tf
4.84 0 Td
[(\242)-167(\242)-166(\242)]TJ
/T1_0 10.91 Tf
16.36 0 Td
(;)Tj
/T1_3 10.91 Tf
4.85 0 Td
(U)Tj
/T1_4 7.97 Tf
5.73 -1.78 Td
(l)Tj
/T1_9 5.98 Tf
2.52 -1.4 Td
(`)Tj
/T1_1 10.91 Tf
4.1 3.18 Td
(g)Tj
/T1_2 10.91 Tf
9.46 0 Td
(with)Tj
/T1_1 10.91 Tf
25.22 0 Td
(f)Tj
/T1_0 10.91 Tf
(l)Tj
/T1_5 7.97 Tf
8.7 -1.64 Td
(1)Tj
/T1_0 10.91 Tf
4.74 1.64 Td
(;)Tj
/T1_1 10.91 Tf
4.84 0 Td
[(\242)-166(\242)-167(\242)]TJ
/T1_0 10.91 Tf
16.36 0 Td
[(;)-166(l)]TJ
/T1_4 7.97 Tf
8.1 -1.78 Td
(`)Tj
/T1_1 10.91 Tf
3.96 1.78 Td
[(g)-334(\275)-335(f)]TJ
/T1_2 10.91 Tf
26.69 0 Td
(1)Tj
/T1_0 10.91 Tf
(;)Tj
/T1_2 10.91 Tf
10.3 0 Td
(2)Tj
/T1_0 10.91 Tf
(;)Tj
/T1_1 10.91 Tf
10.3 0 Td
[(\242)-167(\242)-166(\242)]TJ
/T1_0 10.91 Tf
16.36 0 Td
[(;)-166(n)]TJ
/T1_1 10.91 Tf
11.4 0 Td
(g)Tj
/T1_2 10.91 Tf
9.46 0 Td
[(wishes)-367(to)-368(lea)27(v)28(e)-367(group)]TJ
/T1_1 10.91 Tf
-365.11 -21.92 Td
(G)Tj
/T1_2 10.91 Tf
10.16 0 Td
(=)Tj
/T1_1 10.91 Tf
11.52 0 Td
(f)Tj
/T1_3 10.91 Tf
(U)Tj
/T1_5 7.97 Tf
11.17 -1.63 Td
(1)Tj
/T1_0 10.91 Tf
4.74 1.63 Td
(;)Tj
/T1_1 10.91 Tf
4.84 0 Td
[(\242)-166(\242)-167(\242)]TJ
/T1_0 10.91 Tf
16.36 0 Td
(;)Tj
/T1_3 10.91 Tf
4.85 0 Td
(U)Tj
/T1_4 7.97 Tf
5.72 -1.63 Td
(n)Tj
/T1_1 10.91 Tf
5.64 1.63 Td
(g)Tj
/T1_2 10.91 Tf
[(.)-435(Let)]TJ
/T1_1 10.91 Tf
32.46 0 Td
(N)Tj
/T1_2 10.91 Tf
10.56 0 Td
(\()Tj
/T1_1 10.91 Tf
(R)Tj
/T1_2 10.91 Tf
13.48 0 Td
[(\))-305(b)-28(e)-306(the)-305(set)-306(of)-305(all)-306(left)-306(and)-305(righ)27(t)-305(neigh)27(b)-27(ors)-305(of)-306(lea)27(ving)-305(users,)-311(i.e.)]TJ
/T1_1 10.91 Tf
296.58 0 Td
(N)Tj
/T1_2 10.91 Tf
10.55 0 Td
(\()Tj
/T1_1 10.91 Tf
(R)Tj
/T1_2 10.91 Tf
[(\))-277(=)]TJ
/T1_1 10.91 Tf
-438.63 -21.91 Td
(f)Tj
/T1_3 10.91 Tf
(U)Tj
/T1_4 7.97 Tf
11.18 -1.78 Td
(l)Tj
/T1_10 5.98 Tf
2.53 -1.11 Td
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9.43 0 Td
(\267)Tj
/T1_0 10.91 Tf
11.89 0 Td
(`)Tj
/T1_5 10.91 Tf
[(.)-506(Then)-354(eac)27(h)]TJ
-405.16 -21.91 Td
[(mem)27(b)-26(er)]TJ
/T1_8 10.91 Tf
42.62 0 Td
(V)Tj
/T1_1 7.97 Tf
5.73 -1.64 Td
(i)Tj
/T1_9 10.91 Tf
7.72 1.64 Td
[(2)-398(G)]TJ
/T1_3 7.97 Tf
18.75 3.96 Td
(0)Tj
/T1_5 10.91 Tf
7.22 -3.96 Td
(computes)Tj
/T1_0 10.91 Tf
49.32 0 Td
(L)Tj
/T1_3 7.97 Tf
7.42 3.96 Td
(0)Tj
/T1_1 7.97 Tf
0 -7.02 TD
(i)Tj
/T1_5 10.91 Tf
7.72 3.06 Td
(=)Tj
/T1_10 10.91 Tf
12.82 0 Td
(H)Tj
/T1_5 10.91 Tf
7.73 0 Td
(\()Tj
/T1_0 10.91 Tf
(\256)Tj
/T1_1 7.97 Tf
11.22 -1.64 Td
(i)Tj
/T1_9 10.91 Tf
3.38 1.64 Td
(jj)Tj
/T1_0 10.91 Tf
6.06 0 Td
(I)Tj
/T1_1 7.97 Tf
4.79 -1.64 Td
(v)Tj
/T1_9 10.91 Tf
4.91 1.64 Td
(jj)Tj
/T1_0 10.91 Tf
6.06 0 Td
(v)Tj
/T1_5 10.91 Tf
5.67 0 Td
(\),)Tj
/T1_0 10.91 Tf
11.89 0 Td
(R)Tj
/T1_3 7.97 Tf
8.37 3.96 Td
(0)Tj
/T1_1 7.97 Tf
-0.09 -7.02 Td
(i)Tj
/T1_5 10.91 Tf
7.73 3.06 Td
(=)Tj
/T1_10 10.91 Tf
12.82 0 Td
(H)Tj
/T1_5 10.91 Tf
7.73 0 Td
(\()Tj
/T1_0 10.91 Tf
(\257)Tj
/T1_1 7.97 Tf
10.41 -1.64 Td
(i)Tj
/T1_9 10.91 Tf
3.38 1.64 Td
(jj)Tj
/T1_0 10.91 Tf
6.06 0 Td
(I)Tj
/T1_1 7.97 Tf
4.79 -1.64 Td
(v)Tj
/T1_9 10.91 Tf
4.91 1.64 Td
(jj)Tj
/T1_0 10.91 Tf
6.05 0 Td
(v)Tj
/T1_5 10.91 Tf
5.68 0 Td
[(\))-405(and)]TJ
/T1_0 10.91 Tf
30.66 0 Td
(X)Tj
/T1_3 7.97 Tf
9.89 3.96 Td
(0)Tj
/T1_1 7.97 Tf
-0.85 -7.02 Td
(i)Tj
/T1_5 10.91 Tf
7.99 3.06 Td
(=)Tj
/T1_0 10.91 Tf
12.82 0 Td
(L)Tj
/T1_3 7.97 Tf
7.42 3.96 Td
(0)Tj
/T1_1 7.97 Tf
T*
(i)Tj
/T1_9 10.91 Tf
6.33 3.06 Td
(\251)Tj
/T1_0 10.91 Tf
11.43 0 Td
(R)Tj
/T1_3 7.97 Tf
8.37 3.96 Td
(0)Tj
/T1_1 7.97 Tf
-0.09 -7.02 Td
(i)Tj
/T1_5 10.91 Tf
3.38 3.06 Td
[(.)-661(The)-406(mem)27(b)-27(er)]TJ
/T1_8 10.91 Tf
-396.22 -21.92 Td
(U)Tj
/T1_1 7.97 Tf
5.73 -1.78 Td
(l)Tj
/T1_2 5.98 Tf
2.52 -1.4 Td
(`)Tj
/T1_4 7.97 Tf
3.6 1.4 Td
(+1)Tj
/T1_5 10.91 Tf
16.03 1.78 Td
[(additionally)-432(computes)]TJ
/T1_11 10.91 Tf
111.86 2.88 Td
(c)Tj
/T1_0 10.91 Tf
-0.89 -2.88 Td
(X)Tj
/T1_3 7.97 Tf
9.9 3.15 Td
(0)Tj
/T1_5 10.91 Tf
7.62 -3.15 Td
(=)Tj
/T1_0 10.91 Tf
13.31 0 Td
(\267)Tj
/T1_1 7.97 Tf
6.28 -1.78 Td
(l)Tj
/T1_2 5.98 Tf
2.53 -1.4 Td
(`)Tj
/T1_4 7.97 Tf
3.59 1.4 Td
(+1)Tj
/T1_9 10.91 Tf
14.46 1.78 Td
(\251)Tj
/T1_0 10.91 Tf
11.63 0 Td
(R)Tj
/T1_1 7.97 Tf
8.28 -1.78 Td
(l)Tj
/T1_2 5.98 Tf
2.52 -1.4 Td
(`)Tj
/T1_4 7.97 Tf
3.6 1.4 Td
(+1)Tj
/T1_5 10.91 Tf
11.32 1.78 Td
[(.)-740(Eac)27(h)-432(mem)27(b)-27(er)]TJ
/T1_8 10.91 Tf
82.21 0 Td
(U)Tj
/T1_1 7.97 Tf
5.73 -1.63 Td
(j)Tj
/T1_9 10.91 Tf
9.21 1.63 Td
(6)Tj
/T1_5 10.91 Tf
(=)Tj
/T1_8 10.91 Tf
13.31 0 Td
(U)Tj
/T1_1 7.97 Tf
5.72 -1.78 Td
(l)Tj
/T1_2 5.98 Tf
2.53 -1.4 Td
(`)Tj
/T1_4 7.97 Tf
3.6 1.4 Td
(+1)Tj
/T1_9 10.91 Tf
16.14 1.78 Td
[(2)-442(N)]TJ
/T1_5 10.91 Tf
22.65 0 Td
(\()Tj
/T1_9 10.91 Tf
(R)Tj
/T1_5 10.91 Tf
[(\))-431(broadcasts)]TJ
/T1_9 10.91 Tf
-394.99 -21.92 Td
(f)Tj
/T1_0 10.91 Tf
(\267)Tj
/T1_1 7.97 Tf
11.74 -1.63 Td
(j)Tj
/T1_9 10.91 Tf
4.38 1.63 Td
(jj)Tj
/T1_0 10.91 Tf
6.06 0 Td
(X)Tj
/T1_3 7.97 Tf
9.89 3.96 Td
(0)Tj
/T1_1 7.97 Tf
-0.86 -7.01 Td
(j)Tj
/T1_9 10.91 Tf
4.38 3.05 Td
(jj)Tj
/T1_0 10.91 Tf
6.06 0 Td
(\276)Tj
/T1_3 7.97 Tf
6.63 3.96 Td
(0)Tj
/T1_1 7.97 Tf
-0.4 -7.01 Td
(j)Tj
/T1_9 10.91 Tf
4.38 3.05 Td
(g)Tj
/T1_5 10.91 Tf
(,)Tj
/T1_8 10.91 Tf
12.19 0 Td
(U)Tj
/T1_1 7.97 Tf
5.73 -1.77 Td
(l)Tj
/T1_2 5.98 Tf
2.52 -1.41 Td
(`)Tj
/T1_4 7.97 Tf
3.6 1.41 Td
(+1)Tj
/T1_5 10.91 Tf
15 1.77 Td
(broadcast)Tj
/T1_9 10.91 Tf
49.83 0 Td
(f)Tj
/T1_11 10.91 Tf
6.35 2.89 Td
(c)Tj
/T1_0 10.91 Tf
-0.89 -2.89 Td
(X)Tj
/T1_3 7.97 Tf
9.89 3.16 Td
(0)Tj
/T1_9 10.91 Tf
2.79 -3.16 Td
(jj)Tj
/T1_0 10.91 Tf
6.06 0 Td
(X)Tj
/T1_3 7.97 Tf
9.89 3.96 Td
(0)Tj
/T1_1 7.97 Tf
-0.85 -7.28 Td
(l)Tj
/T1_2 5.98 Tf
2.52 -1.4 Td
(`)Tj
/T1_4 7.97 Tf
3.6 1.4 Td
(+1)Tj
/T1_9 10.91 Tf
11.31 3.32 Td
(jj)Tj
/T1_0 10.91 Tf
6.06 0 Td
(\276)Tj
/T1_3 7.97 Tf
6.63 3.96 Td
(0)Tj
/T1_1 7.97 Tf
-0.39 -7.28 Td
(l)Tj
/T1_2 5.98 Tf
2.52 -1.4 Td
(`)Tj
/T1_4 7.97 Tf
3.6 1.4 Td
(+1)Tj
/T1_9 10.91 Tf
11.31 3.32 Td
(g)Tj
/T1_5 10.91 Tf
9.15 0 Td
[(and)-338(mem)27(b)-27(ers)]TJ
/T1_8 10.91 Tf
67.45 0 Td
(V)Tj
/T1_1 7.97 Tf
5.73 -1.63 Td
(j)Tj
/T1_9 10.91 Tf
7.5 1.63 Td
[(2)-285(G)]TJ
/T1_3 7.97 Tf
17.52 3.96 Td
(0)Tj
/T1_9 10.91 Tf
5.26 -3.96 Td
[(n)-225(N)]TJ
/T1_5 10.91 Tf
18.46 0 Td
(\()Tj
/T1_9 10.91 Tf
4.25 0 Td
(R)Tj
/T1_5 10.91 Tf
9.24 0 Td
[(\))-338(broadcast)]TJ
/T1_9 10.91 Tf
57.76 0 Td
(f)Tj
/T1_0 10.91 Tf
(X)Tj
/T1_3 7.97 Tf
15.34 3.96 Td
(0)Tj
/T1_1 7.97 Tf
-0.85 -7.01 Td
(j)Tj
/T1_9 10.91 Tf
4.38 3.05 Td
(jj)Tj
/T1_0 10.91 Tf
6.06 0 Td
(\276)Tj
/T1_3 7.97 Tf
6.62 3.96 Td
(0)Tj
/T1_1 7.97 Tf
-0.39 -7.01 Td
(j)Tj
/T1_9 10.91 Tf
4.38 3.05 Td
(g)Tj
/T1_5 10.91 Tf
(,)Tj
-459.39 -21.91 Td
[(where)-333(signature)]TJ
/T1_0 10.91 Tf
78.89 0 Td
(\276)Tj
/T1_3 7.97 Tf
6.62 3.96 Td
(0)Tj
/T1_1 7.97 Tf
-0.39 -7.02 Td
(j)Tj
/T1_5 10.91 Tf
7.41 3.06 Td
(=)Tj
/T1_9 10.91 Tf
11.51 0 Td
(S)Tj
/T1_5 10.91 Tf
7.42 0 Td
(\()Tj
/T1_0 10.91 Tf
(\267)Tj
/T1_1 7.97 Tf
10.53 -1.64 Td
(j)Tj
/T1_9 10.91 Tf
4.38 1.64 Td
(jj)Tj
/T1_0 10.91 Tf
6.06 0 Td
(X)Tj
/T1_3 7.97 Tf
9.89 3.96 Td
(0)Tj
/T1_1 7.97 Tf
-0.86 -7.02 Td
(j)Tj
/T1_9 10.91 Tf
4.38 3.06 Td
(jj)Tj
/T1_0 10.91 Tf
6.06 0 Td
(I)Tj
/T1_1 7.97 Tf
4.8 -1.64 Td
(v)Tj
/T1_9 10.91 Tf
4.9 1.64 Td
(jj)Tj
/T1_0 10.91 Tf
6.06 0 Td
(v)Tj
/T1_5 10.91 Tf
5.68 0 Td
(\),)Tj
/T1_0 10.91 Tf
10.91 0 Td
(\276)Tj
/T1_3 7.97 Tf
6.62 3.96 Td
(0)Tj
/T1_1 7.97 Tf
-0.39 -7.28 Td
(l)Tj
/T1_2 5.98 Tf
2.53 -1.41 Td
(`)Tj
/T1_4 7.97 Tf
3.59 1.41 Td
(+1)Tj
/T1_5 10.91 Tf
14.35 3.32 Td
(=)Tj
/T1_9 10.91 Tf
11.51 0 Td
(S)Tj
/T1_5 10.91 Tf
7.42 0 Td
(\()Tj
/T1_11 10.91 Tf
5.13 2.88 Td
(c)Tj
/T1_0 10.91 Tf
-0.89 -2.88 Td
(X)Tj
/T1_3 7.97 Tf
9.89 3.15 Td
(0)Tj
/T1_9 10.91 Tf
2.8 -3.15 Td
(jj)Tj
/T1_0 10.91 Tf
6.06 0 Td
(X)Tj
/T1_3 7.97 Tf
9.89 3.96 Td
(0)Tj
/T1_1 7.97 Tf
-0.86 -7.28 Td
(l)Tj
/T1_2 5.98 Tf
2.53 -1.41 Td
(`)Tj
/T1_4 7.97 Tf
3.6 1.41 Td
(+1)Tj
/T1_9 10.91 Tf
11.31 3.32 Td
(jj)Tj
/T1_0 10.91 Tf
6.06 0 Td
(I)Tj
/T1_1 7.97 Tf
4.79 -1.64 Td
(v)Tj
/T1_9 10.91 Tf
4.91 1.64 Td
(jj)Tj
/T1_0 10.91 Tf
6.06 0 Td
(v)Tj
/T1_5 10.91 Tf
5.68 0 Td
[(\))-333(and)]TJ
/T1_0 10.91 Tf
29.08 0 Td
(\276)Tj
/T1_3 7.97 Tf
6.62 3.96 Td
(0)Tj
/T1_1 7.97 Tf
-0.39 -7.02 Td
(j)Tj
/T1_5 10.91 Tf
7.41 3.06 Td
(=)Tj
/T1_9 10.91 Tf
11.51 0 Td
(S)Tj
/T1_5 10.91 Tf
7.43 0 Td
(\()Tj
/T1_0 10.91 Tf
(X)Tj
/T1_3 7.97 Tf
14.13 3.96 Td
(0)Tj
/T1_1 7.97 Tf
-0.86 -7.02 Td
(j)Tj
/T1_9 10.91 Tf
4.38 3.06 Td
(jj)Tj
/T1_0 10.91 Tf
6.06 0 Td
(I)Tj
/T1_1 7.97 Tf
4.8 -1.64 Td
(v)Tj
/T1_9 10.91 Tf
4.9 1.64 Td
(jj)Tj
/T1_0 10.91 Tf
6.06 0 Td
(v)Tj
/T1_5 10.91 Tf
5.68 0 Td
(\).)Tj
-413.65 -21.92 Td
[(Key)-333(Computation)]TJ
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 0 -124.19 cm
0 0 m
85.73 0 l
S
Q
Q
BT
/T1_5 10.91 Tf
1.0003 0 0 1.0003 157.754 649.2462 Tm
(:)Tj
1.0003 0 0 1.0003 72 769.82 Tm
95.342 -120.54 Td
[(All)-413(mem)27(b)-27(ers)]TJ
/T1_8 10.91 Tf
65.748 0 Td
(V)Tj
/T1_1 7.97 Tf
5.72 -1.63 Td
(i)Tj
/T1_9 10.91 Tf
7.86 1.63 Td
[(2)-410(G)]TJ
/T1_3 7.97 Tf
18.88 3.96 Td
(0)Tj
/T1_5 10.91 Tf
7.29 -3.96 Td
[(for)-413(1)]TJ
/T1_9 10.91 Tf
27.49 0 Td
(\267)Tj
/T1_0 10.91 Tf
12.95 0 Td
(i)Tj
/T1_9 10.91 Tf
8.24 0 Td
(\267)Tj
/T1_0 10.91 Tf
12.95 0 Td
(n)Tj
/T1_9 10.91 Tf
9.55 0 Td
(\241)Tj
/T1_0 10.91 Tf
11.48 0 Td
(`)Tj
/T1_5 10.91 Tf
9.05 0 Td
[(v)27(erify)-411(the)-413(receiv)27(ed)-412(signatures.)-683(If)-413(all)]TJ
-292.55 -21.91 Td
[(signatures)-333(are)-333(v)54(alid,)]TJ
/T1_8 10.91 Tf
99.25 0 Td
(V)Tj
/T1_1 7.97 Tf
5.72 -1.64 Td
(i)Tj
/T1_9 10.91 Tf
6.41 1.64 Td
[(2)-277(G)]TJ
/T1_3 7.97 Tf
17.44 3.95 Td
(0)Tj
/T1_5 10.91 Tf
6.43 -3.95 Td
(computes)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 66.84 -173.12 cm
0 0 m
8.36 0 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 138.8587 587.669 Tm
(R)Tj
/T1_1 7.97 Tf
8.36 -1.63 Td
(i)Tj
/T1_4 7.97 Tf
2.89 0 Td
(+1)Tj
/T1_5 10.91 Tf
14.34 1.63 Td
(=)Tj
/T1_0 10.91 Tf
11.51 0 Td
(X)Tj
/T1_1 7.97 Tf
9.04 -1.63 Td
(i)Tj
/T1_4 7.97 Tf
2.88 0 Td
(+1)Tj
/T1_9 10.91 Tf
13.74 1.63 Td
(\251)Tj
/T1_0 10.91 Tf
10.91 0 Td
(R)Tj
/T1_1 7.97 Tf
8.28 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
3.38 1.63 Td
(;)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 165.52 -173.12 cm
0 0 m
8.36 0 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 237.5663 587.669 Tm
(R)Tj
/T1_1 7.97 Tf
8.36 -1.63 Td
(i)Tj
/T1_4 7.97 Tf
2.88 0 Td
(+2)Tj
/T1_5 10.91 Tf
14.35 1.63 Td
(=)Tj
/T1_0 10.91 Tf
11.51 0 Td
(X)Tj
/T1_1 7.97 Tf
9.03 -1.63 Td
(i)Tj
/T1_4 7.97 Tf
2.89 0 Td
(+2)Tj
/T1_9 10.91 Tf
13.74 1.63 Td
(\251)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 239.18 -173.12 cm
0 0 m
8.37 0 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 311.247 587.669 Tm
(R)Tj
/T1_1 7.97 Tf
8.37 -1.63 Td
(i)Tj
/T1_4 7.97 Tf
2.88 0 Td
(+1)Tj
/T1_0 10.91 Tf
11.32 1.63 Td
(;)Tj
/T1_9 10.91 Tf
13.34 0 Td
(\242)Tj
1.0003 0 0 1.0003 72 769.82 Tm
279.945 -182.1 Td
[(\242)-166(\242)]TJ
/T1_0 10.91 Tf
11.505 0 Td
(;)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 304.8 -173.12 cm
0 0 m
8.37 0 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 376.8853 587.669 Tm
(R)Tj
/T1_1 7.97 Tf
8.37 -1.63 Td
(i)Tj
/T1_3 7.97 Tf
2.88 0 Td
(\241)Tj
/T1_4 7.97 Tf
(1)Tj
/T1_5 10.91 Tf
14.34 1.63 Td
(=)Tj
/T1_0 10.91 Tf
11.52 0 Td
(X)Tj
/T1_1 7.97 Tf
9.03 -1.63 Td
(i)Tj
/T1_3 7.97 Tf
2.88 0 Td
(\241)Tj
/T1_4 7.97 Tf
6.59 0 Td
(1)Tj
/T1_9 10.91 Tf
7.15 1.63 Td
(\251)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 378.47 -173.12 cm
0 0 m
8.36 0 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 450.576 587.669 Tm
(R)Tj
/T1_1 7.97 Tf
8.36 -1.63 Td
(i)Tj
/T1_3 7.97 Tf
2.89 0 Td
(\241)Tj
/T1_4 7.97 Tf
(2)Tj
/T1_5 10.91 Tf
-389.72 -38.01 Td
(and)Tj
1.0003 0 0 1.0003 72 769.82 Tm
20.86 -221.74 Td
[(c)27(hec)28(k)-301(if)]TJ
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 59.55 -212.76 cm
0 0 m
8.36 0 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 131.5667 548.0179 Tm
(R)Tj
/T1_1 7.97 Tf
8.36 -1.64 Td
(i)Tj
/T1_3 7.97 Tf
2.88 0 Td
(\241)Tj
/T1_4 7.97 Tf
6.59 0 Td
(1)Tj
/T1_5 10.91 Tf
7.76 1.64 Td
(=)Tj
/T1_0 10.91 Tf
11.51 0 Td
(L)Tj
/T1_1 7.97 Tf
7.42 -1.64 Td
(i)Tj
/T1_5 10.91 Tf
6.67 1.64 Td
(holds.)Tj
1.0003 0 0 1.0003 72 769.82 Tm
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[(Then)-302(all)-301(mem)27(b)-27(ers)-301(can)-302(obtain)]TJ
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/T1_1 10.91 Tf
(sk)Tj
/T1_0 10.91 Tf
23.1 0 Td
[(\))-348(and)-349(also)-348(stores)-349(left)-348(and)-349(righ)27(t)-348(k)27(ey)]TJ
/T1_1 10.91 Tf
169.71 0 Td
(K)Tj
/T1_2 7.97 Tf
10.04 3.95 Td
(L)Tj
-0.78 -7.01 Td
(i)Tj
/T1_0 10.91 Tf
10.84 3.06 Td
(and)Tj
/T1_1 10.91 Tf
21.37 0 Td
(K)Tj
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10.05 3.95 Td
(R)Tj
-0.78 -7.01 Td
(i)Tj
/T1_0 10.91 Tf
-460.17 -18.86 Td
[(in)-333(secure)-333(storage.)]TJ
16.93 -26.27 Td
[(F)83(rom)-333(the)-333(observ)55(ation)-333(of)-333(equation)-333(\(2.7\),)-334(w)27(e)-332(immediately)-334(ha)27(v)28(e)-332(the)-334(follo)27(wing)-332(lemma:)]TJ
/T1_11 10.91 Tf
-16.93 -29.02 Td
[(Lemma)-383(1)]TJ
/T1_12 10.91 Tf
56.2 0 Td
[(F)77(or)-300(e)50(ach)-299(user)]TJ
/T1_4 10.91 Tf
66.83 0 Td
(U)Tj
/T1_2 7.97 Tf
5.72 -1.64 Td
(i)Tj
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6.65 1.64 Td
(for)Tj
/T1_0 10.91 Tf
16.8 0 Td
(1)Tj
/T1_3 10.91 Tf
8.48 0 Td
(\267)Tj
/T1_1 10.91 Tf
11.51 0 Td
(i)Tj
/T1_3 10.91 Tf
6.79 0 Td
(\267)Tj
/T1_1 10.91 Tf
11.51 0 Td
(n)Tj
/T1_12 10.91 Tf
[(,)-311(wher)50(e)]TJ
/T1_4 10.91 Tf
43.46 0 Td
(U)Tj
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5.72 -1.64 Td
(0)Tj
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7.76 1.64 Td
(=)Tj
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11.52 0 Td
(U)Tj
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5.72 -1.64 Td
(n)Tj
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8.91 1.64 Td
(and)Tj
/T1_4 10.91 Tf
20.55 0 Td
(U)Tj
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5.73 -1.64 Td
(n)Tj
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(+1)Tj
/T1_0 10.91 Tf
19.48 1.64 Td
(=)Tj
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11.51 0 Td
(U)Tj
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5.73 -1.64 Td
(1)Tj
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4.73 1.64 Td
[(,)-311(user)]TJ
/T1_4 10.91 Tf
29.94 0 Td
(U)Tj
/T1_2 7.97 Tf
5.73 -1.64 Td
(i)Tj
/T1_12 10.91 Tf
6.65 1.64 Td
[(is)-300(able)-300(to)-300(c)50(ompute)]TJ
-383.63 -21.92 Td
[(the)-357(right)-358(keys)]TJ
/T1_0 10.91 Tf
70.77 2.76 Td
(\271)Tj
/T1_1 10.91 Tf
-2.9 -2.76 Td
(K)Tj
/T1_2 7.97 Tf
10.04 3.96 Td
(R)Tj
-0.78 -7.01 Td
(i)Tj
/T1_6 7.97 Tf
2.88 0 Td
(+)Tj
/T1_2 7.97 Tf
6.59 0 Td
(j)Tj
/T1_0 10.91 Tf
7.41 3.05 Td
(=)Tj
/T1_1 10.91 Tf
11.51 0 Td
(g)Tj
/T1_2 7.97 Tf
5.59 4.41 Td
(r)Tj
/T1_9 5.98 Tf
3.82 -1.22 Td
(i)Tj
/T1_7 5.98 Tf
2.66 0 Td
(+)Tj
/T1_9 5.98 Tf
(j)Tj
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9.49 1.22 Td
(r)Tj
/T1_7 5.98 Tf
3.82 -1.74 Td
(\()Tj
/T1_9 5.98 Tf
(i)Tj
/T1_7 5.98 Tf
5.54 0 Td
(+)Tj
/T1_9 5.98 Tf
(j)Tj
/T1_7 5.98 Tf
9 0 Td
(\)+1)Tj
/T1_0 10.91 Tf
16.14 -2.67 Td
[(mo)-27(d)]TJ
/T1_1 10.91 Tf
23.93 0 Td
(p)Tj
/T1_12 10.91 Tf
9.39 0 Td
(for)Tj
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17.42 0 Td
(1)Tj
/T1_3 10.91 Tf
8.48 0 Td
(\267)Tj
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11.52 0 Td
(j)Tj
/T1_3 10.91 Tf
8.14 0 Td
(\267)Tj
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11.51 0 Td
(n)Tj
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8.97 0 Td
(\241)Tj
/T1_0 10.91 Tf
10.91 0 Td
(1)Tj
/T1_12 10.91 Tf
(.)Tj
/T1_11 10.91 Tf
-271.85 -36.41 Td
[(Lea)31(v)32(e)-382(Proto)-32(col)]TJ
/T1_0 10.91 Tf
0 -28.96 TD
[(Supp)-27(ose)-411(a)-411(group)-411(of)]TJ
/T1_1 10.91 Tf
98.6 0 Td
(m)Tj
/T1_0 10.91 Tf
14.06 0 Td
(users)Tj
/T1_3 10.91 Tf
28.26 0 Td
(L)Tj
/T1_0 10.91 Tf
11.96 0 Td
(=)Tj
/T1_3 10.91 Tf
12.92 0 Td
(f)Tj
/T1_4 10.91 Tf
(U)Tj
/T1_2 7.97 Tf
11.18 -1.78 Td
(l)Tj
/T1_7 5.98 Tf
2.53 -1.1 Td
(1)Tj
/T1_1 10.91 Tf
4.65 2.88 Td
[(;)-166(:)-166(:)-167(:)-167(;)]TJ
/T1_4 10.91 Tf
24.23 0 Td
(U)Tj
/T1_2 7.97 Tf
5.73 -1.78 Td
(l)Tj
/T1_9 5.98 Tf
2.52 -0.99 Td
(m)Tj
/T1_3 10.91 Tf
7.54 2.77 Td
(g)Tj
/T1_0 10.91 Tf
9.93 0 Td
[(w)27(an)28(ts)-410(to)-411(lea)27(v)28(e)-410(the)-411(group)]TJ
/T1_3 10.91 Tf
125.2 0 Td
(G)Tj
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11.57 0 Td
(=)Tj
/T1_3 10.91 Tf
12.92 0 Td
(f)Tj
/T1_4 10.91 Tf
(U)Tj
/T1_6 7.97 Tf
11.18 -1.64 Td
(1)Tj
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4.73 1.64 Td
[(;)-166(:)-167(:)-167(:)-166(;)]TJ
/T1_4 10.91 Tf
24.24 0 Td
(U)Tj
/T1_2 7.97 Tf
5.72 -1.64 Td
(n)Tj
/T1_3 10.91 Tf
5.64 1.64 Td
(g)Tj
/T1_0 10.91 Tf
[(,)-430(who)]TJ
-435.31 -21.92 Td
[(has)-319(already)-320(established)-320(a)-319(session)-320(k)27(ey)-319(in)-320(the)-320(previous)-319(group)-320(k)27(ey)-319(agreemen)27(t.)-439(Then)-320(the)-320(new)-319(group)-320(of)]TJ
0 -21.91 TD
[(users)-292(are)]TJ
/T1_3 10.91 Tf
44.74 0 Td
(f)Tj
/T1_4 10.91 Tf
(U)Tj
/T1_6 7.97 Tf
11.18 -1.64 Td
(1)Tj
/T1_1 10.91 Tf
4.73 1.64 Td
[(;)-166(:)-167(:)-167(:)-166(;)]TJ
/T1_4 10.91 Tf
24.24 0 Td
(U)Tj
/T1_2 7.97 Tf
5.72 3.95 Td
(L)Tj
0 -7.27 TD
(l)Tj
/T1_7 5.98 Tf
2.53 -1.11 Td
(1)Tj
/T1_3 10.91 Tf
4.65 4.43 Td
[(g)-141([)-141(f)]TJ
/T1_4 10.91 Tf
(U)Tj
/T1_2 7.97 Tf
26.99 3.95 Td
(R)Tj
T*
(l)Tj
/T1_7 5.98 Tf
2.52 -1.11 Td
(1)Tj
/T1_1 10.91 Tf
4.65 4.43 Td
[(;)-166(:)-167(:)-167(:)-166(;)]TJ
/T1_4 10.91 Tf
24.24 0 Td
(U)Tj
/T1_2 7.97 Tf
5.72 3.95 Td
(L)Tj
T*
(l)Tj
/T1_7 5.98 Tf
2.53 -1.11 Td
(2)Tj
/T1_3 10.91 Tf
4.65 4.43 Td
[(g)-141([)]TJ
/T1_1 10.91 Tf
15.81 0 Td
[(:)-166(:)-167(:)-166(:)-167(:)-167(:)]TJ
/T1_3 10.91 Tf
29.08 0 Td
[([)-292(f)]TJ
/T1_4 10.91 Tf
(U)Tj
/T1_2 7.97 Tf
21.64 3.95 Td
(R)Tj
T*
(l)Tj
/T1_9 5.98 Tf
2.53 -1 Td
(m)Tj
/T1_1 10.91 Tf
7.53 4.32 Td
[(;)-167(:)-166(:)-167(:)-167(;)]TJ
/T1_4 10.91 Tf
24.24 0 Td
(U)Tj
/T1_2 7.97 Tf
5.73 -1.64 Td
(n)Tj
/T1_3 10.91 Tf
5.63 1.64 Td
(g)Tj
/T1_0 10.91 Tf
[(,)-301(where)]TJ
/T1_4 10.91 Tf
42.86 0 Td
(U)Tj
/T1_2 7.97 Tf
5.73 3.95 Td
(L)Tj
T*
(l)Tj
/T1_9 5.98 Tf
2.52 -1.22 Td
(i)Tj
/T1_0 10.91 Tf
6.93 4.54 Td
(and)Tj
/T1_4 10.91 Tf
20.76 0 Td
(U)Tj
/T1_2 7.97 Tf
5.73 3.95 Td
(R)Tj
T*
(l)Tj
/T1_9 5.98 Tf
2.53 -1.22 Td
(i)Tj
/T1_0 10.91 Tf
7.59 4.54 Td
[(are)-292(resp)-28(ectiv)27(ely)-292(the)]TJ
-375.93 -21.92 Td
[(left)-318(and)-318(righ)27(t)-317(neigh)27(b)-27(ors)-318(of)-318(lea)27(ving)-318(user)]TJ
/T1_4 10.91 Tf
187.18 0 Td
(U)Tj
/T1_2 7.97 Tf
5.72 -1.78 Td
(l)Tj
/T1_9 5.98 Tf
2.53 -1.21 Td
(i)Tj
/T1_0 10.91 Tf
7.13 2.99 Td
[(for)-318(1)]TJ
/T1_3 10.91 Tf
25.01 0 Td
(\267)Tj
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11.51 0 Td
(i)Tj
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6.79 0 Td
(\267)Tj
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11.51 0 Td
(m)Tj
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9.57 0 Td
[(.)-439(Then)-318(for)-318(an)26(y)-317(lea)27(ving)-317(user)]TJ
/T1_4 10.91 Tf
132.84 0 Td
(U)Tj
/T1_2 7.97 Tf
5.72 -1.78 Td
(l)Tj
/T1_9 5.98 Tf
2.53 -1.21 Td
(i)Tj
/T1_0 10.91 Tf
3.66 2.99 Td
(,)Tj
/T1_4 10.91 Tf
6.53 0 Td
(U)Tj
/T1_2 7.97 Tf
5.73 3.96 Td
(L)Tj
0 -7.28 TD
(l)Tj
/T1_9 5.98 Tf
2.52 -1.22 Td
(i)Tj
/T1_0 10.91 Tf
6.76 4.54 Td
(=)Tj
/T1_4 10.91 Tf
11.51 0 Td
(U)Tj
/T1_2 7.97 Tf
5.73 -1.78 Td
(l)Tj
/T1_9 5.98 Tf
2.53 -1.21 Td
(i)Tj
/T1_8 7.97 Tf
3.16 1.21 Td
(\241)Tj
/T1_2 7.97 Tf
(k)Tj
/T1_0 10.91 Tf
-456.17 -20.14 Td
[(if)-344(the)]TJ
/T1_1 10.91 Tf
29.02 0 Td
(k)Tj
/T1_0 10.91 Tf
9.78 0 Td
[(consecutiv)27(e)-343(users)]TJ
/T1_4 10.91 Tf
85.28 0 Td
(U)Tj
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5.73 -1.77 Td
(l)Tj
/T1_9 5.98 Tf
2.52 -1.22 Td
(i)Tj
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3.66 2.99 Td
(;)Tj
/T1_4 10.91 Tf
4.85 0 Td
(U)Tj
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5.73 -1.77 Td
(l)Tj
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2.52 -1.22 Td
(i)Tj
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3.16 1.22 Td
(\241)Tj
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6.59 0 Td
(1)Tj
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4.73 1.77 Td
[(;)-166(:)-167(:)-166(:)-167(;)]TJ
/T1_4 10.91 Tf
24.24 0 Td
(U)Tj
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5.72 -2.22 Td
(l)Tj
/T1_9 5.98 Tf
2.53 -1.21 Td
(i)Tj
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3.16 1.21 Td
(\241)Tj
/T1_6 7.97 Tf
(\()Tj
/T1_2 7.97 Tf
9.88 0 Td
(k)Tj
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4.62 0 Td
(\241)Tj
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(1\))Tj
/T1_0 10.91 Tf
18.36 2.22 Td
[(are)-344(all)-345(lea)27(ving)-343(and)]TJ
/T1_4 10.91 Tf
92.01 0 Td
(U)Tj
/T1_2 7.97 Tf
5.72 -1.77 Td
(l)Tj
/T1_9 5.98 Tf
2.53 -1.22 Td
(i)Tj
/T1_8 7.97 Tf
3.16 1.22 Td
(\241)Tj
/T1_2 7.97 Tf
6.59 0 Td
(k)Tj
/T1_0 10.91 Tf
8.87 1.77 Td
[(is)-344(not)-345(lea)27(ving)-343(the)-345(group.)]TJ
-350.96 -21.91 Td
[(Similarly)83(,)]TJ
/T1_4 10.91 Tf
48.35 0 Td
(U)Tj
/T1_2 7.97 Tf
5.73 3.95 Td
(R)Tj
0 -7.27 TD
(l)Tj
/T1_9 5.98 Tf
2.53 -1.22 Td
(i)Tj
/T1_0 10.91 Tf
7.42 4.54 Td
(=)Tj
/T1_4 10.91 Tf
11.51 0 Td
(U)Tj
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5.73 -1.83 Td
(l)Tj
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2.53 -1.22 Td
(i)Tj
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3.16 1.22 Td
(+)Tj
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(k)Tj
/T1_13 5.98 Tf
11.2 2.26 Td
(0)Tj
/T1_0 10.91 Tf
6.63 -0.43 Td
[(if)-316(the)]TJ
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28.41 0 Td
(k)Tj
/T1_8 7.97 Tf
6.02 3.95 Td
(0)Tj
/T1_0 10.91 Tf
6.25 -3.95 Td
[(consecutiv)27(e)-315(users)]TJ
/T1_4 10.91 Tf
84.67 0 Td
(U)Tj
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5.72 -1.78 Td
(l)Tj
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2.53 -1.21 Td
(i)Tj
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3.66 2.99 Td
(;)Tj
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4.84 0 Td
(U)Tj
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5.73 -1.78 Td
(l)Tj
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2.53 -1.21 Td
(i)Tj
/T1_6 7.97 Tf
3.16 1.21 Td
(+1)Tj
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11.31 1.78 Td
[(;)-166(:)-167(:)-167(:)-166(;)]TJ
/T1_4 10.91 Tf
24.24 0 Td
(U)Tj
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5.72 -2.22 Td
(l)Tj
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2.53 -1.22 Td
(i)Tj
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3.16 1.22 Td
(+\()Tj
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(k)Tj
/T1_13 5.98 Tf
14.5 2.27 Td
(0)Tj
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2.68 -2.27 Td
(\241)Tj
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6.59 0 Td
(1\))Tj
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11.47 2.22 Td
[(are)-316(all)-316(lea)27(ving)-316(and)]TJ
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90.78 0 Td
(U)Tj
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5.73 -1.83 Td
(l)Tj
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2.52 -1.22 Td
(i)Tj
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3.16 1.22 Td
(+)Tj
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6.59 0 Td
(k)Tj
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4.62 2.26 Td
(0)Tj
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6.63 -0.43 Td
(is)Tj
-460.54 -21.92 Td
[(not)-348(lea)26(ving)-347(the)-349(group.)-491(The)]TJ
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133.9 0 Td
(n)Tj
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9.09 0 Td
(\241)Tj
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11.01 0 Td
(m)Tj
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13.38 0 Td
[(remaining)-349(users)-349(are)-348(reindexed)-349(and)-349(denoted)-349(in)-349(the)-349(new)-348(user)-349(set)]TJ
/T1_3 10.91 Tf
-167.38 -21.92 Td
(G)Tj
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7.13 3.96 Td
(0)Tj
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5.83 -3.96 Td
(=)Tj
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11.51 0 Td
(f)Tj
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(V)Tj
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11.18 -1.63 Td
(1)Tj
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4.73 1.63 Td
[(;)-166(:)-167(:)-166(:)-167(;)]TJ
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24.24 0 Td
(V)Tj
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5.72 -1.63 Td
(n)Tj
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(\241)Tj
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(m)Tj
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19.71 1.63 Td
(g)Tj
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[(.)-432(The)-298(left)-298(and)-298(righ)26(t)-297(k)27(eys)-297(of)-298(remaining)-298(users)-298(are)-298(re-indexed)-298(and)-298(denoted)-298(b)27(y)-297(t)26(w)28(o)]TJ
-90.05 -21.91 Td
[(arra)27(ys)]TJ
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32.43 0 Td
(f)Tj
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8.36 2.75 Td
(^)Tj
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-2.91 -2.75 Td
(K)Tj
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10.05 3.96 Td
(L)Tj
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-0.78 -6.88 Td
(1)Tj
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7.03 2.92 Td
[(;)-166(:)-167(:)-167(:)-166(;)]TJ
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27.14 2.75 Td
(^)Tj
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(K)Tj
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10.04 3.96 Td
(L)Tj
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(n)Tj
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(\241)Tj
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(m)Tj
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19.71 2.7 Td
(g)Tj
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8.68 0 Td
(and)Tj
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20.8 0 Td
(f)Tj
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8.35 2.75 Td
(^)Tj
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-2.9 -2.75 Td
(K)Tj
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10.04 3.96 Td
(R)Tj
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-0.78 -6.88 Td
(1)Tj
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7.71 2.92 Td
[(;)-166(:)-167(:)-166(:)-167(;)]TJ
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27.13 2.75 Td
(^)Tj
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-2.9 -2.75 Td
(K)Tj
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10.05 3.96 Td
(R)Tj
-0.78 -6.66 Td
(n)Tj
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5.13 0 Td
(\241)Tj
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6.59 0 Td
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-0.78 -7.01 Td
(j)Tj
/T1_3 5.98 Tf
3.42 -1.34 Td
(L)Tj
/T1_0 10.91 Tf
9.08 4.39 Td
[(=)-338(^)]TJ
/T1_1 10.91 Tf
11.51 0 Td
(z)Tj
/T1_6 7.97 Tf
5.94 7 Td
(^)Tj
/T1_2 7.97 Tf
-0.38 0 Td
(r)Tj
/T1_3 5.98 Tf
3.82 -1.22 Td
(j)Tj
3.05 -2.02 Td
(L)Tj
/T1_2 7.97 Tf
-7.35 -7.01 Td
(j)Tj
/T1_3 5.98 Tf
3.42 -1.34 Td
(R)Tj
/T1_0 10.91 Tf
13.51 4.59 Td
[(mo)-28(d)]TJ
/T1_1 10.91 Tf
23.94 0 Td
(p)Tj
/T1_0 10.91 Tf
8.82 0 Td
[(where)-366(^)]TJ
/T1_1 10.91 Tf
31.24 0 Td
(z)Tj
/T1_2 7.97 Tf
5.07 -1.77 Td
(j)Tj
/T1_3 5.98 Tf
3.43 -1.34 Td
(L)Tj
/T1_5 7.97 Tf
5.55 1.34 Td
(\241)Tj
/T1_2 7.97 Tf
6.59 0 Td
(k)Tj
/T1_0 10.91 Tf
8.14 1.77 Td
(=)Tj
/T1_1 10.91 Tf
11.52 0 Td
(z)Tj
/T1_2 7.97 Tf
5.07 -1.77 Td
(j)Tj
/T1_3 5.98 Tf
3.42 -1.34 Td
(L)Tj
/T1_5 7.97 Tf
5.56 1.34 Td
(\241)Tj
/T1_2 7.97 Tf
(k)Tj
/T1_0 10.91 Tf
15.04 1.77 Td
[(if)-305(the)-307(left)-306(neigh)27(b)-27(or)-306(of)]TJ
/T1_4 10.91 Tf
103.67 0 Td
(U)Tj
/T1_2 7.97 Tf
5.72 -1.77 Td
(j)Tj
/T1_3 5.98 Tf
3.42 -1.34 Td
(L)Tj
/T1_5 7.97 Tf
5.56 1.34 Td
(\241)Tj
/T1_2 7.97 Tf
(k)Tj
/T1_0 10.91 Tf
15.04 1.77 Td
[(did)-306(not)-306(lea)27(v)28(e)-305(the)]TJ
-388.48 -21.91 Td
[(group.)-426(Similarly)83(,)-288(user)]TJ
/T1_4 10.91 Tf
105.51 0 Td
(U)Tj
/T1_2 7.97 Tf
5.72 -1.64 Td
(j)Tj
/T1_3 5.98 Tf
3.43 -1.34 Td
(R)Tj
/T1_0 10.91 Tf
9.56 2.98 Td
[(mo)-27(di\257es)-278(its)-279(left)-278(k)27(ey)]TJ
97.26 2.75 Td
(^)Tj
/T1_1 10.91 Tf
-2.9 -2.75 Td
(K)Tj
/T1_2 7.97 Tf
10.04 3.95 Td
(L)Tj
-0.78 -7.01 Td
(j)Tj
/T1_3 5.98 Tf
3.42 -1.34 Td
(R)Tj
/T1_0 10.91 Tf
9.56 4.4 Td
[(=)-337(^)]TJ
/T1_1 10.91 Tf
11.51 0 Td
(z)Tj
/T1_6 7.97 Tf
5.94 6.99 Td
(^)Tj
/T1_2 7.97 Tf
-0.39 0 Td
(r)Tj
/T1_3 5.98 Tf
3.82 -1.21 Td
(j)Tj
3.06 -2.03 Td
(R)Tj
/T1_2 7.97 Tf
-7.36 -7.01 Td
(j)Tj
/T1_3 5.98 Tf
3.43 -1.34 Td
(L)Tj
/T1_0 10.91 Tf
13.99 4.6 Td
[(mo)-27(d)]TJ
/T1_1 10.91 Tf
23.93 0 Td
(p)Tj
/T1_0 10.91 Tf
8.52 0 Td
[(and)-278(righ)27(t)-277(k)27(ey)]TJ
68.38 2.75 Td
(^)Tj
/T1_1 10.91 Tf
-2.9 -2.75 Td
(K)Tj
/T1_2 7.97 Tf
10.05 3.95 Td
(R)Tj
-0.79 -7.01 Td
(j)Tj
/T1_3 5.98 Tf
3.43 -1.34 Td
(R)Tj
/T1_0 10.91 Tf
9.56 4.4 Td
[(=)-337(^)]TJ
/T1_1 10.91 Tf
11.51 0 Td
(z)Tj
/T1_6 7.97 Tf
5.93 6.99 Td
(^)Tj
/T1_2 7.97 Tf
-0.38 0 Td
(r)Tj
/T1_3 5.98 Tf
3.82 -1.21 Td
(j)Tj
3.06 -2.03 Td
(R)Tj
/T1_2 7.97 Tf
-7.36 -7.33 Td
(j)Tj
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3.42 -1.34 Td
(R)Tj
/T1_6 7.97 Tf
6.03 1.34 Td
(+)Tj
/T1_2 7.97 Tf
6.59 0 Td
(k)Tj
/T1_7 5.98 Tf
4.62 2.27 Td
(0)Tj
/T1_0 10.91 Tf
6.21 1.31 Td
[(mo)-27(d)]TJ
/T1_1 10.91 Tf
23.93 0 Td
(p)Tj
/T1_0 10.91 Tf
-462.38 -21.92 Td
[(where)-393(^)]TJ
/T1_1 10.91 Tf
31.54 0 Td
(z)Tj
/T1_2 7.97 Tf
5.07 -1.83 Td
(j)Tj
/T1_3 5.98 Tf
3.42 -1.34 Td
(R)Tj
/T1_6 7.97 Tf
6.03 1.34 Td
(+)Tj
/T1_2 7.97 Tf
6.59 0 Td
(k)Tj
/T1_7 5.98 Tf
4.62 2.27 Td
(0)Tj
/T1_0 10.91 Tf
6.21 -0.44 Td
(=)Tj
/T1_1 10.91 Tf
11.51 0 Td
(z)Tj
/T1_2 7.97 Tf
5.07 -1.83 Td
(j)Tj
/T1_3 5.98 Tf
3.43 -1.34 Td
(R)Tj
/T1_6 7.97 Tf
6.03 1.34 Td
(+)Tj
/T1_2 7.97 Tf
(k)Tj
/T1_7 5.98 Tf
11.2 2.27 Td
(0)Tj
/T1_0 10.91 Tf
6.82 -0.44 Td
[(if)-333(the)-333(righ)27(t)-333(neigh)27(b)-27(or)-333(of)]TJ
/T1_4 10.91 Tf
112.45 0 Td
(U)Tj
/T1_2 7.97 Tf
5.73 -1.83 Td
(j)Tj
/T1_3 5.98 Tf
3.42 -1.34 Td
(R)Tj
/T1_6 7.97 Tf
6.03 1.34 Td
(+)Tj
/T1_2 7.97 Tf
6.59 0 Td
(k)Tj
/T1_7 5.98 Tf
4.62 2.27 Td
(0)Tj
/T1_0 10.91 Tf
6.81 -0.44 Td
[(did)-333(not)-334(lea)27(v)28(e)-332(the)-334(group.)]TJ
-253.19 -27.89 Td
(\()Tj
/T1_1 10.91 Tf
(ii)Tj
/T1_0 10.91 Tf
[(\))-497(After)-499(receiving)-498(the)-498(messages)-498(from)-498(its)-498(neigh)26(b)-26(ors,)]TJ
/T1_4 10.91 Tf
266.95 0 Td
(U)Tj
/T1_2 7.97 Tf
5.72 -1.78 Td
(j)Tj
/T1_3 5.98 Tf
3.43 -1.34 Td
(L)Tj
/T1_5 7.97 Tf
5.55 1.34 Td
(\241)Tj
/T1_2 7.97 Tf
6.59 0 Td
(k)Tj
/T1_0 10.91 Tf
5.12 1.78 Td
[(,)-538(the)-499(left)-498(neigh)27(b)-27(or)-498(of)]TJ
/T1_4 10.91 Tf
111.26 0 Td
(U)Tj
/T1_2 7.97 Tf
5.72 -1.64 Td
(j)Tj
/T1_3 5.98 Tf
3.42 -1.34 Td
(L)Tj
/T1_0 10.91 Tf
6.06 2.98 Td
[(,)-539(mo)-27(di\257es)]TJ
-419.82 -21.92 Td
[(its)-445(righ)27(t)-445(k)27(ey)]TJ
67.86 2.76 Td
(^)Tj
/T1_1 10.91 Tf
-2.9 -2.76 Td
(K)Tj
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10.04 3.96 Td
(R)Tj
-0.78 -7.28 Td
(j)Tj
/T1_3 5.98 Tf
3.43 -1.34 Td
(L)Tj
/T1_5 7.97 Tf
5.55 1.34 Td
(\241)Tj
/T1_2 7.97 Tf
6.59 0 Td
(k)Tj
/T1_0 10.91 Tf
10.19 3.32 Td
[(=)-524(^)]TJ
/T1_1 10.91 Tf
13.55 0 Td
(z)Tj
/T1_6 7.97 Tf
5.93 7.19 Td
(^)Tj
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-0.38 0 Td
(r)Tj
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3.82 -1.41 Td
(j)Tj
3.06 -2.02 Td
(L)Tj
/T1_7 5.98 Tf
5.55 2.02 Td
(\241)Tj
/T1_3 5.98 Tf
(k)Tj
/T1_2 7.97 Tf
-12.91 -9.04 Td
(j)Tj
/T1_3 5.98 Tf
3.42 -1.33 Td
(L)Tj
/T1_0 10.91 Tf
23.35 4.59 Td
[(mo)-27(d)]TJ
/T1_1 10.91 Tf
23.93 0 Td
(p)Tj
/T1_0 10.91 Tf
10.35 0 Td
(and)Tj
/T1_4 10.91 Tf
22.43 0 Td
(U)Tj
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5.72 -1.83 Td
(j)Tj
/T1_3 5.98 Tf
3.43 -1.34 Td
(R)Tj
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6.03 1.34 Td
(+)Tj
/T1_2 7.97 Tf
(k)Tj
/T1_7 5.98 Tf
11.2 2.27 Td
(0)Tj
/T1_0 10.91 Tf
3.18 -0.44 Td
[(,)-474(the)-445(righ)26(t)-444(neigh)27(b)-27(or)-446(of)]TJ
/T1_4 10.91 Tf
115.56 0 Td
(U)Tj
/T1_2 7.97 Tf
5.72 -1.64 Td
(j)Tj
/T1_3 5.98 Tf
3.43 -1.33 Td
(R)Tj
/T1_0 10.91 Tf
6.52 2.97 Td
[(,)-474(mo)-27(di\257es)-446(its)-446(left)-445(k)26(ey)]TJ
-359.97 -19.16 Td
(^)Tj
/T1_1 10.91 Tf
-2.9 -2.76 Td
(K)Tj
/T1_2 7.97 Tf
10.04 3.96 Td
(L)Tj
-0.78 -7.33 Td
(j)Tj
/T1_3 5.98 Tf
3.43 -1.34 Td
(R)Tj
/T1_6 7.97 Tf
6.03 1.34 Td
(+)Tj
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(k)Tj
/T1_7 5.98 Tf
11.2 2.27 Td
(0)Tj
/T1_0 10.91 Tf
6.21 1.1 Td
[(=)-338(^)]TJ
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11.51 0 Td
(z)Tj
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5.94 8.08 Td
(^)Tj
/T1_2 7.97 Tf
-0.38 0 Td
(r)Tj
/T1_3 5.98 Tf
3.82 -2.29 Td
(j)Tj
3.05 -2.03 Td
(R)Tj
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6.03 2.03 Td
(+)Tj
/T1_3 5.98 Tf
(k)Tj
/T1_7 5.98 Tf
9.67 1.71 Td
(0)Tj
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-23.05 -10.75 Td
(j)Tj
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3.42 -1.34 Td
(R)Tj
/T1_0 10.91 Tf
26.34 4.59 Td
[(mo)-27(d)]TJ
/T1_1 10.91 Tf
23.93 0 Td
(p)Tj
/T1_0 10.91 Tf
8.73 0 Td
[(resp)-27(ectiv)27(ely)-296(where)-342(^)]TJ
/T1_1 10.91 Tf
90.21 0 Td
(r)Tj
/T1_2 7.97 Tf
4.92 -1.77 Td
(j)Tj
/T1_3 5.98 Tf
3.42 -1.34 Td
(L)Tj
/T1_5 7.97 Tf
5.56 1.34 Td
(\241)Tj
/T1_2 7.97 Tf
(k)Tj
/T1_0 10.91 Tf
14.73 1.77 Td
(=)Tj
/T1_1 10.91 Tf
11.51 0 Td
(r)Tj
/T1_2 7.97 Tf
4.93 -1.77 Td
(j)Tj
/T1_3 5.98 Tf
3.42 -1.34 Td
(L)Tj
/T1_5 7.97 Tf
5.55 1.34 Td
(\241)Tj
/T1_2 7.97 Tf
6.59 0 Td
(k)Tj
/T1_0 10.91 Tf
8.36 1.77 Td
[(if)-296(the)-297(left)-298(neigh)27(b)-27(or)-297(of)]TJ
/T1_4 10.91 Tf
103.17 0 Td
(U)Tj
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5.73 -1.77 Td
(j)Tj
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3.42 -1.34 Td
(L)Tj
/T1_5 7.97 Tf
5.56 1.34 Td
(\241)Tj
/T1_2 7.97 Tf
(k)Tj
/T1_0 10.91 Tf
14.94 1.77 Td
[(did)-297(not)-297(lea)27(v)28(e)]TJ
-407.16 -21.91 Td
[(the)-333(group)-333(and)-379(^)]TJ
/T1_1 10.91 Tf
70.92 0 Td
(r)Tj
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4.92 -1.83 Td
(j)Tj
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3.42 -1.34 Td
(R)Tj
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6.03 1.34 Td
(+)Tj
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6.59 0 Td
(k)Tj
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4.62 2.26 Td
(0)Tj
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6.21 -0.43 Td
(=)Tj
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11.51 0 Td
(r)Tj
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4.92 -1.83 Td
(j)Tj
/T1_3 5.98 Tf
3.43 -1.34 Td
(R)Tj
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6.03 1.34 Td
(+)Tj
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(k)Tj
/T1_7 5.98 Tf
11.2 2.26 Td
(0)Tj
/T1_0 10.91 Tf
6.82 -0.43 Td
[(if)-333(the)-333(righ)27(t)-333(neigh)27(b)-27(or)-333(of)]TJ
/T1_4 10.91 Tf
112.45 0 Td
(U)Tj
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5.73 -1.83 Td
(j)Tj
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3.42 -1.34 Td
(R)Tj
/T1_6 7.97 Tf
6.03 1.34 Td
(+)Tj
/T1_2 7.97 Tf
6.59 0 Td
(k)Tj
/T1_7 5.98 Tf
4.62 2.26 Td
(0)Tj
/T1_0 10.91 Tf
6.81 -0.43 Td
[(did)-333(not)-334(lea)27(v)28(e)-332(the)-334(group.)]TJ
-292.27 -27.89 Td
(\()Tj
/T1_1 10.91 Tf
(iii)Tj
/T1_0 10.91 Tf
15.51 0 Td
[(\))-372(Eac)26(h)-371(user)]TJ
/T1_4 10.91 Tf
59.4 0 Td
(V)Tj
/T1_2 7.97 Tf
5.72 -1.64 Td
(i)Tj
/T1_9 10.91 Tf
7.13 1.64 Td
[(2)-343(G)]TJ
/T1_5 7.97 Tf
18.15 3.95 Td
(0)Tj
/T1_0 10.91 Tf
6.86 -3.95 Td
[(for)-372(1)]TJ
/T1_9 10.91 Tf
26.32 0 Td
(\267)Tj
/T1_1 10.91 Tf
12.23 0 Td
(i)Tj
/T1_9 10.91 Tf
7.5 0 Td
(\267)Tj
/T1_1 10.91 Tf
12.23 0 Td
(n)Tj
/T1_9 10.91 Tf
9.25 0 Td
(\241)Tj
/T1_1 10.91 Tf
11.19 0 Td
(m)Tj
/T1_0 10.91 Tf
13.64 0 Td
(computes)Tj
50.62 2.75 Td
(^)Tj
/T1_1 10.91 Tf
-1.65 -2.75 Td
(Y)Tj
/T1_2 7.97 Tf
6.33 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
7.12 1.64 Td
(=)Tj
15.13 2.75 Td
(^)Tj
/T1_1 10.91 Tf
-2.9 -2.75 Td
(K)Tj
/T1_2 7.97 Tf
10.04 3.95 Td
(R)Tj
-0.78 -7.01 Td
(i)Tj
/T1_1 10.91 Tf
7.71 3.06 Td
(=)Tj
/T1_0 10.91 Tf
8.35 2.75 Td
(^)Tj
/T1_1 10.91 Tf
-2.9 -2.75 Td
(K)Tj
/T1_2 7.97 Tf
10.04 3.95 Td
(L)Tj
-0.78 -7.01 Td
(i)Tj
/T1_0 10.91 Tf
11.1 3.06 Td
[(and)-372(sends)]TJ
52.92 2.75 Td
(^)Tj
/T1_1 10.91 Tf
-1.65 -2.75 Td
(Y)Tj
/T1_2 7.97 Tf
6.33 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
7.45 1.64 Td
[(to)-372(the)-373(remaining)]TJ
-387.61 -21.92 Td
[(users.)-444(Note)-333(that)]TJ
84.54 2.76 Td
(^)Tj
/T1_1 10.91 Tf
-2.9 -2.76 Td
(K)Tj
/T1_2 7.97 Tf
10.05 3.96 Td
(R)Tj
-0.78 -7.02 Td
(i)Tj
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10.73 3.06 Td
(=)Tj
14.41 2.76 Td
(^)Tj
/T1_1 10.91 Tf
-2.9 -2.76 Td
(K)Tj
/T1_2 7.97 Tf
10.04 3.96 Td
(L)Tj
-0.78 -7.02 Td
(i)Tj
/T1_6 7.97 Tf
2.89 0 Td
(+1)Tj
/T1_0 10.91 Tf
14.95 3.06 Td
[(for)-333(1)]TJ
/T1_9 10.91 Tf
25.17 0 Td
(\267)Tj
/T1_1 10.91 Tf
11.51 0 Td
(i)Tj
/T1_9 10.91 Tf
6.79 0 Td
(\267)Tj
/T1_1 10.91 Tf
11.51 0 Td
(n)Tj
/T1_9 10.91 Tf
8.97 0 Td
(\241)Tj
/T1_1 10.91 Tf
10.91 0 Td
(m)Tj
/T1_9 10.91 Tf
12 0 Td
(\241)Tj
/T1_0 10.91 Tf
10.9 0 Td
(1,)Tj
15.02 2.76 Td
(^)Tj
/T1_1 10.91 Tf
-2.9 -2.76 Td
(K)Tj
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10.04 3.96 Td
(R)Tj
-0.78 -6.66 Td
(n)Tj
/T1_5 7.97 Tf
(\241)Tj
/T1_2 7.97 Tf
11.73 0 Td
(m)Tj
/T1_0 10.91 Tf
11.01 2.7 Td
(=)Tj
14.41 2.76 Td
(^)Tj
/T1_1 10.91 Tf
-2.9 -2.76 Td
(K)Tj
/T1_2 7.97 Tf
10.05 3.96 Td
(L)Tj
/T1_6 7.97 Tf
-0.78 -6.88 Td
(1)Tj
/T1_0 10.91 Tf
10.67 2.92 Td
(and)Tj
24.1 2.76 Td
(^)Tj
/T1_1 10.91 Tf
-2.9 -2.76 Td
(K)Tj
/T1_2 7.97 Tf
10.05 3.96 Td
(R)Tj
-0.78 -7.72 Td
(i)Tj
/T1_6 7.97 Tf
2.88 0 Td
(+\()Tj
/T1_2 7.97 Tf
(n)Tj
/T1_5 7.97 Tf
15.01 0 Td
(\241)Tj
/T1_2 7.97 Tf
6.59 0 Td
(m)Tj
/T1_5 7.97 Tf
(\241)Tj
/T1_6 7.97 Tf
(1\))Tj
/T1_0 10.91 Tf
25.12 3.76 Td
(=)Tj
14.42 2.76 Td
(^)Tj
/T1_1 10.91 Tf
-2.91 -2.76 Td
(K)Tj
/T1_2 7.97 Tf
10.05 3.96 Td
(L)Tj
-0.78 -7.02 Td
(i)Tj
/T1_0 10.91 Tf
7.03 3.06 Td
(.)Tj
-421.46 -27.89 Td
[(Key)-333(Computation)]TJ
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 0 -323.42 cm
0 0 m
85.73 0 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 157.754 449.9605 Tm
(:)Tj
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T*
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16.93 -21.92 Td
[(In)-261(2003,)-275(Bresson)-261(et)-261(al)-261([BCEP04])-260(prop)-28(osed)-261(a)-261(group)-261(k)27(ey)-260(agreemen)27(t)-260(proto)-28(col)-261(for)-261(lo)27(w-p)-27(o)27(w)28(er)-260(devices)]TJ
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[(where)-332(one)-333(mem)27(b)-27(er)-333(p)-27(erforms)-333(most)-333(of)-333(the)-332(computations)-333(while)-333(the)-333(other)-332(mem)26(b)-26(ers)-333(are)-333(only)-333(required)]TJ
T*
[(to)-312(p)-28(erform)-313(a)-313(\257xed)-313(amoun)27(t)-312(of)-313(computations.)-437(Bo)27(yd)-312(and)-313(Nieto)-313([BN03])-313(in)27(tro)-27(duced)-313(a)-312(computationally)]TJ
0 -21.92 TD
[(asymmetric)-345(one-round)-346(group)-345(k)27(ey)-345(agreemen)27(t)-344(proto)-28(col)-346(that)-345(app)-28(ears)-346(to)-345(easily)-346(extend)-345(to)-346(address)-345(the)]TJ
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[(dynamic)-333(case.)-444(Ho)27(w)27(ev)28(er,)-332(this)-334(proto)-27(col)-334(do)-27(es)-334(not)-333(ac)27(hiev)27(e)-332(forw)27(ard)-332(secrecy)-334([BCP07].)]TJ
16.93 -21.92 Td
[(In)-482(2004,)-519(Bresson)-482(and)-483(Catalano)-482([BC04])-482(presen)27(ted)-481(a)-483(t)27(w)28(o)-481(round)-483(proto)-27(col)-483(that)-482(is)-482(constructed)]TJ
-16.93 -21.92 Td
[(b)27(y)-366(com)26(bining)-366(the)-368(prop)-27(erties)-368(of)-368(ElGamal)-367(encryption)-368(sc)27(heme)-367([Gam85])-367(and)-368(standard)-367(secret)-368(sharing)]TJ
T*
[(tec)27(hniques)-460([Sha79].)-828(Ho)27(w)28(ev)27(er,)-492(Cho)-461(et)-461(al.)-461([CNKW05])-462(p)-27(oin)26(ted)-460(out)-461(that)-461(with)-461(the)-462(increase)-461(in)-461(the)]TJ
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[(n)27(um)28(b)-27(er)-359(of)-359(users,)-365(the)-359(complexit)26(y)-358(of)-359(the)-359(proto)-28(col)-359(go)-27(es)-359(b)-28(ey)27(ond)-359(the)-359(capabilities)-359(of)-359(lo)27(w-p)-27(o)27(w)28(er)-358(mobile)]TJ
T*
[(devices.)-510(Zhou)-355(and)-356(Ra)27(vishank)56(ar)-355([ZR04])-355(presen)27(ted)-355(an)-355(authen)27(ticated)-354(and)-356(fault-toleran)27(t)-354(proto)-28(col)-355(for)]TJ
228.48 -43.35 Td
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[(k)27(ey)-324(agreemen)27(t.)-441(Their)-325(proto)-28(col)-325(uses)-325(RSA)-326(public)-325(and)-325(priv)54(ate)-324(k)27(ey)-324(pairs)-325(to)-326(pro)27(vide)-324(source)]TJ
-52.128 -21.91 Td
[(authen)27(tication.)-842(Eac)27(h)-465(no)-28(de)-466(in)-467(the)-466(tree)-466(has)-466(a)-466(small)-467(subgroup)-466(kno)27(wn)-465(as)-467(its)-466(trust)-466(set.)-843(Shamir's)]TJ
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[(threshold)-494(secret)-495(sharing)-494(sc)26(heme)-493([Sha79])-495(is)-495(then)-494(used)-495(to)-494(distribute)-495(the)-495(function)-494(of)-495(the)-495(trusted)]TJ
T*
[(authorit)27(y)-368(across)-370(the)-370(trust)-370(sets.)-553(It)-370(should)-370(b)-28(e)-369(noted)-370(that)-370(the)-369(use)-370(of)-370(a)-370(secret)-369(sharing)-370(sc)27(heme)-369(w)27(ould)]TJ
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[(require)-261(the)-262(presence)-262(of)-262(a)-262(trusted)-262(third)-262(part)27(y)-261(that)-262(is)-262(resp)-28(onsible)-261(to)-262(generate)-262(the)-262(secret)-262(share.)-421(Nam)-262(et)]TJ
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[(al.)-238([NLKW04])-238(applied)-238(a)-238(v)55(arian)28(t)-237(of)-238(the)-238(compiler)-238(presen)26(ted)-237(b)27(y)-237(Katz)-238(and)-238(Y)83(ung)-238(in)-238([KY03])-238(and)-238(prop)-27(osed)]TJ
0 -21.91 TD
[(an)-312(authen)27(ticated)-311(group)-312(k)27(ey)-312(exc)27(hange)-311(proto)-28(col.)-437(Lik)27(e)-312(the)-312(proto)-28(col)-312(of)-312(Bresson)-312(et)-312(al.)-312([BCEP04],)-317(their)]TJ
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[(proto)-27(col)-400(has)-399(a)-400(con)27(troller)-398(that)-400(p)-27(erforms)-400(most)-399(of)-400(the)-399(computations.)-643(Ho)27(w)28(ev)28(er,)-415(their)-400(authen)27(ticated)]TJ
T*
[(proto)-27(col)-386(requires)-385(an)-385(extra)-385(round)-386(of)-385(comm)27(unication.)-600(In)-385(2005,)-398(Cho)-385(et)-386(al.)-385([CNKW05])-385(prop)-28(osed)-385(an)]TJ
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[(e\261cien)27(t)-294(GKA)-295(proto)-28(col)-295(for)-295(lo)26(w-p)-26(o)26(w)28(er)-294(mobile)-295(devices.)-432(Ho)27(w)28(ev)27(er,)-301(this)-296(proto)-27(col)-296(requires)-295(a)-295(sp)-28(ecial)-295(user)]TJ
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[(who)-257(will)-258(p)-28(erform)-258(most)-258(of)-258(the)-258(computation)-258(on)-258(b)-28(ehalf)-258(of)-258(other)-258(users)-257(in)-258(the)-258(group.)]TJ
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[(Also)-398(in)-399(2005,)-415(T)82(rapp)-27(e)-398(et)-399(al)-399([TWL05])-398(prop)-28(osed)-399(a)-399(resource-a)27(w)28(are)-398(conference)-399(k)27(ey)-398(establishmen)27(t)-398(for)]TJ
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[(heterogeneous)-304(net)27(w)27(orks.)-433(In)-305(2006,)-310(Lee)-305(et)-305(al)-304([LL)82(Y06])-304(considered)-304(sev)26(eral)-303(collab)-28(orativ)27(e)-304(k)27(ey)-304(agreemen)27(t)]TJ
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[(and)-472(authen)27(tication)-471(proto)-28(cols)-472(for)-473(dynamic)-472(p)-28(eer)-472(groups)-472(while)-472(Ghosh)-473(et)-472(al)-472([GPR)]TJ
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[(et)-446(al)-447([PMB06])-447(prop)-28(osed)-446(group)-447(k)27(ey)-446(agreemen)27(t)-446(proto)-28(cols)-446(for)-447(wireless)-447(sensor)-447(net)27(w)28(orks,)-474(whic)27(h)-446(are)]TJ
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[(di\256eren)27(t)-266(from)-266(heterogeneous)-267(net)27(w)27(orks.)-421(Also)-267(in)-266(2006,)-281(Liao)-266(et)-267(al)-267([LM06])-267(prop)-28(osed)-266(a)-267(T)82(ree-based)-266(GKA)]TJ
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T*
[(and)-336(protection)-337(against)-337(DoS)-337(attac)27(ks.)-454(F)83(urthermore,)-337(most)-337(curren)27(t)-336(GKA)-337(proto)-27(cols)-337(except)-337([DPSW06])]TJ
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[(discuss)-333(only)-333(on)-333(securit)26(y)-332(against)-333(outsider)-334(and)-333(do)-333(not)-334(fo)-27(cus)-334(on)-333(attac)27(ks)-333(b)27(y)-332(malicious)-334(group)-333(insiders.)]TJ
16.93 -21.92 Td
[(The)-381(IEEE)-382(802.11i)-381(standard)-382(sp)-27(eci\257es)-382(a)-381(GKA)-382(proto)-27(col)-382(for)-381(Wireless)-382(LAN)-381(\(WLAN\))-382(but)-381(not)-382(for)]TJ
-16.93 -21.92 Td
[(Heterogeneous)-391(Wireless)-391(Net)27(w)27(orks)-390(\(HWNs\).)-618(It)-391(w)26(as)-390(also)-391(men)27(tioned)-391(in)-391([CJL05])-391(that)-392(more)-391(w)27(ork)-390(is)]TJ
T*
[(needed)-440(in)-440(IEEE)-440(802.11i)-441(to)-440(dev)27(elop)-439(a)-441(more)-440(secure)-440(WLAN)-440(en)26(vironmen)28(t.)-764(Most)-440(recen)26(tly)-439(in)-440(2006,)]TJ
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[(Hegland)-302(et)-302(al)-302([HWM)]TJ
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(+)Tj
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7.08 -3.96 Td
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[(HWNs)-392(whic)27(h)-391(discuss)-392(v)54(arious)-391(con)27(tributory)-391(and)-392(distributiv)26(e)-391(k)27(ey)-391(managemen)27(t)-392(proto)-27(cols)-393(in)-392(curren)27(t)]TJ
T*
[(literature.)-426(Besides)-279(these,)-290(there)-280(are)-279(also)-279(other)-280(GKM)-279(proto)-28(cols)-279(suc)27(h)-279(as)-279([SSKV06,)-82(DSL06])-279(prop)-28(osed)-279(in)]TJ
T*
[(2006.)-444(Ho)27(w)28(ev)27(er,)-332(all)-333(the)-334(ab)-27(o)26(v)28(e-men)28(tioned)-332(proto)-28(cols)-333(do)-334(not)-333(pro)27(vide)-333(protection)-333(against)-333(DoS)-334(attac)27(ks.)]TJ
16.93 -21.91 Td
[(Gangw)27(ar)-395(and)-395(Sarje)-396([GS06])-396(brie\260y)-396(presen)27(ted)-394(some)-396(group)-396(k)27(ey)-395(agreemen)27(t)-395(proto)-28(cols)-395(\(CLIQUES)]TJ
-16.93 -21.92 Td
[(proto)-27(col)-436(suite,)-462(TGDH,)-435(STR)-436(and)-436(NA)27(GKA\))-435(and)-436(analyze)-436(them)-435(for)-436(e\261cien)26(t)-434(dynamic)-436(mem)27(b)-27(ership)]TJ
T*
[(ev)27(en)28(ts)-403(for)-404(judging)-404(their)-404(suitabilit)27(y)-403(for)-404(an)-404(ad)-404(ho)-28(c)-404(net)27(w)28(ork.)-656(Choudhary)-404(et)-404(al)-404([CAR)83(T07])-403(prop)-28(osed)]TJ
228.48 -43.35 Td
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[(GKA)-473(proto)-27(col)-473(for)-473(Ad)-472(Ho)-28(c)-473(Sensor)-472(Net)26(w)28(orks)-471(that)-473(adapts)-473(existing)-472(w)27(ork)-472(on)-473(T)83(ree-based)-472(Group)]TJ
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[(Key)-330(Agreemen)26(t)-330(that)-331(com)27(bines)-330(k)27(ey)-330(trees)-331(with)-331(Di\261e-Hellman)-331(k)27(ey)-330(exc)27(hange,)-331(b)27(y)-330(replacing)-331(exp)-28(ensiv)27(e)]TJ
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[(public)-392(k)26(ey)-391(op)-28(erations)-393(with)-393(relativ)27(ely)-392(c)27(heap)-27(er)-393(symmetric)-393(k)27(ey)-392(op)-28(erations.)-623(Niu)-392([Niu07])-393(prop)-28(osed)-393(a)]TJ
T*
[(GKA)-227(proto)-27(col)-227(using)-228(ECDH)-227(\(Elliptic)-227(Curv)27(e)-226(Di\261e-Hellman\))-227(based)-228(on)-227(GDH.3)-227(\(Group)-227(Di\261e-Hellman\))]TJ
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[(proto)-27(col)-383(for)-382(Mobile)-383(Ad)-382(Ho)-28(c)-382(Net)26(w)28(orks,)-394(ho)27(w)28(ev)28(er)-382(Niu)-382(did)-383(not)-382(based)-382(their)-383(sim)27(ulation)-382(on)-382(lo)27(w-p)-27(o)27(w)28(er)]TJ
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[(energy)-459(constrained)-460(user)-460(device)-460(suc)26(h)-459(as)-460(PD)27(As)-459(whic)27(h)-459(are)-460(used)-460(in)-460(Mobile)-460(Ad)-460(Ho)-28(c)-459(Net)26(w)28(orks.)-823(In)]TJ
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[(2007,)-463(Y)82(u)-437(et)-437(al)-438([YSL07])-438(prop)-28(osed)-437(a)-438(con)27(tributory)-437(GKA)-438(proto)-27(col)-438(that)-438(optimizes)-438(rek)27(eying)-437(cost)-437(b)27(y)]TJ
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[(utilizing)-461(a)-462(no)27(v)27(el)-460(logical)-462(k)26(ey)-460(tree)-462(structure)-462(kno)27(wn)-461(as)-462(PFMH,)-462(and)-462(the)-462(concept)-461(of)-462(phan)27(tom)-461(user)]TJ
T*
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[(limited)-433(mobile)-433(no)-28(des,)-458(ho)27(w)28(ev)28(er)-432(they)-434(did)-433(not)-433(pro)27(vide)-432(energy)-433(analysis)-433(to)-434(analyze)-433(the)-433(energy)-433(used)]TJ
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[(for)-454(computation)-455(and)-455(comm)27(unication)-453(\(b)-28(oth)-455(transmission)-455(and)-454(reception\))-455(in)-455(their)-454(GKA)-455(proto)-28(col.)]TJ
T*
[(Lazos)-444(and)-445(P)26(o)-26(o)26(v)28(endran)-444([LP07])-445(prop)-27(osed)-445(a)-445(p)-28(o)27(w)28(er)-444(pro)26(ximit)28(y)-444(based)-445(k)27(ey)-444(managemen)27(t)-444(proto)-28(col)-444(for)]TJ
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[(secure)-415(m)27(ulticast)-415(in)-415(ad)-416(ho)-27(c)-416(net)27(w)28(orks)-415(while)-415(W)82(ang)-414(et)-416(al)-415([WFH07])-416(prop)-28(osed)-415(a)-416(hierarc)27(h)28(y-based)-414(k)26(ey)]TJ
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[(managemen)27(t)-399(proto)-28(col)-401(for)-401(secure)-400(group)-401(comm)27(unications)-400(in)-401(mobile)-400(ad)-401(ho)-28(c)-400(net)26(w)28(orks.)-645(Other)-401(GKA)]TJ
T*
[(proto)-27(cols)-364([SLS07,)-148(KK07,)-148(NHSC07])-363(ha)27(v)28(e)-363(also)-363(b)-28(een)-363(b)-28(een)-363(prop)-28(osed)-363(most)-364(recen)27(tly)-362(in)-364(2007.)-534(Ho)27(w)27(ev)28(er,)]TJ
0 -21.91 TD
[(they)-333(do)-333(not)-333(p)-28(erform)-334(an)27(y)-332(energy)-333(analysis)-334(nor)-333(o\256er)-333(protection)-334(against)-333(DoS)-333(attac)26(ks.)]TJ
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[(2.7.14)-1125(P)31(assw)31(ord-based)-374(GKA)-375(Proto)-31(cols)-375(in)-375(Curren)30(t)-374(Literature)]TJ
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[(Most)-252(curren)26(t)-251(passw)26(ord-based)-251(k)26(ey)-251(exc)26(hange)-252(proto)-27(cols)-253(suc)27(h)-252(as)-253([Mac02,)-58(AP05,)-57(A)27(CP05,)-57(MPS00,)-57(AFP06,)]TJ
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T*
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[(solution)-364(to)-365(the)-365(group)-365(Di\261e-Hellman)-365(k)27(ey)-364(exc)27(hange)-364(problem.)-539(Ho)27(w)28(ev)28(er)-364(the)-365(total)-365(n)27(um)28(b)-27(er)-365(of)-364(rounds)]TJ
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[(in)-412(their)-412(proto)-28(col)-412(w)27(as)-411(linear)-412(to)-412(the)-412(total)-413(n)27(um)28(b)-27(er)-412(of)-412(no)-28(des.)-681(Lee)-412(et)-412(al)-412([LHL04])-412(and)-412(more)-412(recen)26(tly)]TJ
T*
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T*
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[(whic)27(h)-432(is)-433(a)-433(simple)-432(v)54(arian)28(t)-432(of)-433(the)-433(Burmester-Desmedt)-433(proto)-28(col)-433([BD95].)-743(All)-433(the)-433(ab)-27(o)26(v)28(e-men)28(tioned)]TJ
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[(not)-233(b)-28(e)-234(easy)-234(to)-233(securely)-234(up)-28(date)-234(ev)27(ery)-233(remaining)-233(group)-234(mem)27(b)-27(er)-234(with)-233(the)-234(new)-234(passw)27(ord.)-410(F)82(urthermore,)]TJ
0 -21.92 TD
[(all)-270(the)-271(ab)-28(o)27(v)27(e-men)28(tioned)-270(passw)27(ord-based)-270(GKA)-271(proto)-28(cols)-271(also)-271(do)-270(not)-271(pro)26(vide)-270(protection)-271(against)-271(DoS)]TJ
T*
[(attac)27(ks)-332(and)-333(on-line)-334(passw)27(ord)-332(guessing)-334(attac)27(ks.)]TJ
16.93 -21.91 Td
[(W)83(e)-396(shall)-397(no)27(w)-396(presen)26(t)-396(t)27(w)28(o)-396(P)27(assw)28(ord-based)-396(GKA)-397(proto)-28(cols,)-413(namely)-397(Ab)-28(dalla)-397(et)-397(al's)-397(P)27(assw)28(ord-)]TJ
-16.93 -21.92 Td
[(based)-333(GKA)-333(Proto)-28(col)-333([ABCP06])-334(and)-333(Byun)-333(et)-334(al's)-333(EKE-D)-333(Proto)-28(col)-333([BLLH06])-334(in)-333(details)-333(b)-28(elo)27(w:)]TJ
/T1_1 11.95 Tf
0 -37.82 TD
[(2.7.15)-1125(Ab)-31(dalla)-375(et)-375(al's)-375(P)30(assw)32(ord-based)-374(GKA)-375(Proto)-32(col)]TJ
/T1_0 10.91 Tf
0 -28.96 TD
[(Ab)-27(dalla)-394(et)-394(al)-394([ABCP06])-394(prop)-28(osed)-394(a)-394(passw)27(ord-based)-393(constan)27(t)-393(round)-394(GKA)-394(proto)-27(col)-394(that)-394(is)-394(based)]TJ
0 -21.92 TD
[(on)-366(the)-366(BD)-366(proto)-28(col.)-544(Their)-366(proto)-28(col)-366(requires)-366(only)-367(four)-366(rounds)-366(of)-367(comm)27(unications)-365(and)-366(four)-367(m)27(ulti-)]TJ
0 -21.91 TD
[(exp)-27(onen)27(tiations)-436(p)-28(er)-437(user.)-754(Ho)27(w)27(ev)28(er,)-461(they)-437(did)-437(not)-437(prop)-27(ose)-437(an)27(y)-436(dynamic)-437(GKA)-436(proto)-28(cols)-437(in)-437(their)]TJ
0 -21.92 TD
[(pap)-27(er)-334([ABCP06].)]TJ
16.93 -21.92 Td
[(Tw)27(o)-270(random)-271(large)-272(primes,)]TJ
/T1_2 10.91 Tf
126.94 0 Td
(q)Tj
/T1_0 10.91 Tf
8.22 0 Td
(and)Tj
/T1_2 10.91 Tf
20.53 0 Td
(p)Tj
/T1_0 10.91 Tf
[(,)-283(are)-271(selected)-271(suc)26(h)-270(that)]TJ
/T1_2 10.91 Tf
115.99 0 Td
(q)Tj
/T1_0 10.91 Tf
8.22 0 Td
(divides)Tj
/T1_2 10.91 Tf
36.04 0 Td
(p)Tj
/T1_3 10.91 Tf
6.56 0 Td
(\241)Tj
/T1_0 10.91 Tf
9.55 0 Td
[(1)-271(\()]TJ
/T1_2 10.91 Tf
12.65 0 Td
(p)Tj
/T1_0 10.91 Tf
8.45 0 Td
[(is)-271(normally)-271(1024)-271(bits)]TJ
-370.08 -21.91 Td
(and)Tj
/T1_2 10.91 Tf
20.5 0 Td
(q)Tj
/T1_0 10.91 Tf
8.19 0 Td
[(is)-268(normally)-269(160)-268(bits\).)-423(Next,)-282(an)-268(elemen)27(t)]TJ
/T1_2 10.91 Tf
187.28 0 Td
(g)Tj
/T1_3 10.91 Tf
8.62 0 Td
(2)Tj
/T1_2 10.91 Tf
10.3 0 Td
(Z)Tj
/T1_4 7.97 Tf
8.23 3.96 Td
(\244)Tj
/T1_5 7.97 Tf
-0.78 -6.66 Td
(p)Tj
/T1_0 10.91 Tf
8.44 2.7 Td
[(of)-268(order)]TJ
/T1_2 10.91 Tf
39.55 0 Td
(q)Tj
/T1_0 10.91 Tf
8.18 0 Td
[(is)-268(selected.)-423(Tw)26(o)-267(cryptographic)-269(hash)]TJ
-298.51 -21.92 Td
(functions)Tj
/T1_6 10.91 Tf
47.35 0 Td
(H)Tj
/T1_7 7.97 Tf
7.73 -1.63 Td
(1)Tj
/T1_0 10.91 Tf
8.7 1.63 Td
(and)Tj
/T1_6 10.91 Tf
21.54 0 Td
(H)Tj
/T1_7 7.97 Tf
7.72 -1.63 Td
(2)Tj
/T1_0 10.91 Tf
8.7 1.63 Td
[(are)-364(de\257ned)-364(as)-364(follo)27(ws:)]TJ
/T1_6 10.91 Tf
110.89 0 Td
(H)Tj
/T1_7 7.97 Tf
7.72 -1.63 Td
(1)Tj
/T1_0 10.91 Tf
8.32 1.63 Td
(:)Tj
/T1_3 10.91 Tf
6.61 0 Td
(f)Tj
/T1_0 10.91 Tf
(0)Tj
/T1_2 10.91 Tf
(;)Tj
/T1_0 10.91 Tf
15.76 0 Td
(1)Tj
/T1_3 10.91 Tf
(g)Tj
/T1_4 7.97 Tf
10.9 3.96 Td
(\244)Tj
/T1_3 10.91 Tf
8.32 -3.96 Td
[(!)-328(f)]TJ
/T1_0 10.91 Tf
19.95 0 Td
(0)Tj
/T1_2 10.91 Tf
(;)Tj
/T1_0 10.91 Tf
10.3 0 Td
(1)Tj
/T1_3 10.91 Tf
(g)Tj
/T1_5 7.97 Tf
10.9 4.37 Td
(\270)Tj
/T1_8 5.98 Tf
4.94 -1.4 Td
(H)Tj
/T1_9 5.98 Tf
4.48 -1.79 Td
(1)Tj
/T1_0 10.91 Tf
9.12 -1.18 Td
(and)Tj
/T1_6 10.91 Tf
21.54 0 Td
(H)Tj
/T1_7 7.97 Tf
7.72 -1.63 Td
(2)Tj
/T1_0 10.91 Tf
8.32 1.63 Td
(:)Tj
/T1_3 10.91 Tf
6.62 0 Td
(f)Tj
/T1_0 10.91 Tf
(0)Tj
/T1_2 10.91 Tf
(;)Tj
/T1_0 10.91 Tf
15.75 0 Td
(1)Tj
/T1_3 10.91 Tf
(g)Tj
/T1_4 7.97 Tf
10.91 3.96 Td
(\244)Tj
/T1_3 10.91 Tf
8.31 -3.96 Td
[(!)-329(f)]TJ
/T1_0 10.91 Tf
(0)Tj
/T1_2 10.91 Tf
(;)Tj
/T1_0 10.91 Tf
30.25 0 Td
(1)Tj
/T1_3 10.91 Tf
(g)Tj
/T1_5 7.97 Tf
10.9 4.37 Td
(\270)Tj
/T1_8 5.98 Tf
4.94 -1.4 Td
(H)Tj
/T1_9 5.98 Tf
4.49 -1.79 Td
(2)Tj
/T1_0 10.91 Tf
5.14 -1.18 Td
(,)Tj
-464.84 -21.92 Td
(where)Tj
/T1_2 10.91 Tf
31.72 0 Td
(\270)Tj
/T1_8 7.97 Tf
6.37 -1.77 Td
(H)Tj
/T1_9 5.98 Tf
5.97 -1.11 Td
(1)Tj
/T1_0 10.91 Tf
8.47 2.88 Td
(and)Tj
/T1_2 10.91 Tf
21.4 0 Td
(\270)Tj
/T1_8 7.97 Tf
6.36 -1.77 Td
(H)Tj
/T1_9 5.98 Tf
5.97 -1.11 Td
(2)Tj
/T1_0 10.91 Tf
8.48 2.88 Td
[(are)-350(in)27(tegers.)-495(The)-350(k)26(ey)-349(con\257rmation)-351(uses)-350(function)]TJ
/T1_3 10.91 Tf
236.13 0 Td
(A)Tj
/T1_2 10.91 Tf
8.71 0 Td
(uth)Tj
/T1_0 10.91 Tf
19.81 0 Td
(:)Tj
/T1_3 10.91 Tf
6.37 0 Td
(f)Tj
/T1_0 10.91 Tf
(0)Tj
/T1_2 10.91 Tf
(;)Tj
/T1_0 10.91 Tf
15.75 0 Td
(1)Tj
/T1_3 10.91 Tf
(g)Tj
/T1_4 7.97 Tf
10.91 3.96 Td
(\244)Tj
/T1_3 10.91 Tf
8.07 -3.96 Td
[(!)-306(f)]TJ
/T1_0 10.91 Tf
(0)Tj
/T1_2 10.91 Tf
(;)Tj
/T1_0 10.91 Tf
30 0 Td
(1)Tj
/T1_3 10.91 Tf
(g)Tj
/T1_5 7.97 Tf
10.91 3.96 Td
(\270)Tj
/T1_10 5.98 Tf
4.94 -1.4 Td
(A)Tj
/T1_11 5.98 Tf
5.91 0 Td
(uth)Tj
/T1_0 10.91 Tf
12.59 -2.56 Td
(,)Tj
-464.84 -21.91 Td
(where)Tj
/T1_2 10.91 Tf
32.72 0 Td
(\270)Tj
/T1_4 7.97 Tf
6.36 -1.78 Td
(A)Tj
/T1_5 7.97 Tf
6.77 0 Td
(uth)Tj
/T1_0 10.91 Tf
18.15 1.78 Td
[(is)-441(an)-441(in)27(teger.)-768(Their)-442(GKA)-441(proto)-28(col)-441(also)-442(mak)27(es)-441(use)-441(of)-442(a)-441(symmetric)-442(k)27(ey)-440(encryption)]TJ
-64 -21.92 Td
[(sc)27(heme)]TJ
/T1_6 10.91 Tf
37.1 0 Td
(SKE)Tj
/T1_0 10.91 Tf
23.56 0 Td
[(as)-312(de\257ned)-313(in)-313(Section)-313(2.3.3.)-437(F)82(or)-312(simplicit)27(y)83(,)-316(\\)-278(mo)-27(d)]TJ
/T1_2 10.91 Tf
234.62 0 Td
(p)Tj
/T1_0 10.91 Tf
[(")-313(is)-312(omitted)-313(from)-313(the)-313(expressions)-313(if)]TJ
-295.28 -21.91 Td
[(no)-333(confusion)-333(arises.)-445(Their)-333(GKA)-333(proto)-28(col)-333(is)-334(describ)-27(ed)-334(as)-333(follo)27(ws:)]TJ
16.93 -21.92 Td
[(In)-365(Round)-366(1,)-374(eac)27(h)]TJ
/T1_12 10.91 Tf
87.09 0 Td
(U)Tj
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5.73 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
8.72 1.64 Td
[(selects)-365(random)-366(nonce)]TJ
/T1_2 10.91 Tf
106.03 0 Td
(N)Tj
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8.76 -1.64 Td
(i)Tj
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7.37 1.64 Td
[(and)-366(sends)]TJ
/T1_12 10.91 Tf
51.12 0 Td
(U)Tj
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5.73 -1.64 Td
(i)Tj
/T1_2 10.91 Tf
4.73 1.64 Td
[(;)-166(N)]TJ
/T1_5 7.97 Tf
13.61 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
3.38 1.64 Td
[(.)-541(Next)-366(in)-366(Round)-366(2,)-374(the)-366(session)]TJ
/T1_2 10.91 Tf
-319.2 -21.92 Td
(S)Tj
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10.58 0 Td
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11.75 0 Td
(U)Tj
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5.73 -1.63 Td
(1)Tj
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4.73 1.63 Td
(jj)Tj
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6.06 0 Td
(N)Tj
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8.76 -1.63 Td
(1)Tj
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4.73 1.63 Td
[(jj)-166(\242)-167(\242)-167(\242)-166(jj)]TJ
/T1_12 10.91 Tf
28.48 0 Td
(U)Tj
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5.72 -1.63 Td
(n)Tj
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4.73 1.63 Td
(jj)Tj
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6.06 0 Td
(N)Tj
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8.77 -1.63 Td
(n)Tj
/T1_0 10.91 Tf
9.41 1.63 Td
[(is)-346(de\257ned)-346(in)-347(whic)27(h)-345(eac)27(h)]TJ
/T1_12 10.91 Tf
117.71 0 Td
(U)Tj
/T1_5 7.97 Tf
5.72 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
7.16 1.63 Td
[(has)-346(a)-346(sp)-28(eci\257c)-347(symmetric)-346(k)27(ey)]TJ
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139.98 0 Td
(k)Tj
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5.68 -1.63 Td
(i)Tj
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6.64 1.63 Td
(=)Tj
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11.75 0 Td
(H)Tj
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7.73 -1.63 Td
(1)Tj
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4.73 1.63 Td
(\()Tj
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[(S)-2(;)-166(i;)-167(pw)]TJ
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37.99 0 Td
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(where)Tj
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33.13 0 Td
(pw)Tj
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18.81 0 Td
[(is)-479(the)-479(passw)27(ord.)-881(Eac)27(h)]TJ
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117.76 0 Td
(U)Tj
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5.72 -1.64 Td
(i)Tj
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8.61 1.64 Td
[(then)-479(selects)-479(random)]TJ
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103.68 0 Td
(r)Tj
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4.92 -1.64 Td
(i)Tj
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9.06 1.64 Td
(2)Tj
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12.95 0 Td
(Z)Tj
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8.23 3.95 Td
(\244)Tj
/T1_5 7.97 Tf
-0.78 -6.65 Td
(q)Tj
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10.74 2.7 Td
[(and)-478(broadcast)]TJ
/T1_2 10.91 Tf
74.16 0 Td
(z)Tj
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5.55 3.95 Td
(\244)Tj
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(i)Tj
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10.89 3.06 Td
(=)Tj
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14.16 0 Td
(E)Tj
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5.76 -1.78 Td
(k)Tj
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4.41 -1.22 Td
(i)Tj
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3.66 3 Td
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(z)Tj
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9.31 -1.64 Td
(i)Tj
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3.38 1.64 Td
(\))Tj
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(where)Tj
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32.65 0 Td
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13.36 0 Td
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5.59 3.96 Td
(r)Tj
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3.82 -1.22 Td
(i)Tj
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3.66 -2.74 Td
[(.)-749(Next)-435(in)-435(Round)-435(3,)-461(eac)27(h)]TJ
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128.36 0 Td
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(i)Tj
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9.48 1.64 Td
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42.7 0 Td
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2.88 0 Td
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6.59 0 Td
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9.61 1.64 Td
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13.36 0 Td
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(z)Tj
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9.79 3.96 Td
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6.59 0 Td
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4.73 3.06 Td
[(\))-434(and)]TJ
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31.3 0 Td
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(i)Tj
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16.2 1.64 Td
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13.36 0 Td
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8.41 -1.78 Td
(k)Tj
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(i)Tj
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2.66 0 Td
(+1)Tj
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10.24 2.99 Td
(\()Tj
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(z)Tj
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9.79 3.96 Td
(\244)Tj
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-0.48 -7.02 Td
(i)Tj
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2.88 0 Td
(+1)Tj
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11.32 3.06 Td
(\))Tj
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[(and)-490(computes)]TJ
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73.16 0 Td
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7.44 -1.63 Td
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14.37 0 Td
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(r)Tj
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(i)Tj
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(i)Tj
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2.88 0 Td
(\241)Tj
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6.59 0 Td
(1)Tj
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10.07 3.25 Td
(and)Tj
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22.92 0 Td
(Z)Tj
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7.44 -1.63 Td
(i)Tj
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17.19 1.63 Td
(=)Tj
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14.36 0 Td
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5.55 4.97 Td
(r)Tj
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3.83 -1.21 Td
(i)Tj
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-4.3 -7.01 Td
(i)Tj
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2.88 0 Td
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11.31 3.25 Td
(.)Tj
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13.01 0 Td
(U)Tj
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5.73 -1.63 Td
(i)Tj
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10.07 1.63 Td
[(then)-490(broadcasts)]TJ
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82.34 0 Td
(X)Tj
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9.04 -1.63 Td
(i)Tj
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9.26 1.63 Td
(=)Tj
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14.36 0 Td
(Z)Tj
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7.44 -1.63 Td
(i)Tj
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2.89 0 Td
(+1)Tj
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11.31 1.63 Td
[(=)55(Z)]TJ
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12.29 -1.63 Td
(i)Tj
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3.38 1.63 Td
[(.)-915(In)-490(Round)-490(4,)]TJ
-394.03 -21.91 Td
[(eac)27(h)]TJ
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25.64 0 Td
(U)Tj
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5.72 -1.64 Td
(i)Tj
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9.46 1.64 Td
(computes)Tj
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49.63 0 Td
(K)Tj
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/T1_1 10.91 Tf
10.39 0 Td
(=)Tj
/T1_0 10.91 Tf
11.73 0 Td
(f)Tj
/T1_2 10.91 Tf
(U)Tj
/T1_4 7.97 Tf
11.18 -1.63 Td
(1)Tj
/T1_5 10.91 Tf
4.73 1.63 Td
(;)Tj
/T1_0 10.91 Tf
4.84 0 Td
[(\242)-166(\242)-167(\242)]TJ
/T1_5 10.91 Tf
16.36 0 Td
(;)Tj
/T1_2 10.91 Tf
4.85 0 Td
(U)Tj
/T1_3 7.97 Tf
5.73 -1.63 Td
(n)Tj
/T1_0 10.91 Tf
5.63 1.63 Td
(g)Tj
/T1_1 10.91 Tf
[(.)-480(The)-346(EKE-D)-345(Join)-345(Proto)-28(col)-346(will)]TJ
-307.42 -21.91 Td
[(c)27(hange)-359(the)-359(curren)26(t)-358(group)-360(k)27(ey)-359(to)-360(a)-360(new)-360(group)-359(k)26(ey)-358(to)-360(ensure)-360(that)-360(the)-359(joining)-360(users)-360(are)-360(not)-360(able)-359(to)]TJ
0 -21.92 TD
[(compute)-355(the)-355(previous)-355(group)-355(k)27(eys)-354(used.)-510(The)-355(EKE-D)-356(Join)-355(Proto)-27(col)-356(will)-355(also)-355(up)-28(dates)]TJ
/T1_0 10.91 Tf
406.73 0 Td
(G)Tj
/T1_6 7.97 Tf
7.13 3.96 Td
(0)Tj
/T1_1 10.91 Tf
6.22 -3.96 Td
(=)Tj
/T1_0 10.91 Tf
11.91 0 Td
[(G)-296([)-237(J)]TJ
/T1_1 10.91 Tf
32.85 0 Td
(.)Tj
-464.84 -21.92 Td
[(The)-333(EKE-D)-333(Join)-333(Proto)-28(col)-334(is)-333(describ)-28(ed)-333(as)-333(follo)26(ws:)]TJ
/T1_7 10.91 Tf
0 -27.89 TD
[(EKE-D)-326(Join)-327(Proto)-32(col)]TJ
/T1_1 10.91 Tf
120.38 0 Td
[(In)-283(Round)-285(1,)-294(the)-284(Join)-284(Proto)-28(col)-284(will)-284(execute)-284(Round)-284(1)-285(of)-284(the)-284(Setup)-284(Proto)-28(col)]TJ
-120.38 -21.91 Td
[(with)-420(the)-420(new)-420(user)]TJ
/T1_0 10.91 Tf
92.94 0 Td
(J)Tj
/T1_1 10.91 Tf
14.01 0 Td
(=)Tj
/T1_0 10.91 Tf
13.09 0 Td
(f)Tj
/T1_2 10.91 Tf
(U)Tj
/T1_3 7.97 Tf
11.18 -1.64 Td
(n)Tj
/T1_4 7.97 Tf
5.13 0 Td
(+1)Tj
/T1_5 10.91 Tf
11.32 1.64 Td
(;)Tj
/T1_0 10.91 Tf
4.85 0 Td
[(\242)-166(\242)-167(\242)]TJ
/T1_5 10.91 Tf
16.36 0 Td
(;)Tj
/T1_2 10.91 Tf
4.84 0 Td
(U)Tj
/T1_3 7.97 Tf
5.73 -1.64 Td
(n)Tj
/T1_4 7.97 Tf
(+)Tj
/T1_3 7.97 Tf
(m)Tj
/T1_0 10.91 Tf
19.71 1.64 Td
(g)Tj
/T1_1 10.91 Tf
(.)Tj
/T1_2 10.91 Tf
16.16 0 Td
(C)Tj
/T1_1 10.91 Tf
10.31 0 Td
[(gets)-420(the)-420(new)-420(set)]TJ
/T1_8 10.91 Tf
84.49 0 Td
(LIST)Tj
/T1_9 7.97 Tf
22.42 -1.78 Td
(J)Tj
/T1_1 10.91 Tf
9.1 1.78 Td
(=)Tj
/T1_0 10.91 Tf
13.09 0 Td
(f)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 360.18 -118.28 cm
0 0 m
3.94 0 l
S
Q
Q
BT
/T1_5 10.91 Tf
1.0003 0 0 1.0003 432.2809 643.2746 Tm
(t)Tj
/T1_3 7.97 Tf
3.94 -1.64 Td
(n)Tj
/T1_4 7.97 Tf
5.13 0 Td
(+1)Tj
/T1_5 10.91 Tf
11.32 1.64 Td
(;)Tj
/T1_0 10.91 Tf
4.85 0 Td
(\242)Tj
1.0003 0 0 1.0003 72 769.82 Tm
390.264 -126.51 Td
[(\242)-166(\242)]TJ
/T1_5 10.91 Tf
11.516 0 Td
(;)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 406.62 -118.28 cm
0 0 m
3.94 0 l
S
Q
Q
BT
/T1_5 10.91 Tf
1.0003 0 0 1.0003 478.7339 643.2746 Tm
(t)Tj
/T1_3 7.97 Tf
3.94 -1.64 Td
(n)Tj
/T1_4 7.97 Tf
(+)Tj
/T1_3 7.97 Tf
(m)Tj
/T1_0 10.91 Tf
19.71 1.64 Td
(g)Tj
/T1_1 10.91 Tf
10.03 0 Td
(whic)Tj
1.0003 0 0 1.0003 72 769.82 Tm
461.825 -126.51 Td
(h)Tj
-461.825 -21.92 Td
[(consists)-413(of)-414(in)27(termediate)-412(DH)-414(k)27(eys)]TJ
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 164.45 -140.2 cm
0 0 m
3.94 0 l
S
Q
Q
BT
/T1_5 10.91 Tf
1.0003 0 0 1.0003 236.496 621.3484 Tm
(t)Tj
/T1_3 7.97 Tf
3.94 -1.64 Td
(j)Tj
/T1_1 10.91 Tf
8.89 1.64 Td
(for)Tj
/T1_5 10.91 Tf
17.57 0 Td
(n)Tj
/T1_1 10.91 Tf
9.55 0 Td
(+)Tj
1.0003 0 0 1.0003 72 769.82 Tm
215.899 -148.43 Td
(1)Tj
/T1_0 10.91 Tf
9.931 0 Td
(\267)Tj
/T1_5 10.91 Tf
12.97 0 Td
(j)Tj
/T1_0 10.91 Tf
9.61 0 Td
(\267)Tj
/T1_5 10.91 Tf
12.97 0 Td
(n)Tj
/T1_1 10.91 Tf
9.55 0 Td
(+)Tj
/T1_5 10.91 Tf
11.49 0 Td
(m)Tj
/T1_1 10.91 Tf
(.)Tj
/T1_2 10.91 Tf
20.08 0 Td
(C)Tj
/T1_1 10.91 Tf
10.24 0 Td
[(then)-413(up)-27(dates)]TJ
/T1_8 10.91 Tf
67.55 0 Td
(LIST)Tj
/T1_6 7.97 Tf
22.41 4.42 Td
(0)Tj
/T1_9 7.97 Tf
0 -7.12 TD
(sc)Tj
/T1_1 10.91 Tf
12 2.7 Td
(=)Tj
/T1_8 10.91 Tf
12.97 0 Td
(LIST)Tj
/T1_9 7.97 Tf
22.42 -1.64 Td
(sc)Tj
/T1_0 10.91 Tf
10.51 1.64 Td
([)Tj
/T1_8 10.91 Tf
-460.6 -21.92 Td
(LIST)Tj
/T1_9 7.97 Tf
22.42 -1.77 Td
(J)Tj
/T1_1 10.91 Tf
4.49 1.77 Td
[(.)-513(In)-356(the)-356(second)-357(round,)]TJ
/T1_2 10.91 Tf
111.87 0 Td
(C)Tj
/T1_1 10.91 Tf
9.62 0 Td
[(selects)-355(new)-357(random)]TJ
/T1_5 10.91 Tf
97.23 0 Td
(N)Tj
/T1_6 7.97 Tf
9.95 3.96 Td
(0)Tj
/T1_0 10.91 Tf
6.24 -3.96 Td
(2)Tj
/T1_5 10.91 Tf
10.72 0 Td
(Z)Tj
/T1_6 7.97 Tf
8.23 3.96 Td
(\244)Tj
/T1_3 7.97 Tf
-0.78 -6.65 Td
(q)Tj
/T1_1 10.91 Tf
9.39 2.69 Td
[(and)-356(computes)]TJ
/T1_5 10.91 Tf
70.24 0 Td
(N)Tj
/T1_6 7.97 Tf
9.95 3.96 Td
(0)Tj
/T1_0 10.91 Tf
5.39 -3.96 Td
(\251)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 386.03 -162.11 cm
0 0 m
3.94 0 l
S
Q
Q
BT
/T1_5 10.91 Tf
1.0003 0 0 1.0003 458.1381 599.4223 Tm
(t)Tj
/T1_3 7.97 Tf
3.94 -1.63 Td
(i)Tj
/T1_1 10.91 Tf
7.26 1.63 Td
(using)Tj
/T1_8 10.91 Tf
28.79 0 Td
(LIST)Tj
/T1_6 7.97 Tf
22.42 4.42 Td
(0)Tj
/T1_9 7.97 Tf
0 -7.11 TD
(sc)Tj
/T1_1 10.91 Tf
10.95 2.69 Td
(=)Tj
/T1_0 10.91 Tf
-459.39 -21.91 Td
(f)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 5.45 -184.03 cm
0 0 m
3.94 0 l
S
Q
Q
BT
/T1_5 10.91 Tf
1.0003 0 0 1.0003 77.4515 577.5062 Tm
(t)Tj
/T1_4 7.97 Tf
3.94 -1.64 Td
(1)Tj
/T1_5 10.91 Tf
4.73 1.64 Td
(;)Tj
/T1_0 10.91 Tf
4.85 0 Td
(\242)Tj
1.0003 0 0 1.0003 72 769.82 Tm
23.814 -192.26 Td
[(\242)-167(\242)]TJ
/T1_5 10.91 Tf
11.516 0 Td
(;)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 40.18 -184.03 cm
0 0 m
3.93 0 l
S
Q
Q
BT
/T1_5 10.91 Tf
1.0003 0 0 1.0003 112.1913 577.5062 Tm
(t)Tj
/T1_3 7.97 Tf
3.93 -1.64 Td
(n)Tj
/T1_4 7.97 Tf
(+)Tj
/T1_3 7.97 Tf
11.73 0 Td
(m)Tj
/T1_0 10.91 Tf
7.98 1.64 Td
(g)Tj
/T1_1 10.91 Tf
(.)Tj
/T1_2 10.91 Tf
15.94 0 Td
(C)Tj
/T1_1 10.91 Tf
10.23 0 Td
(then)Tj
1.0003 0 0 1.0003 72 769.82 Tm
115.705 -192.26 Td
(broadcast)Tj
/T1_5 10.91 Tf
50.635 0 Td
(N)Tj
/T1_6 7.97 Tf
9.95 3.95 Td
(0)Tj
/T1_0 10.91 Tf
5.8 -3.95 Td
(\251)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 193.57 -184.03 cm
0 0 m
3.94 0 l
S
Q
Q
BT
/T1_5 10.91 Tf
1.0003 0 0 1.0003 265.6242 577.5062 Tm
(t)Tj
/T1_3 7.97 Tf
3.94 -1.64 Td
(i)Tj
/T1_1 10.91 Tf
7.89 1.64 Td
(and)Tj
1.0003 0 0 1.0003 72 769.82 Tm
227.471 -192.26 Td
[(authen)26(ticators)]TJ
/T1_8 10.91 Tf
72.759 0 Td
(H)Tj
/T1_4 7.97 Tf
7.73 -1.64 Td
(2)Tj
/T1_1 10.91 Tf
4.73 1.64 Td
(\()Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 316.93 -184.03 cm
0 0 m
3.94 0 l
S
Q
Q
BT
/T1_5 10.91 Tf
1.0003 0 0 1.0003 389.0187 577.5062 Tm
(t)Tj
/T1_3 7.97 Tf
3.94 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
3.38 1.64 Td
(jj)Tj
/T1_2 10.91 Tf
6.06 0 Td
(C)Tj
/T1_1 10.91 Tf
5.72 0 Td
(\))Tj
1.0003 0 0 1.0003 72 769.82 Tm
344.78 -192.26 Td
(to)Tj
/T1_2 10.91 Tf
14.2 0 Td
(U)Tj
/T1_3 7.97 Tf
5.72 -1.64 Td
(i)Tj
/T1_1 10.91 Tf
7.89 1.64 Td
[(for)-412(1)]TJ
/T1_0 10.91 Tf
27.49 0 Td
(\267)Tj
/T1_5 10.91 Tf
12.96 0 Td
(i)Tj
/T1_0 10.91 Tf
8.23 0 Td
(\267)Tj
/T1_5 10.91 Tf
12.96 0 Td
(n)Tj
/T1_1 10.91 Tf
9.55 0 Td
(+)Tj
/T1_5 10.91 Tf
11.49 0 Td
(m)Tj
/T1_1 10.91 Tf
9.57 0 Td
(.)Tj
-464.84 -21.92 Td
[(Concurren)27(tly)84(,)]TJ
/T1_2 10.91 Tf
67.7 0 Td
(U)Tj
/T1_3 7.97 Tf
5.72 -1.64 Td
(i)Tj
/T1_1 10.91 Tf
6.36 1.64 Td
[(computes)-273(and)-273(sends)-273(authen)27(ticator)]TJ
/T1_8 10.91 Tf
163.91 0 Td
(H)Tj
/T1_4 7.97 Tf
7.72 -1.64 Td
(2)Tj
/T1_1 10.91 Tf
4.73 1.64 Td
(\()Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 260.38 -205.95 cm
0 0 m
3.94 0 l
S
Q
Q
BT
/T1_5 10.91 Tf
1.0003 0 0 1.0003 332.4529 555.58 Tm
(t)Tj
/T1_3 7.97 Tf
3.94 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
3.38 1.64 Td
(jj)Tj
/T1_2 10.91 Tf
6.06 0 Td
(U)Tj
/T1_3 7.97 Tf
5.73 -1.64 Td
(i)Tj
/T1_1 10.91 Tf
3.38 1.64 Td
(\))Tj
1.0003 0 0 1.0003 72 769.82 Tm
290.082 -214.18 Td
(to)Tj
/T1_2 10.91 Tf
12.678 0 Td
(C)Tj
/T1_1 10.91 Tf
[(.)-424(Finally)-273(in)-273(the)-273(Key)-273(Computation)]TJ
-302.76 -21.92 Td
[(Round,)-315(all)-310(no)-28(des)-311(c)27(hec)28(k)-310(if)-311(the)-311(authen)27(ticator)-309(is)-311(v)54(alid)-309(b)26(y)-309(using)]TJ
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 288.22 -227.86 cm
0 0 m
3.94 0 l
S
Q
Q
BT
/T1_5 10.91 Tf
1.0003 0 0 1.0003 360.3007 533.6539 Tm
(t)Tj
/T1_3 7.97 Tf
3.94 -1.63 Td
(i)Tj
/T1_1 10.91 Tf
3.38 1.63 Td
(.)Tj
1.0003 0 0 1.0003 72 769.82 Tm
303.341 -236.1 Td
[(Next,)-315(all)-311(no)-27(des)-311(obtains)]TJ
/T1_5 10.91 Tf
112.789 0 Td
(N)Tj
/T1_6 7.97 Tf
9.95 3.96 Td
(0)Tj
/T1_1 10.91 Tf
6.18 -3.96 Td
(using)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 460.55 -227.86 cm
0 0 m
3.94 0 l
S
Q
Q
BT
/T1_5 10.91 Tf
1.0003 0 0 1.0003 532.679 533.6539 Tm
(t)Tj
/T1_3 7.97 Tf
3.94 -1.63 Td
(i)Tj
/T1_1 10.91 Tf
-464.49 -20.28 Td
(and)Tj
1.0003 0 0 1.0003 72 769.82 Tm
20.609 -258.01 Td
[(generates)-279(the)-279(new)-279(k)27(ey)]TJ
/T1_5 10.91 Tf
106.481 0 Td
(sk)Tj
/T1_6 7.97 Tf
11.13 3.95 Td
(0)Tj
/T1_1 10.91 Tf
5.82 -3.95 Td
(=)Tj
/T1_8 10.91 Tf
11.52 0 Td
(H)Tj
/T1_4 7.97 Tf
7.72 -1.64 Td
(3)Tj
/T1_1 10.91 Tf
4.73 1.64 Td
(\()Tj
/T1_2 10.91 Tf
(SIDS)Tj
/T1_6 7.97 Tf
27.15 3.95 Td
(0)Tj
/T1_0 10.91 Tf
2.79 -3.95 Td
(jj)Tj
/T1_5 10.91 Tf
6.06 0 Td
(N)Tj
/T1_6 7.97 Tf
9.95 3.95 Td
(0)Tj
/T1_1 10.91 Tf
2.79 -3.95 Td
[(\))-279(where)]TJ
/T1_2 10.91 Tf
38.23 0 Td
(SIDS)Tj
/T1_6 7.97 Tf
22.9 3.95 Td
(0)Tj
/T1_1 10.91 Tf
5.83 -3.95 Td
(=)Tj
/T1_2 10.91 Tf
11.51 0 Td
(sid)Tj
/T1_6 7.97 Tf
17.18 3.95 Td
(0)Tj
/T1_0 10.91 Tf
2.79 -3.95 Td
(jj)Tj
/T1_5 10.91 Tf
6.06 0 Td
(t)Tj
/T1_4 7.97 Tf
3.94 -1.64 Td
(1)Tj
/T1_0 10.91 Tf
5.96 1.64 Td
(\251)Tj
/T1_5 10.91 Tf
9.72 0 Td
(N)Tj
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9.95 3.95 Td
(0)Tj
/T1_0 10.91 Tf
2.8 -3.95 Td
(jj)Tj
/T1_5 10.91 Tf
6.06 0 Td
(t)Tj
/T1_4 7.97 Tf
3.94 -1.64 Td
(2)Tj
/T1_0 10.91 Tf
5.96 1.64 Td
(\251)Tj
/T1_5 10.91 Tf
9.72 0 Td
(N)Tj
/T1_6 7.97 Tf
9.95 3.95 Td
(0)Tj
/T1_0 10.91 Tf
2.8 -3.95 Td
[(jj)-166(\242)-167(\242)-166(\242)-167(jj)]TJ
/T1_5 10.91 Tf
28.47 0 Td
(t)Tj
/T1_3 7.97 Tf
3.94 -1.64 Td
(n)Tj
/T1_4 7.97 Tf
(+)Tj
/T1_3 7.97 Tf
(m)Tj
/T1_0 10.91 Tf
20.95 1.64 Td
(\251)Tj
/T1_5 10.91 Tf
9.71 0 Td
(N)Tj
/T1_6 7.97 Tf
9.96 3.95 Td
(0)Tj
/T1_1 10.91 Tf
-465.08 -25.87 Td
(and)Tj
/T1_2 10.91 Tf
21.21 0 Td
(sid)Tj
/T1_6 7.97 Tf
17.17 3.96 Td
(0)Tj
/T1_1 10.91 Tf
5.83 -3.96 Td
(=)Tj
/T1_0 10.91 Tf
11.51 0 Td
(E)Tj
/T1_3 7.97 Tf
5.75 -1.64 Td
(pw)Tj
/T1_10 5.98 Tf
10.34 -1.1 Td
(1)Tj
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4.65 2.74 Td
(\()Tj
/T1_5 10.91 Tf
(g)Tj
/T1_3 7.97 Tf
9.83 3.96 Td
(r)Tj
/T1_10 5.98 Tf
3.82 -1.11 Td
(1)Tj
/T1_1 10.91 Tf
4.65 -2.85 Td
(\))Tj
/T1_0 10.91 Tf
(jjE)Tj
/T1_3 7.97 Tf
16.06 -1.64 Td
(pw)Tj
/T1_10 5.98 Tf
10.34 -1.1 Td
(2)Tj
/T1_1 10.91 Tf
4.64 2.74 Td
(\()Tj
/T1_5 10.91 Tf
(g)Tj
/T1_3 7.97 Tf
9.84 3.96 Td
(r)Tj
/T1_10 5.98 Tf
3.82 -1.11 Td
(2)Tj
/T1_1 10.91 Tf
4.65 -2.85 Td
(\))Tj
/T1_0 10.91 Tf
[(jj)-166(\242)-167(\242)-166(\242)-167(jjE)]TJ
/T1_3 7.97 Tf
38.47 -1.64 Td
(pw)Tj
/T1_11 5.98 Tf
10.34 -1.07 Td
(n)Tj
/T1_10 5.98 Tf
4.6 0 Td
(+)Tj
/T1_11 5.98 Tf
5.58 0 Td
(m)Tj
/T1_1 10.91 Tf
7.54 2.71 Td
(\()Tj
/T1_5 10.91 Tf
(g)Tj
/T1_3 7.97 Tf
9.83 3.96 Td
(r)Tj
/T1_11 5.98 Tf
3.82 -1.08 Td
(n)Tj
/T1_10 5.98 Tf
4.6 0 Td
(+)Tj
/T1_11 5.98 Tf
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[(the)-330(ring)-330(top)-28(ology)-330(are)-331(the)-330(BD)-330(proto)-28(col)-331([BD95],)-330(SSN)-331(proto)-28(col)-330([SSN98],)-331(Kim-Lee-Lee)-330(GKA)-331(proto)-27(col)]TJ
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[([KLL04],)-247(Dutta)-227(and)-226(Barua's)-226(GKA)-227(proto)-27(col)-227([DB05])-226(and)-226(Ab)-28(dalla)-227(et)-226(al's)-226(passw)26(ord-baed)-225(GKA)-226(proto)-28(col)]TJ
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[(Ring)-456(top)-28(ology)-456(uses)-457(broadcast)-456(for)-457(comm)27(unications,)-487(whic)27(h)-455(is)-457(suitable)-456(for)-457(wireless)]TJ
-74.05 -21.91 Td
[(net)27(w)28(orks.)-709(F)82(urthermore,)-443(there)-422(is)-421(no)-422(single)-422(p)-28(oin)27(t)-421(of)-422(failure)-422(b)-28(ecause)-421(there)-422(is)-422(usually)-422(no)-422(con)27(troller)]TJ
T*
[(no)-27(de)-334(in)-333(the)-333(ring)-334(top)-27(ology)82(.)]TJ
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[(Not)-333(e\261cien)27(t)-333(in)-333(handling)-333(user)-334(join)-333(and)-333(user)-334(lea)27(v)28(e)-333(ev)27(en)28(ts.)]TJ
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[(2.9.4)-1125(Star)-375(T)93(op)-30(ology)]TJ
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[(Figure)-303(2.10)-304(illustrates)-304(the)-304(star)-304(top)-28(ology)-304(whic)27(h)-303(is)-304(c)27(haracterized)-303(b)27(y)-303(the)-304(presence)-304(of)-303(a)-304(con)26(troller)-302(no)-28(de)]TJ
0 -21.91 TD
[(that)-335(eases)-335(the)-335(computational)-336(and)-335(comm)27(unication)-335(burden)-335(of)-335(user)-336(no)-27(des)-336(b)27(y)-334(p)-28(erforming)-335(most)-336(of)-335(the)]TJ
0 -21.92 TD
[(computation)-387(and)-388(comm)26(unication)-387(w)27(orkload.)-607(Examples)-388(of)-388(GKA)-388(proto)-27(cols)-388(using)-388(the)-388(star)-388(top)-28(ology)]TJ
T*
[(includes)-436(NLKW)-437(proto)-28(col)-437([NLKW05],)-462(NLKKW)-437(proto)-28(col)-437([NLK)]TJ
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[(04],)-462(NHS)-437([NKW05])-437(and)-437(EKE-D)]TJ
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[(proto)-27(col)-334([BLLH06].)]TJ
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T*
[(Adv)63(an)32(tages:)]TJ
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71.1 0 Td
[(Presence)-285(of)-285(con)27(troller)-284(no)-28(de)-285(impro)27(v)27(es)-284(the)-285(computation)-285(and)-285(comm)26(unication)-284(e\261ciency)]TJ
-71.1 -21.92 Td
[(of)-333(user)-333(no)-28(des.)-444(The)-334(con)27(troller)-332(no)-28(de)-333(can)-334(also)-333(handle)-333(user)-334(join)-333(and)-333(lea)26(v)28(e)-332(ev)27(en)27(ts)-332(more)-333(e\261cien)27(tly)83(.)]TJ
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(Limitations:)Tj
/T1_1 10.91 Tf
70.81 0 Td
[(Con)27(troller)-332(no)-28(de)-334(ma)27(y)-332(b)-28(e)-333(a)-334(single)-333(p)-28(oin)27(t)-332(of)-334(failure.)]TJ
/T1_2 14.34 Tf
-70.81 -45.44 Td
[(2.10)-1124(A)30(ttac)31(ks)-374(on)-375(Group)-375(Key)-375(Managemen)30(t)-374(Proto)-31(cols)]TJ
/T1_1 10.91 Tf
0 -32.72 TD
[(Group)-416(k)27(ey)-416(managemen)27(t)-416(\(GKM\))-417(proto)-27(cols)-417(in)-417(wireless)-416(net)26(w)28(orks)-415(are)-417(vulnerable)-417(to)-416(sev)26(eral)-415(attac)26(ks)]TJ
0 -21.92 TD
[(due)-422(to)-422(the)-422(nature)-422(of)-422(the)-422(transmission)-422(medium)-422(in)-422(wireless)-422(net)27(w)27(orks.)-709(In)-422(this)-422(section,)-445(w)27(e)-421(presen)27(t)]TJ
0 -21.91 TD
[(some)-333(of)-333(the)-333(securit)26(y)-332(attac)27(ks)-333(that)-333(targets)-333(GKM)-334(proto)-27(cols)-334(in)-333(wireless)-333(net)26(w)28(orks.)]TJ
228.48 -50.8 Td
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T*
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[(Repla)27(y)-262(attac)27(ks)-263(includes)-263(an)27(y)-263(situation)-263(where)-264(the)-263(adv)26(ersary)-262(in)27(terferes)-263(with)-263(a)-264(GKM)]TJ
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[(proto)-27(col)-345(b)27(y)-344(insertion)-345(of)-345(a)-344(message,)-348(or)-345(part)-344(of)-345(a)-345(message,)-348(that)-344(has)-345(b)-28(een)-345(previously)-344(sen)26(t)-343(in)-345(another)]TJ
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[(GKM)-452(proto)-28(col)-453(run.)-803(The)-453(common)-453(coun)27(termeasure)-452(against)-453(repla)27(y)-452(attac)27(ks)-452(is)-453(through)-453(the)-453(use)-452(of)]TJ
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[(nonces)-333(and)-333(timestamps)-333(to)-334(ensure)-333(that)-333(the)-334(session)-333(k)27(ey)-333(generation)-333(is)-333(fresh)-334(for)-333(ev)27(ery)-333(proto)-27(col)-334(run.)]TJ
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[(The)-278(goal)-279(of)-279(this)-278(attac)26(k)-277(is)-279(for)-279(the)-279(adv)27(ersary)-278(to)-278(obtain)-279(v)54(aluable)-277(infor-)]TJ
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[(mem)27(b)-26(ers)-411(when)-411(they)-411(are)-411(in)-411(fact)-411(comm)27(unicating)-410(with)-411(the)-411(adv)27(ersary)83(.)-676(The)-411(adv)27(ersary's)-410(device)-411(pre-)]TJ
T*
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[(This)-427(attac)26(k)-427(is)-428(p)-28(ossible)-428(if)-428(the)-429(proto)-27(col)-429(is)-428(w)27(eak)-427(or)-428(if)-429(the)-428(k)27(ey)-427(generated)-429(is)-428(w)27(eak)]TJ
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[(and)-453(is)-454(relativ)27(ely)-453(easy)-453(to)-454(guess)-454(once)-453(su\261cien)27(t)-453(evidence)-454(is)-453(a)26(v)56(ailable.)-804(Examples)-454(of)-454(`evidence')-453(are)]TJ
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[(pairs)-436(of)-436(information)-436(suc)26(h)-435(as)-436(a)-436(plain)26(text)-435(and)-436(its)-437(corresp)-27(onding)-437(ciphertext)-436(or)-436(a)-437(plain)27(text)-435(and)-436(its)]TJ
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[(formed)-368(from)-368(a)-368(passw)27(ord)-367(that)-368(is)-368(easily)-369(remem)27(b)-27(ered)-368(b)27(y)-367(h)27(uman.)-548(In)-368(this)-368(situation,)-377(the)-368(attac)27(k)27(er)-367(can)]TJ
T*
[(guess)-400(the)-400(set)-400(of)-401(v)55(alues)-400(that)-400(are)-400(practically)-401(used)-400(for)-400(passw)27(ords)-400(as)-400(the)-400(e\256ectiv)26(e)-399(k)27(ey)-399(length)-401(in)-400(this)]TJ
0 -21.91 TD
[(case)-333(w)27(ould)-332(b)-28(e)-333(m)26(uc)28(h)-332(smaller)-334(than)-333(the)-333(acceptable)-334(k)27(ey)-332(length)-333(in)-334(mo)-28(dern)-333(cryptosystem.)]TJ
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[(Denial-of-Service)-395(\(DoS\))-395(A)31(ttac)32(k)]TJ
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182.14 0 Td
[(GKM)-344(proto)-27(cols)-344(for)-344(wireless)-344(net)27(w)28(orks)-343(are)-344(vulnerable)-344(to)-343(DoS)]TJ
-182.14 -21.92 Td
[(attac)27(ks)-470(as)-472(DoS)-471(attac)26(ks)-470(can)-472(b)-28(e)-471(easily)-472(launc)27(hed)-471(b)27(y)-470(the)-472(adv)27(ersary)-471(to)-471(disrupt)-472(GKM)-471(services)-472(and)]TJ
0 -21.91 TD
[(halt)-437(secure)-438(group)-438(comm)27(unications.)-757(Ho)27(w)28(ev)28(er,)-463(most)-438(GKM)-437(proto)-28(cols)-438(in)-438(curren)27(t)-437(literature)-437(do)-438(not)]TJ
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[(discuss)-327(DoS)-327(attac)27(ks.)-441(W)82(e)-326(examined)-328(the)-327(problem)-327(of)-327(DoS)-327(attac)27(ks)-327(against)-327(GKM)-327(proto)-28(cols)-327(in)-327(wireless)]TJ
228.48 -48.06 Td
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[(2.11)-1124(Denial-of-Service)-375(A)30(ttac)31(ks)-374(and)-375(Coun)30(termeasures)]TJ
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[(users)-451(from)-452(completing)-452(the)-452(proto)-27(col)-452(and)-452(establishing)-452(a)-452(group)-451(k)26(ey)84(,)-481(th)27(us)-451(prev)27(en)28(ting)-451(secure)-452(group)]TJ
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[(comm)27(unications)-420(from)-420(taking)-421(place.)-707(DoS)-421(attac)27(ks)-420(are)-421(usually)-421(targeted)-421(against)-420(serv)26(ers/con)28(trollers)]TJ
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[(who)-362(are)-363(required)-363(to)-363(in)27(teract)-362(with)-363(the)-363(user)-363(no)-28(des.)-533(Examples)-363(of)-363(DoS)-363(attac)27(ks)-362(include)-363(depleting)-363(the)]TJ
T*
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[(to)-395(accept)-396(new)-396(connections)-395(and)-396(depleting)-396(the)-396(storage)-395(resources)-396(of)-396(the)-396(serv)27(er/con)28(troller.)-631(T)83(o)-395(date,)]TJ
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[(there)-367(ha)26(v)28(e)-367(b)-27(een)-368(sev)27(eral)-367(measures)-368(prop)-28(osed)-368(to)-367(reduce)-368(and)-368(prev)27(en)28(t)-367(the)-368(impact)-368(of)-368(DoS)-367(attac)26(ks.)-547(As)]TJ
T*
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13.33 -33.87 Td
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13.94 -21.92 Td
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T*
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T*
[(the)-399(state)-400(information)-400(returned)-400(to)-400(the)-400(serv)27(er)-399(to)-400(b)-28(e)-400(authen)27(ticated)-399(and)-400(this)-400(information)-400(ma)27(y)]TJ
0 -21.91 TD
[(also)-443(ha)27(v)28(e)-443(to)-444(b)-27(e)-444(con\257den)27(tial.)-775(Therefore,)-471(there)-444(is)-444(an)-443(o)26(v)28(erhead)-443(in)-443(b)-28(oth)-444(comm)27(unication)-443(and)]TJ
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[(computation)-357(incurred)-357(b)26(y)-356(transforming)-358(proto)-28(cols)-357(to)-358(pro)27(vide)-357(stateless)-357(connections.)-518(Karn)-357(and)]TJ
T*
[(Simpson)-304([KS99])-305(suggested)-305(a)-305(w)27(a)27(y)-304(for)-305(dela)27(ying)-304(the)-305(need)-305(for)-305(state)-305(at)-305(the)-305(serv)27(er)-304(through)-305(the)-305(use)]TJ
0 -21.91 TD
[(of)-302(co)-28(okies.)-434(Their)-303(idea)-303(is)-303(for)-303(the)-302(serv)26(er)-302(to)-302(send)-303(a)-303(co)-28(okie)-303(to)-303(the)-303(clien)27(t)-302(when)-303(the)-302(clien)26(t)-302(attempts)]TJ
0 -21.92 TD
[(to)-413(mak)27(e)-412(a)-414(connection.)-685(This)-414(pro)-28(cedure)-413(is)-414(similar)-413(to)-414(the)-413(use)-414(of)-414(co)-27(okies)-414(b)27(y)-413(the)-413(W)82(orld)-413(Wide)]TJ
T*
[(W)83(eb)-298(serv)27(ers)-298(but)-299(the)-299(co)-28(okies)-299(in)-299([KS99])-299(are)-299(a)-299(function)-299(of)-300(a)-299(secret)-299(kno)27(wn)-298(only)-299(to)-299(the)-299(serv)27(er)-298(and)]TJ
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0 -21.92 TD
[(connection)-342(state)-343(information)-342(for)-343(this)-343(request)-343(while)-342(the)-343(clien)27(t)-342(has)-343(to)-343(return)-343(the)-342(co)-28(okie)-343(in)-343(the)]TJ
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0 -21.92 TD
[(The)-310(idea)-311(is)-311(to)-311(ensure)-311(that)-311(b)-28(efore)-311(in)27(v)28(esting)-310(signi\257can)27(t)-310(resources,)-316(the)-311(serv)27(er)-310(is)-311(certain)-311(that)-311(the)]TJ
201.21 -40.91 Td
(77)Tj
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T*
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T*
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T*
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T*
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T*
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(n)Tj
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10.17 0 Td
(where)Tj
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31.53 0 Td
(r)Tj
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4.92 -1.63 Td
(0)Tj
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7.76 1.63 Td
(=)Tj
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11.51 0 Td
(r)Tj
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4.92 -1.63 Td
(n)Tj
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9.27 1.63 Td
(and)Tj
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21.19 0 Td
(r)Tj
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4.92 -1.63 Td
(n)Tj
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(+1)Tj
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19.49 1.63 Td
(=)Tj
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11.51 0 Td
(r)Tj
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4.92 -1.63 Td
(1)Tj
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8.36 1.63 Td
[(and)-332(for)-332(an)27(y)]TJ
/T1_3 10.91 Tf
-413.03 -21.91 Td
[(j)-335(<)-277(n)]TJ
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26.2 0 Td
[(,)-333(w)27(e)-333(consider)-333(the)-333(follo)26(wing)-332(t)27(w)28(o)-333(cases:)]TJ
-26.2 -21.92 Td
[(Case)-380(\(i\))]TJ
/T1_3 10.91 Tf
42.28 0 Td
[(j)-413(<)-356(k)]TJ
/T1_2 10.91 Tf
31.53 0 Td
[(:)-538(Then,)-392(compute)]TJ
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85.79 0 Td
(X)Tj
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13.78 0 Td
(=)Tj
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12.36 8.18 Td
(Q)Tj
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10.3 -3.15 Td
(k)Tj
0 -8.25 TD
(i)Tj
/T1_10 7.97 Tf
2.88 0 Td
(=)Tj
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6.59 0 Td
(j)Tj
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6.2 3.22 Td
(X)Tj
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9.03 -1.63 Td
(i)Tj
/T1_2 10.91 Tf
6.41 1.63 Td
[(mo)-27(d)]TJ
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23.93 0 Td
(p)Tj
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9.37 0 Td
(=)Tj
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12.37 0 Td
(g)Tj
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5.59 3.96 Td
(r)Tj
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3.82 -1.41 Td
(k)Tj
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4.57 1.41 Td
(r)Tj
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3.82 -1.41 Td
(k)Tj
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4.08 0 Td
(+1)Tj
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9.74 1.41 Td
(\241)Tj
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(r)Tj
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10.4 -1.22 Td
(j)Tj
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3.4 0 Td
(\241)Tj
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(1)Tj
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9.91 1.22 Td
(r)Tj
/T1_5 5.98 Tf
3.82 -1.22 Td
(j)Tj
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7.43 -2.74 Td
[(mo)-27(d)]TJ
/T1_3 10.91 Tf
23.93 0 Td
(p)Tj
/T1_2 10.91 Tf
[(.)-584(Since,)-392(the)-381(mem)27(b)-27(er)]TJ
/T1_12 10.91 Tf
-363.33 -21.92 Td
(U)Tj
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5.73 -1.77 Td
(k)Tj
/T1_2 10.91 Tf
10.39 1.77 Td
[(kno)28(ws)]TJ
/T1_3 10.91 Tf
34.41 0 Td
(r)Tj
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4.92 -1.77 Td
(k)Tj
/T1_2 10.91 Tf
5.12 1.77 Td
[(,)-521(then)-483(he)-484(also)-483(kno)26(ws)]TJ
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109.3 0 Td
(g)Tj
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5.59 3.96 Td
(r)Tj
/T1_5 5.98 Tf
3.82 -1.4 Td
(k)Tj
/T1_4 7.97 Tf
4.58 1.4 Td
(r)Tj
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3.82 -1.4 Td
(k)Tj
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4.07 0 Td
(+1)Tj
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10.24 -2.56 Td
[(.)-894(Therefore,)-521(the)-484(mem)27(b)-27(er)]TJ
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131.2 0 Td
(U)Tj
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5.73 -1.77 Td
(k)Tj
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10.39 1.77 Td
(obtains)Tj
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39.87 0 Td
(g)Tj
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5.59 3.96 Td
(r)Tj
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3.82 -1.21 Td
(j)Tj
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3.4 0 Td
(\241)Tj
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(1)Tj
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9.91 1.21 Td
(r)Tj
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3.82 -1.21 Td
(j)Tj
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10.16 -2.75 Td
(=)Tj
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14.24 0 Td
(X)Tj
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9.89 3.96 Td
(\241)Tj
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(1)Tj
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14.83 -3.96 Td
(\242)Tj
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-464.84 -21.91 Td
(g)Tj
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5.59 3.96 Td
(r)Tj
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3.82 -1.41 Td
(k)Tj
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4.58 1.41 Td
(r)Tj
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3.82 -1.41 Td
(k)Tj
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4.07 0 Td
(+1)Tj
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13.27 -2.55 Td
[(mo)-27(d)]TJ
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23.93 0 Td
(p)Tj
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9.12 0 Td
(\(if)Tj
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14.24 0 Td
(k)Tj
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9.05 0 Td
(=)Tj
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11.51 0 Td
(n)Tj
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[(,)-333(then)]TJ
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38.05 0 Td
(r)Tj
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4.92 -1.78 Td
(k)Tj
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4.62 0 Td
(+1)Tj
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14.35 1.78 Td
(=)Tj
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11.51 0 Td
(r)Tj
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4.92 -1.64 Td
(1)Tj
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4.73 1.64 Td
(\).)Tj
-186.1 -21.92 Td
[(Case)-457(\(ii\))]TJ
/T1_3 10.91 Tf
46.99 0 Td
[(j)-541(>)-484(k)]TJ
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35.16 0 Td
[(:)-691(Then,)-489(compute)]TJ
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89.35 0 Td
(X)Tj
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15.17 0 Td
(=)Tj
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13.76 8.18 Td
(Q)Tj
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10.3 -2.87 Td
(j)Tj
0 -8.83 TD
(i)Tj
/T1_10 7.97 Tf
2.88 0 Td
(=)Tj
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6.59 0 Td
(k)Tj
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6.93 3.52 Td
(X)Tj
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9.04 -1.63 Td
(i)Tj
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6.41 1.63 Td
[(mo)-27(d)]TJ
/T1_3 10.91 Tf
23.93 0 Td
(p)Tj
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10.77 0 Td
(=)Tj
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13.76 0 Td
(g)Tj
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5.59 3.96 Td
(r)Tj
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3.82 -1.22 Td
(j)Tj
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3.9 1.22 Td
(r)Tj
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3.82 -1.22 Td
(j)Tj
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3.41 0 Td
(+1)Tj
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9.74 1.22 Td
(\241)Tj
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(r)Tj
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10.4 -1.41 Td
(k)Tj
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4.07 0 Td
(\241)Tj
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(1)Tj
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9.91 1.41 Td
(r)Tj
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3.82 -1.41 Td
(k)Tj
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8.1 -2.55 Td
[(mo)-27(d)]TJ
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23.93 0 Td
(p)Tj
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10.47 0 Td
(\(if)Tj
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15.59 0 Td
(j)Tj
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10.4 0 Td
(=)Tj
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13.76 0 Td
(n)Tj
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6.54 0 Td
[(,)-488(then)]TJ
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(r)Tj
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4.92 -1.64 Td
(j)Tj
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3.88 0 Td
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14.35 1.64 Td
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11.51 0 Td
(r)Tj
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4.92 -1.64 Td
(1)Tj
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4.73 1.64 Td
[(\).)-438(Since,)-317(the)-314(mem)27(b)-27(er)]TJ
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103.58 0 Td
(U)Tj
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5.73 -1.78 Td
(k)Tj
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8.54 1.78 Td
[(kno)28(ws)]TJ
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32.56 0 Td
(r)Tj
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4.92 -1.78 Td
(k)Tj
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5.12 1.78 Td
[(,)-318(then)-313(he)-314(also)-314(kno)27(ws)]TJ
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99.68 0 Td
(g)Tj
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5.6 3.95 Td
(r)Tj
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3.82 -1.4 Td
(k)Tj
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4.07 0 Td
(\241)Tj
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(1)Tj
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9.91 1.4 Td
(r)Tj
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3.82 -1.4 Td
(k)Tj
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5.07 -2.55 Td
[(.)-437(Therefore,)-318(the)-314(mem)27(b)-27(er)]TJ
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120.3 0 Td
(U)Tj
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5.72 -1.78 Td
(k)Tj
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-462.75 -20.14 Td
(obtains)Tj
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38.23 0 Td
(g)Tj
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5.6 3.96 Td
(r)Tj
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3.82 -1.22 Td
(j)Tj
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3.9 1.22 Td
(r)Tj
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3.82 -1.22 Td
(j)Tj
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3.4 0 Td
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13.27 -2.74 Td
(=)Tj
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11.51 0 Td
(X)Tj
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12.31 0 Td
(\242)Tj
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5.46 0 Td
(g)Tj
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5.59 3.96 Td
(r)Tj
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3.82 -1.41 Td
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4.07 0 Td
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(1)Tj
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9.91 1.41 Td
(r)Tj
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3.82 -1.41 Td
(k)Tj
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8.1 -2.55 Td
[(mo)-27(d)]TJ
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23.93 0 Td
(p)Tj
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9.12 0 Td
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14.24 0 Td
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8.15 0 Td
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11.51 0 Td
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6.54 0 Td
[(,)-333(then)]TJ
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31.51 0 Td
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4.92 -1.64 Td
(j)Tj
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14.35 1.64 Td
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4.92 -1.64 Td
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4.73 1.64 Td
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[(Hence,)-333(the)-333(mem)27(b)-27(er)]TJ
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96.06 0 Td
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5.73 -1.77 Td
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8.75 1.77 Td
[(could)-333(obtain)]TJ
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63.02 0 Td
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3.82 -1.21 Td
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8.03 -2.75 Td
[(for)-333(all)-334(1)]TJ
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40.33 0 Td
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7.76 1.63 Td
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[(F)83(rom)-353(Lemma)-353(3,)-359(w)27(e)-353(kno)27(w)-352(that)-354(eac)27(h)-353(mem)27(b)-27(er)-353(can)-354(obtain)]TJ
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3.82 -1.21 Td
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(r)Tj
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3.82 -1.21 Td
(j)Tj
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8.25 -2.74 Td
[(for)-353(all)-354(1)]TJ
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41.13 0 Td
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(\267)Tj
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(n)Tj
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[(for)-353(an)26(y)-352(giv)27(en)]TJ
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[(for)-328(1)]TJ
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25.13 0 Td
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4.92 -1.64 Td
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7.76 1.64 Td
(=)Tj
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4.92 -1.64 Td
(n)Tj
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[(.)-442(Therefore,)-330(eac)26(h)-328(mem)27(b)-27(er)-328(can)-329(compute)-329(the)-329(agreed)-329(group)-329(k)26(ey)-328(in)-329(BD)-329(as)]TJ
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13.07 0 Td
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11.51 8.18 Td
(Q)Tj
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10.3 -3.15 Td
(n)Tj
0 -8.25 TD
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3.89 0 Td
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13.13 3.22 Td
(g)Tj
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5.59 3.96 Td
(r)Tj
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3.82 -1.21 Td
(j)Tj
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(\241)Tj
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3.82 -1.21 Td
(j)Tj
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7.81 -2.75 Td
(where)Tj
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31.31 0 Td
(r)Tj
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4.92 -1.63 Td
(0)Tj
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7.76 1.63 Td
(=)Tj
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11.51 0 Td
(r)Tj
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4.93 -1.63 Td
(n)Tj
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5.63 1.63 Td
[(.)-437(Hence,)-317(it)-312(is)-313(not)-313(necessary)-312(to)-313(carry)-312(out)-313(another)-313(exp)-27(onen)26(tiation)-311(as)]TJ
-152.31 -21.91 Td
[(in)-271(equation)-271(\(2.3\))-272(in)-271(Chapter)-271(2)-272(Section)-271(2.7.6.)-424(This)-271(will)-272(reduce)-271(b)27(y)]TJ
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20.5 0 Td
[(the)-271(n)27(um)28(b)-27(er)-271(of)-272(exp)-28(onen)27(tiations)]TJ
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[(required)-333(to)-333(compute)-333(group)-334(k)27(ey)]TJ
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[(in)-333(BD)-333(.)]TJ
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[(4.3)-1124(Authen)30(tication)-374(T)93(ec)31(hniques)-374(for)-375(Burmester-Desmedt)-375(\(BD\))]TJ
/T1_2 10.91 Tf
0 -32.72 TD
[(In)-332(this)-333(section,)-333(w)26(e)-332(describ)-27(e)-333(t)26(w)28(o)-332(curren)27(t)-332(metho)-28(ds)-333(of)-333(pro)27(viding)-332(authen)27(tication)-332(for)-333(the)-333(BD.)-333(The)-333(\257rst)]TJ
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T*
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[(w)27(a)28(y)-396(of)-397(pro)26(viding)-396(authen)27(tication)-396(for)-398(the)-397(BD)-397(is)-397(b)27(y)-397(the)-397(in)27(tuitiv)28(e)-396(metho)-28(d)-397(also)-398(men)27(tioned)-396(in)-397(pap)-28(ers)]TJ
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[(cation.)-512(This)-356(metho)-28(d)-356(has)-357(also)-356(b)-27(een)-357(used)-356(in)-356(pap)-28(ers)-356([KY03])-356(and)-356([NLKW04].)-513(The)-356(adv)54(an)28(tage)-355(of)-356(this)]TJ
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T*
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[(b)-27(e)-334(executed)-333(b)-28(efore)-333(the)-333(proto)-28(col)-334(is)-333(ran)-333(for)-334(the)-333(\257rst)-333(time.)-445(This)-333(metho)-28(d)-333(is)-333(describ)-28(ed)-334(as)-333(follo)27(ws:)]TJ
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129.82 0 Td
(y)Tj
/T1_3 7.97 Tf
5.35 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
6.74 1.64 Td
(=)Tj
/T1_4 10.91 Tf
11.84 0 Td
(g)Tj
/T1_3 7.97 Tf
5.59 3.95 Td
(x)Tj
/T1_5 5.98 Tf
4.77 -1.21 Td
(i)Tj
/T1_4 10.91 Tf
3.66 -2.74 Td
[(;)-166(x)]TJ
/T1_3 7.97 Tf
11.08 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
3.38 1.64 Td
[(\).)-498(First,)]TJ
/T1_2 10.91 Tf
42.59 0 Td
(U)Tj
/T1_3 7.97 Tf
5.72 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
7.22 1.64 Td
[(c)28(ho)-27(oses)]TJ
/T1_4 10.91 Tf
39.09 0 Td
(r)Tj
/T1_3 7.97 Tf
4.92 -1.64 Td
(i)Tj
/T1_1 10.91 Tf
6.74 1.64 Td
(2)Tj
/T1_4 10.91 Tf
10.63 0 Td
(Z)Tj
/T1_6 7.97 Tf
8.23 3.95 Td
(\244)Tj
/T1_3 7.97 Tf
-0.78 -6.65 Td
(q)Tj
/T1_0 10.91 Tf
-462.36 -19.22 Td
[(and)-333(computes)]TJ
/T1_4 10.91 Tf
69.74 0 Td
(z)Tj
/T1_3 7.97 Tf
5.07 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
6.41 1.64 Td
(=)Tj
/T1_4 10.91 Tf
11.51 0 Td
(g)Tj
/T1_3 7.97 Tf
5.6 3.96 Td
(r)Tj
/T1_5 5.98 Tf
3.82 -1.22 Td
(i)Tj
/T1_0 10.91 Tf
3.65 -2.74 Td
[(,)-333(sends)-334(out)]TJ
/T1_4 10.91 Tf
55.26 0 Td
(z)Tj
/T1_3 7.97 Tf
5.07 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
7.02 1.64 Td
(and)Tj
/T1_4 10.91 Tf
21.21 0 Td
(y)Tj
/T1_3 7.97 Tf
5.34 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
3.38 1.64 Td
(.)Tj
/T1_2 10.91 Tf
-203.08 -27.89 Td
[(Round)-524(2)]TJ
/T1_0 10.91 Tf
[(:)-444(Up)-28(on)-333(receipt)-333(of)-334(all)]TJ
/T1_4 10.91 Tf
140.99 0 Td
(z)Tj
/T1_3 7.97 Tf
5.07 -1.64 Td
(j)Tj
/T1_0 10.91 Tf
8.02 1.64 Td
(\(1)Tj
/T1_1 10.91 Tf
12.72 0 Td
(\267)Tj
/T1_4 10.91 Tf
11.51 0 Td
(j)Tj
/T1_1 10.91 Tf
8.15 0 Td
(\267)Tj
/T1_4 10.91 Tf
11.51 0 Td
(n)Tj
/T1_0 10.91 Tf
[(\),)-333(eac)27(h)]TJ
/T1_2 10.91 Tf
41.99 0 Td
(U)Tj
/T1_3 7.97 Tf
5.73 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
7.01 1.64 Td
(\(1)Tj
/T1_1 10.91 Tf
12.73 0 Td
(\267)Tj
/T1_4 10.91 Tf
11.51 0 Td
(i)Tj
/T1_1 10.91 Tf
6.79 0 Td
(\267)Tj
/T1_4 10.91 Tf
11.51 0 Td
(n)Tj
/T1_0 10.91 Tf
6.54 0 Td
[(\))-333(computes)]TJ
/T1_4 10.91 Tf
-130.37 -43.84 Td
(X)Tj
/T1_3 7.97 Tf
9.04 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
6.41 1.63 Td
(=)Tj
/T1_7 10.91 Tf
11.51 18.65 Td
(\303)Tj
/T1_4 10.91 Tf
9.91 -10.31 Td
(z)Tj
/T1_3 7.97 Tf
5.07 -1.63 Td
(i)Tj
/T1_8 7.97 Tf
2.88 0 Td
(+1)Tj
/T1_1 10.91 Tf
13.74 1.63 Td
(\242)Tj
/T1_4 10.91 Tf
5.46 0 Td
(y)Tj
/T1_3 7.97 Tf
5.73 5.8 Td
(c)Tj
/T1_5 5.98 Tf
3.67 -1.21 Td
(i)Tj
/T1_9 5.98 Tf
2.66 0 Td
(+1)Tj
/T1_3 7.97 Tf
-6.72 -7.84 Td
(i)Tj
/T1_8 7.97 Tf
2.89 0 Td
(+1)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 208.2 -151.68 cm
0 0 m
49.61 0 l
S
Q
Q
BT
/T1_4 10.91 Tf
1.0003 0 0 1.0003 280.2583 607.3345 Tm
(z)Tj
/T1_3 7.97 Tf
5.07 -1.63 Td
(i)Tj
/T1_6 7.97 Tf
2.88 0 Td
(\241)Tj
/T1_8 7.97 Tf
6.59 0 Td
(1)Tj
/T1_1 10.91 Tf
7.15 1.63 Td
(\242)Tj
/T1_4 10.91 Tf
5.45 0 Td
(y)Tj
/T1_3 7.97 Tf
5.74 5.8 Td
(c)Tj
/T1_5 5.98 Tf
3.67 -1.21 Td
(i)Tj
/T1_10 5.98 Tf
2.66 0 Td
(\241)Tj
/T1_9 5.98 Tf
(1)Tj
/T1_3 7.97 Tf
-6.72 -7.84 Td
(i)Tj
/T1_8 7.97 Tf
2.88 0 Td
(+1)Tj
/T1_7 10.91 Tf
15.44 29.93 Td
(!)Tj
/T1_3 7.97 Tf
8.63 -2.71 Td
(r)Tj
/T1_5 5.98 Tf
3.82 -1.22 Td
(i)Tj
/T1_8 7.97 Tf
3.16 1.22 Td
(+)Tj
/T1_3 7.97 Tf
6.59 0 Td
(c)Tj
/T1_5 5.98 Tf
3.66 -1.22 Td
(i)Tj
/T1_3 7.97 Tf
3.17 1.22 Td
(x)Tj
/T1_5 5.98 Tf
4.76 -1.22 Td
(i)Tj
/T1_0 10.91 Tf
-292.8 -47.11 Td
(where)Tj
/T1_4 10.91 Tf
31.54 0 Td
(c)Tj
/T1_3 7.97 Tf
4.72 -1.63 Td
(j)Tj
/T1_0 10.91 Tf
7.41 1.63 Td
(=)Tj
/T1_11 10.91 Tf
11.51 0 Td
(H)Tj
/T1_0 10.91 Tf
(\()Tj
/T1_4 10.91 Tf
11.97 0 Td
(z)Tj
/T1_3 7.97 Tf
5.07 -1.63 Td
(j)Tj
/T1_0 10.91 Tf
4.38 1.63 Td
(\))Tj
1.0003 0 0 1.0003 72 769.82 Tm
84.477 -186.8 Td
(for)Tj
/T1_4 10.91 Tf
16.693 0 Td
(j)Tj
/T1_0 10.91 Tf
8.14 0 Td
(=)Tj
/T1_4 10.91 Tf
11.51 0 Td
[(i;)-167(i)]TJ
/T1_1 10.91 Tf
14.79 0 Td
(\241)Tj
/T1_0 10.91 Tf
10.91 0 Td
(1)Tj
/T1_4 10.91 Tf
[(;)-166(i)]TJ
/T1_0 10.91 Tf
16.48 0 Td
[(+)-221(1)-334(and)-333(sends)-333(out)]TJ
/T1_4 10.91 Tf
89.79 0 Td
(X)Tj
/T1_3 7.97 Tf
9.03 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
3.39 1.63 Td
(.)Tj
/T1_2 10.91 Tf
-265.21 -27.89 Td
[(Computation)-524(of)-525(Key)]TJ
/T1_0 10.91 Tf
103.06 0 Td
(:)Tj
/T1_4 10.91 Tf
7.88 0 Td
(K)Tj
/T1_0 10.91 Tf
13.07 0 Td
(=)Tj
/T1_4 10.91 Tf
11.51 0 Td
(g)Tj
/T1_8 7.97 Tf
5.6 3.96 Td
(\()Tj
/T1_3 7.97 Tf
(r)Tj
/T1_5 5.98 Tf
7.11 -1 Td
(n)Tj
/T1_8 7.97 Tf
5.1 1 Td
(+)Tj
/T1_3 7.97 Tf
(c)Tj
/T1_5 5.98 Tf
10.25 -1 Td
(n)Tj
/T1_3 7.97 Tf
5.09 1 Td
(x)Tj
/T1_5 5.98 Tf
4.77 -1 Td
(n)Tj
/T1_8 7.97 Tf
5.1 1 Td
(\)\()Tj
/T1_3 7.97 Tf
(r)Tj
/T1_9 5.98 Tf
10.4 -1.11 Td
(1)Tj
/T1_8 7.97 Tf
4.15 1.11 Td
(+)Tj
/T1_3 7.97 Tf
6.59 0 Td
(c)Tj
/T1_9 5.98 Tf
3.66 -1.11 Td
(1)Tj
/T1_3 7.97 Tf
4.15 1.11 Td
(x)Tj
/T1_9 5.98 Tf
4.77 -1.11 Td
(1)Tj
/T1_8 7.97 Tf
4.15 1.11 Td
(\)+)Tj
/T1_12 7.97 Tf
9.88 5.97 Td
(P)Tj
/T1_5 5.98 Tf
8.93 -2.4 Td
(n)Tj
/T1_10 5.98 Tf
4.6 0 Td
(\241)Tj
/T1_9 5.98 Tf
(1)Tj
/T1_5 5.98 Tf
-4.6 -6.22 Td
(i)Tj
/T1_9 5.98 Tf
(=1)Tj
/T1_8 7.97 Tf
14.51 2.65 Td
(\()Tj
/T1_3 7.97 Tf
(r)Tj
/T1_5 5.98 Tf
7.11 -1.22 Td
(i)Tj
/T1_8 7.97 Tf
3.16 1.22 Td
(+)Tj
/T1_3 7.97 Tf
(c)Tj
/T1_5 5.98 Tf
10.25 -1.22 Td
(i)Tj
/T1_3 7.97 Tf
3.16 1.22 Td
(x)Tj
/T1_5 5.98 Tf
4.77 -1.22 Td
(i)Tj
/T1_8 7.97 Tf
3.16 1.22 Td
(\)\()Tj
/T1_3 7.97 Tf
(r)Tj
/T1_5 5.98 Tf
10.4 -1.22 Td
(i)Tj
/T1_9 5.98 Tf
(+1)Tj
/T1_8 7.97 Tf
12.4 1.22 Td
(+)Tj
/T1_3 7.97 Tf
6.59 0 Td
(c)Tj
/T1_5 5.98 Tf
3.67 -1.22 Td
(i)Tj
/T1_9 5.98 Tf
2.66 0 Td
(+1)Tj
/T1_3 7.97 Tf
9.74 1.22 Td
(x)Tj
/T1_5 5.98 Tf
4.76 -1.22 Td
(i)Tj
/T1_9 5.98 Tf
(+1)Tj
/T1_8 7.97 Tf
12.4 1.22 Td
(\))Tj
/T1_0 10.91 Tf
3.79 -3.96 Td
(.)Tj
-330.82 -27.89 Td
[(No)27(w,)-299(w)27(e)-290(con)26(v)28(ert)-290(the)-292(ab)-28(o)27(v)28(e)-290(VBD)-292(proto)-28(col)-291(in)27(to)-291(BD)-291(proto)-28(col)-291(as)-292(follo)27(ws:)-423(eac)27(h)-290(user)]TJ
/T1_2 10.91 Tf
382.31 0 Td
(U)Tj
/T1_3 7.97 Tf
5.72 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
6.56 1.64 Td
(\(1)Tj
/T1_1 10.91 Tf
12.72 0 Td
(\267)Tj
/T1_4 10.91 Tf
11.52 0 Td
(i)Tj
/T1_1 10.91 Tf
6.78 0 Td
(\267)Tj
/T1_4 10.91 Tf
11.51 0 Td
(n)Tj
/T1_0 10.91 Tf
(\),)Tj
-454.05 -21.92 Td
[(set)-389(\271)]TJ
/T1_4 10.91 Tf
16.99 0 Td
(z)Tj
/T1_3 7.97 Tf
5.07 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
6.41 1.63 Td
(=)Tj
/T1_4 10.91 Tf
11.51 0 Td
(z)Tj
/T1_3 7.97 Tf
5.07 -1.63 Td
(i)Tj
/T1_1 10.91 Tf
5.73 1.63 Td
(\242)Tj
/T1_4 10.91 Tf
5.37 0 Td
(y)Tj
/T1_3 7.97 Tf
5.74 4.97 Td
(c)Tj
/T1_5 5.98 Tf
3.67 -1.21 Td
(i)Tj
/T1_3 7.97 Tf
-4.06 -7.01 Td
(i)Tj
/T1_0 10.91 Tf
11.31 3.25 Td
(and)Tj
/T1_4 10.91 Tf
21.17 0 Td
(a)Tj
/T1_3 7.97 Tf
5.77 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
6.41 1.63 Td
(=)Tj
/T1_4 10.91 Tf
11.51 0 Td
(r)Tj
/T1_3 7.97 Tf
4.92 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
5.72 1.63 Td
(+)Tj
/T1_4 10.91 Tf
10.83 0 Td
(c)Tj
/T1_3 7.97 Tf
4.72 -1.63 Td
(i)Tj
/T1_4 10.91 Tf
3.38 1.63 Td
(x)Tj
/T1_3 7.97 Tf
6.24 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
6.41 1.63 Td
[(mo)-27(d)]TJ
/T1_4 10.91 Tf
23.93 0 Td
(q)Tj
/T1_0 10.91 Tf
8.86 0 Td
(where)Tj
/T1_4 10.91 Tf
31.49 0 Td
(c)Tj
/T1_3 7.97 Tf
4.72 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
6.41 1.63 Td
(=)Tj
/T1_11 10.91 Tf
11.51 0 Td
(H)Tj
/T1_0 10.91 Tf
7.73 0 Td
(\()Tj
/T1_4 10.91 Tf
(z)Tj
/T1_3 7.97 Tf
9.31 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
3.38 1.63 Td
[(\).)-443(Then,)-331(c)27(hanging)-329(round)-329(1)-330(and)-330(round)-330(2)-329(in)]TJ
-267.23 -21.92 Td
[(VBD)-333(as)-333(follo)27(ws:)]TJ
/T1_2 10.91 Tf
T*
[(Round)-524(1')]TJ
/T1_0 10.91 Tf
[(:)-443(Eac)26(h)-332(user)]TJ
/T1_2 10.91 Tf
103.91 0 Td
(U)Tj
/T1_3 7.97 Tf
5.73 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
7.01 1.63 Td
(\(1)Tj
/T1_1 10.91 Tf
12.73 0 Td
(\267)Tj
/T1_4 10.91 Tf
11.51 0 Td
(i)Tj
/T1_1 10.91 Tf
6.78 0 Td
(\267)Tj
/T1_4 10.91 Tf
11.52 0 Td
(n)Tj
/T1_0 10.91 Tf
6.54 0 Td
[(\))-333(sends)-333(out)-394(\271)]TJ
/T1_4 10.91 Tf
56.47 0 Td
(z)Tj
/T1_3 7.97 Tf
5.07 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
3.38 1.63 Td
(.)Tj
/T1_2 10.91 Tf
-230.65 -27.89 Td
[(Round)-524(2')]TJ
/T1_0 10.91 Tf
[(:)-443(Up)-28(on)-334(receipt)-333(of)-333(all)-471(\271)]TJ
/T1_4 10.91 Tf
146.72 0 Td
(z)Tj
/T1_3 7.97 Tf
5.07 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
3.38 1.64 Td
[(,)-333(eac)27(h)]TJ
/T1_2 10.91 Tf
31.2 0 Td
(U)Tj
/T1_3 7.97 Tf
5.73 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
7.01 1.64 Td
(\(1)Tj
/T1_1 10.91 Tf
12.73 0 Td
(\267)Tj
/T1_4 10.91 Tf
11.51 0 Td
(i)Tj
/T1_1 10.91 Tf
6.79 0 Td
(\267)Tj
/T1_4 10.91 Tf
11.51 0 Td
(n)Tj
/T1_0 10.91 Tf
6.54 0 Td
[(\))-333(computes)]TJ
59.54 2.76 Td
(\271)Tj
/T1_4 10.91 Tf
-3.13 -2.76 Td
(X)Tj
/T1_3 7.97 Tf
9.04 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
6.41 1.64 Td
[(=)-277(\()-60(\271)]TJ
/T1_4 10.91 Tf
15.75 0 Td
(z)Tj
/T1_3 7.97 Tf
5.07 -1.64 Td
(i)Tj
/T1_8 7.97 Tf
2.89 0 Td
(+1)Tj
/T1_4 10.91 Tf
11.31 1.64 Td
(=)Tj
/T1_0 10.91 Tf
6.11 0 Td
(\271)Tj
/T1_4 10.91 Tf
-0.66 0 Td
(z)Tj
/T1_3 7.97 Tf
5.08 -1.64 Td
(i)Tj
/T1_6 7.97 Tf
2.88 0 Td
(\241)Tj
/T1_8 7.97 Tf
(1)Tj
/T1_0 10.91 Tf
11.31 1.64 Td
(\))Tj
/T1_3 7.97 Tf
4.25 3.96 Td
(a)Tj
/T1_5 5.98 Tf
4.49 -1.22 Td
(i)Tj
/T1_0 10.91 Tf
7.3 -2.74 Td
[(and)-332(sends)]TJ
53.53 2.76 Td
(\271)Tj
/T1_4 10.91 Tf
-3.12 -2.76 Td
(X)Tj
/T1_3 7.97 Tf
9.03 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
3.38 1.64 Td
(.)Tj
/T1_2 10.91 Tf
-458.65 -27.89 Td
[(Computation)-524(of)-525(Key)]TJ
/T1_0 10.91 Tf
103.06 0 Td
(:)Tj
/T1_4 10.91 Tf
7.88 0 Td
(K)Tj
/T1_0 10.91 Tf
13.07 0 Td
(=)Tj
/T1_4 10.91 Tf
11.51 0 Td
(g)Tj
/T1_3 7.97 Tf
5.6 3.96 Td
(a)Tj
/T1_5 5.98 Tf
4.49 -1 Td
(n)Tj
/T1_3 7.97 Tf
5.1 1 Td
(a)Tj
/T1_9 5.98 Tf
4.5 -1.11 Td
(1)Tj
/T1_8 7.97 Tf
4.15 1.11 Td
(+)Tj
/T1_12 7.97 Tf
6.58 5.97 Td
(P)Tj
/T1_5 5.98 Tf
8.94 -2.4 Td
(n)Tj
/T1_10 5.98 Tf
4.6 0 Td
(\241)Tj
/T1_9 5.98 Tf
5.75 0 Td
(1)Tj
/T1_5 5.98 Tf
-10.35 -6.22 Td
(i)Tj
/T1_9 5.98 Tf
2.66 0 Td
(=1)Tj
/T1_3 7.97 Tf
13.25 2.65 Td
(a)Tj
/T1_5 5.98 Tf
4.5 -1.22 Td
(i)Tj
/T1_3 7.97 Tf
3.16 1.22 Td
(a)Tj
/T1_5 5.98 Tf
4.5 -1.22 Td
(i)Tj
/T1_9 5.98 Tf
2.66 0 Td
(+1)Tj
/T1_0 10.91 Tf
10.24 -2.74 Td
(.)Tj
-198.92 -27.89 Td
[(Then,)-333(w)27(e)-333(obtain)-333(a)-333(BD)-334(proto)-27(col.)-445(Hence,)-333(VBD)-333(proto)-28(col)-334(is)-333(secure)-333(if)-334(BD)-333(proto)-28(col)-333(is)-333(secure.)]TJ
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
6.1 w
q 1 0 0 1 464.82 -397.98 cm
0 0 m
0 6.1 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 88.9347 349.8024 Tm
(Next,)Tj
1.0003 0 0 1.0003 72 769.82 Tm
46.911 -419.9 Td
[(w)27(e)-352(pro)26(v)28(e)-353(that)-353(an)-354(adv)27(ersary)]TJ
/T1_1 10.91 Tf
134.849 0 Td
(A)Tj
/T1_0 10.91 Tf
12.57 0 Td
[(is)-353(not)-354(able)-354(to)-353(obtain)-354(the)-354(group)-354(k)27(ey)]TJ
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T*
[(m)27(ust)-363(b)-28(e)-364(con\257gured)-364(with)-365(unique)-364(net)27(w)28(ork)-364(la)27(y)28(er)-363(\(IP\))-365(addresses.)-537(Since)-364(MANETs)-365(are)-364(self-organizing)]TJ
0 -21.92 TD
[(and)-321(ha)26(v)28(e)-321(dynamic)-321(net)26(w)28(ork)-321(top)-27(ology)82(,)-323(the)-322(IP)-322(address)-322(assignmen)27(t)-321(should)-322(b)-27(e)-322(done)-322(automatically)-322(and)]TJ
T*
[(dynamically)83(.)-568(Hence,)-385(b)-28(esides)-375(handling)-375(dynamic)-374(ev)26(en)28(ts,)-384(GKA)-375(proto)-27(cols)-375(for)-375(wireless)-375(net)27(w)28(orks)-374(suc)27(h)]TJ
0 -21.91 TD
[(as)-333(MANETs)-333(should)-333(also)-334(address)-333(issues)-333(suc)26(h)-332(as)-333(IP)-334(address)-333(assignmen)27(t)-333(in)-333(the)-333(net)27(w)27(ork.)]TJ
225.76 -47.37 Td
(113)Tj
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[(04],)-364(the)-358(authors)-358(prop)-28(osed)-359(a)-358(secure)-358(auto)-28(con\257guration)-358(proto)-28(col)-358(for)-359(MANET)-358(that)-358(uses)]TJ
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[(threshold)-381(cryptograph)27(y)-381(tec)27(hniques.)-588(Ho)27(w)27(ev)28(er,)-392(that)-382(pap)-28(er)-381(did)-382(not)-381(describ)-28(e)-382(net)27(w)28(ork)-381(merging)-381(tec)27(h-)]TJ
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T*
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[(do)-27(es)-334(not)-333(describ)-28(e)-333(GKA)-333(for)-334(secure)-333(group)-333(comm)26(unication.)]TJ
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[(The)-319(most)-320(in)27(tuitiv)28(e)-319(metho)-28(d)-319(of)-320(pro)27(viding)-319(GKA)-319(with)-320(secure)-319(IP)-320(address)-319(auto)-28(con\257guration)-320(will)-319(b)-28(e)]TJ
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[(will)-309(result)-310(in)-309(a)-310(w)27(aste)-309(of)-310(energy)-309(for)-310(MANET)-309(no)-28(des)-310(that)-310(ha)27(v)28(e)-309(limited)-309(p)-28(o)27(w)28(er)-309(capabilities)-310(as)-309(they)-310(will)]TJ
T*
[(ha)27(v)28(e)-332(to)-334(p)-27(erform)-334(comm)27(unication)-332(and)-334(computation)-333(t)27(wice.)]TJ
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[(In)-428(the)-428(previous)-429(c)27(hapter,)-451(w)27(e)-427(ha)26(v)28(e)-427(seen)-429(that)-428(the)-428(BD)-428(proto)-28(col)-428(is)-429(suitable)-428(for)-428(GKA)-429(in)-428(wireless)]TJ
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T*
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[(to)-358(extend)-358(the)-358(BD)-359(proto)-27(col)-359(to)-358(handle)-358(dynamic)-359(ev)27(en)28(ts.)-518(In)-359([STW98],)-364(Steiner)-358(et)-359(al)-358(brie\260y)-358(suggested)]TJ
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[(a)-355(Join)-356(Proto)-27(col)-356(for)-355(adding)-356(a)-356(new)-355(mem)27(b)-27(er)-356(for)-355(the)-356(BD)-355(proto)-28(col)-356(while)-355(in)-356([DB05],)-361(Dutta)-355(and)-356(Barua)]TJ
T*
[(prop)-27(osed)-364(pro)27(v)56(ably)-362(secure)-364(constan)27(t)-362(round)-363(dynamic)-364(authen)27(ticated)-362(GKA)-363(proto)-28(cols)-363(\(Join)-364(and)-363(Lea)27(v)28(e)]TJ
0 -21.91 TD
[(Proto)-27(cols\))-310(based)-310(on)-310(the)-309(BD)-310(for)-310(dynamic)-310(scenario.)-436(Dutta)-310(and)-310(Barua's)-310(Lea)27(v)28(e)-309(proto)-28(col)-310(requires)-309(only)]TJ
0 -21.92 TD
[(the)-333(left)-333(and)-333(righ)26(t)-332(neigh)27(b)-27(ors)-333(of)-334(lea)27(ving)-332(users)-334(to)-333(c)27(hange)-332(their)-334(random)-333(secrets.)]TJ
16.93 -21.92 Td
[(In)-405(the)-405(\257rst)-405(part)-405(of)-405(this)-405(c)27(hapter,)-422(w)27(e)-404(sho)27(w)-404(that)-405(the)-405(suggested)-405(Join)-405(metho)-28(d)-405(for)-405(BD)-405(b)27(y)-404(Steiner)]TJ
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[(et)-357(al)-358(in)-358([STW98])-358(do)-27(es)-358(not)-358(pro)27(vide)-357(bac)27(kw)28(ard)-357(secrecy)-358(\(new)-358(users)-357(can)-358(disco)27(v)27(er)-356(previous)-358(k)27(eys)-357(used\).)]TJ
T*
[(Next,)-332(w)27(e)-332(sho)27(w)-332(that)-332(Dutta)-333(and)-333(Barua's)-332(Lea)27(v)27(e)-331(proto)-28(col)-333(in)-332([DB05])-333(do)-27(es)-333(not)-333(ac)27(hiev)28(e)-332(forw)27(ard)-331(secrecy)]TJ
T*
[(\(a)-317(lea)27(ving)-316(user)-317(can)-317(disco)27(v)28(er)-316(the)-317(new)-317(session)-317(k)27(ey)-316(used)-318(in)-317(subsequen)27(t)-316(sessions)-317(if)-317(an)27(y)-316(t)27(w)28(o)-316(consecutiv)26(e)]TJ
0 -21.91 TD
[(remaining)-333(users)-333(do)-333(not)-334(c)27(hange)-332(their)-334(random)-333(secrets\).)]TJ
16.93 -21.92 Td
[(In)-387(the)-388(second)-387(part)-388(of)-387(this)-387(c)26(hapter,)-400(w)27(e)-386(prop)-28(ose)-388(four)-387(e\261cien)27(t)-387(proto)-28(cols,)-401(namely)-387(the)-388(Initial)-387(k)27(ey)]TJ
-16.93 -21.91 Td
[(agreemen)27(t,)-461(Join,)-462(Lea)27(v)28(e)-435(and)-437(Merge)-436(proto)-28(cols,)-462(that)-436(pro)27(vide)-436(b)-27(oth)-437(authen)27(ticated)-435(GKA)-436(and)-437(secure)]TJ
0 -21.92 TD
[(IP)-448(address)-449(auto)-28(con\257guration)-449(sim)27(ultaneously)-448(for)-449(symmetric)-449(wireless)-449(net)27(w)28(orks)-448(suc)27(h)-448(as)-449(MANETs)]TJ
T*
[(where)-474(all)-474(no)-28(des)-474(ha)26(v)28(e)-473(equal)-475(limited)-474(computing)-475(capabilities.)-867(As)-475(compared)-474(to)-474(existing)-475(proto)-28(cols)]TJ
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[(proto)-27(cols,)-308(also)-301(pro)27(vide)-300(e\256ectiv)27(e)-300(and)-301(e\261cien)27(t)-300(solutions)-301(to)-301(the)-301(problem)-301(of)-301(frequen)26(t)-300(net)27(w)28(ork)-300(top)-28(ology)]TJ
225.76 -43.35 Td
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[(sim)27(ultaneously)-224(whenev)27(er)-225(a)-226(dynamic)-225(ev)27(en)27(t)-224(o)-28(ccurs.)-408(Our)-226(dynamic)-225(proto)-28(cols)-226(also)-225(reduce)-226(computational)]TJ
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[(and)-345(comm)26(unication)-344(costs)-346(for)-346(the)-346(no)-28(des)-345(as)-346(only)-346(certain)-346(no)-28(des)-346(p)-27(erform)-346(exp)-28(onen)27(tiations)-345(in)-346(the)-346(Join)]TJ
T*
[(and)-384(Merge)-385(Proto)-28(cols)-384(and)-385(only)-385(half)-385(the)-384(group)-385(broadcast)-385(messages)-384(in)-385(the)-385(\257rst)-385(round)-384(of)-385(the)-385(Lea)27(v)28(e)]TJ
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[(Proto)-27(col.)]TJ
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[(Our)-430(prop)-28(osed)-431(proto)-28(cols)-431(tak)27(e)-430(adv)55(an)28(tage)-430(of)-431(the)-431(broadcast)-430(nature)-431(of)-431(MANET)-431(as)-431(compared)-430(to)]TJ
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[(GDH)-484(where)-484(the)-484(mo)-28(de)-484(of)-485(comm)27(unication)-483(is)-485(unicast)-484(and)-484(eac)27(h)-484(user)]TJ
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T*
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T*
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T*
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[(and)-356(discussion)-357(section,)-362(w)27(e)-356(sho)27(w)-356(that)-356(despite)-357(ha)27(ving)-356(additional)-356(capabilities,)-363(our)-356(proto)-28(cols)-357(are)-356(still)]TJ
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[(5.2)-1124(Cryptanalysis)-375(of)-375(Steiner)-375(et)-375(al.)-500(Join)-375(Proto)-32(col)-375(for)-375(BD)]TJ
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-0.85 -7.2 Td
(n)Tj
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5.13 0 Td
(+1)Tj
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21.28 2.7 Td
(=)Tj
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18.44 0 Td
(g)Tj
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5.6 4.5 Td
(r)Tj
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3.82 -1.11 Td
(n)Tj
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4.6 0 Td
(+1)Tj
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9.73 1.11 Td
(r)Tj
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3.82 -1.11 Td
(1)Tj
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4.15 1.11 Td
(\241)Tj
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6.59 0 Td
(r)Tj
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4.05 2.81 Td
(0)Tj
/T1_7 5.98 Tf
-0.23 -4.8 Td
(n)Tj
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5.1 1.99 Td
(r)Tj
/T1_7 5.98 Tf
3.82 -1.11 Td
(n)Tj
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4.6 0 Td
(+1)Tj
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13.26 -3.39 Td
[(mo)-27(d)]TJ
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23.93 0 Td
(p;)Tj
-135.91 -24.91 Td
(X)Tj
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9.89 4.51 Td
(0)Tj
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-0.85 -7.2 Td
(n)Tj
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15.59 2.69 Td
(=)Tj
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18.44 0 Td
(g)Tj
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5.6 4.51 Td
(r)Tj
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4.05 2.81 Td
(0)Tj
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-0.23 -4.81 Td
(n)Tj
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5.09 2 Td
(r)Tj
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3.82 -1.11 Td
(n)Tj
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4.6 0 Td
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9.74 1.11 Td
(\241)Tj
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6.59 0 Td
(r)Tj
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3.82 -1.11 Td
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4.6 0 Td
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5.75 0 Td
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(r)Tj
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4.06 2.81 Td
(0)Tj
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(n)Tj
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8.63 -2.51 Td
[(mo)-27(d)]TJ
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23.93 0 Td
(p;)Tj
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(X)Tj
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9.89 4.5 Td
(0)Tj
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(n)Tj
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6.59 0 Td
(1)Tj
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14.69 2.7 Td
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5.6 4.5 Td
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3.82 -1.11 Td
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4.6 0 Td
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(1)Tj
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4.15 1.11 Td
(r)Tj
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4.06 2.81 Td
(0)Tj
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-0.24 -4.8 Td
(n)Tj
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5.1 1.99 Td
(\241)Tj
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(r)Tj
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10.4 -1.11 Td
(n)Tj
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4.6 0 Td
(\241)Tj
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(1)Tj
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9.91 1.11 Td
(r)Tj
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3.82 -1.11 Td
(n)Tj
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4.6 0 Td
(\241)Tj
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5.75 0 Td
(2)Tj
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7.68 -3.39 Td
[(mo)-27(d)]TJ
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23.93 0 Td
(p)Tj
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-309.9 -39.65 Td
[(resp)-27(ectiv)27(ely)83(.)-551(All)-369(other)]TJ
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111.13 0 Td
(X)Tj
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9.04 -1.63 Td
(i)Tj
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7.4 1.63 Td
[(for)-369(2)]TJ
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26.22 0 Td
(\267)Tj
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12.16 0 Td
(i)Tj
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7.44 0 Td
(\267)Tj
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12.16 0 Td
(n)Tj
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9.23 0 Td
(\241)Tj
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11.17 0 Td
[(2)-368(are)-370(tak)27(en)-368(from)-369(the)-369(previous)-369(run)-369(of)-370(the)-369(BD)-369(proto)-28(col.)]TJ
-205.95 -21.91 Td
[(Finally)83(,)-341(all)-341(group)-340(mem)27(b)-27(ers,)-342(including)]TJ
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182.16 0 Td
(U)Tj
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5.72 -1.64 Td
(n)Tj
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(+1)Tj
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20.17 1.64 Td
[(compute)-339(the)-341(new)-340(group)-340(k)26(ey)-339(in)-340(the)-340(usual)-341(BD)-340(approac)27(h)]TJ
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[(as)-333(describ)-28(ed)-333(in)-333(Section)-334(2.7.6,)-333(where)-333(the)-334(new)-333(group)-333(k)27(ey)83(,)]TJ
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267.11 0 Td
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10.04 3.96 Td
(0)Tj
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6.43 -3.96 Td
(is:)Tj
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-160.27 -39.64 Td
(K)Tj
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(0)Tj
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5.82 -4.5 Td
(=)Tj
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11.52 0 Td
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5.59 4.5 Td
(r)Tj
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3.82 -1.1 Td
(1)Tj
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4.15 1.1 Td
(r)Tj
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3.82 -1.1 Td
(2)Tj
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4.15 1.1 Td
(+)Tj
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(r)Tj
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10.41 -1.1 Td
(2)Tj
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4.14 1.1 Td
(r)Tj
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3.83 -1.1 Td
(3)Tj
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4.15 1.1 Td
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(\242\242\242)Tj
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20.22 0 Td
(r)Tj
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3.82 -1.1 Td
(n)Tj
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4.6 0 Td
(\241)Tj
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4.06 2.81 Td
(0)Tj
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-0.24 -4.8 Td
(n)Tj
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5.1 1.99 Td
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6.59 0 Td
(r)Tj
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4.05 2.81 Td
(0)Tj
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(n)Tj
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5.09 1.99 Td
(r)Tj
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3.82 -1.1 Td
(n)Tj
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9.74 1.1 Td
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3.82 -1.1 Td
(n)Tj
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9.74 1.1 Td
(r)Tj
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3.82 -1.1 Td
(1)Tj
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7.67 -3.4 Td
[(mo)-28(d)]TJ
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23.94 0 Td
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[(Ho)27(w)28(ev)28(er)-328(this)-329(metho)-28(d)-329(do)-28(es)-329(not)-329(pro)27(vide)-328(bac)26(kw)28(ard)-328(secrecy)-329(as)-329(the)-329(new)-329(mem)27(b)-27(er)]TJ
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14.91 1.64 Td
[(can)-328(reco)26(v)28(er)-328(the)]TJ
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[(previous)-395(group)-396(k)27(ey)-395(shared)-396(b)27(y)-395(the)-395(group)-396(mem)27(b)-27(er)]TJ
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240.81 0 Td
(U)Tj
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5.72 -1.64 Td
(i)Tj
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7.7 1.64 Td
[(for)-395(1)]TJ
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26.99 0 Td
(\267)Tj
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12.64 0 Td
(i)Tj
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(\267)Tj
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12.64 0 Td
(n)Tj
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[(.)-631(W)82(e)-395(sho)27(w)-394(this)-396(as)-396(follo)27(ws)-395(\(for)]TJ
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[(simplicit)27(y)84(,)-347(\\)-278(mo)-28(d)]TJ
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84.44 0 Td
(p)Tj
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[(")-344(is)-345(omitted)-345(from)-345(the)-345(expressions)-345(if)-345(no)-345(confusion)-345(arises\):)-467(As)]TJ
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296.9 0 Td
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5.72 -1.63 Td
(n)Tj
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(+1)Tj
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20.22 1.63 Td
[(kno)28(ws)-344(all)]TJ
51.3 2.76 Td
(\271)Tj
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-3.12 -2.76 Td
(X)Tj
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(i)Tj
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-464.49 -20.28 Td
[(for)-333(1)]TJ
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25.17 0 Td
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11.52 0 Td
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6.78 0 Td
(\267)Tj
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11.52 0 Td
(n)Tj
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8.97 0 Td
[(+)-221(1)-334(where)]TJ
81.8 -45.79 Td
(\271)Tj
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-3.13 -2.76 Td
(X)Tj
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(i)Tj
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6.4 1.63 Td
(=)Tj
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11.52 25.63 Td
(8)Tj
0 -9.81 TD
(>)Tj
0 -3.27 TD
(<)Tj
0 -19.63 TD
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0 -3.28 TD
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14.67 19.67 Td
(X)Tj
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9.04 -1.64 Td
(i)Tj
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17.24 1.64 Td
[(if)-333(2)]TJ
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18.48 0 Td
(\267)Tj
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11.51 0 Td
(i)Tj
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6.79 0 Td
(\267)Tj
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11.51 0 Td
(n)Tj
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8.97 0 Td
(\241)Tj
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10.91 0 Td
(2)Tj
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(;)Tj
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(X)Tj
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9.89 3.96 Td
(0)Tj
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-0.85 -7.01 Td
(i)Tj
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17.24 3.05 Td
(if)Tj
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10 0 Td
(i)Tj
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6.79 0 Td
[(=)-277(1)]TJ
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[(;)-166(n;)-167(n)]TJ
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42.17 0 Td
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10.91 0 Td
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[(;)-166(n)]TJ
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19.27 0 Td
[(+)-221(1)]TJ
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16.36 0 Td
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-316.04 -29.12 Td
[(The)-363(mem)27(b)-27(er)]TJ
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64.92 0 Td
(U)Tj
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5.72 -1.64 Td
(n)Tj
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(+1)Tj
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20.42 1.64 Td
[(\257rst)-364(computes)]TJ
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71.71 0 Td
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5.59 3.96 Td
(r)Tj
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3.82 -1.11 Td
(n)Tj
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9.74 1.11 Td
(r)Tj
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3.82 -1.11 Td
(1)Tj
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8.23 -2.85 Td
(=)Tj
15.19 2.75 Td
(\271)Tj
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(X)Tj
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(n)Tj
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19.1 1.64 Td
(\242)Tj
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5.67 0 Td
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(r)Tj
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4.05 2.81 Td
(0)Tj
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(n)Tj
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5.09 2 Td
(r)Tj
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(n)Tj
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4.6 0 Td
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14.21 -2.85 Td
[(and)-363(recursiv)27(ely)-363(compute)]TJ
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120.78 0 Td
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5.97 3.96 Td
(\271)Tj
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3.82 -1.22 Td
(j)Tj
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4.28 1.22 Td
(\271)Tj
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13.82 -2.74 Td
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15.19 2.75 Td
(\271)Tj
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(X)Tj
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(j)Tj
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7.02 1.64 Td
(\242)Tj
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(g)Tj
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5.97 3.96 Td
(\271)Tj
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3.82 -1.22 Td
(j)Tj
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3.41 0 Td
(\241)Tj
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5.75 0 Td
(1)Tj
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4.53 1.22 Td
(\271)Tj
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-0.38 0 Td
(r)Tj
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3.82 -1.22 Td
(j)Tj
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7.2 -2.74 Td
[(for)-256(1)]TJ
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24.34 0 Td
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11.51 0 Td
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8.15 0 Td
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11.51 0 Td
(n)Tj
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7.29 0 Td
[(+)-69(1)-256(where)-302(\271)]TJ
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48.19 0 Td
(r)Tj
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4.92 -1.63 Td
(n)Tj
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(+2)Tj
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19.48 1.63 Td
(=)Tj
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11.51 0 Td
(r)Tj
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4.92 -1.63 Td
(1)Tj
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4.73 1.63 Td
[(,)-317(\271)]TJ
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6 0 Td
(r)Tj
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(n)Tj
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8.66 1.63 Td
(=)Tj
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11.52 0 Td
(r)Tj
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5.22 3.96 Td
(0)Tj
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(n)Tj
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5.63 2.69 Td
[(,)-317(\271)]TJ
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6 0 Td
(r)Tj
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4.92 -1.63 Td
(n)Tj
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14.35 1.63 Td
(=)Tj
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(r)Tj
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4.92 -1.63 Td
(n)Tj
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(+1)Tj
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19.25 1.63 Td
[(and)-301(\271)]TJ
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20.37 0 Td
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(i)Tj
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(r)Tj
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4.92 -1.63 Td
(i)Tj
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6.18 1.63 Td
[(for)-256(1)]TJ
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24.34 0 Td
(\267)Tj
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11.51 0 Td
(i)Tj
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(n)Tj
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7.3 0 Td
(\241)Tj
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[(1.)-418(Hence,)]TJ
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5.73 -1.63 Td
(n)Tj
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14.96 1.63 Td
[(kno)27(ws)]TJ
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32.79 0 Td
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5.59 3.96 Td
(r)Tj
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3.83 -1.21 Td
(j)Tj
/T1_1 7.97 Tf
3.9 1.21 Td
(r)Tj
/T1_7 5.98 Tf
3.82 -1.21 Td
(j)Tj
/T1_6 5.98 Tf
3.4 0 Td
(+1)Tj
/T1_2 10.91 Tf
13.88 -2.75 Td
[(for)-334(1)]TJ
/T1_9 10.91 Tf
25.2 0 Td
(\267)Tj
/T1_5 10.91 Tf
11.53 0 Td
(j)Tj
/T1_9 10.91 Tf
8.16 0 Td
(\267)Tj
/T1_5 10.91 Tf
11.53 0 Td
(n)Tj
/T1_9 10.91 Tf
8.98 0 Td
(\241)Tj
/T1_2 10.91 Tf
10.91 0 Td
[(2)-334(so)]TJ
/T1_0 10.91 Tf
22.5 0 Td
(U)Tj
/T1_1 7.97 Tf
5.72 -1.63 Td
(n)Tj
/T1_4 7.97 Tf
(+1)Tj
/T1_2 10.91 Tf
20.1 1.63 Td
[(w)27(ould)-333(obtain)]TJ
/T1_5 10.91 Tf
65.76 0 Td
(g)Tj
/T1_1 7.97 Tf
5.59 3.96 Td
(r)Tj
/T1_7 5.98 Tf
3.82 -0.99 Td
(n)Tj
/T1_1 7.97 Tf
5.1 0.99 Td
(r)Tj
/T1_6 5.98 Tf
3.82 -1.1 Td
(1)Tj
/T1_2 10.91 Tf
8.29 -2.86 Td
(and)Tj
/T1_5 10.91 Tf
21.22 0 Td
(g)Tj
/T1_1 7.97 Tf
5.59 3.96 Td
(r)Tj
/T1_7 5.98 Tf
3.82 -1.1 Td
(n)Tj
/T1_8 5.98 Tf
4.6 0 Td
(\241)Tj
/T1_6 5.98 Tf
(1)Tj
/T1_1 7.97 Tf
9.91 1.1 Td
(r)Tj
/T1_7 5.98 Tf
3.82 -0.99 Td
(n)Tj
/T1_2 10.91 Tf
9.24 -2.97 Td
(from)Tj
/T1_5 10.91 Tf
25.79 0 Td
(X)Tj
/T1_4 7.97 Tf
9.03 -1.63 Td
(1)Tj
/T1_2 10.91 Tf
7.78 1.63 Td
(=)Tj
/T1_5 10.91 Tf
11.53 0 Td
(g)Tj
/T1_1 7.97 Tf
5.59 3.96 Td
(r)Tj
/T1_6 5.98 Tf
3.82 -1.1 Td
(1)Tj
/T1_1 7.97 Tf
4.15 1.1 Td
(r)Tj
/T1_6 5.98 Tf
3.82 -1.1 Td
(2)Tj
/T1_3 7.97 Tf
4.15 1.1 Td
(\241)Tj
/T1_1 7.97 Tf
(r)Tj
/T1_7 5.98 Tf
10.41 -0.99 Td
(n)Tj
/T1_1 7.97 Tf
5.09 0.99 Td
(r)Tj
/T1_6 5.98 Tf
3.82 -1.1 Td
(1)Tj
/T1_2 10.91 Tf
-463.22 -24.77 Td
(and)Tj
/T1_5 10.91 Tf
21.86 0 Td
(X)Tj
/T1_1 7.97 Tf
9.04 -1.64 Td
(n)Tj
/T1_3 7.97 Tf
(\241)Tj
/T1_4 7.97 Tf
(1)Tj
/T1_2 10.91 Tf
20.58 1.64 Td
(=)Tj
/T1_5 10.91 Tf
12.61 0 Td
(g)Tj
/T1_1 7.97 Tf
5.59 3.96 Td
(r)Tj
/T1_7 5.98 Tf
3.82 -1.11 Td
(n)Tj
/T1_8 5.98 Tf
4.6 0 Td
(\241)Tj
/T1_6 5.98 Tf
(1)Tj
/T1_1 7.97 Tf
9.91 1.11 Td
(r)Tj
/T1_7 5.98 Tf
3.82 -1 Td
(n)Tj
/T1_3 7.97 Tf
5.09 1 Td
(\241)Tj
/T1_1 7.97 Tf
6.59 0 Td
(r)Tj
/T1_7 5.98 Tf
3.82 -1.11 Td
(n)Tj
/T1_8 5.98 Tf
4.6 0 Td
(\241)Tj
/T1_6 5.98 Tf
5.75 0 Td
(2)Tj
/T1_1 7.97 Tf
4.15 1.11 Td
(r)Tj
/T1_7 5.98 Tf
3.82 -1.11 Td
(n)Tj
/T1_8 5.98 Tf
4.6 0 Td
(\241)Tj
/T1_6 5.98 Tf
(1)Tj
/T1_2 10.91 Tf
14.7 -2.85 Td
[(resp)-27(ectiv)27(ely)-393(as)]TJ
/T1_0 10.91 Tf
74.17 0 Td
(U)Tj
/T1_1 7.97 Tf
5.73 -1.64 Td
(n)Tj
/T1_4 7.97 Tf
(+1)Tj
/T1_2 10.91 Tf
20.75 1.64 Td
[(kno)28(ws)]TJ
/T1_5 10.91 Tf
33.43 0 Td
(g)Tj
/T1_1 7.97 Tf
5.6 3.96 Td
(r)Tj
/T1_6 5.98 Tf
3.82 -1.11 Td
(1)Tj
/T1_1 7.97 Tf
4.15 1.11 Td
(r)Tj
/T1_6 5.98 Tf
3.82 -1.11 Td
(2)Tj
/T1_2 10.91 Tf
8.94 -2.85 Td
(and)Tj
/T1_5 10.91 Tf
21.86 0 Td
(g)Tj
/T1_1 7.97 Tf
5.6 3.96 Td
(r)Tj
/T1_7 5.98 Tf
3.82 -1.11 Td
(n)Tj
/T1_8 5.98 Tf
4.6 0 Td
(\241)Tj
/T1_6 5.98 Tf
5.75 0 Td
(2)Tj
/T1_1 7.97 Tf
4.15 1.11 Td
(r)Tj
/T1_7 5.98 Tf
3.82 -1.11 Td
(n)Tj
/T1_8 5.98 Tf
4.6 0 Td
(\241)Tj
/T1_6 5.98 Tf
5.75 0 Td
(1)Tj
/T1_2 10.91 Tf
4.65 -2.85 Td
[(.)-625(As)-394(suc)27(h,)]TJ
/T1_0 10.91 Tf
55.08 0 Td
(U)Tj
/T1_1 7.97 Tf
5.73 -1.64 Td
(n)Tj
/T1_4 7.97 Tf
5.13 0 Td
(+1)Tj
/T1_2 10.91 Tf
15.61 1.64 Td
(can)Tj
-451.51 -21.92 Td
[(obtain)-364(the)-364(previous)-365(group)-364(k)27(ey)-364(as)]TJ
/T1_5 10.91 Tf
162.17 0 Td
(K)Tj
/T1_2 10.91 Tf
13.64 0 Td
(=)Tj
/T1_5 10.91 Tf
12.08 0 Td
(g)Tj
/T1_1 7.97 Tf
5.59 3.96 Td
(r)Tj
/T1_7 5.98 Tf
3.82 -1 Td
(n)Tj
/T1_1 7.97 Tf
5.1 1 Td
(r)Tj
/T1_6 5.98 Tf
3.82 -1.11 Td
(1)Tj
/T1_9 10.91 Tf
7.29 -2.85 Td
(\242)Tj
/T1_10 10.91 Tf
5.68 8.18 Td
(Q)Tj
/T1_1 7.97 Tf
10.3 -3.15 Td
(n)Tj
/T1_3 7.97 Tf
(\241)Tj
/T1_4 7.97 Tf
(1)Tj
/T1_1 7.97 Tf
0 -8.25 TD
(j)Tj
/T1_4 7.97 Tf
3.89 0 Td
(=1)Tj
/T1_5 10.91 Tf
14.38 3.22 Td
(g)Tj
/T1_1 7.97 Tf
5.6 3.96 Td
(r)Tj
/T1_7 5.98 Tf
3.82 -1.22 Td
(j)Tj
/T1_1 7.97 Tf
3.9 1.22 Td
(r)Tj
/T1_7 5.98 Tf
3.82 -1.22 Td
(j)Tj
/T1_6 5.98 Tf
3.4 0 Td
(+1)Tj
/T1_2 10.91 Tf
10.24 -2.74 Td
[(.)-537(Therefore,)-372(Steiner)-365(el)-364(al.)-538(metho)-28(d)-364(do)-28(es)]TJ
-278.54 -21.91 Td
[(not)-333(pro)27(vide)-332(bac)26(kw)28(ard)-332(secrecy)-333(in)-334(the)-333(group)-333(k)26(ey)-332(agreemen)27(t.)]TJ
225.76 -114.29 Td
(116)Tj
ET
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1 0 0 1 -62.5 824 cm
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BT
/T1_0 14.34 Tf
1.0003 0 0 1.0003 72 758.8569 Tm
(5.3)Tj
1.0003 0 0 1.0003 72 769.82 Tm
36.739 -10.96 Td
[(Cryptanalysis)-375(of)-375(Dutta)-375(and)-375(Barua's)-375(Lea)30(v)31(e)-374(Proto)-31(col)]TJ
/T1_1 10.91 Tf
-36.739 -32.71 Td
[(In)-359([DB05],)-365(Dutta)-360(and)-359(Barua)-359(extended)-360(the)-359(w)27(ork)-358(of)-360(Burmester)-359(and)-359(Desmedt)-359([BD95])-360(and)-359(prop)-28(osed)]TJ
0 -21.92 TD
[(pro)27(v)56(ably)-281(secure)-282(constan)26(t)-281(round)-282(authen)27(ticated)-281(GKA)-282(proto)-28(cols)-282(in)-282(dynamic)-283(scenario,)-292(where)-282(users)-282(can)]TJ
T*
[(join)-335(or)-335(lea)27(v)27(e)-334(the)-335(group)-336(at)-335(their)-336(desire)-335(and)-335(the)-336(session)-335(k)27(ey)-335(is)-335(up)-28(dated.)-450(They)-336(also)-335(pro)27(vided)-335(securit)27(y)]TJ
0 -21.91 TD
[(pro)-27(ofs)-306(for)-306(their)-305(dynamic)-306(authen)27(ticated)-305(GKA,)-306(namely)-306(Join)-305(and)-306(Lea)27(v)27(e)-304(Proto)-28(col.)-435(Dutta)-306(and)-306(Barua's)]TJ
0 -21.92 TD
[(Lea)27(v)28(e)-363(proto)-28(col)-363(as)-364(describ)-28(ed)-364(in)-364(Section)-364(2.7.12)-364(requires)-364(only)-363(the)-364(left)-364(and)-364(righ)27(t)-363(neigh)27(b)-27(ors)-364(of)-364(lea)27(ving)]TJ
0 -21.91 TD
[(users)-401(to)-402(c)27(hange)-401(their)-402(random)-402(secrets.)-650(W)83(e)-401(shall)-402(sho)27(w)-401(that)-402(their)-401(Lea)26(v)28(e)-401(proto)-27(col)-402(do)-28(es)-402(not)-402(ac)27(hiev)28(e)]TJ
0 -21.92 TD
[(forw)27(ard)-317(secrecy)-317(\(a)-318(lea)26(ving)-316(user)-318(can)-318(still)-318(disco)27(v)27(er)-316(the)-318(new)-318(session)-318(k)27(ey)-317(used)-318(in)-318(subsequen)27(t)-317(sessions)-318(if)]TJ
T*
[(an)27(y)-332(t)27(w)28(o)-333(consecutiv)27(e)-332(remaining)-334(users)-333(do)-333(not)-334(c)27(hange)-332(their)-334(random)-333(secret\).)]TJ
/T1_0 11.95 Tf
0 -37.24 TD
[(5.3.1)-1125(A)31(ttac)31(k)-374(on)-375(the)-375(Dutta)-375(and)-375(Barua's)-375(Lea)30(v)31(e)-374(Proto)-31(col)]TJ
/T1_1 10.91 Tf
0 -28.96 TD
[(In)-236(Dutta)-236(and)-236(Barua's)-236(Lea)26(v)28(e)-235(Proto)-28(col)-236(as)-236(men)27(tioned)-236(in)-236(Section)-236(2.7.12,)-256(w)27(e)-235(ha)27(v)28(e)-236(a)-236(group)-236(of)]TJ
/T1_2 10.91 Tf
410.33 0 Td
(m)Tj
/T1_1 10.91 Tf
12.15 0 Td
(users)Tj
/T1_3 10.91 Tf
26.36 0 Td
(L)Tj
/T1_1 10.91 Tf
10.55 0 Td
(=)Tj
/T1_3 10.91 Tf
-459.39 -21.92 Td
(f)Tj
/T1_4 10.91 Tf
(U)Tj
/T1_5 7.97 Tf
11.18 -1.77 Td
(l)Tj
/T1_6 5.98 Tf
2.53 -1.11 Td
(1)Tj
/T1_2 10.91 Tf
4.64 2.88 Td
[(;)-166(:)-167(:)-167(:)-166(;)]TJ
/T1_4 10.91 Tf
24.24 0 Td
(U)Tj
/T1_5 7.97 Tf
5.72 -1.77 Td
(l)Tj
/T1_7 5.98 Tf
2.53 -1 Td
(m)Tj
/T1_3 10.91 Tf
7.53 2.77 Td
(g)Tj
/T1_1 10.91 Tf
9.02 0 Td
[(lea)28(ving)-326(the)-326(group)]TJ
/T1_3 10.91 Tf
86.44 0 Td
(G)Tj
/T1_1 10.91 Tf
10.16 0 Td
(=)Tj
/T1_3 10.91 Tf
11.51 0 Td
(f)Tj
/T1_4 10.91 Tf
(U)Tj
/T1_8 7.97 Tf
11.18 -1.63 Td
(1)Tj
/T1_2 10.91 Tf
4.73 1.63 Td
[(;)-166(:)-167(:)-167(:)-166(;)]TJ
/T1_4 10.91 Tf
24.24 0 Td
(U)Tj
/T1_5 7.97 Tf
5.72 -1.63 Td
(n)Tj
/T1_3 10.91 Tf
5.64 1.63 Td
(g)Tj
/T1_1 10.91 Tf
[(,)-327(who)-327(has)-326(already)-326(established)-326(a)-327(session)-326(k)27(ey)-325(in)-327(the)]TJ
-227.01 -21.91 Td
[(previous)-225(group)-226(k)27(ey)-225(agreemen)27(t.)-407(Then)-226(the)-226(new)-225(group)-226(of)-226(users)-225(are)]TJ
/T1_3 10.91 Tf
297.24 0 Td
(f)Tj
/T1_4 10.91 Tf
(U)Tj
/T1_8 7.97 Tf
11.17 -1.64 Td
(1)Tj
/T1_2 10.91 Tf
4.73 1.64 Td
[(;)-167(:)-166(:)-167(:)-167(;)]TJ
/T1_4 10.91 Tf
24.24 0 Td
(U)Tj
/T1_5 7.97 Tf
5.73 3.95 Td
(L)Tj
0 -7.28 TD
(l)Tj
/T1_6 5.98 Tf
2.52 -1.1 Td
(1)Tj
/T1_3 10.91 Tf
4.65 4.43 Td
[(g)-6([)-7(f)]TJ
/T1_4 10.91 Tf
(U)Tj
/T1_5 7.97 Tf
24.05 3.95 Td
(R)Tj
T*
(l)Tj
/T1_6 5.98 Tf
2.53 -1.1 Td
(1)Tj
/T1_2 10.91 Tf
4.65 4.43 Td
[(;)-166(:)-167(:)-166(:)-167(;)]TJ
/T1_4 10.91 Tf
24.23 0 Td
(U)Tj
/T1_5 7.97 Tf
5.73 3.95 Td
(L)Tj
T*
(l)Tj
/T1_6 5.98 Tf
2.53 -1.1 Td
(2)Tj
/T1_3 10.91 Tf
4.64 4.43 Td
[(g)-7([)]TJ
/T1_2 10.91 Tf
12.88 0 Td
[(:)-166(:)-167(:)-166(:)-167(:)-167(:)]TJ
/T1_3 10.91 Tf
29.08 0 Td
([)Tj
-460.6 -21.92 Td
(f)Tj
/T1_4 10.91 Tf
(U)Tj
/T1_5 7.97 Tf
11.18 3.96 Td
(R)Tj
T*
(l)Tj
/T1_7 5.98 Tf
2.53 -1 Td
(m)Tj
/T1_2 10.91 Tf
7.53 4.32 Td
[(;)-166(:)-167(:)-166(:)-167(;)]TJ
/T1_4 10.91 Tf
24.23 0 Td
(U)Tj
/T1_5 7.97 Tf
5.73 -1.64 Td
(n)Tj
/T1_3 10.91 Tf
5.63 1.64 Td
(g)Tj
/T1_1 10.91 Tf
[(,)-339(where)]TJ
/T1_4 10.91 Tf
43.78 0 Td
(U)Tj
/T1_5 7.97 Tf
5.72 3.96 Td
(L)Tj
T*
(l)Tj
/T1_7 5.98 Tf
2.53 -1.22 Td
(i)Tj
/T1_1 10.91 Tf
7.42 4.54 Td
(and)Tj
/T1_4 10.91 Tf
21.26 0 Td
(U)Tj
/T1_5 7.97 Tf
5.72 3.96 Td
(R)Tj
T*
(l)Tj
/T1_7 5.98 Tf
2.53 -1.22 Td
(i)Tj
/T1_1 10.91 Tf
8.09 4.54 Td
[(are)-337(resp)-28(ectiv)27(ely)-338(the)-338(left)-338(and)-338(righ)26(t)-337(neigh)27(b)-27(ors)-338(of)-338(lea)26(ving)-337(user)]TJ
/T1_4 10.91 Tf
285.33 0 Td
(U)Tj
/T1_5 7.97 Tf
5.73 -1.78 Td
(l)Tj
/T1_7 5.98 Tf
2.53 -1.21 Td
(i)Tj
/T1_1 10.91 Tf
7.34 2.99 Td
(for)Tj
-454.81 -21.92 Td
(1)Tj
/T1_3 10.91 Tf
8.48 0 Td
(\267)Tj
/T1_2 10.91 Tf
11.51 0 Td
(i)Tj
/T1_3 10.91 Tf
6.79 0 Td
(\267)Tj
/T1_2 10.91 Tf
11.51 0 Td
(m)Tj
/T1_1 10.91 Tf
[(.)-410(Then)-233(for)-233(an)27(y)-232(lea)26(ving)-232(user)]TJ
/T1_4 10.91 Tf
137.46 0 Td
(U)Tj
/T1_5 7.97 Tf
5.73 -1.77 Td
(l)Tj
/T1_7 5.98 Tf
2.52 -1.22 Td
(i)Tj
/T1_1 10.91 Tf
3.66 2.99 Td
(,)Tj
/T1_4 10.91 Tf
5.79 0 Td
(U)Tj
/T1_5 7.97 Tf
5.73 3.96 Td
(L)Tj
T*
(l)Tj
/T1_7 5.98 Tf
2.52 -1.21 Td
(i)Tj
/T1_1 10.91 Tf
6.76 4.53 Td
(=)Tj
/T1_4 10.91 Tf
11.51 0 Td
(U)Tj
/T1_5 7.97 Tf
5.73 -1.77 Td
(l)Tj
/T1_7 5.98 Tf
2.53 -1.22 Td
(i)Tj
/T1_9 7.97 Tf
3.16 1.22 Td
(\241)Tj
/T1_5 7.97 Tf
(k)Tj
/T1_1 10.91 Tf
14.24 1.77 Td
[(if)-232(the)]TJ
/T1_2 10.91 Tf
26.59 0 Td
(k)Tj
/T1_1 10.91 Tf
8.56 0 Td
[(consecutiv)27(e)-232(users)]TJ
/T1_4 10.91 Tf
82.85 0 Td
(U)Tj
/T1_5 7.97 Tf
5.72 -1.77 Td
(l)Tj
/T1_7 5.98 Tf
2.53 -1.22 Td
(i)Tj
/T1_2 10.91 Tf
3.66 2.99 Td
(;)Tj
/T1_4 10.91 Tf
4.85 0 Td
(U)Tj
/T1_5 7.97 Tf
5.72 -1.77 Td
(l)Tj
/T1_7 5.98 Tf
2.53 -1.22 Td
(i)Tj
/T1_9 7.97 Tf
3.16 1.22 Td
(\241)Tj
/T1_8 7.97 Tf
6.59 0 Td
(1)Tj
/T1_2 10.91 Tf
4.73 1.77 Td
[(;)-166(:)-166(:)-167(:)-167(;)]TJ
/T1_4 10.91 Tf
24.23 0 Td
(U)Tj
/T1_5 7.97 Tf
5.73 -2.22 Td
(l)Tj
/T1_7 5.98 Tf
2.52 -1.21 Td
(i)Tj
/T1_9 7.97 Tf
3.17 1.21 Td
(\241)Tj
/T1_8 7.97 Tf
(\()Tj
/T1_5 7.97 Tf
(k)Tj
/T1_9 7.97 Tf
14.49 0 Td
(\241)Tj
/T1_8 7.97 Tf
6.59 0 Td
(1\))Tj
/T1_1 10.91 Tf
-459.85 -19.69 Td
[(are)-335(all)-336(lea)27(ving)-335(and)]TJ
/T1_4 10.91 Tf
91.63 0 Td
(U)Tj
/T1_5 7.97 Tf
5.72 -1.78 Td
(l)Tj
/T1_7 5.98 Tf
2.53 -1.22 Td
(i)Tj
/T1_9 7.97 Tf
3.16 1.22 Td
(\241)Tj
/T1_5 7.97 Tf
(k)Tj
/T1_1 10.91 Tf
15.36 1.78 Td
[(is)-336(not)-335(lea)26(ving)-334(the)-336(group.)-452(Similarly)83(,)]TJ
/T1_4 10.91 Tf
169.99 0 Td
(U)Tj
/T1_5 7.97 Tf
5.73 3.95 Td
(R)Tj
0 -7.27 TD
(l)Tj
/T1_7 5.98 Tf
2.53 -1.22 Td
(i)Tj
/T1_1 10.91 Tf
7.47 4.54 Td
(=)Tj
/T1_4 10.91 Tf
11.55 0 Td
(U)Tj
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[(5.3.2)-1125(Fla)31(w)-374(in)-375(Dutta)-375(and)-375(Barua's)-375(securit)30(y)-374(pro)-31(of)]TJ
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[(In)-358(the)-359(Lea)27(v)28(e)-358(Proto)-28(col)-359(b)27(y)-358(Dutta)-358(and)-359(Barua)-359(in)-359(Section)-358(2.7.12,)-366(some)-358(of)-359(the)-359(left)-359(and)-358(righ)26(t)-357(k)27(eys)-358(that)]TJ
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[(are)-448(curren)27(tly)-448(used)-448(b)27(y)-448(remaining)-448(users)-449(w)27(ere)-447(created)-449(and)-448(used)-448(in)-449(a)-448(previous)-449(GKA)-448(proto)-28(col)-448(run.)]TJ
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[(Ho)27(w)28(ev)28(er,)-466(the)-441(re-use)-440(of)-440(these)-441(information)-440(\(left)-440(and)-441(righ)27(t)-439(k)27(eys)-440(that)-440(w)27(ere)-440(created)-440(in)-440(earlier)-441(GKA)]TJ
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[(proto)-27(col)-480(run)-479(and)-479(are)-479(curren)26(tly)-478(b)-28(eing)-479(used)-479(b)27(y)-479(remaining)-479(users\))-479(in)-479(the)-480(Lea)27(v)28(e)-478(Proto)-28(col)-479(w)26(as)-478(not)]TJ
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[(included)-372(in)-372(the)-372(securit)27(y)-372(analysis)-372(b)-28(ecause)-372(the)-372(securit)27(y)-371(analysis)-373(do)-27(es)-373(not)-372(tak)27(e)-371(care)-373(of)-372(lea)27(ving)-371(users)]TJ
T*
[(who)-333(kno)27(w)-332(additional)-334(information.)]TJ
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[(As)-433(a)-433(result,)-459(Dutta)-433(and)-433(Barua's)-434(securit)27(y)-432(pro)-28(of)-433(fails)-434(to)-433(consider)-433(the)-434(abilit)27(y)-432(of)-434(a)-433(lea)27(ving)-433(user,)]TJ
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[(who)-358(is)-359(no)-359(longer)-359(part)-359(of)-359(the)-358(group,)-366(b)-27(eing)-359(able)-359(to)-359(obtain)-359(the)-359(new)-358(group)-359(k)26(ey)-357(b)26(y)-357(making)-359(use)-359(of)-359(the)]TJ
T*
[(re-use)-348(information)-348(\(i.e.)-490(left)-348(and)-349(righ)27(t)-347(k)27(eys)-348(that)-348(w)27(ere)-348(created)-348(in)-349(earlier)-348(GKA)-348(proto)-28(col)-348(run)-349(and)-348(are)]TJ
0 -21.91 TD
[(curren)27(tly)-332(b)-28(eing)-333(used)-333(b)26(y)-332(remaining)-333(users\))-334(and)-333(using)-333(the)-334(tec)27(hnique)-332(men)27(tioned)-333(in)-333(Section)-333(5.3.1.)]TJ
225.76 -115.36 Td
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0 -21.92 TD
[(address)-389(auto)-28(con\257guration)-389(and)-389(sho)27(w)-389(the)-389(requiremen)27(ts)-389(\(including)-389(securit)27(y)-388(requiremen)26(ts\))-388(for)-389(GKA)]TJ
0 -21.91 TD
[(proto)-27(cols)-334(to)-333(b)-28(e)-333(applied)-333(to)-334(MANETs.)]TJ
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[(5.4.1)-1125(IP)-375(Address)-375(Auto)-31(con\257guration)-375(Classes)]TJ
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[(IP)-465(address)-466(auto)-28(con\257guration)-466(proto)-27(cols)-466(can)-466(b)-28(e)-466(classi\257ed)-465(in)26(to)-464(three)-466(t)26(yp)-26(es)-466(of)-466(approac)27(hes:)-709(State-)]TJ
0 -21.92 TD
[(ful,)-456(stateless)-433(and)-432(h)27(ybrid)-431(proto)-28(col.)-741(Stateful)-432(approac)27(hes)-432(suc)27(h)-431(as)-432([BPS)]TJ
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0 -21.91 TD
[(ab)-27(out)-347(curren)26(tly)-346(assigned)-347(addresses)-347(in)-348(an)-347(address)-347(allo)-28(cation)-347(table.)-486(Stateful)-347(approac)26(hes)-346(are)-347(further)]TJ
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[(distinguished)-356(b)26(y)-355(three)-357(categories:)]TJ
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165.11 0 Td
[(Centr)50(alize)51(d)-378(maintenanc)50(e)-378(of)-380(al)-51(lo)50(c)52(ation)-379(table)]TJ
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290.7 0 Td
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[(assigns)-277(an)-277(address)-278(and)-277(v)27(eri\257es)-277(its)-277(uniqueness)-277(in)-278(a)-277(distributed)-277(manner)-278(using)-277(the)-278(Duplicated)-277(Address)]TJ
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[(01].)-622(The)-392(h)27(ybrid)-392(approac)27(h)-392([W)83(en05],)-407(com)27(bines)-392(elemen)27(ts)-391(from)]TJ
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/T1_0 11.95 Tf
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[(5.4.2)-1125(Requiremen)31(ts)]TJ
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[(Sev)27(eral)-445(requiremen)27(ts)-445(m)27(ust)-445(b)-27(e)-446(satis\257ed)-446(b)-28(efore)-446(w)27(e)-445(can)-445(apply)-446(our)-446(proto)-28(col)-446(in)-445(MANET.)-446(First,)-474(w)27(e)]TJ
0 -21.92 TD
[(require)-321(that)-321(a)-321(Public)-321(Key)-321(Infrastructure)-321(\(PKI\))-321(should)-321(b)-28(e)-321(in)-321(place.)-441(All)-321(MANET)-321(no)-28(des)-321(taking)-321(part)]TJ
T*
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0 -21.91 TD
[(with)-292(the)-292(Certi\257cation)-293(Authorit)27(y)-291(\(CA\))-293(to)-292(certify)-293(their)-292(public)-292(k)26(ey)-291(and)-292(obtain)-293(a)-292(public)-293(k)27(ey)-291(certi\257cate)]TJ
0 -21.92 TD
[(through)-387(a)-388(secure)-388(c)27(hannel)-386(b)-28(efore)-388(taking)-388(part)-387(in)-388(group)-388(comm)27(unications.)-606(The)-388(CA)-388(could)-387(simply)-388(b)-28(e)]TJ
T*
[(the)-333(o)27(wner)-332(of)-334(the)-333(MANET.)]TJ
16.93 -21.91 Td
[(As)-416(the)-416(net)27(w)28(ork)-415(top)-28(ology)-416(of)-416(MANET)-416(is)-417(dynamic,)-436(one)-417(requiremen)27(t)-415(for)-416(GKA)-416(in)-416(MANET)-416(will)]TJ
-16.93 -21.92 Td
[(b)-27(e)-338(to)-337(e\261cien)26(tly)-336(handle)-338(dynamic)-337(ev)27(en)27(ts.)-456(F)83(urthermore,)-338(to)-337(prev)26(en)28(t)-336(address)-338(con\260icts)-337(that)-338(are)-337(caused)]TJ
T*
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[(;)-166(n)]TJ
/T1_5 10.91 Tf
(g)Tj
/T1_0 10.91 Tf
[(.)-443(W)83(e)-330(also)]TJ
-406.17 -21.92 Td
[(assume)-418(that)-418(the)-419(IP)-418(addresses)]TJ
/T1_6 10.91 Tf
147.81 0 Td
(addr)Tj
/T1_0 10.91 Tf
20.39 0 Td
([)Tj
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(U)Tj
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8.76 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
3.38 1.63 Td
[(])-418(of)]TJ
/T1_3 10.91 Tf
20.94 0 Td
(U)Tj
/T1_2 7.97 Tf
5.72 -1.63 Td
(i)Tj
/T1_5 10.91 Tf
7.96 1.63 Td
[(2)-419(G)]TJ
/T1_0 10.91 Tf
23.55 0 Td
[(for)-418(1)]TJ
/T1_5 10.91 Tf
27.65 0 Td
(\267)Tj
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13.06 0 Td
(i)Tj
/T1_5 10.91 Tf
8.33 0 Td
(\267)Tj
/T1_1 10.91 Tf
13.06 0 Td
(n)Tj
/T1_0 10.91 Tf
11.11 0 Td
[(b)-27(elong)-418(to)-419(the)-418(same)-419(subnet.)-700(F)83(or)]TJ
-311.72 -21.91 Td
[(example,)-397(the)-385(IP)-385(address)]TJ
/T1_6 10.91 Tf
120.84 0 Td
(addr)Tj
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20.39 0 Td
([)Tj
/T1_3 10.91 Tf
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5.73 -1.64 Td
(i)Tj
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3.38 1.64 Td
[(])-384(of)]TJ
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20.21 0 Td
(U)Tj
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5.72 -1.64 Td
(i)Tj
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7.35 1.64 Td
[(2)-363(G)]TJ
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22.57 0 Td
[(for)-384(1)]TJ
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26.67 0 Td
(\267)Tj
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12.44 0 Td
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7.73 0 Td
(\267)Tj
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12.44 0 Td
(n)Tj
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10.75 0 Td
[(will)-384(b)-28(egin)-385(with)-384(\(179)]TJ
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97.11 0 Td
(:)Tj
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(156)Tj
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(:)Tj
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(0)Tj
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(:i)Tj
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[(\))-384(and)-385(hence)]TJ
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[(do)-384(not)-385(ha)27(v)28(e)-384(address)-385(con\260icts.)-598(The)-385(Initial)-385(Key)-385(Agreemen)27(t)-384(\(IKA\))-384(proto)-28(col)-385(consists)-384(of)-385(t)27(w)27(o)-383(rounds)]TJ
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[(during)-366(whic)27(h)-365(eac)27(h)-365(user)]TJ
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114.85 0 Td
(U)Tj
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5.73 -1.63 Td
(i)Tj
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7.37 1.63 Td
[(will)-366(broadcast)-366(their)-366(IP)-366(address)]TJ
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152.17 0 Td
(addr)Tj
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(U)Tj
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(i)Tj
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3.38 1.63 Td
[(])-366(and)-366(k)27(eying)-365(materials)-366(for)-366(group)]TJ
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[(k)27(ey)-402(computation.)-655(A)27(t)-403(the)-403(end)-403(of)-404(the)-403(second)-404(round,)-421(all)-403(users)]TJ
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296.35 0 Td
(U)Tj
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7.68 1.64 Td
[(2)-394(G)]TJ
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23.11 0 Td
[(will)-403(b)-28(e)-403(able)-404(to)-403(compute)-404(the)]TJ
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[(common)-306(group)-307(k)27(ey)]TJ
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93.38 0 Td
(K)Tj
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13.39 0 Td
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[(allo)-27(cation)-334(table)]TJ
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77.25 0 Td
(LIST)Tj
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[(.)-444(The)-334(Initial)-333(Key)-333(Agreemen)26(t)-332(\(IKA\))-333(Proto)-28(col)-333(is)-334(describ)-27(ed)-334(b)-28(elo)27(w:)]TJ
-100.15 -21.91 Td
[(Round)-333(1)]TJ
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 0 -364.18 cm
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40.75 0 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 112.7614 407.0685 Tm
(:)Tj
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49.729 -362.65 Td
[(Eac)27(h)-384(user)]TJ
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51.341 0 Td
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7.57 1.64 Td
[(for)-384(1)]TJ
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26.66 0 Td
(\267)Tj
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12.43 0 Td
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12.44 0 Td
(n)Tj
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10.73 0 Td
[(\257rst)-384(selects)]TJ
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57.67 0 Td
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(\244)Tj
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-0.78 -6.66 Td
(q)Tj
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9.7 2.7 Td
[(and)-384(computes)]TJ
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(i)Tj
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6.69 -2.74 Td
[(mo)-27(d)]TJ
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23.93 0 Td
(p)Tj
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(.)Tj
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(jj)Tj
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(z)Tj
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(i)Tj
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3.38 1.63 Td
(jj)Tj
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6.06 0 Td
(addr)Tj
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20.38 0 Td
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(U)Tj
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(i)Tj
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(])Tj
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(jj)Tj
/T1_3 10.91 Tf
9.09 0 Td
(cert)Tj
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22.9 0 Td
([)Tj
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(U)Tj
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(i)Tj
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(])Tj
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3.02 0 Td
(g)Tj
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(.)Tj
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[(Round)-333(2)]TJ
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 0 -408.01 cm
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S
Q
Q
BT
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1.0003 0 0 1.0003 112.7614 363.2262 Tm
(:)Tj
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50.362 -406.48 Td
[(Eac)27(h)]TJ
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27.978 0 Td
(U)Tj
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5.73 -1.64 Td
(i)Tj
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7.88 1.64 Td
[(for)-412(1)]TJ
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27.49 0 Td
(\267)Tj
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12.96 0 Td
(i)Tj
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8.23 0 Td
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12.96 0 Td
(n)Tj
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11.05 0 Td
[(\257rst)-412(v)27(eri\257es)-412(the)]TJ
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80.34 0 Td
(cert)Tj
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22.9 0 Td
([)Tj
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(U)Tj
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(j)Tj
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4.39 1.64 Td
[(])-412(of)-413(other)-413(users)]TJ
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78.48 0 Td
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[(for)-412(1)]TJ
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12.95 0 Td
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9.6 0 Td
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(=)Tj
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(i)Tj
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(.)Tj
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[(If)-388(the)-388(v)26(eri\257cation)-387(is)-388(not)-389(correct,)]TJ
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34.93 0 Td
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4.38 1.64 Td
[(.)-609(Otherwise,)]TJ
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65.05 0 Td
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[(stores)-388(the)-388(IP)-388(address)]TJ
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106.16 0 Td
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(U)Tj
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(j)Tj
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[(])-388(of)-388(all)]TJ
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8.34 1.63 Td
[(for)-362(1)]TJ
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26.02 0 Td
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[(.)-531(Then)-363(user)]TJ
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[(\))-362(for)]TJ
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ET
q
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S
Q
Q
BT
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(n)Tj
0 -8.25 TD
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7.41 1.64 Td
[(mo)-28(d)]TJ
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[(and)-316(signs)]TJ
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47.62 0 Td
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[(.)-745(Ho)27(w)28(ev)28(er,)-458(if)]TJ
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[(detects)-433(that)]TJ
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[(the)-482(signature)-482(\()]TJ
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[(;)-166(\277)]TJ
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[(\))-482(is)-482(incorrect,)-520(then)-482(user)]TJ
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[(will)-482(b)-27(e)-483(excluded)-482(from)-483(the)-482(GKA.)]TJ
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[(will)-482(re-)]TJ
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7.68 -2.85 Td
[(mo)-27(d)]TJ
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23.93 0 Td
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[(will)-459(recompute)]TJ
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[(;)-166(\277)]TJ
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[(;)-166(\277)]TJ
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[(.)-733(All)-429(users)]TJ
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[(from)-332(GKA)-334(b)27(y)-332(using)-334(new)]TJ
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[(and)-333(remo)27(ving)]TJ
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[(b)-27(e)-312(the)-313(new)-312(user)-313(joining)-313(the)-312(group.)-438(W)83(e)-312(divide)]TJ
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[(,)-493(whic)27(h)-460(are)-461(the)-461(t)27(w)28(o)-460(users)-461(activ)26(ely)-460(in)27(v)28(olv)28(ed)-460(in)-461(the)-461(Join)-461(Proto)-28(col)-461(and)]TJ
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[(,)-438(whic)27(h)-416(consist)-418(of)-417(the)-417(rest)-417(of)-417(the)-418(group.)-696(W)83(e)-416(consider)-418(a)-417(ring)-417(structure)-417(among)-417(the)]TJ
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/T1_2 7.97 Tf
5.72 -1.63 Td
(1)Tj
/T1_0 10.91 Tf
8.29 1.63 Td
[(c)28(ho)-27(oses)-326(a)-325(new)-326(random)]TJ
/T1_5 10.91 Tf
110.08 0 Td
(r)Tj
/T1_6 7.97 Tf
5.23 3.96 Td
(0)Tj
/T1_2 7.97 Tf
-0.31 -6.88 Td
(1)Tj
/T1_4 10.91 Tf
7.76 2.92 Td
(2)Tj
/T1_5 10.91 Tf
10.3 0 Td
(Z)Tj
/T1_6 7.97 Tf
8.23 3.96 Td
(\244)Tj
/T1_3 7.97 Tf
-0.78 -6.65 Td
(q)Tj
/T1_0 10.91 Tf
9.06 2.69 Td
[(and)-325(computes)]TJ
/T1_5 10.91 Tf
-401.85 -21.91 Td
(K)Tj
/T1_6 7.97 Tf
10.04 3.95 Td
(\244)Tj
/T1_0 10.91 Tf
8.37 -3.95 Td
[(as)-333(follo)27(ws:)]TJ
/T1_5 10.91 Tf
77.04 -39.65 Td
(K)Tj
/T1_6 7.97 Tf
10.04 4.51 Td
(\244)Tj
/T1_0 10.91 Tf
14.69 -4.51 Td
(=)Tj
/T1_5 10.91 Tf
18.44 0 Td
(K)Tj
/T1_4 10.91 Tf
12.47 0 Td
(\242)Tj
/T1_0 10.91 Tf
5.45 0 Td
(\()Tj
/T1_5 10.91 Tf
4.25 0 Td
(z)Tj
/T1_2 7.97 Tf
5.07 -1.63 Td
(2)Tj
/T1_4 10.91 Tf
7.15 1.63 Td
(\242)Tj
/T1_5 10.91 Tf
5.45 0 Td
(y)Tj
/T1_3 7.97 Tf
5.74 4.87 Td
(c)Tj
/T1_8 5.98 Tf
3.67 -1.11 Td
(2)Tj
/T1_2 7.97 Tf
-4.06 -6.88 Td
(2)Tj
/T1_4 10.91 Tf
11.13 3.12 Td
(\242)Tj
/T1_5 10.91 Tf
5.45 0 Td
(z)Tj
/T1_3 7.97 Tf
5.08 -1.63 Td
(n)Tj
/T1_4 10.91 Tf
8.05 1.63 Td
(\242)Tj
/T1_5 10.91 Tf
5.46 0 Td
(y)Tj
/T1_3 7.97 Tf
5.74 4.51 Td
(c)Tj
/T1_7 5.98 Tf
3.66 -1 Td
(n)Tj
/T1_3 7.97 Tf
-4.06 -6.2 Td
(n)Tj
/T1_0 10.91 Tf
9.66 2.69 Td
(\))Tj
/T1_6 7.97 Tf
4.24 4.51 Td
(\241)Tj
/T1_3 7.97 Tf
(d)Tj
/T1_8 5.98 Tf
10.94 -1.11 Td
(1)Tj
/T1_4 10.91 Tf
7.07 -3.4 Td
(\242)Tj
/T1_0 10.91 Tf
5.45 0 Td
(\()Tj
/T1_5 10.91 Tf
4.25 0 Td
(z)Tj
/T1_2 7.97 Tf
5.07 -1.63 Td
(2)Tj
/T1_4 10.91 Tf
7.15 1.63 Td
(\242)Tj
/T1_5 10.91 Tf
5.45 0 Td
(y)Tj
/T1_3 7.97 Tf
5.74 4.87 Td
(c)Tj
/T1_8 5.98 Tf
3.67 -1.11 Td
(2)Tj
/T1_2 7.97 Tf
-4.06 -6.88 Td
(2)Tj
/T1_4 10.91 Tf
11.13 3.12 Td
(\242)Tj
/T1_5 10.91 Tf
5.45 0 Td
(z)Tj
/T1_3 7.97 Tf
5.08 -1.63 Td
(n)Tj
/T1_2 7.97 Tf
5.13 0 Td
(+1)Tj
/T1_4 10.91 Tf
13.74 1.63 Td
(\242)Tj
/T1_5 10.91 Tf
5.46 0 Td
(y)Tj
/T1_3 7.97 Tf
5.73 5.7 Td
(c)Tj
/T1_7 5.98 Tf
3.67 -1.11 Td
(n)Tj
/T1_8 5.98 Tf
4.6 0 Td
(+1)Tj
/T1_3 7.97 Tf
-8.66 -7.71 Td
(n)Tj
/T1_2 7.97 Tf
(+1)Tj
/T1_0 10.91 Tf
18.9 3.12 Td
(\))Tj
/T1_3 7.97 Tf
4.24 4.51 Td
(d)Tj
/T1_10 5.98 Tf
4.35 2.81 Td
(0)Tj
/T1_8 5.98 Tf
0 -5.29 TD
(1)Tj
/T1_0 10.91 Tf
-247.59 -26.93 Td
(=)Tj
/T1_5 10.91 Tf
18.44 0 Td
(g)Tj
/T1_3 7.97 Tf
5.6 4.5 Td
(d)Tj
/T1_10 5.98 Tf
4.35 2.81 Td
(0)Tj
/T1_8 5.98 Tf
0 -5.28 TD
(1)Tj
/T1_3 7.97 Tf
4.15 2.47 Td
(d)Tj
/T1_8 5.98 Tf
4.36 -1.1 Td
(2)Tj
/T1_2 7.97 Tf
4.15 1.1 Td
(+)Tj
/T1_3 7.97 Tf
(d)Tj
/T1_8 5.98 Tf
10.94 -1.1 Td
(2)Tj
/T1_3 7.97 Tf
4.15 1.1 Td
(d)Tj
/T1_8 5.98 Tf
4.36 -1.1 Td
(3)Tj
/T1_2 7.97 Tf
4.15 1.1 Td
(+)Tj
/T1_6 7.97 Tf
(\242\242\242)Tj
/T1_2 7.97 Tf
13.64 0 Td
(+)Tj
/T1_3 7.97 Tf
(d)Tj
/T1_7 5.98 Tf
10.94 -1.1 Td
(n)Tj
/T1_10 5.98 Tf
4.6 0 Td
(\241)Tj
/T1_8 5.98 Tf
5.75 0 Td
(1)Tj
/T1_3 7.97 Tf
4.15 1.1 Td
(d)Tj
/T1_7 5.98 Tf
4.36 -0.99 Td
(n)Tj
/T1_2 7.97 Tf
5.09 0.99 Td
(+)Tj
/T1_3 7.97 Tf
6.59 0 Td
(d)Tj
/T1_7 5.98 Tf
4.36 -1.1 Td
(n)Tj
/T1_8 5.98 Tf
4.59 0 Td
(+1)Tj
/T1_3 7.97 Tf
9.74 1.1 Td
(d)Tj
/T1_10 5.98 Tf
4.36 2.81 Td
(0)Tj
/T1_8 5.98 Tf
T*
(1)Tj
/T1_0 10.91 Tf
7.68 -2.03 Td
[(mo)-27(d)]TJ
/T1_5 10.91 Tf
23.93 0 Td
(p:)Tj
/T1_0 10.91 Tf
150.84 0 Td
(\(5.3\))Tj
-445.45 -39.64 Td
(where)Tj
/T1_5 10.91 Tf
32.11 0 Td
(d)Tj
/T1_3 7.97 Tf
5.68 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
7.37 1.64 Td
(=)Tj
/T1_5 10.91 Tf
12.48 0 Td
(r)Tj
/T1_3 7.97 Tf
4.92 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
6.19 1.64 Td
(+)Tj
/T1_5 10.91 Tf
11.29 0 Td
(c)Tj
/T1_3 7.97 Tf
4.72 -1.64 Td
(i)Tj
/T1_5 10.91 Tf
3.38 1.64 Td
(x)Tj
/T1_3 7.97 Tf
6.23 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
7.6 1.64 Td
(and)Tj
/T1_5 10.91 Tf
21.78 0 Td
(c)Tj
/T1_3 7.97 Tf
4.72 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
7.38 1.64 Td
(=)Tj
/T1_9 10.91 Tf
12.47 0 Td
(H)Tj
/T1_0 10.91 Tf
7.73 0 Td
(\()Tj
/T1_5 10.91 Tf
(z)Tj
/T1_3 7.97 Tf
9.31 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
3.38 1.64 Td
[(\))-386(for)-386(2)]TJ
/T1_4 10.91 Tf
35.17 0 Td
(\267)Tj
/T1_5 10.91 Tf
12.48 0 Td
(i)Tj
/T1_4 10.91 Tf
7.75 0 Td
(\267)Tj
/T1_5 10.91 Tf
12.47 0 Td
(n)Tj
/T1_0 10.91 Tf
10.76 0 Td
(and)Tj
/T1_5 10.91 Tf
21.79 0 Td
(d)Tj
/T1_6 7.97 Tf
5.67 3.95 Td
(0)Tj
/T1_2 7.97 Tf
0 -6.88 TD
(1)Tj
/T1_0 10.91 Tf
8.73 2.93 Td
(=)Tj
/T1_5 10.91 Tf
12.47 0 Td
(r)Tj
/T1_6 7.97 Tf
5.22 3.95 Td
(0)Tj
/T1_2 7.97 Tf
-0.3 -6.88 Td
(1)Tj
/T1_0 10.91 Tf
7.54 2.93 Td
(+)Tj
/T1_5 10.91 Tf
11.29 0 Td
(c)Tj
/T1_6 7.97 Tf
4.72 3.95 Td
(0)Tj
/T1_2 7.97 Tf
T*
(1)Tj
/T1_5 10.91 Tf
4.73 2.93 Td
(x)Tj
/T1_2 7.97 Tf
6.24 -1.64 Td
(1)Tj
/T1_0 10.91 Tf
8.94 1.64 Td
(and)Tj
/T1_5 10.91 Tf
21.79 0 Td
(c)Tj
/T1_6 7.97 Tf
4.71 3.95 Td
(0)Tj
/T1_2 7.97 Tf
T*
(1)Tj
/T1_0 10.91 Tf
8.73 2.93 Td
(=)Tj
/T1_9 10.91 Tf
12.47 0 Td
(H)Tj
/T1_0 10.91 Tf
7.73 0 Td
(\()Tj
/T1_5 10.91 Tf
(g)Tj
/T1_3 7.97 Tf
9.83 3.95 Td
(r)Tj
/T1_10 5.98 Tf
4.06 2.82 Td
(0)Tj
/T1_8 5.98 Tf
-0.24 -5.29 Td
(1)Tj
/T1_0 10.91 Tf
4.65 -1.48 Td
(\).)Tj
/T1_1 10.91 Tf
13.85 0 Td
(U)Tj
/T1_2 7.97 Tf
5.73 -1.64 Td
(1)Tj
/T1_0 10.91 Tf
8.94 1.64 Td
(then)Tj
-446.66 -21.92 Td
(encrypts)Tj
/T1_5 10.91 Tf
43.82 0 Td
(K)Tj
/T1_6 7.97 Tf
10.04 3.96 Td
(\244)Tj
/T1_4 10.91 Tf
4.73 -3.96 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(U)Tj
/T1_2 7.97 Tf
5.73 -1.64 Td
(1)Tj
/T1_0 10.91 Tf
8.16 1.64 Td
[(using)-315(previously)-315(established)-315(group)-315(k)27(ey)]TJ
/T1_5 10.91 Tf
186.23 0 Td
(K)Tj
/T1_0 10.91 Tf
13.47 0 Td
[(and)-315(a)-315(symmetric)-315(k)27(ey)-314(encryption)]TJ
/T1_9 10.91 Tf
156.36 0 Td
(SKE)Tj
/T1_0 10.91 Tf
23.58 0 Td
(to)Tj
-458.18 -21.92 Td
(obtain)Tj
/T1_1 10.91 Tf
33.93 0 Td
(c)Tj
/T1_2 7.97 Tf
5.73 -1.63 Td
(1)Tj
/T1_0 10.91 Tf
7.76 1.63 Td
(=)Tj
/T1_4 10.91 Tf
11.51 0 Td
(E)Tj
/T1_3 7.97 Tf
5.75 -1.68 Td
(K)Tj
/T1_0 10.91 Tf
8.2 1.68 Td
(\()Tj
/T1_5 10.91 Tf
4.25 0 Td
(K)Tj
/T1_6 7.97 Tf
10.04 3.96 Td
(\244)Tj
/T1_4 10.91 Tf
4.73 -3.96 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(U)Tj
/T1_2 7.97 Tf
5.72 -1.63 Td
(1)Tj
/T1_0 10.91 Tf
4.73 1.63 Td
[(\))-333(and)-334(broadcasts)]TJ
/T1_4 10.91 Tf
83.16 0 Td
(f)Tj
/T1_1 10.91 Tf
(U)Tj
/T1_2 7.97 Tf
11.18 -1.63 Td
(1)Tj
/T1_4 10.91 Tf
4.73 1.63 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(c)Tj
/T1_2 7.97 Tf
5.73 -1.63 Td
(1)Tj
/T1_4 10.91 Tf
4.73 1.63 Td
(g)Tj
/T1_0 10.91 Tf
(.)Tj
-224 -21.91 Td
[(Round)-333(3)]TJ
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 0 -445.42 cm
0 0 m
40.75 0 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 118.6831 325.8057 Tm
(:)Tj
/T1_1 10.91 Tf
12.47 0 Td
(U)Tj
/T1_3 7.97 Tf
5.72 -1.64 Td
(n)Tj
/T1_0 10.91 Tf
11.57 1.64 Td
(v)Tj
1.0003 0 0 1.0003 72 769.82 Tm
81.885 -443.89 Td
[(eri\257es)-543(the)]TJ
/T1_1 10.91 Tf
54.355 0 Td
(cert)Tj
/T1_0 10.91 Tf
22.9 0 Td
([)Tj
/T1_1 10.91 Tf
(U)Tj
/T1_3 7.97 Tf
8.76 -1.64 Td
(n)Tj
/T1_2 7.97 Tf
5.13 0 Td
(+1)Tj
/T1_0 10.91 Tf
11.32 1.64 Td
[(])-543(and)-543(signature)-544(\()]TJ
/T1_5 10.91 Tf
86.34 0 Td
(\276)Tj
/T1_3 7.97 Tf
6.23 -1.64 Td
(n)Tj
/T1_2 7.97 Tf
(+1)Tj
/T1_5 10.91 Tf
16.45 1.64 Td
[(;)-166(\277)]TJ
/T1_3 7.97 Tf
9.62 -1.64 Td
(n)Tj
/T1_2 7.97 Tf
(+1)Tj
/T1_0 10.91 Tf
16.45 1.64 Td
[(\))-543(from)]TJ
/T1_1 10.91 Tf
38.24 0 Td
(U)Tj
/T1_3 7.97 Tf
5.73 -1.64 Td
(n)Tj
/T1_2 7.97 Tf
(+1)Tj
/T1_0 10.91 Tf
16.45 1.64 Td
[(.)-1075(If)-543(they)-544(are)-543(in-)]TJ
-379.86 -21.92 Td
[(v)55(alid,)-458(then)]TJ
/T1_1 10.91 Tf
56.69 0 Td
(U)Tj
/T1_3 7.97 Tf
5.73 -1.64 Td
(n)Tj
/T1_0 10.91 Tf
10.36 1.64 Td
(rejects)Tj
/T1_1 10.91 Tf
35.42 0 Td
(U)Tj
/T1_3 7.97 Tf
5.72 -1.64 Td
(n)Tj
/T1_2 7.97 Tf
(+1)Tj
/T1_0 10.91 Tf
16.46 1.64 Td
[(.)-745(Otherwise,)]TJ
/T1_1 10.91 Tf
67.15 0 Td
(U)Tj
/T1_3 7.97 Tf
5.72 -1.64 Td
(n)Tj
/T1_0 10.91 Tf
10.37 1.64 Td
[(computes)-433(the)-434(DH)-433(k)27(ey)]TJ
/T1_5 10.91 Tf
111.53 0 Td
(K)Tj
/T1_11 7.97 Tf
9.26 -1.64 Td
(U)Tj
/T1_7 5.98 Tf
4.23 -0.99 Td
(n)Tj
/T1_11 7.97 Tf
5.1 0.99 Td
(U)Tj
/T1_7 5.98 Tf
4.23 -1.1 Td
(n)Tj
/T1_8 5.98 Tf
4.6 0 Td
(+1)Tj
/T1_0 10.91 Tf
15.09 2.74 Td
[(=)-445(\()]TJ
/T1_5 10.91 Tf
17.58 0 Td
(z)Tj
/T1_3 7.97 Tf
5.07 -1.64 Td
(n)Tj
/T1_2 7.97 Tf
(+1)Tj
/T1_4 10.91 Tf
19.61 1.64 Td
(\242)Tj
/T1_5 10.91 Tf
6.18 0 Td
(y)Tj
/T1_3 7.97 Tf
5.74 5.69 Td
(c)Tj
/T1_7 5.98 Tf
3.67 -1.1 Td
(n)Tj
/T1_8 5.98 Tf
4.6 0 Td
(+1)Tj
/T1_3 7.97 Tf
-8.66 -7.71 Td
(n)Tj
/T1_2 7.97 Tf
5.13 0 Td
(+1)Tj
/T1_0 10.91 Tf
13.76 3.12 Td
(\))Tj
/T1_3 7.97 Tf
4.24 3.96 Td
(d)Tj
/T1_7 5.98 Tf
4.36 -1 Td
(n)Tj
/T1_0 10.91 Tf
10.45 -2.96 Td
(=)Tj
/T1_5 10.91 Tf
-459.39 -21.92 Td
(g)Tj
/T1_3 7.97 Tf
5.59 3.96 Td
(d)Tj
/T1_7 5.98 Tf
4.36 -0.99 Td
(n)Tj
/T1_3 7.97 Tf
5.1 0.99 Td
(d)Tj
/T1_7 5.98 Tf
4.35 -1.11 Td
(n)Tj
/T1_8 5.98 Tf
4.6 0 Td
(+1)Tj
/T1_0 10.91 Tf
13.27 -2.85 Td
[(mo)-27(d)]TJ
/T1_5 10.91 Tf
23.93 0 Td
(p)Tj
/T1_0 10.91 Tf
10.97 0 Td
[(that)-502(it)-502(shares)-503(with)]TJ
/T1_1 10.91 Tf
99.62 0 Td
(U)Tj
/T1_3 7.97 Tf
5.73 -1.63 Td
(n)Tj
/T1_2 7.97 Tf
5.13 0 Td
(+1)Tj
/T1_0 10.91 Tf
11.32 1.63 Td
[(,)-544(where)]TJ
/T1_5 10.91 Tf
42.35 0 Td
(d)Tj
/T1_3 7.97 Tf
5.68 -1.77 Td
(k)Tj
/T1_0 10.91 Tf
11.22 1.77 Td
(=)Tj
/T1_5 10.91 Tf
14.58 0 Td
(r)Tj
/T1_3 7.97 Tf
4.92 -1.77 Td
(k)Tj
/T1_0 10.91 Tf
8.77 1.77 Td
(+)Tj
/T1_5 10.91 Tf
12.14 0 Td
(c)Tj
/T1_3 7.97 Tf
4.72 -1.77 Td
(k)Tj
/T1_5 10.91 Tf
5.12 1.77 Td
(x)Tj
/T1_3 7.97 Tf
6.23 -1.77 Td
(k)Tj
/T1_0 10.91 Tf
10.6 1.77 Td
(for)Tj
/T1_5 10.91 Tf
18.54 0 Td
(k)Tj
/T1_0 10.91 Tf
12.12 0 Td
(=)Tj
/T1_5 10.91 Tf
14.58 0 Td
(n)Tj
/T1_0 10.91 Tf
12.03 0 Td
(and)Tj
/T1_5 10.91 Tf
23.05 0 Td
(n)Tj
/T1_0 10.91 Tf
10.2 0 Td
[(+)-334(1.)-952(Next,)]TJ
/T1_1 10.91 Tf
-410.82 -21.91 Td
(U)Tj
/T1_3 7.97 Tf
5.73 -1.64 Td
(n)Tj
/T1_0 10.91 Tf
11.08 1.64 Td
(encrypts)Tj
/T1_5 10.91 Tf
45.84 0 Td
(K)Tj
/T1_11 7.97 Tf
9.26 -1.64 Td
(U)Tj
/T1_7 5.98 Tf
4.23 -0.99 Td
(n)Tj
/T1_11 7.97 Tf
5.1 0.99 Td
(U)Tj
/T1_7 5.98 Tf
4.23 -1.11 Td
(n)Tj
/T1_8 5.98 Tf
4.6 0 Td
(+1)Tj
/T1_4 10.91 Tf
10.24 2.75 Td
(jj)Tj
/T1_9 10.91 Tf
6.06 0 Td
(addr)Tj
/T1_0 10.91 Tf
20.38 0 Td
([)Tj
/T1_1 10.91 Tf
(U)Tj
/T1_3 7.97 Tf
8.76 -1.64 Td
(n)Tj
/T1_2 7.97 Tf
(+1)Tj
/T1_0 10.91 Tf
16.45 1.64 Td
(])Tj
/T1_4 10.91 Tf
(jj)Tj
/T1_1 10.91 Tf
9.09 0 Td
(U)Tj
/T1_3 7.97 Tf
5.73 -1.64 Td
(n)Tj
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(U)Tj
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5.72 -1.64 Td
(1)Tj
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8.52 1.64 Td
[(is)-347(not)-348(decrypted)-347(correctly)82(,)-350(then)]TJ
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153.95 0 Td
(U)Tj
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5.72 -1.64 Td
(i)Tj
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7.17 1.64 Td
(rejects)Tj
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34.48 0 Td
(c)Tj
/T1_4 7.97 Tf
5.73 -1.64 Td
(1)Tj
/T1_0 10.91 Tf
4.73 1.64 Td
[(.)-486(Otherwise,)]TJ
/T1_2 10.91 Tf
63.14 0 Td
(U)Tj
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5.73 -1.64 Td
(i)Tj
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-464.49 -20.28 Td
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38.69 0 Td
(K)Tj
/T1_5 7.97 Tf
10.04 3.96 Td
(\244)Tj
/T1_0 10.91 Tf
4.73 -3.96 Td
[(.)-569(Next,)-386(users)]TJ
/T1_2 10.91 Tf
67.38 0 Td
(U)Tj
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5.72 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
7.47 1.64 Td
[(for)-375(1)]TJ
/T1_10 10.91 Tf
26.39 0 Td
(\267)Tj
/T1_1 10.91 Tf
12.27 0 Td
(i)Tj
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7.55 0 Td
(\267)Tj
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12.27 0 Td
(n)Tj
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9.27 0 Td
(\241)Tj
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11.21 0 Td
[(1)-375(decrypts)]TJ
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54.02 0 Td
(c)Tj
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5.73 -1.64 Td
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9.72 1.64 Td
[(using)-375(previously)-375(established)-375(group)-375(k)27(ey)]TJ
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(K)Tj
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14.38 0 Td
[(and)-397(obtain)]TJ
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56.54 0 Td
(K)Tj
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9.26 -1.63 Td
(U)Tj
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4.23 -1 Td
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5.1 1 Td
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4.23 -1.11 Td
(n)Tj
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4.6 0 Td
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10.24 2.74 Td
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7.54 0 Td
(addr)Tj
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20.39 0 Td
([)Tj
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(U)Tj
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(+1)Tj
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16.46 1.63 Td
[(])-397(and)-397(iden)26(tit)28(y)]TJ
/T1_2 10.91 Tf
70.26 0 Td
(U)Tj
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5.73 -1.63 Td
(n)Tj
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5.63 1.63 Td
[(.)-637(If)-398(the)-397(iden)26(tit)28(y)]TJ
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82.07 0 Td
(U)Tj
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5.72 -1.63 Td
(n)Tj
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9.97 1.63 Td
[(is)-398(not)-397(decrypted)-398(correctly)83(,)]TJ
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25.17 0 Td
(U)Tj
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5.72 -1.64 Td
(i)Tj
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7.34 1.64 Td
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34.65 0 Td
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5.73 -1.64 Td
(n)Tj
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5.63 1.64 Td
[(.)-533(Otherwise,)]TJ
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63.88 0 Td
(U)Tj
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5.72 -1.64 Td
(i)Tj
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7.34 1.64 Td
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38.56 0 Td
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4.24 -1.11 Td
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4.59 0 Td
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14.2 2.75 Td
[(and)-363(up)-27(dates)]TJ
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62.81 0 Td
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(to)Tj
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22.9 3.95 Td
(0)Tj
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6.76 -3.95 Td
[(b)28(y)-363(including)-363(the)-363(IP)]TJ
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16.45 1.64 Td
[(])-333(of)-334(the)-333(new)-333(user)]TJ
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20.09 1.64 Td
[(and)-333(pro)-28(ceed)-333(to)-333(compute)-334(the)-333(new)-333(group)-334(k)27(ey)]TJ
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15.51 0 Td
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(U)Tj
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5.72 -1.63 Td
(i)Tj
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7.02 1.63 Td
[(for)-333(1)]TJ
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25.17 0 Td
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21.21 0 Td
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5.13 0 Td
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14.95 1.63 Td
[(compute)-333(the)-333(new)-334(group)-333(k)27(ey)]TJ
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136.06 0 Td
(K)Tj
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(0)Tj
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(K)Tj
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10.05 4.5 Td
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12.75 -4.5 Td
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18.44 0 Td
(K)Tj
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10.04 4.5 Td
(\244)Tj
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7.16 -4.5 Td
(\242)Tj
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5.45 0 Td
(K)Tj
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4.24 -0.99 Td
(n)Tj
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5.1 0.99 Td
(U)Tj
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4.23 -1.1 Td
(n)Tj
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18.44 0 Td
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4.35 2.81 Td
(0)Tj
/T1_9 5.98 Tf
0 -5.28 TD
(1)Tj
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4.15 2.47 Td
(d)Tj
/T1_9 5.98 Tf
4.36 -1.11 Td
(2)Tj
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4.15 1.11 Td
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(d)Tj
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10.94 -1.11 Td
(2)Tj
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4.15 1.11 Td
(d)Tj
/T1_9 5.98 Tf
4.35 -1.11 Td
(3)Tj
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4.15 1.11 Td
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6.59 0 Td
(\242\242\242)Tj
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13.64 0 Td
(d)Tj
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4.35 -1 Td
(n)Tj
/T1_3 7.97 Tf
5.1 1 Td
(d)Tj
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4.36 -1.11 Td
(n)Tj
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4.6 0 Td
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(d)Tj
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(n)Tj
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4.6 0 Td
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9.73 1.11 Td
(d)Tj
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4.36 2.81 Td
(0)Tj
/T1_9 5.98 Tf
T*
(1)Tj
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7.68 -2.03 Td
[(mo)-27(d)]TJ
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23.93 0 Td
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115.73 0 Td
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-445.45 -39.65 Td
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5.67 -1.63 Td
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6.41 1.63 Td
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11.51 0 Td
(r)Tj
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4.93 -1.63 Td
(i)Tj
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5.8 1.63 Td
(+)Tj
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10.91 0 Td
(c)Tj
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4.71 -1.63 Td
(i)Tj
/T1_1 10.91 Tf
3.39 1.63 Td
(x)Tj
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6.23 -1.63 Td
(i)Tj
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7.01 1.63 Td
(and)Tj
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21.21 0 Td
(c)Tj
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4.72 -1.63 Td
(i)Tj
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6.41 1.63 Td
(=)Tj
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11.51 0 Td
(H)Tj
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7.73 0 Td
(\()Tj
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(z)Tj
/T1_3 7.97 Tf
9.31 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
3.38 1.63 Td
[(\))-333(for)-333(2)]TJ
/T1_10 10.91 Tf
33.05 0 Td
(\267)Tj
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11.51 0 Td
(i)Tj
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6.79 0 Td
(\267)Tj
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11.51 0 Td
(n)Tj
/T1_0 10.91 Tf
8.97 0 Td
[(+)-222(1)-333(and)]TJ
/T1_1 10.91 Tf
41.2 0 Td
(d)Tj
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5.68 3.96 Td
(0)Tj
/T1_4 7.97 Tf
0 -6.88 TD
(1)Tj
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7.76 2.92 Td
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11.51 0 Td
(r)Tj
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5.22 3.96 Td
(0)Tj
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-0.3 -6.88 Td
(1)Tj
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7.16 2.92 Td
(+)Tj
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10.9 0 Td
(c)Tj
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4.72 3.96 Td
(0)Tj
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T*
(1)Tj
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4.73 2.92 Td
(x)Tj
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6.24 -1.63 Td
(1)Tj
/T1_0 10.91 Tf
8.36 1.63 Td
(and)Tj
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21.21 0 Td
(c)Tj
/T1_5 7.97 Tf
4.72 3.96 Td
(0)Tj
/T1_4 7.97 Tf
T*
(1)Tj
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7.76 2.92 Td
(=)Tj
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11.51 0 Td
(H)Tj
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7.73 0 Td
(\()Tj
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(g)Tj
/T1_3 7.97 Tf
9.83 3.96 Td
(r)Tj
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4.06 2.81 Td
(0)Tj
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-0.24 -5.28 Td
(1)Tj
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4.65 -1.49 Td
(\).)Tj
/T1_12 11.95 Tf
-418.62 -37.82 Td
[(5.5.3)-1125(Merge)-375(Proto)-31(col)]TJ
/T1_0 10.91 Tf
0 -28.96 TD
[(A)-260(merge)-261(o)-28(ccurs)-261(when)-261(t)27(w)28(o)-260(or)-261(more)-261(subgroups)-261(are)-260(com)26(bined)-260(in)27(to)-260(a)-260(single)-261(group;)-285(it)-261(can)-261(also)-261(b)-28(e)-261(seen)-260(as)]TJ
0 -21.92 TD
[(m)27(ultiple)-282(users)-284(joining)-284(a)-283(group.)-428(Let)]TJ
/T1_10 10.91 Tf
167.09 0 Td
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6.49 -1.68 Td
(A)Tj
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9.87 1.68 Td
(=)Tj
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11.51 0 Td
(f)Tj
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(U)Tj
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11.18 -1.63 Td
(1)Tj
/T1_1 10.91 Tf
4.73 1.63 Td
(;)Tj
/T1_10 10.91 Tf
4.85 0 Td
[(\242)-166(\242)-167(\242)]TJ
/T1_1 10.91 Tf
16.36 0 Td
(;)Tj
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4.84 0 Td
(U)Tj
/T1_3 7.97 Tf
5.73 -1.63 Td
(n)Tj
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5.64 1.63 Td
(g)Tj
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8.54 0 Td
[(denote)-283(all)-284(users)-284(in)-283(Group)]TJ
/T1_10 10.91 Tf
121.76 0 Td
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/T1_3 7.97 Tf
6.49 -1.68 Td
(A)Tj
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9.93 1.68 Td
[(with)-283(previously)]TJ
-395.01 -21.91 Td
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103.8 0 Td
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9.27 -1.69 Td
(A)Tj
/T1_0 10.91 Tf
9.58 1.69 Td
[(and)-251(IP)-251(address)-251(allo)-28(cation)-252(table)]TJ
/T1_2 10.91 Tf
147.91 0 Td
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(;)Tj
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4.84 0 Td
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(n)Tj
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(+2)Tj
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16.45 1.64 Td
(;)Tj
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4.85 0 Td
[(\242)-166(\242)-167(\242)]TJ
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16.36 0 Td
(;)Tj
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(g)Tj
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-462.42 -21.92 Td
[(denote)-338(all)-338(users)-339(in)-338(Group)]TJ
/T1_10 10.91 Tf
124.74 0 Td
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6.49 -1.69 Td
(B)Tj
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10.96 1.69 Td
[(with)-338(previously)-339(established)-338(group)-338(k)26(ey)]TJ
/T1_1 10.91 Tf
183.81 0 Td
(K)Tj
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9.26 -1.69 Td
(B)Tj
/T1_0 10.91 Tf
10.96 1.69 Td
[(and)-338(IP)-339(address)-338(allo)-28(cation)]TJ
-346.22 -21.92 Td
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27.02 0 Td
(LIST_B)Tj
/T1_0 10.91 Tf
34.35 0 Td
[(.)-437(W)83(e)-310(divide)]TJ
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58.51 0 Td
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6.48 -1.68 Td
(A)Tj
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10.23 1.68 Td
[(in)27(to)-310(t)27(w)28(o)-310(parts,)]TJ
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73.02 0 Td
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(U)Tj
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11.18 -1.63 Td
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4.73 1.63 Td
(;)Tj
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(U)Tj
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(n)Tj
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(g)Tj
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8.84 0 Td
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(U)Tj
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(2)Tj
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4.74 1.63 Td
(;)Tj
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4.84 0 Td
[(\242)-166(\242)-167(\242)]TJ
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(;)Tj
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(U)Tj
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5.72 -1.63 Td
(n)Tj
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(\241)Tj
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(1)Tj
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(g)Tj
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8.84 0 Td
(and)Tj
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20.96 0 Td
(G)Tj
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6.49 -1.68 Td
(B)Tj
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10.67 1.68 Td
[(in)28(to)]TJ
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21.87 0 Td
(f)Tj
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(U)Tj
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[(w)27(as)-308(stored)-310(from)-309(the)-310(previous)-309(GKA)-309(proto)-28(col)-309(run\))-310(and)-309(obtains)-309(the)-310(Ra-)]TJ
-137.79 -21.91 Td
[(bin's)-333(signature)-333(\()]TJ
/T1_1 10.91 Tf
77.71 0 Td
(\276)Tj
/T1_4 7.97 Tf
6.62 3.95 Td
(0)Tj
/T1_2 7.97 Tf
-0.39 -6.88 Td
(n)Tj
/T1_6 7.97 Tf
5.13 0 Td
(+1)Tj
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11.32 2.93 Td
[(;)-166(\277)]TJ
/T1_4 7.97 Tf
10.85 3.95 Td
(0)Tj
/T1_2 7.97 Tf
-1.23 -6.88 Td
(n)Tj
/T1_6 7.97 Tf
5.13 0 Td
(+1)Tj
/T1_0 10.91 Tf
11.32 2.93 Td
[(\).)-444(Next,)]TJ
/T1_5 10.91 Tf
41.8 0 Td
(U)Tj
/T1_2 7.97 Tf
5.73 -1.64 Td
(n)Tj
/T1_6 7.97 Tf
(+1)Tj
/T1_0 10.91 Tf
20.09 1.64 Td
(broadcasts)Tj
/T1_3 10.91 Tf
54.07 0 Td
(f)Tj
/T1_5 10.91 Tf
(U)Tj
/T1_2 7.97 Tf
11.18 -1.64 Td
(n)Tj
/T1_6 7.97 Tf
(+1)Tj
/T1_3 10.91 Tf
16.45 1.64 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(z)Tj
/T1_4 7.97 Tf
5.56 3.95 Td
(0)Tj
/T1_2 7.97 Tf
-0.48 -6.88 Td
(n)Tj
/T1_6 7.97 Tf
5.13 0 Td
(+1)Tj
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11.32 2.93 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(z)Tj
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5.07 -1.64 Td
(n)Tj
/T1_6 7.97 Tf
(+)Tj
/T1_2 7.97 Tf
(m)Tj
/T1_3 10.91 Tf
19.71 1.64 Td
(jj)Tj
/T1_0 10.91 Tf
6.06 0 Td
(\()Tj
/T1_1 10.91 Tf
(\276)Tj
/T1_4 7.97 Tf
10.86 3.95 Td
(0)Tj
/T1_2 7.97 Tf
-0.39 -6.88 Td
(n)Tj
/T1_6 7.97 Tf
(+1)Tj
/T1_1 10.91 Tf
16.45 2.93 Td
[(;)-166(\277)]TJ
/T1_4 7.97 Tf
10.85 3.95 Td
(0)Tj
/T1_2 7.97 Tf
-1.23 -6.88 Td
(n)Tj
/T1_6 7.97 Tf
5.13 0 Td
(+1)Tj
/T1_0 10.91 Tf
11.32 2.93 Td
(\))Tj
/T1_3 10.91 Tf
(jj)Tj
/T1_5 10.91 Tf
10.3 0 Td
(cert)Tj
/T1_0 10.91 Tf
22.9 0 Td
([)Tj
/T1_5 10.91 Tf
(U)Tj
/T1_2 7.97 Tf
8.76 -1.64 Td
(n)Tj
/T1_6 7.97 Tf
5.13 0 Td
(+1)Tj
/T1_0 10.91 Tf
11.32 1.64 Td
(])Tj
/T1_3 10.91 Tf
(g)Tj
/T1_0 10.91 Tf
(.)Tj
-451.67 -21.92 Td
[(Round)-333(2)]TJ
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 0 -297.4 cm
0 0 m
40.75 0 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 116.3924 473.8672 Tm
(:)Tj
-44.38 -21.92 Td
(\()Tj
/T1_1 10.91 Tf
(i)Tj
/T1_0 10.91 Tf
(\))Tj
/T1_5 10.91 Tf
15.87 0 Td
(U)Tj
/T1_6 7.97 Tf
5.73 -1.63 Td
(1)Tj
/T1_0 10.91 Tf
8.36 1.63 Td
(v)Tj
1.0003 0 0 1.0003 72 769.82 Tm
35.426 -317.79 Td
(eri\257es)Tj
/T1_5 10.91 Tf
30.984 0 Td
(cert)Tj
/T1_0 10.91 Tf
22.9 0 Td
([)Tj
/T1_5 10.91 Tf
(U)Tj
/T1_2 7.97 Tf
8.75 -1.63 Td
(n)Tj
/T1_6 7.97 Tf
(+1)Tj
/T1_0 10.91 Tf
16.46 1.63 Td
[(])-332(and)-334(signature)-333(\()]TJ
/T1_1 10.91 Tf
79.45 0 Td
(\276)Tj
/T1_4 7.97 Tf
6.63 3.96 Td
(0)Tj
/T1_2 7.97 Tf
-0.39 -6.88 Td
(n)Tj
/T1_6 7.97 Tf
5.13 0 Td
(+1)Tj
/T1_1 10.91 Tf
11.32 2.92 Td
[(;)-166(\277)]TJ
/T1_4 7.97 Tf
10.85 3.96 Td
(0)Tj
/T1_2 7.97 Tf
-1.24 -6.88 Td
(n)Tj
/T1_6 7.97 Tf
(+1)Tj
/T1_0 10.91 Tf
16.46 2.92 Td
[(\))-332(from)]TJ
/T1_5 10.91 Tf
33.65 0 Td
(U)Tj
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5.73 -1.63 Td
(n)Tj
/T1_6 7.97 Tf
5.13 0 Td
(+1)Tj
/T1_0 10.91 Tf
11.32 1.63 Td
[(.)-444(If)-333(they)-333(are)-333(in)26(v)56(alid,)-332(then)]TJ
/T1_5 10.91 Tf
124.53 0 Td
(U)Tj
/T1_6 7.97 Tf
5.73 -1.63 Td
(1)Tj
/T1_0 10.91 Tf
8.36 1.63 Td
(rejects)Tj
/T1_5 10.91 Tf
-437.18 -21.91 Td
(U)Tj
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5.73 -1.64 Td
(n)Tj
/T1_6 7.97 Tf
5.13 0 Td
(+1)Tj
/T1_0 10.91 Tf
11.32 1.64 Td
[(.)-551(Otherwise,)]TJ
/T1_5 10.91 Tf
64.16 0 Td
(U)Tj
/T1_6 7.97 Tf
5.72 -1.64 Td
(1)Tj
/T1_0 10.91 Tf
8.76 1.64 Td
[(computes)-369(DH)-369(k)27(ey)]TJ
/T1_1 10.91 Tf
89.54 0 Td
(K)Tj
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9.27 -1.64 Td
(U)Tj
/T1_8 5.98 Tf
4.23 -1.11 Td
(1)Tj
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4.15 1.11 Td
(U)Tj
/T1_10 5.98 Tf
4.23 -1.11 Td
(n)Tj
/T1_8 5.98 Tf
4.6 0 Td
(+1)Tj
/T1_0 10.91 Tf
13.92 2.75 Td
[(=)-337(\()]TJ
/T1_1 10.91 Tf
16.4 0 Td
(z)Tj
/T1_4 7.97 Tf
5.55 3.95 Td
(0)Tj
/T1_2 7.97 Tf
-0.48 -6.87 Td
(n)Tj
/T1_6 7.97 Tf
(+1)Tj
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16.46 2.92 Td
(\))Tj
/T1_2 7.97 Tf
4.24 3.95 Td
(r)Tj
/T1_7 5.98 Tf
4.05 2.82 Td
(0)Tj
/T1_8 5.98 Tf
-0.23 -5.29 Td
(1)Tj
/T1_0 10.91 Tf
8.33 -1.48 Td
(=)Tj
/T1_1 10.91 Tf
12.16 0 Td
(g)Tj
/T1_2 7.97 Tf
5.59 4.47 Td
(r)Tj
/T1_7 5.98 Tf
4.06 2.82 Td
(0)Tj
/T1_8 5.98 Tf
-0.24 -5.29 Td
(1)Tj
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4.15 2.47 Td
(r)Tj
/T1_7 5.98 Tf
4.06 2.82 Td
(0)Tj
/T1_10 5.98 Tf
-0.24 -5.29 Td
(n)Tj
/T1_8 5.98 Tf
4.6 0 Td
(+1)Tj
/T1_0 10.91 Tf
13.27 -2 Td
[(mo)-27(d)]TJ
/T1_1 10.91 Tf
23.93 0 Td
(p)Tj
/T1_0 10.91 Tf
9.52 0 Td
[(shared)-368(with)]TJ
/T1_5 10.91 Tf
60.25 0 Td
(U)Tj
/T1_2 7.97 Tf
5.72 -1.64 Td
(n)Tj
/T1_6 7.97 Tf
(+1)Tj
/T1_0 10.91 Tf
16.45 1.64 Td
(.)Tj
/T1_5 10.91 Tf
9.05 0 Td
(U)Tj
/T1_6 7.97 Tf
5.73 -1.64 Td
(1)Tj
/T1_0 10.91 Tf
-463.14 -20.28 Td
[(then)-333(computes:)]TJ
/T1_1 10.91 Tf
88.69 -39.64 Td
(K)Tj
/T1_4 7.97 Tf
10.04 4.5 Td
(\244)Tj
/T1_2 7.97 Tf
-0.78 -7.2 Td
(A)Tj
/T1_0 10.91 Tf
16.8 2.7 Td
(=)Tj
/T1_1 10.91 Tf
18.44 0 Td
(K)Tj
/T1_2 7.97 Tf
9.26 -1.69 Td
(A)Tj
/T1_3 10.91 Tf
9.26 1.69 Td
(\242)Tj
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5.46 0 Td
(\()Tj
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(z)Tj
/T1_6 7.97 Tf
9.31 -1.64 Td
(2)Tj
/T1_3 10.91 Tf
7.16 1.64 Td
(\242)Tj
/T1_1 10.91 Tf
5.45 0 Td
(y)Tj
/T1_2 7.97 Tf
5.74 4.86 Td
(c)Tj
/T1_8 5.98 Tf
3.66 -1.11 Td
(2)Tj
/T1_6 7.97 Tf
-4.05 -6.88 Td
(2)Tj
/T1_3 10.91 Tf
11.12 3.13 Td
(\242)Tj
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5.46 0 Td
(z)Tj
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5.07 -1.64 Td
(n)Tj
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8.06 1.64 Td
(\242)Tj
/T1_1 10.91 Tf
5.45 0 Td
(y)Tj
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5.74 4.5 Td
(c)Tj
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3.67 -1 Td
(n)Tj
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-4.06 -6.2 Td
(n)Tj
/T1_0 10.91 Tf
9.65 2.7 Td
(\))Tj
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4.24 4.5 Td
(\241)Tj
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6.59 0 Td
(d)Tj
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4.35 -1.11 Td
(1)Tj
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7.08 -3.39 Td
(\242)Tj
/T1_0 10.91 Tf
5.45 0 Td
(\()Tj
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(z)Tj
/T1_6 7.97 Tf
9.31 -1.64 Td
(2)Tj
/T1_3 10.91 Tf
7.16 1.64 Td
(\242)Tj
/T1_1 10.91 Tf
5.45 0 Td
(y)Tj
/T1_2 7.97 Tf
5.74 4.86 Td
(c)Tj
/T1_8 5.98 Tf
3.66 -1.11 Td
(2)Tj
/T1_6 7.97 Tf
-4.05 -6.88 Td
(2)Tj
/T1_3 10.91 Tf
11.13 3.13 Td
(\242)Tj
/T1_1 10.91 Tf
5.45 0 Td
(z)Tj
/T1_2 7.97 Tf
5.07 -1.64 Td
(n)Tj
/T1_6 7.97 Tf
(+)Tj
/T1_2 7.97 Tf
(m)Tj
/T1_3 10.91 Tf
22.13 1.64 Td
(\242)Tj
/T1_1 10.91 Tf
5.45 0 Td
(y)Tj
/T1_2 7.97 Tf
5.74 5.66 Td
(c)Tj
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3.67 -1.08 Td
(n)Tj
/T1_8 5.98 Tf
4.6 0 Td
(+)Tj
/T1_10 5.98 Tf
(m)Tj
/T1_2 7.97 Tf
-8.66 -7.38 Td
(n)Tj
/T1_6 7.97 Tf
(+)Tj
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(m)Tj
/T1_0 10.91 Tf
21.78 2.8 Td
(\))Tj
/T1_2 7.97 Tf
4.24 4.5 Td
(d)Tj
/T1_7 5.98 Tf
4.36 2.81 Td
(0)Tj
/T1_8 5.98 Tf
0 -5.28 TD
(1)Tj
/T1_0 10.91 Tf
-259.79 -26.94 Td
(=)Tj
/T1_1 10.91 Tf
18.44 0 Td
(g)Tj
/T1_2 7.97 Tf
5.59 4.51 Td
(d)Tj
/T1_7 5.98 Tf
4.36 2.81 Td
(0)Tj
/T1_8 5.98 Tf
0 -5.29 TD
(1)Tj
/T1_2 7.97 Tf
4.15 2.48 Td
(d)Tj
/T1_8 5.98 Tf
4.35 -1.11 Td
(2)Tj
/T1_6 7.97 Tf
4.15 1.11 Td
(+)Tj
/T1_2 7.97 Tf
6.59 0 Td
(d)Tj
/T1_8 5.98 Tf
4.36 -1.11 Td
(2)Tj
/T1_2 7.97 Tf
4.15 1.11 Td
(d)Tj
/T1_8 5.98 Tf
4.35 -1.11 Td
(3)Tj
/T1_6 7.97 Tf
4.15 1.11 Td
(+)Tj
/T1_4 7.97 Tf
6.59 0 Td
(\242\242\242)Tj
/T1_6 7.97 Tf
(+)Tj
/T1_2 7.97 Tf
13.64 0 Td
(d)Tj
/T1_10 5.98 Tf
4.35 -1.11 Td
(n)Tj
/T1_7 5.98 Tf
4.6 0 Td
(\241)Tj
/T1_8 5.98 Tf
(1)Tj
/T1_2 7.97 Tf
9.91 1.11 Td
(d)Tj
/T1_10 5.98 Tf
4.35 -1 Td
(n)Tj
/T1_6 7.97 Tf
5.1 1 Td
(+)Tj
/T1_2 7.97 Tf
(d)Tj
/T1_10 5.98 Tf
10.94 -1.08 Td
(n)Tj
/T1_8 5.98 Tf
4.6 0 Td
(+)Tj
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(m)Tj
/T1_2 7.97 Tf
12.62 1.08 Td
(d)Tj
/T1_7 5.98 Tf
4.36 2.81 Td
(0)Tj
/T1_8 5.98 Tf
T*
(1)Tj
/T1_0 10.91 Tf
7.68 -2.03 Td
[(mo)-27(d)]TJ
/T1_1 10.91 Tf
23.93 0 Td
(p:)Tj
/T1_0 10.91 Tf
153.39 0 Td
(\(5.5\))Tj
-445.45 -39.64 Td
(where)Tj
/T1_1 10.91 Tf
30.5 0 Td
(d)Tj
/T1_2 7.97 Tf
5.68 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
6.41 1.64 Td
(=)Tj
/T1_1 10.91 Tf
11.51 0 Td
(r)Tj
/T1_2 7.97 Tf
4.92 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
3.74 1.64 Td
(+)Tj
/T1_1 10.91 Tf
8.84 0 Td
(c)Tj
/T1_2 7.97 Tf
4.72 -1.64 Td
(i)Tj
/T1_1 10.91 Tf
3.38 1.64 Td
(x)Tj
/T1_2 7.97 Tf
6.24 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
5.98 1.64 Td
(and)Tj
/T1_1 10.91 Tf
20.18 0 Td
(c)Tj
/T1_2 7.97 Tf
4.71 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
6.41 1.64 Td
(=)Tj
/T1_9 10.91 Tf
11.52 0 Td
(H)Tj
/T1_0 10.91 Tf
(\()Tj
/T1_1 10.91 Tf
(z)Tj
/T1_2 7.97 Tf
17.03 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
3.39 1.64 Td
[(\))-238(for)]TJ
/T1_1 10.91 Tf
22.5 0 Td
(i)Tj
/T1_0 10.91 Tf
6.79 0 Td
[(=)-277(2)]TJ
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(;)Tj
/T1_3 10.91 Tf
21.81 0 Td
[(\242)-166(\242)-167(\242)]TJ
/T1_1 10.91 Tf
16.36 0 Td
[(;)-166(n;)-167(n)]TJ
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23.14 0 Td
(+)Tj
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8.85 0 Td
(m)Tj
/T1_0 10.91 Tf
12.17 0 Td
(and)Tj
/T1_1 10.91 Tf
20.18 0 Td
(d)Tj
/T1_4 7.97 Tf
5.67 3.96 Td
(0)Tj
/T1_6 7.97 Tf
0 -6.88 TD
(1)Tj
/T1_0 10.91 Tf
7.77 2.92 Td
(=)Tj
/T1_1 10.91 Tf
11.51 0 Td
(r)Tj
/T1_4 7.97 Tf
5.22 3.96 Td
(0)Tj
/T1_6 7.97 Tf
-0.3 -6.88 Td
(1)Tj
/T1_0 10.91 Tf
5.09 2.92 Td
(+)Tj
/T1_1 10.91 Tf
8.84 0 Td
(c)Tj
/T1_4 7.97 Tf
4.72 3.96 Td
(0)Tj
/T1_6 7.97 Tf
T*
(1)Tj
/T1_1 10.91 Tf
4.73 2.92 Td
(x)Tj
/T1_6 7.97 Tf
6.23 -1.64 Td
(1)Tj
/T1_0 10.91 Tf
7.34 1.64 Td
(where)Tj
/T1_1 10.91 Tf
30.5 0 Td
(c)Tj
/T1_4 7.97 Tf
4.72 3.96 Td
(0)Tj
/T1_6 7.97 Tf
T*
(1)Tj
/T1_0 10.91 Tf
7.76 2.92 Td
(=)Tj
/T1_9 10.91 Tf
11.51 0 Td
(H)Tj
/T1_0 10.91 Tf
7.73 0 Td
(\()Tj
/T1_1 10.91 Tf
(z)Tj
/T1_4 7.97 Tf
9.79 3.96 Td
(0)Tj
/T1_6 7.97 Tf
-0.48 -6.88 Td
(1)Tj
/T1_0 10.91 Tf
4.73 2.92 Td
[(\).)-413(Next,)]TJ
/T1_5 10.91 Tf
-430.04 -21.92 Td
(U)Tj
/T1_6 7.97 Tf
5.73 -1.63 Td
(1)Tj
/T1_0 10.91 Tf
7.81 1.63 Td
(encrypts)Tj
/T1_1 10.91 Tf
43.46 0 Td
(K)Tj
/T1_4 7.97 Tf
10.04 3.96 Td
(\244)Tj
/T1_2 7.97 Tf
-0.78 -7.19 Td
(A)Tj
/T1_3 10.91 Tf
6.84 3.23 Td
(jj)Tj
/T1_5 10.91 Tf
6.06 0 Td
(U)Tj
/T1_6 7.97 Tf
5.73 -1.63 Td
(1)Tj
/T1_0 10.91 Tf
7.81 1.63 Td
(and)Tj
/T1_1 10.91 Tf
20.65 0 Td
(K)Tj
/T1_4 7.97 Tf
10.04 3.96 Td
(\244)Tj
/T1_2 7.97 Tf
-0.78 -7.19 Td
(A)Tj
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6.84 3.23 Td
(jj)Tj
/T1_5 10.91 Tf
6.06 0 Td
(LIST_A)Tj
/T1_3 10.91 Tf
34.35 0 Td
(jj)Tj
/T1_5 10.91 Tf
6.06 0 Td
(U)Tj
/T1_6 7.97 Tf
5.73 -1.63 Td
(1)Tj
/T1_0 10.91 Tf
7.81 1.63 Td
[(using)-282(Group)]TJ
/T1_3 10.91 Tf
61.46 0 Td
(G)Tj
/T1_2 7.97 Tf
6.49 -1.68 Td
(A)Tj
/T1_0 10.91 Tf
6.84 1.68 Td
[('s)-282(previously)-282(established)-282(group)-283(k)27(ey)]TJ
/T1_1 10.91 Tf
166.87 0 Td
(K)Tj
/T1_2 7.97 Tf
9.26 -1.68 Td
(A)Tj
/T1_0 10.91 Tf
9.92 1.68 Td
(and)Tj
-450.3 -21.91 Td
[(the)-276(DH)-276(k)27(ey)]TJ
/T1_1 10.91 Tf
56.75 0 Td
(K)Tj
/T1_11 7.97 Tf
9.27 -1.64 Td
(U)Tj
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(+2)Tj
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21.32 3.12 Td
(\242)Tj
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5.45 0 Td
(z)Tj
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5.07 -1.63 Td
(n)Tj
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(+)Tj
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(m)Tj
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22.13 1.63 Td
(\242)Tj
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5.46 0 Td
(y)Tj
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(m)Tj
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(n)Tj
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(m)Tj
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10.05 2.8 Td
(\))Tj
/T1_2 7.97 Tf
4.24 4.5 Td
(\241)Tj
/T1_5 7.97 Tf
6.59 0 Td
(d)Tj
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(=)Tj
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5.6 4.5 Td
(d)Tj
/T1_10 5.98 Tf
4.35 -1 Td
(n)Tj
/T1_5 7.97 Tf
5.1 1 Td
(d)Tj
/T1_11 5.98 Tf
4.35 2.81 Td
(0)Tj
/T1_10 5.98 Tf
0 -5.28 TD
(n)Tj
/T1_9 5.98 Tf
4.6 0 Td
(+1)Tj
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9.74 2.47 Td
(+)Tj
/T1_5 7.97 Tf
6.59 0 Td
(d)Tj
/T1_11 5.98 Tf
4.35 2.81 Td
(0)Tj
/T1_10 5.98 Tf
T*
(n)Tj
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4.6 0 Td
(+1)Tj
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9.74 2.47 Td
(d)Tj
/T1_10 5.98 Tf
4.36 -1.11 Td
(n)Tj
/T1_9 5.98 Tf
4.6 0 Td
(+2)Tj
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9.74 1.11 Td
(+)Tj
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(d)Tj
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10.94 -1.11 Td
(n)Tj
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4.6 0 Td
(+2)Tj
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9.73 1.11 Td
(d)Tj
/T1_10 5.98 Tf
4.36 -1.11 Td
(n)Tj
/T1_9 5.98 Tf
4.6 0 Td
(+3)Tj
/T1_7 7.97 Tf
9.74 1.11 Td
(+)Tj
/T1_2 7.97 Tf
(\242\242\242)Tj
/T1_7 7.97 Tf
13.64 0 Td
(+)Tj
/T1_5 7.97 Tf
(d)Tj
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10.94 -1.11 Td
(n)Tj
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4.6 0 Td
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(m)Tj
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(\241)Tj
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(1)Tj
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4.35 -1.07 Td
(n)Tj
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4.6 0 Td
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(m)Tj
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16.15 -3.43 Td
[(mo)-28(d)]TJ
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23.94 0 Td
(p)Tj
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122.42 0 Td
(\(5.6\))Tj
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(where)Tj
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32.53 0 Td
(d)Tj
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5.68 -1.63 Td
(i)Tj
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8.06 1.63 Td
(=)Tj
/T1_6 10.91 Tf
13.17 0 Td
(r)Tj
/T1_5 7.97 Tf
4.92 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
6.47 1.63 Td
(+)Tj
/T1_6 10.91 Tf
11.57 0 Td
(c)Tj
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4.72 -1.63 Td
(i)Tj
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3.38 1.63 Td
(x)Tj
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6.23 -1.63 Td
(i)Tj
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8.01 1.63 Td
(and)Tj
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22.2 0 Td
(c)Tj
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4.72 -1.63 Td
(i)Tj
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8.07 1.63 Td
(=)Tj
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13.17 0 Td
(H)Tj
/T1_0 10.91 Tf
(\()Tj
/T1_6 10.91 Tf
(z)Tj
/T1_5 7.97 Tf
17.03 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
3.38 1.63 Td
[(\))-424(for)]TJ
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26.56 0 Td
(n)Tj
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11.23 0 Td
(\267)Tj
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13.17 0 Td
(i)Tj
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8.45 0 Td
(6)Tj
/T1_0 10.91 Tf
(=)Tj
/T1_6 10.91 Tf
13.17 0 Td
(n)Tj
/T1_0 10.91 Tf
9.63 0 Td
[(+)-282(1)]TJ
/T1_4 10.91 Tf
21.71 0 Td
(\267)Tj
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13.16 0 Td
(n)Tj
/T1_0 10.91 Tf
9.64 0 Td
(+)Tj
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11.57 0 Td
(m)Tj
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14.2 0 Td
(and)Tj
/T1_6 10.91 Tf
22.2 0 Td
(d)Tj
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5.68 3.96 Td
(0)Tj
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0 -6.88 TD
(n)Tj
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5.13 0 Td
(+1)Tj
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16.01 2.92 Td
(=)Tj
/T1_6 10.91 Tf
13.16 0 Td
(r)Tj
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5.23 3.96 Td
(0)Tj
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-0.3 -6.88 Td
(n)Tj
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5.13 0 Td
(+1)Tj
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14.4 2.92 Td
(+)Tj
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11.57 0 Td
(c)Tj
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4.72 3.96 Td
(0)Tj
/T1_5 7.97 Tf
T*
(n)Tj
/T1_7 7.97 Tf
(+1)Tj
/T1_6 10.91 Tf
16.45 2.92 Td
(x)Tj
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6.24 -1.63 Td
(n)Tj
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5.13 0 Td
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-456.55 -20.28 Td
(where)Tj
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33.03 0 Td
(c)Tj
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4.72 3.96 Td
(0)Tj
/T1_5 7.97 Tf
T*
(n)Tj
/T1_7 7.97 Tf
(+1)Tj
/T1_0 10.91 Tf
21.97 2.92 Td
(=)Tj
/T1_3 10.91 Tf
14 0 Td
(H)Tj
/T1_0 10.91 Tf
7.73 0 Td
(\()Tj
/T1_6 10.91 Tf
(z)Tj
/T1_2 7.97 Tf
9.79 3.96 Td
(0)Tj
/T1_5 7.97 Tf
-0.48 -6.88 Td
(n)Tj
/T1_7 7.97 Tf
(+1)Tj
/T1_0 10.91 Tf
16.45 2.92 Td
[(\).)-855(Next,)]TJ
/T1_1 10.91 Tf
48.16 0 Td
(U)Tj
/T1_5 7.97 Tf
5.72 -1.64 Td
(n)Tj
/T1_7 7.97 Tf
(+1)Tj
/T1_0 10.91 Tf
21.59 1.64 Td
(encrypts)Tj
/T1_6 10.91 Tf
45.51 0 Td
(K)Tj
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10.04 3.96 Td
(\244)Tj
/T1_5 7.97 Tf
-0.78 -7.19 Td
(B)Tj
/T1_4 10.91 Tf
7.28 3.23 Td
(jj)Tj
/T1_3 10.91 Tf
6.05 0 Td
(addr)Tj
/T1_0 10.91 Tf
20.39 0 Td
([)Tj
/T1_4 10.91 Tf
(G)Tj
/T1_5 7.97 Tf
9.52 -1.69 Td
(B)Tj
/T1_0 10.91 Tf
7.28 1.69 Td
(])Tj
/T1_2 7.97 Tf
3.03 3.96 Td
(0)Tj
/T1_4 10.91 Tf
2.79 -3.96 Td
(jj)Tj
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6.06 0 Td
(U)Tj
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5.73 -1.64 Td
(n)Tj
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16.45 1.64 Td
(and)Tj
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22.7 0 Td
(K)Tj
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10.04 3.96 Td
(\244)Tj
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-0.78 -7.19 Td
(B)Tj
/T1_4 10.91 Tf
7.28 3.23 Td
(jj)Tj
/T1_1 10.91 Tf
6.05 0 Td
(LIST_B)Tj
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34.36 3.96 Td
(0)Tj
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2.79 -3.96 Td
(jj)Tj
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6.06 0 Td
(U)Tj
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5.73 -1.64 Td
(n)Tj
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5.13 0 Td
(+1)Tj
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16.45 1.64 Td
(using)Tj
-442.97 -21.92 Td
(Group)Tj
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35.05 0 Td
(G)Tj
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6.49 -1.69 Td
(B)Tj
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7.28 1.69 Td
[('s)-426(previously)-427(established)-426(group)-427(k)27(ey)]TJ
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174.74 0 Td
(K)Tj
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9.26 -1.69 Td
(B)Tj
/T1_0 10.91 Tf
11.93 1.69 Td
[(and)-426(the)-427(DH)-426(k)26(ey)]TJ
/T1_6 10.91 Tf
83.9 0 Td
(K)Tj
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9.26 -1.63 Td
(U)Tj
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4.23 -1.11 Td
(1)Tj
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4.15 1.11 Td
(U)Tj
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4.23 -1.11 Td
(n)Tj
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4.6 0 Td
(+1)Tj
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14.89 2.74 Td
[(resp)-28(ectiv)27(ely)-425(and)-427(ob-)]TJ
-370.01 -21.92 Td
(tains)Tj
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25.65 0 Td
(c)Tj
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5.72 -1.63 Td
(n)Tj
/T1_7 7.97 Tf
(+1)Tj
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19.48 1.63 Td
(=)Tj
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11.52 0 Td
(E)Tj
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5.75 -1.68 Td
(K)Tj
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7.14 -1.34 Td
(B)Tj
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6.82 3.02 Td
(\()Tj
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(K)Tj
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14.28 3.96 Td
(\244)Tj
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-0.78 -7.19 Td
(B)Tj
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7.28 3.23 Td
(jj)Tj
/T1_3 10.91 Tf
6.06 0 Td
(addr)Tj
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20.39 0 Td
([)Tj
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(G)Tj
/T1_5 7.97 Tf
9.52 -1.68 Td
(B)Tj
/T1_0 10.91 Tf
7.27 1.68 Td
(])Tj
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3.03 3.96 Td
(0)Tj
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2.8 -3.96 Td
(jj)Tj
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6.05 0 Td
(U)Tj
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5.73 -1.63 Td
(n)Tj
/T1_7 7.97 Tf
(+1)Tj
/T1_0 10.91 Tf
16.45 1.63 Td
[(\))-235(and)]TJ
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26.94 0 Td
(c)Tj
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5.72 3.96 Td
(0)Tj
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T*
(n)Tj
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19.49 2.92 Td
(=)Tj
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11.51 0 Td
(E)Tj
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5.75 -1.68 Td
(K)Tj
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7.14 -1 Td
(U)Tj
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3.18 -1.79 Td
(1)Tj
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4.15 1.79 Td
(U)Tj
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3.17 -1.79 Td
(n)Tj
/T1_9 5.98 Tf
4.6 0 Td
(+1)Tj
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10.74 4.47 Td
(\()Tj
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(K)Tj
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14.28 3.96 Td
(\244)Tj
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-0.78 -7.19 Td
(B)Tj
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7.28 3.23 Td
(jj)Tj
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6.06 0 Td
(LIST_B)Tj
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34.35 3.96 Td
(0)Tj
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2.79 -3.96 Td
(jj)Tj
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6.06 0 Td
(U)Tj
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5.73 -1.63 Td
(n)Tj
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(+1)Tj
/T1_0 10.91 Tf
16.45 1.63 Td
[(\))-234(resp)-28(ectiv)27(ely)-234(where)]TJ
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-374.77 -21.91 Td
(addr)Tj
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20.39 0 Td
([)Tj
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(G)Tj
/T1_5 7.97 Tf
9.52 -1.69 Td
(B)Tj
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7.27 1.69 Td
(])Tj
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3.03 3.96 Td
(0)Tj
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6.05 -3.96 Td
(=)Tj
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11.74 0 Td
(addr)Tj
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20.39 0 Td
([)Tj
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(G)Tj
/T1_5 7.97 Tf
9.52 -1.69 Td
(B)Tj
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7.27 1.69 Td
[(])-346(and)]TJ
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28.15 0 Td
(LIST_B)Tj
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34.35 3.96 Td
(0)Tj
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6.05 -3.96 Td
(=)Tj
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11.74 0 Td
(LIST_B)Tj
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38.13 0 Td
[(if)-345(there)-346(are)-346(no)-346(address)-346(con\260icts.)-482(Finally)83(,)]TJ
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197.39 0 Td
(U)Tj
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5.73 -1.64 Td
(n)Tj
/T1_7 7.97 Tf
5.13 0 Td
(+1)Tj
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15.09 1.64 Td
(broad-)Tj
-436.94 -21.92 Td
(casts)Tj
/T1_4 10.91 Tf
26.78 0 Td
(f)Tj
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(U)Tj
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11.18 -1.63 Td
(n)Tj
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(+1)Tj
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16.45 1.63 Td
(jj)Tj
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6.06 0 Td
(c)Tj
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5.73 -1.63 Td
(n)Tj
/T1_7 7.97 Tf
5.13 0 Td
(+1)Tj
/T1_4 10.91 Tf
11.32 1.63 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(c)Tj
/T1_2 7.97 Tf
5.72 3.96 Td
(0)Tj
/T1_5 7.97 Tf
T*
(n)Tj
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(+1)Tj
/T1_4 10.91 Tf
16.46 2.92 Td
(g)Tj
/T1_0 10.91 Tf
(.)Tj
-110.89 -21.91 Td
[(Round)-333(3)]TJ
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 0 -313.92 cm
0 0 m
40.75 0 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 116.3924 457.3425 Tm
(:)Tj
-44.38 -21.92 Td
(\()Tj
/T1_6 10.91 Tf
(i)Tj
/T1_0 10.91 Tf
(\))Tj
/T1_1 10.91 Tf
16.49 0 Td
(U)Tj
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5.72 -1.64 Td
(1)Tj
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8.98 1.64 Td
(decrypts)Tj
/T1_1 10.91 Tf
44.63 0 Td
(c)Tj
/T1_2 7.97 Tf
5.73 3.96 Td
(0)Tj
/T1_5 7.97 Tf
T*
(n)Tj
/T1_7 7.97 Tf
(+1)Tj
/T1_0 10.91 Tf
20.7 2.92 Td
(and)Tj
1.0003 0 0 1.0003 72 769.82 Tm
124.07 -334.31 Td
(obtains)Tj
/T1_6 10.91 Tf
38.84 0 Td
(K)Tj
/T1_2 7.97 Tf
10.05 3.96 Td
(\244)Tj
/T1_5 7.97 Tf
-0.78 -7.19 Td
(B)Tj
/T1_0 10.91 Tf
7.27 3.23 Td
(,)Tj
/T1_1 10.91 Tf
7.43 0 Td
(LIST_B)Tj
/T1_2 7.97 Tf
34.36 3.96 Td
(0)Tj
/T1_0 10.91 Tf
7.04 -3.96 Td
[(and)-389(the)-390(iden)27(tit)28(y)]TJ
/T1_1 10.91 Tf
82.12 0 Td
(U)Tj
/T1_5 7.97 Tf
5.73 -1.64 Td
(n)Tj
/T1_7 7.97 Tf
5.13 0 Td
(+1)Tj
/T1_0 10.91 Tf
11.32 1.64 Td
[(.)-612(If)-390(the)-389(iden)26(tit)28(y)]TJ
/T1_1 10.91 Tf
81.53 0 Td
(U)Tj
/T1_5 7.97 Tf
5.73 -1.64 Td
(n)Tj
/T1_7 7.97 Tf
5.13 0 Td
(+1)Tj
/T1_0 10.91 Tf
15.57 1.64 Td
[(is)-389(not)]TJ
-440.54 -21.92 Td
[(decrypted)-403(correctly)83(,)-420(then)]TJ
/T1_1 10.91 Tf
125.26 0 Td
(U)Tj
/T1_7 7.97 Tf
5.72 -1.63 Td
(1)Tj
/T1_0 10.91 Tf
9.13 1.63 Td
(rejects)Tj
/T1_1 10.91 Tf
35.09 0 Td
(c)Tj
/T1_2 7.97 Tf
5.72 3.96 Td
(0)Tj
/T1_5 7.97 Tf
T*
(n)Tj
/T1_7 7.97 Tf
(+1)Tj
/T1_0 10.91 Tf
16.45 2.92 Td
[(.)-654(Otherwise,)]TJ
/T1_1 10.91 Tf
65.74 0 Td
(U)Tj
/T1_7 7.97 Tf
5.72 -1.63 Td
(1)Tj
/T1_0 10.91 Tf
9.13 1.63 Td
[(com)27(bines)]TJ
/T1_1 10.91 Tf
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9.42 0 Td
(+)Tj
/T1_1 10.91 Tf
11.35 0 Td
(m)Tj
/T1_0 10.91 Tf
13.88 0 Td
[(\257rst)-394(decrypt)]TJ
/T1_4 10.91 Tf
63.56 0 Td
(c)Tj
/T1_2 7.97 Tf
5.73 -1.63 Td
(n)Tj
/T1_5 7.97 Tf
5.13 0 Td
(+1)Tj
/T1_0 10.91 Tf
15.62 1.63 Td
[(and)-394(obtain)]TJ
/T1_1 10.91 Tf
56.47 0 Td
(K)Tj
/T1_3 7.97 Tf
10.05 3.96 Td
(\244)Tj
/T1_2 7.97 Tf
-0.78 -7.19 Td
(B)Tj
/T1_0 10.91 Tf
7.27 3.23 Td
(,)Tj
/T1_7 10.91 Tf
7.5 0 Td
(addr)Tj
/T1_0 10.91 Tf
20.39 0 Td
([)Tj
/T1_6 10.91 Tf
(G)Tj
/T1_2 7.97 Tf
9.52 -1.68 Td
(B)Tj
/T1_0 10.91 Tf
7.27 1.68 Td
(])Tj
/T1_3 7.97 Tf
3.03 3.96 Td
(0)Tj
/T1_0 10.91 Tf
7.1 -3.96 Td
(and)Tj
-450.3 -21.91 Td
[(iden)27(tit)28(y)]TJ
/T1_4 10.91 Tf
39.93 0 Td
(U)Tj
/T1_2 7.97 Tf
5.73 -1.64 Td
(n)Tj
/T1_5 7.97 Tf
(+1)Tj
/T1_0 10.91 Tf
16.45 1.64 Td
[(.)-433(If)-301(the)-300(iden)27(tit)27(y)]TJ
/T1_4 10.91 Tf
76.67 0 Td
(U)Tj
/T1_2 7.97 Tf
5.72 -1.64 Td
(n)Tj
/T1_5 7.97 Tf
(+1)Tj
/T1_0 10.91 Tf
19.73 1.64 Td
[(is)-300(not)-301(decrypted)-300(correctly)82(,)-306(eac)27(h)]TJ
/T1_4 10.91 Tf
151.12 0 Td
(U)Tj
/T1_2 7.97 Tf
5.72 -1.64 Td
(j)Tj
/T1_0 10.91 Tf
7.66 1.64 Td
(rejects)Tj
/T1_4 10.91 Tf
33.97 0 Td
(c)Tj
/T1_2 7.97 Tf
5.72 -1.64 Td
(n)Tj
/T1_5 7.97 Tf
(+1)Tj
/T1_0 10.91 Tf
16.46 1.64 Td
[(.)-433(Otherwise,)-307(eac)27(h)]TJ
/T1_4 10.91 Tf
-384.88 -21.92 Td
(U)Tj
/T1_2 7.97 Tf
5.73 -1.63 Td
(j)Tj
/T1_0 10.91 Tf
8.67 1.63 Td
(stores)Tj
/T1_1 10.91 Tf
31.7 0 Td
(K)Tj
/T1_3 7.97 Tf
10.04 3.96 Td
(\244)Tj
/T1_2 7.97 Tf
-0.78 -7.19 Td
(B)Tj
/T1_0 10.91 Tf
11.57 3.23 Td
[(for)-393(k)27(ey)-392(computation)-393(later.)]TJ
/T1_4 10.91 Tf
133.64 0 Td
(U)Tj
/T1_2 7.97 Tf
5.73 -1.63 Td
(j)Tj
/T1_0 10.91 Tf
8.66 1.63 Td
[(also)-393(c)27(hec)27(ks)]TJ
/T1_7 10.91 Tf
56.87 0 Td
(addr)Tj
/T1_0 10.91 Tf
20.39 0 Td
([)Tj
/T1_6 10.91 Tf
(G)Tj
/T1_2 7.97 Tf
9.52 -1.69 Td
(B)Tj
/T1_0 10.91 Tf
7.27 1.69 Td
(])Tj
/T1_3 7.97 Tf
3.03 3.96 Td
(0)Tj
/T1_0 10.91 Tf
7.09 -3.96 Td
[(for)-392(address)-394(con\260ict.)-624(If)-393(there)-393(is)]TJ
-319.13 -21.91 Td
[(an)-390(address)-391(con\260ict,)-405(then)]TJ
/T1_7 10.91 Tf
122.78 0 Td
(addr)Tj
/T1_0 10.91 Tf
20.39 0 Td
([)Tj
/T1_6 10.91 Tf
(G)Tj
/T1_2 7.97 Tf
9.52 -1.69 Td
(B)Tj
/T1_0 10.91 Tf
7.28 1.69 Td
(])Tj
/T1_3 7.97 Tf
3.03 3.95 Td
(0)Tj
/T1_6 10.91 Tf
6.87 -3.95 Td
(6)Tj
/T1_0 10.91 Tf
(=)Tj
/T1_7 10.91 Tf
12.55 0 Td
(addr)Tj
/T1_0 10.91 Tf
20.39 0 Td
([)Tj
/T1_6 10.91 Tf
(G)Tj
/T1_2 7.97 Tf
9.52 -1.69 Td
(B)Tj
/T1_0 10.91 Tf
7.27 1.69 Td
[(],)-405(where)]TJ
/T1_7 10.91 Tf
42.65 0 Td
(addr)Tj
/T1_0 10.91 Tf
20.39 0 Td
([)Tj
/T1_6 10.91 Tf
(G)Tj
/T1_2 7.97 Tf
9.51 -1.69 Td
(B)Tj
/T1_0 10.91 Tf
7.28 1.69 Td
[(])-390(is)-391(the)-391(curren)27(t)-390(Group)]TJ
/T1_6 10.91 Tf
111.52 0 Td
(G)Tj
/T1_2 7.97 Tf
6.48 -1.69 Td
(B)Tj
/T1_0 10.91 Tf
7.28 1.69 Td
[('s)-390(subnet)]TJ
-424.71 -21.92 Td
[(address.)-739(Then)-431(eac)27(h)]TJ
/T1_4 10.91 Tf
101.54 0 Td
(U)Tj
/T1_2 7.97 Tf
5.73 -1.64 Td
(j)Tj
/T1_0 10.91 Tf
9.09 1.64 Td
[(will)-431(c)27(hange)-430(its)-432(IP)-431(address)-432(according)-432(to)]TJ
/T1_7 10.91 Tf
195.71 0 Td
(addr)Tj
/T1_0 10.91 Tf
20.39 0 Td
([)Tj
/T1_6 10.91 Tf
(G)Tj
/T1_2 7.97 Tf
9.52 -1.69 Td
(B)Tj
/T1_0 10.91 Tf
7.28 1.69 Td
(])Tj
/T1_3 7.97 Tf
3.03 3.96 Td
(0)Tj
/T1_0 10.91 Tf
7.5 -3.96 Td
[(and)-431(stores)]TJ
/T1_1 10.91 Tf
54.4 0 Td
(K)Tj
/T1_3 7.97 Tf
10.04 3.96 Td
(\244)Tj
/T1_2 7.97 Tf
-0.78 -7.19 Td
(B)Tj
/T1_0 10.91 Tf
7.28 3.23 Td
[(.)-738(Next,)]TJ
/T1_4 10.91 Tf
-430.73 -21.92 Td
(U)Tj
/T1_2 7.97 Tf
5.73 -1.63 Td
(j)Tj
/T1_0 10.91 Tf
8.52 1.63 Td
(decrypt)Tj
/T1_4 10.91 Tf
40.23 0 Td
(c)Tj
/T1_3 7.97 Tf
5.73 3.96 Td
(00)Tj
/T1_2 7.97 Tf
T*
(n)Tj
/T1_5 7.97 Tf
5.13 0 Td
(+1)Tj
/T1_0 10.91 Tf
15.47 2.92 Td
[(and)-380(obtain)]TJ
/T1_1 10.91 Tf
56.16 0 Td
(K)Tj
/T1_3 7.97 Tf
10.04 3.96 Td
(\244)Tj
/T1_2 7.97 Tf
-0.78 -7.19 Td
(A)Tj
/T1_0 10.91 Tf
6.84 3.23 Td
(,)Tj
/T1_4 10.91 Tf
7.3 0 Td
(LIST)Tj
/T1_3 7.97 Tf
22.91 3.96 Td
(0)Tj
/T1_0 10.91 Tf
6.94 -3.96 Td
[(and)-380(the)-380(iden)27(tit)28(y)]TJ
/T1_4 10.91 Tf
81.82 0 Td
(U)Tj
/T1_2 7.97 Tf
5.72 -1.63 Td
(n)Tj
/T1_5 7.97 Tf
(+1)Tj
/T1_0 10.91 Tf
20.6 1.63 Td
[(resp)-27(ectiv)26(ely)84(.)-584(If)-381(the)-380(iden)27(tit)28(y)]TJ
/T1_4 10.91 Tf
135.85 0 Td
(U)Tj
/T1_2 7.97 Tf
5.73 -1.63 Td
(n)Tj
/T1_5 7.97 Tf
(+1)Tj
/T1_0 10.91 Tf
20.6 1.63 Td
(is)Tj
-460.54 -21.91 Td
[(not)-352(decrypted)-352(correctly)82(,)-355(then)-353(eac)27(h)]TJ
/T1_4 10.91 Tf
167.79 0 Td
(U)Tj
/T1_2 7.97 Tf
5.73 -1.64 Td
(j)Tj
/T1_0 10.91 Tf
8.22 1.64 Td
(rejects)Tj
/T1_4 10.91 Tf
34.53 0 Td
(c)Tj
/T1_3 7.97 Tf
5.72 3.95 Td
(00)Tj
/T1_2 7.97 Tf
T*
(n)Tj
/T1_5 7.97 Tf
(+1)Tj
/T1_0 10.91 Tf
16.46 2.93 Td
[(.)-500(Otherwise,)-357(eac)27(h)]TJ
/T1_4 10.91 Tf
88.11 0 Td
(U)Tj
/T1_2 7.97 Tf
5.73 -1.64 Td
(j)Tj
/T1_0 10.91 Tf
8.22 1.64 Td
(stores)Tj
/T1_4 10.91 Tf
31.26 0 Td
(LIST)Tj
/T1_3 7.97 Tf
22.9 3.95 Td
(0)Tj
/T1_0 10.91 Tf
6.63 -3.95 Td
[(as)-352(the)-352(new)-352(IP)]TJ
-401.3 -21.92 Td
[(allo)-27(cation)-334(table)-333(and)-333(stores)]TJ
/T1_1 10.91 Tf
129.51 0 Td
(K)Tj
/T1_3 7.97 Tf
10.04 3.96 Td
(\244)Tj
/T1_2 7.97 Tf
-0.78 -7.19 Td
(A)Tj
/T1_0 10.91 Tf
10.48 3.23 Td
[(for)-333(k)27(ey)-332(computation)-333(later.)]TJ
-149.25 -21.92 Td
(\()Tj
/T1_1 10.91 Tf
(iii)Tj
/T1_0 10.91 Tf
15.51 0 Td
[(\))-328(Finally)83(,)-328(all)-328(users)]TJ
/T1_4 10.91 Tf
89.45 0 Td
(U)Tj
/T1_2 7.97 Tf
5.73 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
6.95 1.63 Td
[(for)-328(1)]TJ
/T1_6 10.91 Tf
25.12 0 Td
(\267)Tj
/T1_1 10.91 Tf
11.51 0 Td
(i)Tj
/T1_6 10.91 Tf
6.79 0 Td
(\267)Tj
/T1_1 10.91 Tf
11.51 0 Td
(n)Tj
/T1_0 10.91 Tf
8.85 0 Td
(+)Tj
/T1_1 10.91 Tf
10.79 0 Td
(m)Tj
/T1_0 10.91 Tf
13.15 0 Td
[(in)-328(the)-328(merged)-328(group)]TJ
/T1_6 10.91 Tf
100.41 0 Td
(G)Tj
/T1_3 7.97 Tf
7.13 3.96 Td
(0)Tj
/T1_0 10.91 Tf
6.37 -3.96 Td
[(compute)-328(the)-328(new)-328(group)-328(k)27(ey)]TJ
/T1_1 10.91 Tf
135.76 0 Td
(K)Tj
/T1_3 7.97 Tf
10.05 3.96 Td
(0)Tj
/T1_0 10.91 Tf
-465.08 -25.87 Td
[(as)-333(follo)27(ws:)]TJ
/T1_1 10.91 Tf
78.91 -39.65 Td
(K)Tj
/T1_3 7.97 Tf
10.05 4.51 Td
(0)Tj
/T1_0 10.91 Tf
12.75 -4.51 Td
(=)Tj
/T1_1 10.91 Tf
18.44 0 Td
(K)Tj
/T1_3 7.97 Tf
10.05 4.51 Td
(\244)Tj
/T1_2 7.97 Tf
-0.79 -7.2 Td
(A)Tj
/T1_6 10.91 Tf
9.27 2.69 Td
(\242)Tj
/T1_1 10.91 Tf
5.45 0 Td
(K)Tj
/T1_3 7.97 Tf
10.04 4.51 Td
(\244)Tj
/T1_2 7.97 Tf
-0.78 -7.2 Td
(B)Tj
/T1_0 10.91 Tf
-51.68 -22.21 Td
(=)Tj
/T1_1 10.91 Tf
18.44 0 Td
(g)Tj
/T1_2 7.97 Tf
5.6 4.5 Td
(d)Tj
/T1_8 5.98 Tf
4.35 2.81 Td
(0)Tj
/T1_9 5.98 Tf
0 -5.28 TD
(1)Tj
/T1_2 7.97 Tf
4.15 2.47 Td
(d)Tj
/T1_9 5.98 Tf
4.36 -1.1 Td
(2)Tj
/T1_5 7.97 Tf
4.15 1.1 Td
(+)Tj
/T1_2 7.97 Tf
(d)Tj
/T1_9 5.98 Tf
10.94 -1.1 Td
(2)Tj
/T1_2 7.97 Tf
4.15 1.1 Td
(d)Tj
/T1_9 5.98 Tf
4.35 -1.1 Td
(3)Tj
/T1_5 7.97 Tf
4.15 1.1 Td
(+)Tj
/T1_3 7.97 Tf
6.59 0 Td
(\242\242\242)Tj
/T1_5 7.97 Tf
(+)Tj
/T1_2 7.97 Tf
13.64 0 Td
(d)Tj
/T1_10 5.98 Tf
4.35 -0.99 Td
(n)Tj
/T1_2 7.97 Tf
5.1 0.99 Td
(d)Tj
/T1_8 5.98 Tf
4.36 2.81 Td
(0)Tj
/T1_10 5.98 Tf
T*
(n)Tj
/T1_9 5.98 Tf
4.6 0 Td
(+1)Tj
/T1_5 7.97 Tf
9.74 2.47 Td
(+)Tj
/T1_2 7.97 Tf
(d)Tj
/T1_8 5.98 Tf
10.94 2.81 Td
(0)Tj
/T1_10 5.98 Tf
T*
(n)Tj
/T1_9 5.98 Tf
4.6 0 Td
(+1)Tj
/T1_2 7.97 Tf
9.73 2.47 Td
(d)Tj
/T1_10 5.98 Tf
4.36 -1.1 Td
(n)Tj
/T1_9 5.98 Tf
4.6 0 Td
(+2)Tj
/T1_5 7.97 Tf
9.74 1.1 Td
(+)Tj
/T1_2 7.97 Tf
(d)Tj
/T1_10 5.98 Tf
10.94 -1.1 Td
(n)Tj
/T1_9 5.98 Tf
4.6 0 Td
(+2)Tj
/T1_2 7.97 Tf
9.74 1.1 Td
(d)Tj
/T1_10 5.98 Tf
4.35 -1.1 Td
(n)Tj
/T1_9 5.98 Tf
4.6 0 Td
(+3)Tj
/T1_5 7.97 Tf
9.74 1.1 Td
(+)Tj
/T1_3 7.97 Tf
6.59 0 Td
(\242\242\242)Tj
/T1_5 7.97 Tf
(+)Tj
/T1_2 7.97 Tf
13.64 0 Td
(d)Tj
/T1_10 5.98 Tf
4.35 -1.07 Td
(n)Tj
/T1_9 5.98 Tf
4.6 0 Td
(+)Tj
/T1_10 5.98 Tf
(m)Tj
/T1_2 7.97 Tf
12.62 1.07 Td
(d)Tj
/T1_8 5.98 Tf
4.36 2.81 Td
(0)Tj
/T1_9 5.98 Tf
T*
(1)Tj
/T1_0 10.91 Tf
7.68 -2.03 Td
[(mo)-27(d)]TJ
/T1_1 10.91 Tf
23.93 0 Td
(p:)Tj
/T1_0 10.91 Tf
65.01 0 Td
(\(5.7\))Tj
-445.45 -39.64 Td
(where)Tj
/T1_1 10.91 Tf
31.54 0 Td
(d)Tj
/T1_2 7.97 Tf
5.67 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
6.41 1.64 Td
(=)Tj
/T1_1 10.91 Tf
11.51 0 Td
(r)Tj
/T1_2 7.97 Tf
4.93 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
5.8 1.64 Td
(+)Tj
/T1_1 10.91 Tf
10.91 0 Td
(c)Tj
/T1_2 7.97 Tf
4.71 -1.64 Td
(i)Tj
/T1_1 10.91 Tf
3.39 1.64 Td
(x)Tj
/T1_2 7.97 Tf
6.23 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
7.01 1.64 Td
[(for)-333(2)]TJ
/T1_6 10.91 Tf
25.18 0 Td
(\267)Tj
/T1_1 10.91 Tf
11.51 0 Td
(i)Tj
/T1_6 10.91 Tf
6.79 0 Td
(6)Tj
/T1_0 10.91 Tf
(=)Tj
/T1_1 10.91 Tf
11.51 0 Td
(n)Tj
/T1_0 10.91 Tf
8.97 0 Td
[(+)-222(1)]TJ
/T1_6 10.91 Tf
19.39 0 Td
(\267)Tj
/T1_1 10.91 Tf
11.51 0 Td
(n)Tj
/T1_0 10.91 Tf
8.97 0 Td
(+)Tj
/T1_1 10.91 Tf
10.91 0 Td
(m)Tj
/T1_0 10.91 Tf
9.57 0 Td
(,)Tj
/T1_1 10.91 Tf
6.67 0 Td
(d)Tj
/T1_3 7.97 Tf
5.67 3.95 Td
(0)Tj
/T1_5 7.97 Tf
0 -6.88 TD
(1)Tj
/T1_0 10.91 Tf
7.76 2.93 Td
(=)Tj
/T1_1 10.91 Tf
11.51 0 Td
(r)Tj
/T1_3 7.97 Tf
5.23 3.95 Td
(0)Tj
/T1_5 7.97 Tf
-0.3 -6.88 Td
(1)Tj
/T1_0 10.91 Tf
7.15 2.93 Td
(+)Tj
/T1_1 10.91 Tf
10.91 0 Td
(c)Tj
/T1_3 7.97 Tf
4.72 3.95 Td
(0)Tj
/T1_5 7.97 Tf
T*
(1)Tj
/T1_1 10.91 Tf
4.73 2.93 Td
(x)Tj
/T1_5 7.97 Tf
6.23 -1.64 Td
(1)Tj
/T1_0 10.91 Tf
8.37 1.64 Td
(and)Tj
/T1_1 10.91 Tf
21.2 0 Td
(d)Tj
/T1_3 7.97 Tf
5.68 3.95 Td
(0)Tj
/T1_2 7.97 Tf
T*
(n)Tj
/T1_5 7.97 Tf
(+1)Tj
/T1_0 10.91 Tf
19.48 2.93 Td
(=)Tj
/T1_1 10.91 Tf
11.51 0 Td
(r)Tj
/T1_3 7.97 Tf
5.23 3.95 Td
(0)Tj
/T1_2 7.97 Tf
-0.31 -6.88 Td
(n)Tj
/T1_5 7.97 Tf
(+1)Tj
/T1_0 10.91 Tf
18.88 2.93 Td
(+)Tj
/T1_1 10.91 Tf
10.9 0 Td
(c)Tj
/T1_3 7.97 Tf
4.72 3.95 Td
(0)Tj
/T1_2 7.97 Tf
T*
(n)Tj
/T1_5 7.97 Tf
(+1)Tj
/T1_1 10.91 Tf
16.46 2.93 Td
(x)Tj
/T1_2 7.97 Tf
6.23 -1.64 Td
(n)Tj
/T1_5 7.97 Tf
(+1)Tj
/T1_0 10.91 Tf
16.45 1.64 Td
(.)Tj
/T1_11 11.95 Tf
-437.5 -37.83 Td
[(5.5.4)-1125(Lea)31(v)31(e)-374(Proto)-31(col)]TJ
/T1_0 10.91 Tf
0 -28.96 TD
[(A)-430(lea)27(ving)-430(user)]TJ
/T1_4 10.91 Tf
75.07 0 Td
(U)Tj
/T1_2 7.97 Tf
5.73 -1.77 Td
(l)Tj
/T1_0 10.91 Tf
7.82 1.77 Td
[(will)-430(send)-431(a)-430(lea)26(v)28(e)-430(noti\257cation)-430(to)-431(announce)-431(its)-430(departure)-431(from)-431(the)-431(group.)-736(The)]TJ
-88.62 -21.91 Td
[(group)-367(k)27(ey)-366(will)-367(b)-28(e)-367(c)27(hanged)-367(to)-367(protect)-367(future)-367(MANET)-367(comm)26(unications)-366(from)-367(the)-367(lea)27(ving)-367(user.)-546(Let)]TJ
/T1_6 10.91 Tf
0 -21.92 TD
(G)Tj
/T1_0 10.91 Tf
11.69 0 Td
(=)Tj
/T1_6 10.91 Tf
13.04 0 Td
(f)Tj
/T1_4 10.91 Tf
(U)Tj
/T1_5 7.97 Tf
11.18 -1.63 Td
(1)Tj
/T1_1 10.91 Tf
4.73 1.63 Td
(;)Tj
/T1_6 10.91 Tf
4.85 0 Td
[(\242)-166(\242)-167(\242)]TJ
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(0)Tj
/T1_8 5.98 Tf
-0.33 -5.58 Td
(l)Tj
/T1_7 5.98 Tf
2.4 0 Td
(\241)Tj
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5.75 0 Td
(1)Tj
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4.15 2.84 Td
(\242)Tj
/T1_3 7.97 Tf
(y)Tj
/T1_8 5.98 Tf
6.82 6.83 Td
(c)Tj
/T1_7 5.98 Tf
3.35 2.05 Td
(0)Tj
/T1_8 5.98 Tf
T*
(l)Tj
/T1_7 5.98 Tf
2.4 0 Td
(\241)Tj
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5.75 0 Td
(1)Tj
/T1_8 5.98 Tf
-11.78 -6.41 Td
(l)Tj
/T1_7 5.98 Tf
2.4 0 Td
(\241)Tj
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5.75 0 Td
(1)Tj
/T1_9 10.91 Tf
9.47 31.62 Td
(!)Tj
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8.64 -2.55 Td
(d)Tj
/T1_7 5.98 Tf
4.35 2.82 Td
(0)Tj
/T1_8 5.98 Tf
0 -5.59 TD
(l)Tj
/T1_10 5.98 Tf
2.4 0 Td
(+1)Tj
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13.88 -13.33 Td
(if)Tj
/T1_1 10.91 Tf
9.99 0 Td
(i)Tj
/T1_0 10.91 Tf
6.79 0 Td
(=)Tj
/T1_1 10.91 Tf
11.51 0 Td
(l)Tj
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5.89 0 Td
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1.0003 0 0 1.0003 72 769.82 Tm
296.37 -237.42 Td
(1)Tj
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(:)Tj
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149.08 37.36 Td
(\(5.8\))Tj
-445.45 -71.02 Td
(for)Tj
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16.87 0 Td
(d)Tj
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5.68 3.96 Td
(0)Tj
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0 -7.01 TD
(i)Tj
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6.71 3.05 Td
(=)Tj
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11.81 0 Td
(r)Tj
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5.22 3.96 Td
(0)Tj
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-0.3 -7.01 Td
(i)Tj
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5.93 3.05 Td
(+)Tj
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11.02 0 Td
(c)Tj
/T1_5 7.97 Tf
4.72 3.96 Td
(0)Tj
/T1_3 7.97 Tf
T*
(i)Tj
/T1_1 10.91 Tf
3.38 3.05 Td
(x)Tj
/T1_3 7.97 Tf
6.23 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
7.2 1.63 Td
(and)Tj
/T1_1 10.91 Tf
21.39 0 Td
(c)Tj
/T1_5 7.97 Tf
4.72 3.96 Td
(0)Tj
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T*
(i)Tj
/T1_0 10.91 Tf
6.71 3.05 Td
(=)Tj
/T1_11 10.91 Tf
11.81 0 Td
(H)Tj
/T1_0 10.91 Tf
(\()Tj
/T1_1 10.91 Tf
(z)Tj
/T1_5 7.97 Tf
17.52 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.48 -7.01 Td
(i)Tj
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3.38 3.05 Td
[(\))-349(where)]TJ
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39.77 0 Td
(z)Tj
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5.55 3.96 Td
(0)Tj
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-0.48 -7.01 Td
(i)Tj
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(=)Tj
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11.81 0 Td
(z)Tj
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5.08 -1.63 Td
(i)Tj
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3.38 1.63 Td
(,)Tj
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6.89 0 Td
(d)Tj
/T1_5 7.97 Tf
5.67 3.96 Td
(0)Tj
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T*
(i)Tj
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6.71 3.05 Td
(=)Tj
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11.81 0 Td
(d)Tj
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5.68 -1.63 Td
(i)Tj
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3.38 1.63 Td
(,)Tj
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6.89 0 Td
(r)Tj
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5.22 3.96 Td
(0)Tj
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-0.3 -7.01 Td
(i)Tj
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6.71 3.05 Td
(=)Tj
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11.81 0 Td
(r)Tj
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4.92 -1.63 Td
(i)Tj
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7.2 1.63 Td
(and)Tj
/T1_1 10.91 Tf
21.39 0 Td
(c)Tj
/T1_5 7.97 Tf
4.72 3.96 Td
(0)Tj
/T1_3 7.97 Tf
T*
(i)Tj
/T1_0 10.91 Tf
6.71 3.05 Td
(=)Tj
/T1_1 10.91 Tf
11.81 0 Td
(c)Tj
/T1_3 7.97 Tf
4.72 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
7.19 1.63 Td
(for)Tj
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16.88 0 Td
(i)Tj
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7.08 0 Td
(6)Tj
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(=)Tj
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11.81 0 Td
(l)Tj
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7.29 0 Td
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21.39 0 Td
(i)Tj
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7.57 0 Td
[(is)-349(ev)27(en.)]TJ
-432.49 -21.91 Td
[(Finally)83(,)-348(eac)27(h)-345(remaining)-345(user)]TJ
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138.38 0 Td
(U)Tj
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5.72 -1.64 Td
(i)Tj
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6.64 1.64 Td
[(2)-297(G)]TJ
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17.65 3.96 Td
(0)Tj
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6.57 -3.96 Td
[(for)-345(1)]TJ
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25.53 0 Td
(\267)Tj
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11.73 0 Td
(i)Tj
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7.01 0 Td
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11.74 0 Td
(l)Tj
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6.72 0 Td
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11.73 0 Td
(n)Tj
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10.32 0 Td
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48.67 0 Td
(Z)Tj
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8.77 3.96 Td
(0)Tj
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6.04 -3.96 Td
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11.74 8.18 Td
(Q)Tj
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10.3 -3.16 Td
(n)Tj
0 -8.25 TD
(j)Tj
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3.88 0 Td
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(;j)Tj
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(j)Tj
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7.41 3.06 Td
[(mo)-27(d)]TJ
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23.93 0 Td
(p)Tj
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9.26 0 Td
[(and)-345(signs)]TJ
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(U)Tj
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(i)Tj
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(jj)Tj
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(0)Tj
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(i)Tj
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(jj)Tj
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9.18 2.76 Td
(^)Tj
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-3.12 -2.76 Td
(X)Tj
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9.89 3.96 Td
(0)Tj
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(i)Tj
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3.65 3.05 Td
(jjZ)Tj
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14.83 3.96 Td
(0)Tj
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7.25 -3.96 Td
[(to)-407(obtain)-409(Rabin's)-408(signature)-408(\()]TJ
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141.71 0 Td
(\276)Tj
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6.62 3.96 Td
(0)Tj
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-0.39 -7.01 Td
(i)Tj
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3.38 3.05 Td
[(;)-166(\277)]TJ
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10.85 3.96 Td
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(i)Tj
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[(\))-408(and)-408(broadcasts)]TJ
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85.61 0 Td
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9.19 2.76 Td
(^)Tj
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(X)Tj
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(0)Tj
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3.65 3.05 Td
(jj)Tj
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6.05 0 Td
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4.25 0 Td
(\276)Tj
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6.62 3.96 Td
(0)Tj
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-0.39 -7.01 Td
(i)Tj
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3.38 3.05 Td
[(;)-166(\277)]TJ
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10.85 3.96 Td
(0)Tj
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-1.24 -7.01 Td
(i)Tj
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4.03 3.05 Td
(\))Tj
/T1_4 10.91 Tf
(g)Tj
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[(.)-668(All)-408(remaining)]TJ
-381.87 -21.92 Td
[(users)-305(store)]TJ
/T1_4 10.91 Tf
53.56 0 Td
(Z)Tj
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8.77 3.96 Td
(0)Tj
/T1_0 10.91 Tf
6.12 -3.96 Td
[(for)-305(v)27(eri\257cation)-304(in)-306(the)-305(next)-305(round.)-435(W)82(e)-304(assume)]TJ
/T1_2 10.91 Tf
219.12 0 Td
(U)Tj
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5.73 -1.63 Td
(1)Tj
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8.06 1.63 Td
[(to)-305(b)-27(e)-306(a)-305(trusted)-305(con)27(troller)-305(suc)27(h)-304(that)]TJ
/T1_2 10.91 Tf
-301.36 -21.91 Td
(U)Tj
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5.73 -1.64 Td
(1)Tj
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8.36 1.64 Td
[(is)-333(the)-333(last)-334(user)-333(to)-333(broadcast)-334(its)-333(message)-333(after)-334(all)-333(other)-333(users)-334(ha)27(v)28(e)-332(broadcast)-334(their)-333(messages.)]TJ
-14.09 -21.92 Td
[(Authen)27(tication)-332(and)-333(Key)-334(Computation)]TJ
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 0 -384.31 cm
0 0 m
182.07 0 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 254.121 389.0534 Tm
(:)Tj
1.0003 0 0 1.0003 72 769.82 Tm
189.489 -380.66 Td
[(Eac)27(h)]TJ
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(i)Tj
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6.41 1.63 Td
[(2)-277(G)]TJ
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17.43 3.96 Td
(0)Tj
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5.51 -3.96 Td
[(for)-248(1)]TJ
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24.25 0 Td
(\267)Tj
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11.52 0 Td
(i)Tj
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6.78 0 Td
(6)Tj
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(=)Tj
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11.51 0 Td
(l)Tj
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6.5 0 Td
(\267)Tj
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11.51 0 Td
(n)Tj
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9.26 0 Td
[(v)27(eri\257es)-248(the)-249(Rabin's)-249(signature)]TJ
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(0)Tj
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(j)Tj
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4.38 3.06 Td
[(;)-167(\277)]TJ
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(0)Tj
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(j)Tj
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4.38 3.06 Td
[(\))-391(of)-392(message)]TJ
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64.14 0 Td
(U)Tj
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5.73 -1.64 Td
(j)Tj
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4.38 1.64 Td
(jj)Tj
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6.06 0 Td
(z)Tj
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5.55 3.95 Td
(0)Tj
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(j)Tj
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4.38 3.06 Td
(jj)Tj
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9.19 2.75 Td
(^)Tj
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-3.13 -2.75 Td
(X)Tj
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9.89 3.95 Td
(0)Tj
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-0.86 -7.01 Td
(j)Tj
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4.38 3.06 Td
(jjZ)Tj
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14.83 3.95 Td
(0)Tj
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7.07 -3.95 Td
[(for)-392(1)]TJ
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26.88 0 Td
(\267)Tj
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12.58 0 Td
(j)Tj
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9.2 0 Td
(6)Tj
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(=)Tj
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12.58 0 Td
(i)Tj
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7.85 0 Td
(\267)Tj
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12.58 0 Td
(n)Tj
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10.82 0 Td
(and)Tj
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21.84 0 Td
(j)Tj
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9.21 0 Td
(6)Tj
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(=)Tj
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12.58 0 Td
(l)Tj
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3.47 0 Td
[(,)-406(where)]TJ
/T1_4 10.91 Tf
39.64 0 Td
(Z)Tj
/T1_5 7.97 Tf
8.77 3.95 Td
(0)Tj
/T1_0 10.91 Tf
7.06 -3.95 Td
[(w)27(as)-391(stored)-392(in)-392(Round)-392(2.)]TJ
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[(If)-401(the)-402(signature)-402(v)27(eri\257cations)-401(are)-402(correct,)-419(then)-402(from)-402(equation)-402(\(5.8\))-402(and)-402(using)-401(similar)-402(calculations)]TJ
0 -21.92 TD
[(as)-389(men)27(tioned)-389(in)-389(the)-390(Authen)27(tication)-389(and)-389(Key)-390(Computation)-389(Round)-390(of)-389(the)-390(prop)-28(osed)-389(IKA)-390(proto)-27(col)]TJ
0 -21.91 TD
[(in)-401(Section)-401(5.5.1,)-418(eac)27(h)]TJ
/T1_2 10.91 Tf
107.66 0 Td
(U)Tj
/T1_3 7.97 Tf
5.73 -1.64 Td
(i)Tj
/T1_4 10.91 Tf
7.64 1.64 Td
[(2)-390(G)]TJ
/T1_5 7.97 Tf
18.67 3.95 Td
(0)Tj
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7.16 -3.95 Td
[(for)-401(1)]TJ
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27.15 0 Td
(\267)Tj
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12.75 0 Td
(i)Tj
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8.02 0 Td
(6)Tj
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(=)Tj
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12.74 0 Td
(l)Tj
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7.73 0 Td
(\267)Tj
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12.75 0 Td
(n)Tj
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10.92 0 Td
(obtains)Tj
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38.97 0 Td
(g)Tj
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5.59 4.91 Td
(d)Tj
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4.36 2.82 Td
(0)Tj
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0 -5.4 TD
(j)Tj
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3.9 2.58 Td
(d)Tj
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4.35 2.82 Td
(0)Tj
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T*
(j)Tj
/T1_10 5.98 Tf
3.41 0 Td
(+1)Tj
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13.26 -2.33 Td
[(mo)-28(d)]TJ
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23.94 0 Td
(p)Tj
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9.86 0 Td
[(for)-401(1)]TJ
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27.15 0 Td
(\267)Tj
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12.74 0 Td
(j)Tj
/T1_4 10.91 Tf
9.38 0 Td
(6)Tj
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(=)Tj
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12.74 0 Td
(l)Tj
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7.73 0 Td
(\267)Tj
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12.75 0 Td
(n)Tj
/T1_0 10.91 Tf
10.92 0 Td
(where)Tj
/T1_1 10.91 Tf
-439.97 -21.92 Td
(d)Tj
/T1_5 7.97 Tf
5.68 3.96 Td
(0)Tj
/T1_3 7.97 Tf
0 -7.01 TD
(j)Tj
/T1_0 10.91 Tf
8.2 3.05 Td
(=)Tj
/T1_1 10.91 Tf
12.31 0 Td
(r)Tj
/T1_5 7.97 Tf
5.22 3.96 Td
(0)Tj
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-0.3 -7.01 Td
(j)Tj
/T1_0 10.91 Tf
7.12 3.05 Td
(+)Tj
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11.23 0 Td
(c)Tj
/T1_5 7.97 Tf
4.72 3.96 Td
(0)Tj
/T1_3 7.97 Tf
T*
(j)Tj
/T1_1 10.91 Tf
4.38 3.05 Td
(x)Tj
/T1_3 7.97 Tf
6.23 -1.64 Td
(j)Tj
/T1_0 10.91 Tf
8.49 1.64 Td
(and)Tj
/T1_1 10.91 Tf
21.69 0 Td
(d)Tj
/T1_5 7.97 Tf
5.67 3.96 Td
(0)Tj
/T1_3 7.97 Tf
T*
(j)Tj
/T1_0 10.91 Tf
8.21 3.05 Td
(=)Tj
/T1_1 10.91 Tf
12.3 0 Td
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[(insiders)-333(to)-333(imp)-28(ersonate)-333(an)27(y)-333(user)-333(in)-333(the)-334(group)-333(to)-333(establish)-334(a)-333(new)-333(group)-334(k)27(ey)83(.)]TJ
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
6.1 w
q 1 0 0 1 464.82 -377.39 cm
0 0 m
0 6.1 l
S
Q
Q
BT
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1.0003 0 0 1.0003 72 354.6938 Tm
(5.6.2)Tj
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41.084 -415.01 Td
[(Securit)31(y)-374(Analysis)-375(of)-375(Join)-375(Proto)-32(col)]TJ
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[(In)-399(this)-399(section,)-415(w)27(e)-398(\257rst)-399(sho)27(w)-398(that)-399(the)-399(Join)-399(Proto)-28(col)-399(ac)27(hiev)27(es)-398(bac)27(kw)28(ard)-398(secrecy)82(,)-414(that)-399(is,)-416(the)-399(new)]TJ
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[(cannot)-349(obtain)-350(the)-350(previously)-349(established)-350(group)-349(k)26(ey)]TJ
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[(The)-430(pr)50(op)51(ose)51(d)-429(Join)-430(pr)50(oto)51(c)51(ol)-429(achieves)-430(b)50(ackwar)51(d)-429(se)50(cr)51(e)51(cy)-429(in)-430(the)-430(information-the)50(or)51(etic)]TJ
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[(are)-377(indep)-28(enden)27(t)-376(to)-378(eac)27(h)-377(other.)-576(Similarly)82(,)-387(the)-378(terms)]TJ
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T*
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[(b)-27(eing)-337(send)-337(out)-336(except)-337(in)]TJ
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[(Hence,)-304(the)-296(new)-297(user)-297(will)-297(not)-297(b)-27(e)-297(able)-297(to)-297(deriv)27(e)]TJ
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[(.)-432(Therefore,)-304(w)27(e)-296(conclude)-297(that)-297(the)]TJ
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[(Join)-333(proto)-28(col)-333(ac)27(hiev)28(es)-333(bac)27(kw)28(ard)-332(secrecy)-334(in)-333(the)-333(information-theoretic)-334(sense.)]TJ
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
6.1 w
q 1 0 0 1 464.82 -252.04 cm
0 0 m
0 6.11 l
S
Q
Q
BT
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1.0003 0 0 1.0003 88.9347 489.8116 Tm
(Next,)Tj
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46.823 -279.93 Td
[(w)27(e)-347(sho)27(w)-347(that)-347(the)-348(outsider)-347(malicious)-348(adv)27(ersary)]TJ
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[(is)-347(unable)-348(to)-348(obtain)-347(the)-348(new)-348(group)-347(k)27(ey)]TJ
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[(from)-333(the)-333(Join)-334(Proto)-27(col.)]TJ
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[(Theorem)-383(11)]TJ
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[(fr)51(om)-367(the)-369(pr)50(op)51(ose)52(d)-368(Join)]TJ
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[(in)-272(Round)]TJ
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[(\(if)-394(the)]TJ
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[(Rabin)-320(signature)-321(\()]TJ
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[(\))-320(is)-321(not)-320(correct,)-323(then)]TJ
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5.59 3.95 Td
(\()Tj
/T1_2 7.97 Tf
(r)Tj
/T1_7 5.98 Tf
7.11 -0.99 Td
(n)Tj
/T1_5 7.97 Tf
5.1 0.99 Td
(+)Tj
/T1_2 7.97 Tf
6.59 0 Td
(c)Tj
/T1_7 5.98 Tf
3.66 -0.99 Td
(n)Tj
/T1_2 7.97 Tf
5.1 0.99 Td
(x)Tj
/T1_7 5.98 Tf
4.77 -0.99 Td
(n)Tj
/T1_5 7.97 Tf
5.09 0.99 Td
(\)\()Tj
/T1_2 7.97 Tf
6.59 0 Td
(r)Tj
/T1_7 5.98 Tf
3.82 -1.1 Td
(n)Tj
/T1_8 5.98 Tf
4.6 0 Td
(+1)Tj
/T1_5 7.97 Tf
9.74 1.1 Td
(+)Tj
/T1_2 7.97 Tf
(c)Tj
/T1_7 5.98 Tf
10.25 -1.1 Td
(n)Tj
/T1_8 5.98 Tf
4.6 0 Td
(+1)Tj
/T1_2 7.97 Tf
9.74 1.1 Td
(x)Tj
/T1_7 5.98 Tf
4.76 -1.1 Td
(n)Tj
/T1_8 5.98 Tf
4.6 0 Td
(+1)Tj
/T1_5 7.97 Tf
9.74 1.1 Td
(\))Tj
/T1_0 10.91 Tf
7.62 -3.95 Td
[(as)-351(this)-351(is)-351(the)]TJ
/T1_9 10.91 Tf
65.19 0 Td
(CDH)Tj
/T1_0 10.91 Tf
-445.3 -21.92 Td
[(problem)-384(and)-385(is)-385(assumed)-384(to)-385(b)-28(e)-385(di\261cult.)-598(Therefore,)-398(the)-384(adv)26(ersary)]TJ
/T1_4 10.91 Tf
318.38 0 Td
(A)Tj
/T1_0 10.91 Tf
12.91 0 Td
[(is)-384(not)-385(p)-28(ossible)-384(to)-385(obtain)-385(the)]TJ
-331.29 -21.92 Td
[(new)-333(group)-333(k)27(ey)]TJ
/T1_1 10.91 Tf
73.04 0 Td
(K)Tj
/T1_6 7.97 Tf
10.04 3.96 Td
(0)Tj
/T1_0 10.91 Tf
2.8 -3.96 Td
(.)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
6.1 w
q 1 0 0 1 464.82 -252.04 cm
0 0 m
0 6.11 l
S
Q
Q
BT
/T1_10 11.95 Tf
1.0003 0 0 1.0003 72 480.529 Tm
(5.6.3)Tj
1.0003 0 0 1.0003 72 769.82 Tm
41.084 -289.21 Td
[(Securit)31(y)-374(Analysis)-375(of)-375(Merge)-375(Proto)-32(col)]TJ
/T1_0 10.91 Tf
-41.084 -28.96 Td
[(In)-348(this)-349(section,)-353(w)27(e)-348(\257rst)-349(sho)27(w)-348(that)-349(the)-349(Merge)-349(Proto)-28(col)-349(pro)27(vides)-348(bac)27(kw)28(ard)-348(secrecy)82(,)-352(that)-349(is,)-353(users)-348(in)]TJ
0 -21.91 TD
(Group)Tj
/T1_4 10.91 Tf
34.12 0 Td
(G)Tj
/T1_2 7.97 Tf
6.49 -1.69 Td
(B)Tj
/T1_0 10.91 Tf
11 1.69 Td
[(cannot)-341(obtain)-341(Group)]TJ
/T1_4 10.91 Tf
103.97 0 Td
(G)Tj
/T1_2 7.97 Tf
6.49 -1.69 Td
(A)Tj
/T1_0 10.91 Tf
6.84 1.69 Td
[('s)-341(previously)-341(established)-341(group)-341(k)26(ey)]TJ
/T1_1 10.91 Tf
170.08 0 Td
(K)Tj
/T1_2 7.97 Tf
9.26 -1.69 Td
(A)Tj
/T1_0 10.91 Tf
10.57 1.69 Td
[(and)-340(users)-342(in)-341(Group)]TJ
/T1_4 10.91 Tf
95.72 0 Td
(G)Tj
/T1_2 7.97 Tf
6.49 -1.69 Td
(A)Tj
/T1_0 10.91 Tf
-461.03 -20.23 Td
[(cannot)-333(obtain)-333(Group)]TJ
/T1_4 10.91 Tf
103.71 0 Td
(G)Tj
/T1_2 7.97 Tf
6.49 -1.69 Td
(B)Tj
/T1_0 10.91 Tf
7.28 1.69 Td
[('s)-333(previously)-333(established)-333(group)-334(k)27(ey)]TJ
/T1_1 10.91 Tf
169.65 0 Td
(K)Tj
/T1_2 7.97 Tf
9.26 -1.69 Td
(B)Tj
/T1_0 10.91 Tf
7.28 1.69 Td
(.)Tj
/T1_11 10.91 Tf
-303.67 -29.73 Td
[(Theorem)-383(12)]TJ
/T1_12 10.91 Tf
71.25 0 Td
[(The)-415(pr)50(op)51(ose)51(d)-414(Mer)50(ge)-414(pr)50(oto)51(c)51(ol)-414(achieves)-415(b)50(ackwar)51(d)-414(se)50(cr)51(e)51(cy)-414(pr)50(ovide)51(d)-414(the)]TJ
/T1_9 10.91 Tf
332.59 0 Td
(CDH)Tj
/T1_12 10.91 Tf
27.1 0 Td
[(pr)50(oblem)]TJ
-430.94 -21.92 Td
[(is)-357(di\261cult.)]TJ
21.81 -29.72 Td
[(Pr)50(o)52(of:)]TJ
/T1_0 10.91 Tf
43.74 0 Td
[(In)-456(this)-457(theorem,)-487(w)27(e)-456(need)-456(to)-457(sho)27(w)-456(that)-456(an)27(y)-456(user)-456(in)-457(group)]TJ
/T1_4 10.91 Tf
289.69 0 Td
(G)Tj
/T1_2 7.97 Tf
6.48 -1.69 Td
(B)Tj
/T1_0 10.91 Tf
12.26 1.69 Td
(\()Tj
/T1_4 10.91 Tf
(G)Tj
/T1_2 7.97 Tf
10.73 -1.69 Td
(A)Tj
/T1_0 10.91 Tf
6.84 1.69 Td
[(\))-456(is)-456(not)-457(able)-456(to)]TJ
-391.55 -21.92 Td
[(obtain)-488(the)-488(previous)-488(group)-488(k)27(ey)]TJ
/T1_1 10.91 Tf
155.19 0 Td
(K)Tj
/T1_2 7.97 Tf
9.26 -1.69 Td
(A)Tj
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12.16 1.69 Td
(\()Tj
/T1_1 10.91 Tf
(K)Tj
/T1_2 7.97 Tf
13.51 -1.69 Td
(B)Tj
/T1_0 10.91 Tf
7.27 1.69 Td
[(\))-488(of)]TJ
/T1_4 10.91 Tf
23.68 0 Td
(G)Tj
/T1_2 7.97 Tf
6.48 -1.69 Td
(A)Tj
/T1_0 10.91 Tf
12.17 1.69 Td
(\()Tj
/T1_4 10.91 Tf
(G)Tj
/T1_2 7.97 Tf
10.73 -1.69 Td
(B)Tj
/T1_0 10.91 Tf
7.27 1.69 Td
[(\).)-908(Supp)-28(ose)-488(a)-489(user)]TJ
/T1_3 10.91 Tf
97.23 0 Td
(U)Tj
/T1_2 7.97 Tf
5.72 -1.78 Td
(k)Tj
/T1_0 10.91 Tf
10.45 1.78 Td
(\()Tj
/T1_1 10.91 Tf
(n)Tj
/T1_0 10.91 Tf
14.33 0 Td
[(+)-325(1)]TJ
/T1_4 10.91 Tf
23.33 0 Td
(\267)Tj
/T1_1 10.91 Tf
14.32 0 Td
(k)Tj
/T1_4 10.91 Tf
11.87 0 Td
(\267)Tj
/T1_1 10.91 Tf
14.32 0 Td
(n)Tj
/T1_0 10.91 Tf
10.1 0 Td
(+)Tj
/T1_1 10.91 Tf
-459.39 -21.92 Td
(m)Tj
/T1_0 10.91 Tf
[(\))-470(in)-471(group)]TJ
/T1_4 10.91 Tf
65.61 0 Td
(G)Tj
/T1_2 7.97 Tf
6.48 -1.68 Td
(B)Tj
/T1_0 10.91 Tf
12.42 1.68 Td
[(tries)-470(to)-471(obtain)-471(the)-471(previous)-470(group)-471(k)26(ey)]TJ
/T1_1 10.91 Tf
194.9 0 Td
(K)Tj
/T1_2 7.97 Tf
9.26 -1.68 Td
(A)Tj
/T1_0 10.91 Tf
12.37 1.68 Td
(=)Tj
/T1_1 10.91 Tf
14.01 0 Td
(g)Tj
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5.6 3.96 Td
(d)Tj
/T1_8 5.98 Tf
4.35 -1.11 Td
(1)Tj
/T1_2 7.97 Tf
4.15 1.11 Td
(d)Tj
/T1_8 5.98 Tf
4.36 -1.11 Td
(2)Tj
/T1_5 7.97 Tf
4.15 1.11 Td
(+)Tj
/T1_2 7.97 Tf
(d)Tj
/T1_8 5.98 Tf
10.94 -1.11 Td
(2)Tj
/T1_2 7.97 Tf
4.15 1.11 Td
(d)Tj
/T1_8 5.98 Tf
4.35 -1.11 Td
(3)Tj
/T1_5 7.97 Tf
4.15 1.11 Td
(+)Tj
/T1_6 7.97 Tf
6.59 0 Td
(\242\242\242)Tj
/T1_5 7.97 Tf
(+)Tj
/T1_2 7.97 Tf
13.64 0 Td
(d)Tj
/T1_7 5.98 Tf
4.35 -1.11 Td
(n)Tj
/T1_13 5.98 Tf
4.6 0 Td
(\241)Tj
/T1_8 5.98 Tf
(1)Tj
/T1_2 7.97 Tf
9.91 1.11 Td
(d)Tj
/T1_7 5.98 Tf
4.35 -0.99 Td
(n)Tj
/T1_5 7.97 Tf
5.1 0.99 Td
(+)Tj
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6.59 0 Td
(d)Tj
/T1_7 5.98 Tf
4.35 -0.99 Td
(n)Tj
/T1_2 7.97 Tf
5.1 0.99 Td
(d)Tj
/T1_8 5.98 Tf
4.36 -1.11 Td
(1)Tj
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9.78 -2.85 Td
(where)Tj
/T1_1 10.91 Tf
-439.97 -21.91 Td
(d)Tj
/T1_2 7.97 Tf
5.68 -1.64 Td
(i)Tj
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8.39 1.64 Td
(=)Tj
/T1_1 10.91 Tf
13.5 0 Td
(r)Tj
/T1_2 7.97 Tf
4.92 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
6.6 1.64 Td
(+)Tj
/T1_1 10.91 Tf
11.7 0 Td
(c)Tj
/T1_2 7.97 Tf
4.72 -1.64 Td
(i)Tj
/T1_1 10.91 Tf
3.38 1.64 Td
(x)Tj
/T1_2 7.97 Tf
6.23 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
8.21 1.64 Td
(and)Tj
/T1_1 10.91 Tf
22.4 0 Td
(c)Tj
/T1_2 7.97 Tf
4.72 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
8.39 1.64 Td
(=)Tj
/T1_9 10.91 Tf
13.5 0 Td
(H)Tj
/T1_0 10.91 Tf
(\()Tj
/T1_1 10.91 Tf
11.97 0 Td
(z)Tj
/T1_2 7.97 Tf
5.07 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
3.38 1.64 Td
[(\))-442(for)-442(1)]TJ
/T1_4 10.91 Tf
37.42 0 Td
(\267)Tj
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13.49 0 Td
(i)Tj
/T1_4 10.91 Tf
8.78 0 Td
(\267)Tj
/T1_1 10.91 Tf
13.49 0 Td
(n)Tj
/T1_0 10.91 Tf
11.38 0 Td
[(of)-442(group)]TJ
/T1_4 10.91 Tf
45.73 0 Td
(G)Tj
/T1_2 7.97 Tf
6.49 -1.69 Td
(A)Tj
/T1_0 10.91 Tf
11.67 1.69 Td
[(from)-442(the)-442(Merge)-443(proto)-28(col,)-470(then)]TJ
/T1_3 10.91 Tf
154.48 0 Td
(U)Tj
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5.73 -1.64 Td
(n)Tj
/T1_5 7.97 Tf
(+1)Tj
/T1_0 10.91 Tf
-451.42 -20.28 Td
[(\257rst)-407(obtained)]TJ
/T1_1 10.91 Tf
68.96 0 Td
(z)Tj
/T1_6 7.97 Tf
5.55 3.96 Td
(0)Tj
/T1_5 7.97 Tf
-0.48 -6.88 Td
(1)Tj
/T1_0 10.91 Tf
9.17 2.92 Td
(and)Tj
/T1_1 10.91 Tf
22.01 0 Td
(K)Tj
/T1_6 7.97 Tf
10.05 3.96 Td
(\244)Tj
/T1_2 7.97 Tf
-0.79 -7.19 Td
(A)Tj
/T1_0 10.91 Tf
11.22 3.23 Td
(=)Tj
/T1_1 10.91 Tf
12.85 0 Td
(g)Tj
/T1_2 7.97 Tf
5.59 3.96 Td
(d)Tj
/T1_13 5.98 Tf
4.36 2.81 Td
(0)Tj
/T1_8 5.98 Tf
0 -5.29 TD
(1)Tj
/T1_2 7.97 Tf
4.15 2.48 Td
(d)Tj
/T1_8 5.98 Tf
4.36 -1.11 Td
(2)Tj
/T1_5 7.97 Tf
4.15 1.11 Td
(+)Tj
/T1_2 7.97 Tf
(d)Tj
/T1_8 5.98 Tf
10.94 -1.11 Td
(2)Tj
/T1_2 7.97 Tf
4.15 1.11 Td
(d)Tj
/T1_8 5.98 Tf
4.35 -1.11 Td
(3)Tj
/T1_5 7.97 Tf
4.15 1.11 Td
(+)Tj
/T1_6 7.97 Tf
6.59 0 Td
(\242\242\242)Tj
/T1_5 7.97 Tf
(+)Tj
/T1_2 7.97 Tf
13.64 0 Td
(d)Tj
/T1_7 5.98 Tf
4.35 -1.11 Td
(n)Tj
/T1_13 5.98 Tf
4.6 0 Td
(\241)Tj
/T1_8 5.98 Tf
(1)Tj
/T1_2 7.97 Tf
9.91 1.11 Td
(d)Tj
/T1_7 5.98 Tf
4.35 -1 Td
(n)Tj
/T1_5 7.97 Tf
5.1 1 Td
(+)Tj
/T1_2 7.97 Tf
6.59 0 Td
(d)Tj
/T1_7 5.98 Tf
4.35 -1.08 Td
(n)Tj
/T1_8 5.98 Tf
4.6 0 Td
(+)Tj
/T1_7 5.98 Tf
(m)Tj
/T1_2 7.97 Tf
12.62 1.08 Td
(d)Tj
/T1_13 5.98 Tf
4.36 2.81 Td
(0)Tj
/T1_8 5.98 Tf
T*
(1)Tj
/T1_0 10.91 Tf
9.09 -1.48 Td
(where)Tj
/T1_1 10.91 Tf
32.34 0 Td
(d)Tj
/T1_2 7.97 Tf
5.68 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
7.75 1.64 Td
(=)Tj
/T1_1 10.91 Tf
12.85 0 Td
(r)Tj
/T1_2 7.97 Tf
4.93 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
6.34 1.64 Td
(+)Tj
/T1_1 10.91 Tf
11.44 0 Td
(c)Tj
/T1_2 7.97 Tf
4.72 -1.64 Td
(i)Tj
/T1_1 10.91 Tf
3.38 1.64 Td
(x)Tj
/T1_2 7.97 Tf
6.23 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
7.82 1.64 Td
(and)Tj
/T1_1 10.91 Tf
22.02 0 Td
(c)Tj
/T1_2 7.97 Tf
4.72 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
7.75 1.64 Td
(=)Tj
/T1_9 10.91 Tf
12.85 0 Td
(H)Tj
/T1_0 10.91 Tf
7.73 0 Td
(\()Tj
/T1_1 10.91 Tf
(z)Tj
/T1_2 7.97 Tf
9.31 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
3.38 1.64 Td
[(\))-407(for)]TJ
/T1_1 10.91 Tf
-446.13 -21.92 Td
(i)Tj
/T1_0 10.91 Tf
8.27 0 Td
[(=)-413(2)]TJ
/T1_1 10.91 Tf
18.44 0 Td
(;)Tj
/T1_0 10.91 Tf
4.85 0 Td
(3)Tj
/T1_1 10.91 Tf
(;)Tj
/T1_4 10.91 Tf
10.3 0 Td
[(\242)-166(\242)-167(\242)]TJ
/T1_1 10.91 Tf
16.36 0 Td
[(;)-166(n;)-167(n)]TJ
/T1_0 10.91 Tf
25.8 0 Td
(+)Tj
/T1_1 10.91 Tf
11.5 0 Td
(m)Tj
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9.57 0 Td
(,)Tj
/T1_1 10.91 Tf
7.78 0 Td
(d)Tj
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5.68 3.96 Td
(0)Tj
/T1_5 7.97 Tf
0 -6.88 TD
(1)Tj
/T1_0 10.91 Tf
9.24 2.92 Td
(=)Tj
/T1_1 10.91 Tf
12.99 0 Td
(r)Tj
/T1_6 7.97 Tf
5.22 3.96 Td
(0)Tj
/T1_5 7.97 Tf
-0.3 -6.88 Td
(1)Tj
/T1_0 10.91 Tf
7.75 2.92 Td
(+)Tj
/T1_1 10.91 Tf
11.49 0 Td
(c)Tj
/T1_6 7.97 Tf
4.72 3.96 Td
(0)Tj
/T1_5 7.97 Tf
T*
(1)Tj
/T1_1 10.91 Tf
4.73 2.92 Td
(x)Tj
/T1_5 7.97 Tf
6.24 -1.63 Td
(1)Tj
/T1_0 10.91 Tf
9.25 1.63 Td
(and)Tj
/T1_1 10.91 Tf
22.1 0 Td
(c)Tj
/T1_6 7.97 Tf
4.72 3.96 Td
(0)Tj
/T1_5 7.97 Tf
T*
(1)Tj
/T1_0 10.91 Tf
9.24 2.92 Td
(=)Tj
/T1_9 10.91 Tf
12.99 0 Td
(H)Tj
/T1_0 10.91 Tf
(\()Tj
/T1_1 10.91 Tf
11.97 0 Td
(z)Tj
/T1_6 7.97 Tf
5.55 3.96 Td
(0)Tj
/T1_5 7.97 Tf
-0.48 -6.88 Td
(1)Tj
/T1_0 10.91 Tf
4.73 2.92 Td
[(\))-414(from)-415(the)-415(Merge)-414(proto)-28(col.)-689(The)-415(di\256erence)]TJ
-260.7 -21.91 Td
[(b)-27(et)27(w)27(een)]TJ
/T1_1 10.91 Tf
41.8 0 Td
(K)Tj
/T1_2 7.97 Tf
9.26 -1.69 Td
(A)Tj
/T1_0 10.91 Tf
10.16 1.69 Td
(and)Tj
/T1_1 10.91 Tf
20.89 0 Td
(K)Tj
/T1_6 7.97 Tf
10.04 3.96 Td
(\244)Tj
/T1_2 7.97 Tf
-0.78 -7.19 Td
(A)Tj
/T1_0 10.91 Tf
10.16 3.23 Td
[(are)-304(the)-305(terms)]TJ
/T1_1 10.91 Tf
66.43 0 Td
(g)Tj
/T1_5 7.97 Tf
5.6 3.96 Td
(\()Tj
/T1_2 7.97 Tf
(r)Tj
/T1_8 5.98 Tf
7.11 -1.11 Td
(1)Tj
/T1_5 7.97 Tf
4.15 1.11 Td
(+)Tj
/T1_2 7.97 Tf
(c)Tj
/T1_8 5.98 Tf
10.25 -1.11 Td
(1)Tj
/T1_2 7.97 Tf
4.15 1.11 Td
(x)Tj
/T1_8 5.98 Tf
4.77 -1.11 Td
(1)Tj
/T1_5 7.97 Tf
4.15 1.11 Td
(\)\()Tj
/T1_2 7.97 Tf
(r)Tj
/T1_8 5.98 Tf
10.4 -1.11 Td
(2)Tj
/T1_5 7.97 Tf
4.15 1.11 Td
(+)Tj
/T1_2 7.97 Tf
6.59 0 Td
(c)Tj
/T1_8 5.98 Tf
3.66 -1.11 Td
(2)Tj
/T1_2 7.97 Tf
4.15 1.11 Td
(x)Tj
/T1_8 5.98 Tf
4.77 -1.11 Td
(2)Tj
/T1_5 7.97 Tf
4.15 1.11 Td
(\))Tj
/T1_0 10.91 Tf
7.11 -3.96 Td
(and)Tj
/T1_1 10.91 Tf
20.89 0 Td
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(m)Tj
/T1_3 7.97 Tf
12.62 1.08 Td
(\)\()Tj
/T1_4 7.97 Tf
(r)Tj
/T1_5 5.98 Tf
10.64 2.81 Td
(0)Tj
/T1_6 5.98 Tf
-0.24 -5.29 Td
(1)Tj
/T1_3 7.97 Tf
4.15 2.48 Td
(+)Tj
/T1_4 7.97 Tf
6.59 0 Td
(c)Tj
/T1_5 5.98 Tf
3.67 2.81 Td
(0)Tj
/T1_6 5.98 Tf
T*
(1)Tj
/T1_4 7.97 Tf
4.15 2.48 Td
(x)Tj
/T1_6 5.98 Tf
4.76 -1.11 Td
(1)Tj
/T1_3 7.97 Tf
4.15 1.11 Td
(\))Tj
/T1_0 10.91 Tf
7.29 -3.96 Td
[(\(except)-319(user)]TJ
/T1_8 10.91 Tf
61.3 0 Td
(U)Tj
/T1_4 7.97 Tf
5.73 -1.64 Td
(n)Tj
/T1_3 7.97 Tf
5.13 0 Td
(+)Tj
/T1_4 7.97 Tf
6.59 0 Td
(m)Tj
/T1_0 10.91 Tf
11.48 1.64 Td
[(whic)27(h)-319(can)-321(compute)-320(this)-320(as)-321(he)-320(kno)27(ws)]TJ
/T1_1 10.91 Tf
176.42 0 Td
(r)Tj
/T1_4 7.97 Tf
4.92 -1.64 Td
(n)Tj
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5.13 0 Td
(+)Tj
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6.59 0 Td
(m)Tj
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7.99 1.64 Td
(,)Tj
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6.55 0 Td
(c)Tj
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4.72 -1.64 Td
(n)Tj
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5.13 0 Td
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6.59 0 Td
(m)Tj
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11.48 1.64 Td
(and)Tj
/T1_1 10.91 Tf
-450.3 -21.92 Td
(x)Tj
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6.23 -1.63 Td
(n)Tj
/T1_3 7.97 Tf
(+)Tj
/T1_4 7.97 Tf
(m)Tj
/T1_0 10.91 Tf
19.71 1.63 Td
[(\))-294(and)]TJ
/T1_1 10.91 Tf
28.23 0 Td
(g)Tj
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5.59 3.96 Td
(\()Tj
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3.3 0 Td
(r)Tj
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4.05 2.81 Td
(0)Tj
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-0.23 -5.28 Td
(1)Tj
/T1_3 7.97 Tf
4.15 2.47 Td
(+)Tj
/T1_4 7.97 Tf
(c)Tj
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10.25 2.81 Td
(0)Tj
/T1_6 5.98 Tf
0 -5.28 TD
(1)Tj
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4.15 2.47 Td
(x)Tj
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4.76 -1.11 Td
(1)Tj
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4.15 1.11 Td
(\)\()Tj
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6.59 0 Td
(r)Tj
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3.82 -1.11 Td
(2)Tj
/T1_3 7.97 Tf
4.15 1.11 Td
(+)Tj
/T1_4 7.97 Tf
(c)Tj
/T1_6 5.98 Tf
10.25 -1.11 Td
(2)Tj
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4.15 1.11 Td
(x)Tj
/T1_6 5.98 Tf
4.77 -1.11 Td
(2)Tj
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4.14 1.11 Td
(\))Tj
/T1_0 10.91 Tf
7 -3.96 Td
(from)Tj
/T1_1 10.91 Tf
25.36 0 Td
(z)Tj
/T1_4 7.97 Tf
5.07 -1.63 Td
(n)Tj
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5.63 1.63 Td
(,)Tj
/T1_1 10.91 Tf
6.33 0 Td
(y)Tj
/T1_4 7.97 Tf
5.35 -1.63 Td
(n)Tj
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5.63 1.63 Td
(,)Tj
/T1_1 10.91 Tf
6.32 0 Td
(z)Tj
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5.08 -1.63 Td
(1)Tj
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6.32 0 Td
(y)Tj
/T1_3 7.97 Tf
5.35 -1.63 Td
(1)Tj
/T1_0 10.91 Tf
4.73 1.63 Td
(,)Tj
/T1_1 10.91 Tf
6.32 0 Td
(z)Tj
/T1_2 7.97 Tf
5.55 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.48 -6.88 Td
(1)Tj
/T1_0 10.91 Tf
4.73 2.92 Td
(,)Tj
/T1_1 10.91 Tf
6.33 0 Td
(z)Tj
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5.07 -1.63 Td
(n)Tj
/T1_3 7.97 Tf
(+)Tj
/T1_4 7.97 Tf
(m)Tj
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19.71 1.63 Td
(,)Tj
/T1_1 10.91 Tf
6.32 0 Td
(y)Tj
/T1_4 7.97 Tf
5.35 -1.63 Td
(n)Tj
/T1_3 7.97 Tf
(+)Tj
/T1_4 7.97 Tf
(m)Tj
/T1_0 10.91 Tf
19.71 1.63 Td
(,)Tj
/T1_1 10.91 Tf
6.32 0 Td
(z)Tj
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5.07 -1.63 Td
(2)Tj
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7.94 1.63 Td
(and)Tj
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20.78 0 Td
(y)Tj
/T1_3 7.97 Tf
5.35 -1.63 Td
(2)Tj
/T1_0 10.91 Tf
4.73 1.63 Td
[(.)-431(Then,)]TJ
/T1_8 10.91 Tf
38.9 0 Td
(U)Tj
/T1_4 7.97 Tf
5.72 -1.77 Td
(k)Tj
/T1_0 10.91 Tf
8.33 1.77 Td
[(can)-294(solv)27(e)-293(the)]TJ
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-406.86 -21.91 Td
(CDH)Tj
/T1_0 10.91 Tf
26.88 0 Td
[(problem,)-410(but)-395(this)-395(con)27(tradicts)-394(to)-395(the)-395(assumption)-395(that)-395(the)]TJ
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281.3 0 Td
(CDH)Tj
/T1_0 10.91 Tf
26.88 0 Td
[(problem)-394(is)-395(di\261cult.)-630(Hence,)]TJ
-335.06 -21.92 Td
[(the)-360(user)]TJ
/T1_8 10.91 Tf
42.49 0 Td
(U)Tj
/T1_4 7.97 Tf
5.73 -1.78 Td
(k)Tj
/T1_0 10.91 Tf
9.05 1.78 Td
[(in)-360(group)]TJ
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44.25 0 Td
(G)Tj
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6.49 -1.69 Td
(B)Tj
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11.21 1.69 Td
[(will)-360(not)-361(b)-28(e)-360(able)-361(to)-361(deriv)27(e)]TJ
/T1_1 10.91 Tf
125.12 0 Td
(K)Tj
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9.26 -1.69 Td
(A)Tj
/T1_0 10.91 Tf
10.78 1.69 Td
(from)Tj
/T1_1 10.91 Tf
26.08 0 Td
(K)Tj
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10.04 3.96 Td
(\244)Tj
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-0.78 -7.19 Td
(A)Tj
/T1_0 10.91 Tf
6.84 3.23 Td
[(.)-526(The)-361(similar)-360(pro)-28(of)-361(can)-360(b)-28(e)-361(sho)27(wn)]TJ
-306.56 -21.92 Td
[(that)-364(an)26(y)-364(user)-365(in)-364(group)]TJ
/T1_10 10.91 Tf
112.72 0 Td
(G)Tj
/T1_4 7.97 Tf
6.49 -1.69 Td
(A)Tj
/T1_0 10.91 Tf
10.82 1.69 Td
[(is)-364(not)-365(able)-365(to)-365(obtain)-365(the)-365(previous)-365(group)-365(k)27(ey)]TJ
/T1_1 10.91 Tf
216.56 0 Td
(K)Tj
/T1_4 7.97 Tf
9.26 -1.69 Td
(B)Tj
/T1_0 10.91 Tf
11.26 1.69 Td
(of)Tj
/T1_10 10.91 Tf
12.76 0 Td
(G)Tj
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6.49 -1.69 Td
(B)Tj
/T1_0 10.91 Tf
7.28 1.69 Td
[(.)-539(Therefore,)-372(w)26(e)]TJ
-393.64 -21.91 Td
[(conclude)-333(that)-333(the)-333(Merge)-334(proto)-28(col)-333(ac)27(hiev)28(es)-333(bac)27(kw)28(ard)-332(secrecy)-334(if)-333(the)]TJ
/T1_9 10.91 Tf
320.15 0 Td
(CDH)Tj
/T1_0 10.91 Tf
26.21 0 Td
[(problem)-333(is)-333(di\261cult.)]TJ
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
6.1 w
q 1 0 0 1 464.82 -208.2 cm
0 0 m
0 6.1 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 88.9347 533.6539 Tm
(Next,)Tj
1.0003 0 0 1.0003 72 769.82 Tm
46.398 -236.1 Td
[(w)27(e)-306(sho)26(w)-306(that)-307(an)-307(adv)27(ersary)]TJ
/T1_10 10.91 Tf
129.922 0 Td
(A)Tj
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12.06 0 Td
[(is)-307(not)-307(able)-307(to)-307(obtain)-307(the)-308(new)-307(group)-307(k)27(ey)]TJ
/T1_1 10.91 Tf
189.89 0 Td
(K)Tj
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10.05 3.96 Td
(0)Tj
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6.14 -3.96 Td
[(from)-307(the)-307(Merge)]TJ
-394.46 -21.91 Td
[(Proto)-27(col.)]TJ
/T1_11 10.91 Tf
0 -33.87 TD
[(Theorem)-383(13)]TJ
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71.25 0 Td
[(A)25(n)-321(adversary)]TJ
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66.69 0 Td
(A)Tj
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12.22 0 Td
[(is)-322(not)-322(able)-322(to)-322(obtain)-322(the)-322(new)-321(gr)50(oup)-321(key)]TJ
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185.59 0 Td
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10.04 3.96 Td
(0)Tj
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6.31 -3.96 Td
[(fr)51(om)-321(the)-322(pr)50(op)51(ose)51(d)-321(Mer)50(ge)]TJ
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[(Pr)51(oto)51(c)51(ol)-397(pr)50(ovide)51(d)-396(the)-398(R)50(abin)-397(signatur)50(e)-396(scheme)-398(and)-398(the)-398(symmetric)-398(key)-397(encryption)-398(scheme)]TJ
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428.75 0 Td
(SKE)Tj
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24.49 0 Td
[(ar)51(e)]TJ
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[(se)51(cur)51(e)-357(and)-358(the)]TJ
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72.05 0 Td
(CDH)Tj
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26.47 0 Td
[(pr)51(oblem)-357(is)-358(di\261cult.)]TJ
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[(Pr)50(o)52(of:)]TJ
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38.27 0 Td
[(In)-302(this)-303(pro)-28(of,)-309(w)27(e)-302(consider)-303(t)27(w)28(o)-302(cases,)-309(that)-303(is,)-309(\(a\))-303(an)-303(adv)27(ersary)]TJ
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292.08 0 Td
(A)Tj
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12.01 0 Td
[(tries)-302(to)-303(imp)-28(ersonate)-303(a)]TJ
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(user)Tj
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22.14 0 Td
(U)Tj
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5.72 -1.63 Td
(i)Tj
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6.04 1.63 Td
[(\(for)-244(some)]TJ
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46.31 0 Td
(i)Tj
/T1_0 10.91 Tf
6.79 0 Td
[(=)-277(1)-244(or)]TJ
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32 0 Td
(i)Tj
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6.79 0 Td
(=)Tj
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11.51 0 Td
(n)Tj
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7.02 0 Td
[(+)-43(1\))-243(to)-244(establish)-244(a)-244(new)-244(group)-243(k)26(ey)84(,)-261(\(b\))-244(an)-243(adv)26(ersary)]TJ
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238.07 0 Td
(A)Tj
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11.37 0 Td
[(tries)-243(to)-244(obtain)-244(a)]TJ
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[(new)-259(group)-260(k)26(ey)-259(from)-259(the)-260(public)-260(exc)26(hange)-258(information.)-420(F)82(or)-259(case)-260(\(a\),)-275(supp)-27(ose)]TJ
/T1_10 10.91 Tf
355.68 0 Td
(A)Tj
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11.55 0 Td
[(w)28(an)27(ts)-259(to)-260(imp)-27(ersonate)]TJ
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(U)Tj
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5.73 -1.64 Td
(1)Tj
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9.09 1.64 Td
(\()Tj
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(U)Tj
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9.96 -1.64 Td
(n)Tj
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(+1)Tj
/T1_0 10.91 Tf
16.46 1.64 Td
[(\),)-416(then)-399(in)-400(Round)-400(1,)]TJ
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99.87 0 Td
(A)Tj
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13.06 0 Td
(computes)Tj
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49.26 0 Td
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5.55 3.96 Td
(0)Tj
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(1)Tj
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8.97 2.92 Td
(=)Tj
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12.72 0 Td
(g)Tj
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(r)Tj
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4.06 2.81 Td
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(1)Tj
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9.01 -1.48 Td
(\()Tj
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(z)Tj
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9.79 3.96 Td
(0)Tj
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-0.47 -6.88 Td
(n)Tj
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5.13 0 Td
(+1)Tj
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15.56 2.92 Td
(=)Tj
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12.72 0 Td
(g)Tj
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5.59 4.48 Td
(r)Tj
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4.05 2.81 Td
(0)Tj
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-0.23 -5.29 Td
(n)Tj
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4.6 0 Td
(+1)Tj
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10.23 -2 Td
[(\).)-644(Next,)]TJ
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44.89 0 Td
(A)Tj
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13.07 0 Td
[(has)-399(to)-400(compute)-400(the)]TJ
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[(Rabin)-288(signature)-288(\()]TJ
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82.87 0 Td
(\276)Tj
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6.62 3.96 Td
(0)Tj
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(1)Tj
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4.73 2.92 Td
[(;)-166(\277)]TJ
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10.85 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-1.23 -6.88 Td
(1)Tj
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4.73 2.92 Td
[(\))-287(of)-288(the)-288(message)]TJ
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79.03 0 Td
(U)Tj
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5.72 -1.63 Td
(1)Tj
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4.73 1.63 Td
(jj)Tj
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5.55 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.48 -6.88 Td
(1)Tj
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4.74 2.92 Td
(jj)Tj
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6.05 0 Td
(z)Tj
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5.08 -1.63 Td
(n)Tj
/T1_10 10.91 Tf
5.63 1.63 Td
(jj)Tj
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6.06 0 Td
(addr)Tj
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20.39 0 Td
([)Tj
/T1_10 10.91 Tf
(G)Tj
/T1_4 7.97 Tf
9.52 -1.69 Td
(A)Tj
/T1_0 10.91 Tf
6.83 1.69 Td
[(])-288(\(the)-288(Rabin)-288(signature)-288(\()]TJ
/T1_1 10.91 Tf
111.57 0 Td
(\276)Tj
/T1_2 7.97 Tf
6.63 3.96 Td
(0)Tj
/T1_4 7.97 Tf
-0.4 -6.88 Td
(n)Tj
/T1_3 7.97 Tf
(+1)Tj
/T1_1 10.91 Tf
16.46 2.92 Td
[(;)-166(\277)]TJ
/T1_2 7.97 Tf
10.85 3.96 Td
(0)Tj
/T1_4 7.97 Tf
-1.24 -6.88 Td
(n)Tj
/T1_3 7.97 Tf
(+1)Tj
/T1_0 10.91 Tf
16.45 2.92 Td
[(\))-288(of)-288(the)]TJ
-433.41 -21.91 Td
(message)Tj
/T1_8 10.91 Tf
42.73 0 Td
(U)Tj
/T1_4 7.97 Tf
5.73 -1.64 Td
(n)Tj
/T1_3 7.97 Tf
5.13 0 Td
(+1)Tj
/T1_10 10.91 Tf
11.32 1.64 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(z)Tj
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5.55 3.95 Td
(0)Tj
/T1_4 7.97 Tf
-0.48 -6.88 Td
(n)Tj
/T1_3 7.97 Tf
(+1)Tj
/T1_10 10.91 Tf
16.45 2.93 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(z)Tj
/T1_4 7.97 Tf
5.07 -1.64 Td
(n)Tj
/T1_3 7.97 Tf
(+)Tj
/T1_4 7.97 Tf
(m)Tj
/T1_0 10.91 Tf
19.71 1.64 Td
[(\).)-665(The)-407(v)54(alidit)28(y)-406(of)-407(Rabin)-407(signature)-407(\()]TJ
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176.32 0 Td
(\276)Tj
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6.63 3.95 Td
(0)Tj
/T1_3 7.97 Tf
-0.4 -6.88 Td
(1)Tj
/T1_1 10.91 Tf
4.73 2.93 Td
[(;)-167(\277)]TJ
/T1_2 7.97 Tf
10.85 3.95 Td
(0)Tj
/T1_3 7.97 Tf
-1.23 -6.88 Td
(1)Tj
/T1_0 10.91 Tf
4.73 2.93 Td
[(\))-407(\(\()]TJ
/T1_1 10.91 Tf
17.16 0 Td
(\276)Tj
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6.63 3.95 Td
(0)Tj
/T1_4 7.97 Tf
-0.39 -6.88 Td
(n)Tj
/T1_3 7.97 Tf
5.13 0 Td
(+1)Tj
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11.32 2.93 Td
[(;)-166(\277)]TJ
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10.85 3.95 Td
(0)Tj
/T1_4 7.97 Tf
-1.24 -6.88 Td
(n)Tj
/T1_3 7.97 Tf
(+1)Tj
/T1_0 10.91 Tf
16.45 2.93 Td
[(\)\))-407(is)-407(c)27(hec)28(k)27(ed)-406(b)27(y)]TJ
/T1_8 10.91 Tf
-390.87 -21.92 Td
(U)Tj
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5.73 -1.64 Td
(n)Tj
/T1_3 7.97 Tf
5.13 0 Td
(+1)Tj
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/T1_8 5.98 Tf
4.05 2.81 Td
(0)Tj
/T1_10 5.98 Tf
-0.23 -5.28 Td
(n)Tj
/T1_9 5.98 Tf
4.6 0 Td
(+1)Tj
/T1_0 10.91 Tf
14.48 -2 Td
[(as)-388(this)-389(is)-389(the)]TJ
/T1_7 10.91 Tf
66.83 0 Td
(CDH)Tj
/T1_0 10.91 Tf
26.82 0 Td
[(problem)-388(and)-389(is)]TJ
-395.68 -21.92 Td
[(assumed)-313(to)-314(b)-28(e)-314(di\261cult.)-438(Therefore,)-317(the)-314(adv)27(ersary)]TJ
/T1_6 10.91 Tf
235.6 0 Td
(A)Tj
/T1_0 10.91 Tf
12.13 0 Td
[(is)-313(not)-314(p)-28(ossible)-314(to)-314(obtain)-313(new)-314(group)-314(k)27(ey)]TJ
/T1_1 10.91 Tf
189.97 0 Td
(K)Tj
/T1_2 7.97 Tf
10.04 3.96 Td
(0)Tj
/T1_0 10.91 Tf
2.8 -3.96 Td
(.)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
6.1 w
q 1 0 0 1 464.82 -164.37 cm
0 0 m
0 6.1 l
S
Q
Q
BT
/T1_11 11.95 Tf
1.0003 0 0 1.0003 72 568.2236 Tm
(5.6.4)Tj
1.0003 0 0 1.0003 72 769.82 Tm
41.084 -201.54 Td
[(Securit)31(y)-374(Analysis)-375(of)-375(Lea)30(v)31(e)-374(Proto)-31(col)]TJ
/T1_0 10.91 Tf
-41.084 -28.96 Td
[(In)-280(this)-280(section,)-292(w)27(e)-279(\257rst)-281(sho)27(w)-279(that)-281(the)-280(prop)-28(osed)-281(Lea)27(v)28(e)-280(proto)-27(col)-281(ac)27(hiev)28(es)-280(forw)27(ard)-279(secrecy)82(,)-290(that)-281(is,)-291(the)]TJ
0 -21.92 TD
[(lea)27(ving)-250(user)]TJ
/T1_5 10.91 Tf
58.28 0 Td
(U)Tj
/T1_4 7.97 Tf
5.73 -1.78 Td
(l)Tj
/T1_0 10.91 Tf
5.85 1.78 Td
[(cannot)-251(obtain)-251(the)-251(new)-251(group)-251(k)26(ey)]TJ
/T1_1 10.91 Tf
156.12 0 Td
(K)Tj
/T1_2 7.97 Tf
10.05 3.96 Td
(0)Tj
/T1_0 10.91 Tf
5.53 -3.96 Td
[(from)-251(previous)-251(group)-251(k)27(ey)]TJ
/T1_1 10.91 Tf
116.23 0 Td
(K)Tj
/T1_0 10.91 Tf
12.78 0 Td
[(with)-251(the)-251(information)]TJ
-370.57 -21.92 Td
[(kno)27(wn)-385(b)27(y)-385(the)-386(lea)27(ving)-385(user)]TJ
/T1_5 10.91 Tf
131.41 0 Td
(U)Tj
/T1_4 7.97 Tf
5.72 -1.77 Td
(l)Tj
/T1_0 10.91 Tf
3.12 1.77 Td
[(.)-602(Next,)-399(w)27(e)-385(sho)26(w)-385(that)-386(an)-385(adv)26(ersary)]TJ
/T1_6 10.91 Tf
174.23 0 Td
(A)Tj
/T1_0 10.91 Tf
12.92 0 Td
[(cannot)-386(obtain)-386(the)-385(new)-386(group)]TJ
-327.4 -21.91 Td
[(k)27(ey)]TJ
/T1_1 10.91 Tf
19.69 0 Td
(K)Tj
/T1_2 7.97 Tf
10.04 3.96 Td
(0)Tj
/T1_0 10.91 Tf
6.43 -3.96 Td
[(from)-333(the)-334(prop)-27(osed)-334(Lea)27(v)28(e)-332(proto)-28(col.)]TJ
/T1_12 10.91 Tf
-36.16 -29.73 Td
[(Theorem)-383(14)]TJ
/T1_13 10.91 Tf
71.25 0 Td
[(The)-388(pr)50(op)51(ose)52(d)-388(L)51(e)51(ave)-387(pr)50(oto)51(c)51(ol)-387(achieves)-388(forwar)50(d)-387(se)50(cr)51(e)51(cy)-387(pr)50(ovide)51(d)-387(the)]TJ
/T1_7 10.91 Tf
320.85 0 Td
(CDH)Tj
/T1_13 10.91 Tf
26.81 0 Td
[(pr)51(oblem)-387(is)]TJ
-418.91 -21.92 Td
[(di\261cult)-357(and)-358(VBD)-358(pr)50(oto)51(c)52(ol)-357(is)-358(se)50(cur)51(e.)]TJ
21.81 -29.72 Td
[(Pr)50(o)52(of:)]TJ
/T1_0 10.91 Tf
46.67 0 Td
[(As)-526(the)-527(lea)27(ving)-525(user)]TJ
/T1_5 10.91 Tf
103.4 0 Td
(U)Tj
/T1_4 7.97 Tf
5.73 -1.78 Td
(l)Tj
/T1_0 10.91 Tf
8.86 1.78 Td
[(kno)27(ws)-525(the)-526(previous)-527(group)-526(k)26(ey)]TJ
/T1_1 10.91 Tf
156.12 0 Td
(K)Tj
/T1_0 10.91 Tf
16.59 0 Td
(=)Tj
/T1_1 10.91 Tf
15.02 0 Td
(g)Tj
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5.59 3.95 Td
(d)Tj
/T1_10 5.98 Tf
4.36 -0.99 Td
(n)Tj
/T1_4 7.97 Tf
5.1 0.99 Td
(d)Tj
/T1_9 5.98 Tf
4.35 -1.1 Td
(1)Tj
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8.48 -2.85 Td
(\242)Tj
/T1_14 10.91 Tf
6.85 8.18 Td
(Q)Tj
/T1_4 7.97 Tf
10.3 -3.16 Td
(n)Tj
/T1_2 7.97 Tf
(\241)Tj
/T1_3 7.97 Tf
11.73 0 Td
(1)Tj
/T1_4 7.97 Tf
-11.73 -8.25 Td
(i)Tj
/T1_3 7.97 Tf
2.89 0 Td
(=1)Tj
/T1_1 10.91 Tf
15.39 3.23 Td
(g)Tj
/T1_4 7.97 Tf
5.59 3.95 Td
(d)Tj
/T1_10 5.98 Tf
4.35 -1.21 Td
(i)Tj
/T1_4 7.97 Tf
3.17 1.21 Td
(d)Tj
/T1_10 5.98 Tf
4.35 -1.21 Td
(i)Tj
/T1_9 5.98 Tf
2.66 0 Td
(+1)Tj
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-457.63 -24.66 Td
[(\(whic)27(h)-516(is)-517(of)]TJ
/T1_1 10.91 Tf
64.84 0 Td
(n)Tj
/T1_0 10.91 Tf
12.19 0 Td
[(terms)-517(of)-517(the)-517(form)]TJ
/T1_1 10.91 Tf
95.39 0 Td
(g)Tj
/T1_4 7.97 Tf
5.59 3.96 Td
(de)Tj
/T1_0 10.91 Tf
8.78 -3.96 Td
[(\))-517(where)]TJ
/T1_1 10.91 Tf
43.42 0 Td
(d)Tj
/T1_4 7.97 Tf
5.68 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
9.75 1.64 Td
(=)Tj
/T1_1 10.91 Tf
14.85 0 Td
(r)Tj
/T1_4 7.97 Tf
4.92 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
7.14 1.64 Td
(+)Tj
/T1_1 10.91 Tf
12.24 0 Td
(c)Tj
/T1_4 7.97 Tf
4.72 -1.64 Td
(i)Tj
/T1_1 10.91 Tf
3.38 1.64 Td
(x)Tj
/T1_4 7.97 Tf
6.24 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
9.01 1.64 Td
(and)Tj
/T1_1 10.91 Tf
23.21 0 Td
(c)Tj
/T1_4 7.97 Tf
4.72 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
9.75 1.64 Td
(=)Tj
/T1_7 10.91 Tf
14.86 0 Td
(H)Tj
/T1_0 10.91 Tf
(\()Tj
/T1_1 10.91 Tf
(z)Tj
/T1_4 7.97 Tf
17.03 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
3.38 1.64 Td
[(\))-517(for)-517(1)]TJ
/T1_6 10.91 Tf
40.4 0 Td
(\267)Tj
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14.86 0 Td
(i)Tj
/T1_6 10.91 Tf
10.12 0 Td
(\267)Tj
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14.85 0 Td
(n)Tj
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-461.32 -21.92 Td
[(and)-465(all)-465(the)-465(terms)]TJ
/T1_1 10.91 Tf
91.28 0 Td
(g)Tj
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5.59 3.96 Td
(d)Tj
/T1_10 5.98 Tf
4.36 -1.21 Td
(i)Tj
/T1_4 7.97 Tf
3.16 1.21 Td
(d)Tj
/T1_10 5.98 Tf
4.36 -1.21 Td
(i)Tj
/T1_9 5.98 Tf
2.66 0 Td
(+1)Tj
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15.31 -2.75 Td
[(for)-465(1)]TJ
/T1_6 10.91 Tf
29.01 0 Td
(\267)Tj
/T1_1 10.91 Tf
13.91 0 Td
(i)Tj
/T1_6 10.91 Tf
9.19 0 Td
(\267)Tj
/T1_1 10.91 Tf
13.91 0 Td
(n)Tj
/T1_6 10.91 Tf
9.93 0 Td
(\241)Tj
/T1_0 10.91 Tf
11.86 0 Td
[(1)-465(and)]TJ
/T1_1 10.91 Tf
33.18 0 Td
(g)Tj
/T1_4 7.97 Tf
5.59 3.96 Td
(d)Tj
/T1_10 5.98 Tf
4.36 -1 Td
(n)Tj
/T1_4 7.97 Tf
5.09 1 Td
(d)Tj
/T1_9 5.98 Tf
4.36 -1.11 Td
(1)Tj
/T1_0 10.91 Tf
4.65 -2.85 Td
[(,)-498(but)-465(the)-465(new)-466(group)-465(k)27(ey)-464(is)-466(of)-465(the)-465(form)]TJ
/T1_1 10.91 Tf
-271.76 -21.91 Td
(K)Tj
/T1_2 7.97 Tf
10.04 3.95 Td
(0)Tj
/T1_0 10.91 Tf
9.62 -3.95 Td
(=)Tj
/T1_1 10.91 Tf
15.3 0 Td
(g)Tj
/T1_4 7.97 Tf
5.6 4.77 Td
(d)Tj
/T1_8 5.98 Tf
4.35 2.81 Td
(0)Tj
/T1_9 5.98 Tf
0 -5.28 TD
(1)Tj
/T1_4 7.97 Tf
4.15 2.47 Td
(d)Tj
/T1_8 5.98 Tf
4.36 2.81 Td
(0)Tj
/T1_9 5.98 Tf
T*
(2)Tj
/T1_3 7.97 Tf
4.15 2.47 Td
(+)Tj
/T1_4 7.97 Tf
(d)Tj
/T1_8 5.98 Tf
10.94 2.81 Td
(0)Tj
/T1_9 5.98 Tf
T*
(2)Tj
/T1_4 7.97 Tf
4.15 2.47 Td
(d)Tj
/T1_8 5.98 Tf
4.35 2.81 Td
(0)Tj
/T1_9 5.98 Tf
T*
(3)Tj
/T1_3 7.97 Tf
4.15 2.47 Td
(+)Tj
/T1_2 7.97 Tf
6.59 0 Td
(\242\242\242)Tj
/T1_3 7.97 Tf
(+)Tj
/T1_4 7.97 Tf
13.64 0 Td
(d)Tj
/T1_8 5.98 Tf
4.35 2.81 Td
(0)Tj
/T1_10 5.98 Tf
0 -5.58 TD
(l)Tj
/T1_8 5.98 Tf
2.4 0 Td
(\241)Tj
/T1_9 5.98 Tf
(2)Tj
/T1_4 7.97 Tf
9.91 2.77 Td
(d)Tj
/T1_8 5.98 Tf
4.35 2.81 Td
(0)Tj
/T1_10 5.98 Tf
T*
(l)Tj
/T1_8 5.98 Tf
2.41 0 Td
(\241)Tj
/T1_9 5.98 Tf
5.75 0 Td
(1)Tj
/T1_3 7.97 Tf
4.15 2.77 Td
(+)Tj
/T1_4 7.97 Tf
(d)Tj
/T1_8 5.98 Tf
10.94 2.81 Td
(0)Tj
/T1_10 5.98 Tf
T*
(l)Tj
/T1_8 5.98 Tf
2.4 0 Td
(\241)Tj
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5.75 0 Td
(1)Tj
/T1_4 7.97 Tf
4.15 2.77 Td
(d)Tj
/T1_8 5.98 Tf
4.36 2.81 Td
(0)Tj
/T1_10 5.98 Tf
T*
(l)Tj
/T1_9 5.98 Tf
2.4 0 Td
(+1)Tj
/T1_3 7.97 Tf
9.74 2.77 Td
(+)Tj
/T1_2 7.97 Tf
(\242\242\242)Tj
/T1_3 7.97 Tf
13.64 0 Td
(+)Tj
/T1_4 7.97 Tf
(d)Tj
/T1_8 5.98 Tf
10.94 2.81 Td
(0)Tj
/T1_10 5.98 Tf
0 -4.8 TD
(n)Tj
/T1_4 7.97 Tf
5.1 1.99 Td
(d)Tj
/T1_8 5.98 Tf
4.35 2.81 Td
(0)Tj
/T1_9 5.98 Tf
0 -5.28 TD
(1)Tj
/T1_0 10.91 Tf
10.56 -2.3 Td
[(\(whic)27(h)-541(is)-542(of)]TJ
/T1_1 10.91 Tf
65.66 0 Td
(n)Tj
/T1_6 10.91 Tf
10.49 0 Td
(\241)Tj
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12.42 0 Td
[(1)-541(terms)-542(of)-542(the)-542(form)]TJ
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107.83 0 Td
(g)Tj
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5.6 3.95 Td
(de)Tj
/T1_0 10.91 Tf
8.78 -3.95 Td
[(\))-541(where)]TJ
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-429.82 -21.92 Td
(d)Tj
/T1_2 7.97 Tf
5.68 3.96 Td
(0)Tj
/T1_4 7.97 Tf
0 -7.01 TD
(i)Tj
/T1_0 10.91 Tf
9.45 3.05 Td
(=)Tj
/T1_1 10.91 Tf
14.56 0 Td
(r)Tj
/T1_2 7.97 Tf
5.23 3.96 Td
(0)Tj
/T1_4 7.97 Tf
-0.31 -7.01 Td
(i)Tj
/T1_0 10.91 Tf
7.03 3.05 Td
(+)Tj
/T1_1 10.91 Tf
12.12 0 Td
(c)Tj
/T1_2 7.97 Tf
4.72 3.96 Td
(0)Tj
/T1_4 7.97 Tf
T*
(i)Tj
/T1_1 10.91 Tf
3.38 3.05 Td
(x)Tj
/T1_4 7.97 Tf
6.23 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
8.85 1.64 Td
(and)Tj
/T1_1 10.91 Tf
23.03 0 Td
(c)Tj
/T1_2 7.97 Tf
4.72 3.96 Td
(0)Tj
/T1_4 7.97 Tf
T*
(i)Tj
/T1_0 10.91 Tf
9.46 3.05 Td
(=)Tj
/T1_7 10.91 Tf
14.56 0 Td
(H)Tj
/T1_0 10.91 Tf
7.73 0 Td
(\()Tj
/T1_1 10.91 Tf
(z)Tj
/T1_2 7.97 Tf
9.79 3.96 Td
(0)Tj
/T1_4 7.97 Tf
-0.48 -7.01 Td
(i)Tj
/T1_0 10.91 Tf
3.38 3.05 Td
[(\))-500(for)-501(1)]TJ
/T1_6 10.91 Tf
39.76 0 Td
(\267)Tj
/T1_1 10.91 Tf
14.55 0 Td
(i)Tj
/T1_6 10.91 Tf
9.84 0 Td
(6)Tj
/T1_0 10.91 Tf
(=)Tj
/T1_1 10.91 Tf
14.56 0 Td
(l)Tj
/T1_6 10.91 Tf
9.54 0 Td
(\267)Tj
/T1_1 10.91 Tf
14.56 0 Td
(n)Tj
/T1_0 10.91 Tf
(,)Tj
/T1_1 10.91 Tf
15.5 0 Td
(r)Tj
/T1_2 7.97 Tf
5.22 3.96 Td
(0)Tj
/T1_4 7.97 Tf
-0.3 -7.01 Td
(j)Tj
/T1_0 10.91 Tf
10.46 3.05 Td
(=)Tj
/T1_1 10.91 Tf
14.56 0 Td
(r)Tj
/T1_4 7.97 Tf
4.92 -1.64 Td
(j)Tj
/T1_0 10.91 Tf
9.84 1.64 Td
(and)Tj
/T1_1 10.91 Tf
23.04 0 Td
(c)Tj
/T1_2 7.97 Tf
4.72 3.96 Td
(0)Tj
/T1_4 7.97 Tf
T*
(j)Tj
/T1_0 10.91 Tf
10.46 3.05 Td
(=)Tj
/T1_1 10.91 Tf
14.56 0 Td
(c)Tj
/T1_4 7.97 Tf
4.72 -1.64 Td
(j)Tj
/T1_0 10.91 Tf
9.84 1.64 Td
[(for)-500(1)]TJ
/T1_6 10.91 Tf
30.05 0 Td
(\267)Tj
/T1_1 10.91 Tf
14.56 0 Td
(j)Tj
/T1_6 10.91 Tf
11.19 0 Td
(6)Tj
/T1_0 10.91 Tf
(=)Tj
/T1_1 10.91 Tf
14.56 0 Td
(l)Tj
/T1_6 10.91 Tf
9.55 0 Td
(\267)Tj
/T1_1 10.91 Tf
-459.39 -21.92 Td
(n)Tj
/T1_0 10.91 Tf
12.45 0 Td
(and)Tj
/T1_1 10.91 Tf
23.47 0 Td
(j)Tj
/T1_0 10.91 Tf
11.01 0 Td
[(is)-541(ev)27(en.)-1066(F)82(urthermore,)-592(eac)27(h)]TJ
/T1_1 10.91 Tf
145.03 0 Td
(r)Tj
/T1_2 7.97 Tf
5.22 3.96 Td
(0)Tj
/T1_4 7.97 Tf
-0.3 -7.01 Td
(j)Tj
/T1_0 10.91 Tf
10.28 3.05 Td
[(is)-540(indep)-28(enden)27(t)-540(of)]TJ
/T1_1 10.91 Tf
91.98 0 Td
(r)Tj
/T1_4 7.97 Tf
4.92 -1.63 Td
(j)Tj
/T1_0 10.91 Tf
10.28 1.63 Td
[(for)-541(1)]TJ
/T1_6 10.91 Tf
31.22 0 Td
(\267)Tj
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15.28 0 Td
(j)Tj
/T1_6 10.91 Tf
11.92 0 Td
(6)Tj
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(=)Tj
/T1_1 10.91 Tf
15.29 0 Td
(l)Tj
/T1_6 10.91 Tf
10.27 0 Td
(\267)Tj
/T1_1 10.91 Tf
15.29 0 Td
(n)Tj
/T1_0 10.91 Tf
12.44 0 Td
(and)Tj
/T1_1 10.91 Tf
23.47 0 Td
(j)Tj
/T1_0 10.91 Tf
11.02 0 Td
(is)Tj
-460.54 -21.91 Td
[(o)-27(dd,)-499(hence)]TJ
/T1_1 10.91 Tf
58.08 0 Td
(z)Tj
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5.55 3.95 Td
(0)Tj
/T1_4 7.97 Tf
-0.48 -7.01 Td
(j)Tj
/T1_0 10.91 Tf
9.82 3.06 Td
(=)Tj
/T1_1 10.91 Tf
13.91 0 Td
(g)Tj
/T1_4 7.97 Tf
5.59 4.91 Td
(r)Tj
/T1_8 5.98 Tf
4.06 2.82 Td
(0)Tj
/T1_10 5.98 Tf
-0.24 -5.4 Td
(j)Tj
/T1_0 10.91 Tf
9.48 -2.33 Td
(and)Tj
/T1_1 10.91 Tf
22.65 0 Td
(z)Tj
/T1_4 7.97 Tf
5.07 -1.64 Td
(j)Tj
/T1_0 10.91 Tf
9.82 1.64 Td
(=)Tj
/T1_1 10.91 Tf
13.91 0 Td
(g)Tj
/T1_4 7.97 Tf
5.6 3.95 Td
(r)Tj
/T1_10 5.98 Tf
3.82 -1.21 Td
(j)Tj
/T1_0 10.91 Tf
9.47 -2.74 Td
[(are)-466(indep)-27(enden)26(t)-464(to)-466(eac)27(h)-465(other.)-841(Therefore,)]TJ
/T1_1 10.91 Tf
215 0 Td
(c)Tj
/T1_2 7.97 Tf
4.72 3.95 Td
(0)Tj
/T1_4 7.97 Tf
T*
(j)Tj
/T1_0 10.91 Tf
9.82 3.06 Td
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/T1_1 10.91 Tf
120.79 0 Td
(K)Tj
/T1_2 7.97 Tf
10.05 3.96 Td
(0)Tj
/T1_0 10.91 Tf
5.79 -3.96 Td
[(through)-275(the)-275(public)-275(exc)27(hange)-274(information,)-287(that)-275(is,)-287(round)-275(1)-275(and)-275(round)-276(2)]TJ
-136.63 -21.91 Td
[(information)-322(sen)27(t)-322(b)27(y)-321(the)-323(remaining)-323(group)-322(mem)27(b)-27(ers.)-441(But)-322(the)-323(Lea)27(v)28(e)-322(proto)-28(col)-322(\(without)-323(the)-322(signature)]TJ
0 -21.92 TD
[(information)-375(sen)26(t\))-374(is)-376(just)-376(the)-376(VBD)-376(proto)-28(col,)-386(b)27(y)-375(Theorem)-376(5,)-387(it)-376(is)-375(sho)26(wn)-375(that)-375(the)-376(VBD)-376(proto)-28(col)-376(is)]TJ
0 -21.91 TD
[(secure.)-524(Therefore,)-366(the)-360(lea)27(ving)-359(user)]TJ
/T1_3 10.91 Tf
170.48 0 Td
(U)Tj
/T1_4 7.97 Tf
5.72 -1.78 Td
(l)Tj
/T1_0 10.91 Tf
7.04 1.78 Td
[(is)-360(not)-360(able)-359(to)-360(obtain)-360(the)-360(new)-360(group)-360(k)27(ey)]TJ
/T1_1 10.91 Tf
195.07 0 Td
(K)Tj
/T1_2 7.97 Tf
10.04 3.95 Td
(0)Tj
/T1_0 10.91 Tf
2.8 -3.95 Td
[(.)-523(Therefore,)-367(the)]TJ
-391.15 -21.92 Td
[(lea)27(v)28(e)-332(proto)-28(col)-333(ac)26(hiev)28(es)-332(forw)27(ard)-333(secrecy)83(.)]TJ
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
6.1 w
q 1 0 0 1 464.82 -164.37 cm
0 0 m
0 6.1 l
S
Q
Q
BT
/T1_9 10.91 Tf
1.0003 0 0 1.0003 72 575.4756 Tm
(Theorem)Tj
1.0003 0 0 1.0003 72 769.82 Tm
53.274 -194.29 Td
(15)Tj
/T1_10 10.91 Tf
17.976 0 Td
[(A)25(n)-378(adversary)]TJ
/T1_7 10.91 Tf
67.92 0 Td
(A)Tj
/T1_10 10.91 Tf
12.84 0 Td
[(\(not)-378(a)-378(le)50(aving)-378(user)]TJ
/T1_3 10.91 Tf
94.13 0 Td
(U)Tj
/T1_4 7.97 Tf
5.72 -1.78 Td
(l)Tj
/T1_10 10.91 Tf
3.12 1.78 Td
[(\))-378(c)50(annot)-378(obtain)-378(the)-378(new)-379(gr)50(oup)-377(key)]TJ
/T1_1 10.91 Tf
168.11 0 Td
(K)Tj
/T1_2 7.97 Tf
10.04 3.96 Td
(0)Tj
/T1_10 10.91 Tf
6.92 -3.96 Td
[(in)-378(the)]TJ
-440.05 -21.92 Td
[(pr)51(op)51(ose)51(d)-351(L)50(e)51(ave)-350(pr)50(oto)51(c)51(ol)-351(pr)51(ovide)51(d)-351(that)-352(the)]TJ
/T1_8 10.91 Tf
198.05 0 Td
(CDH)Tj
/T1_10 10.91 Tf
26.41 0 Td
[(pr)51(oblem)-351(is)-351(di\261cult)-352(and)-352(the)-351(R)50(abin)-351(signatur)50(e)-350(scheme)]TJ
-224.46 -21.91 Td
[(and)-357(the)-358(VBD)-358(pr)50(oto)51(c)52(ol)-357(ar)50(e)-357(se)50(cur)51(e.)]TJ
21.81 -29.92 Td
[(Pr)50(o)52(of:)]TJ
/T1_0 10.91 Tf
39.3 0 Td
[(In)-350(this)-351(pro)-28(of,)-354(w)26(e)-349(consider)-351(t)27(w)28(o)-349(cases,)-355(that)-351(is,)-354(\(a\))-351(an)-350(adv)26(ersary)]TJ
/T1_7 10.91 Tf
298.25 0 Td
(A)Tj
/T1_0 10.91 Tf
12.53 0 Td
[(tries)-350(to)-350(imp)-28(ersonate)]TJ
-371.89 -21.92 Td
[(a)-326(user)]TJ
/T1_3 10.91 Tf
32.06 0 Td
(U)Tj
/T1_4 7.97 Tf
5.73 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
6.94 1.63 Td
[(\(for)-327(some)]TJ
/T1_1 10.91 Tf
48.12 0 Td
(i)Tj
/T1_0 10.91 Tf
7.32 0 Td
[(is)-327(o)-27(dd)-327(suc)27(h)-326(that)]TJ
/T1_1 10.91 Tf
80.42 0 Td
(i)Tj
/T1_7 10.91 Tf
6.79 0 Td
(6)Tj
/T1_0 10.91 Tf
(=)Tj
/T1_1 10.91 Tf
11.51 0 Td
(l)Tj
/T1_0 10.91 Tf
3.47 0 Td
[(\))-326(to)-327(establish)-327(a)-327(new)-327(group)-327(k)27(ey)83(,)-327(\(b\))-327(an)-326(adv)26(ersary)]TJ
/T1_7 10.91 Tf
232.55 0 Td
(A)Tj
/T1_0 10.91 Tf
12.27 0 Td
(tries)Tj
-447.18 -21.92 Td
[(to)-322(obtain)-323(a)-322(new)-323(group)-323(k)27(ey)-322(from)-322(the)-323(public)-323(exc)27(hange)-322(information.)-440(F)82(or)-322(case)-322(\(a\),)-325(it)-323(is)-322(already)-323(sho)27(wn)]TJ
T*
[(in)-373(Theorem)-373(8)-374(that)-373(no)-374(adv)27(ersary)-372(can)-374(imp)-28(ersonate)-373(an)27(y)-373(user)-373(in)-374(the)-373(group)-374(as)-373(they)-374(do)-373(not)-373(kno)26(w)-372(the)]TJ
0 -21.92 TD
[(priv)55(ate)-276(k)27(ey)]TJ
/T1_1 10.91 Tf
55.15 0 Td
(x)Tj
/T1_4 7.97 Tf
6.23 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
6.41 1.63 Td
(of)Tj
/T1_3 10.91 Tf
11.8 0 Td
(U)Tj
/T1_4 7.97 Tf
5.73 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
6.4 1.63 Td
[(to)-277(compute)-277(a)-277(v)54(alid)]TJ
93.68 2.76 Td
(^)Tj
/T1_1 10.91 Tf
-3.13 -2.76 Td
(X)Tj
/T1_2 7.97 Tf
9.9 3.96 Td
(0)Tj
/T1_4 7.97 Tf
-0.86 -7.01 Td
(i)Tj
/T1_0 10.91 Tf
6.67 3.05 Td
[(pro)27(vided)-276(that)-277(the)]TJ
/T1_8 10.91 Tf
85.44 0 Td
(CDH)Tj
/T1_0 10.91 Tf
25.59 0 Td
[(problem)-277(is)-277(di\261cult.)-426(F)83(urthermore,)]TJ
/T1_7 10.91 Tf
-309.01 -21.91 Td
(A)Tj
/T1_0 10.91 Tf
11.58 0 Td
[(cannot)-263(compute)-263(a)-263(v)55(alid)-263(signature)-263(\()]TJ
/T1_1 10.91 Tf
163.19 0 Td
(\276)Tj
/T1_2 7.97 Tf
6.62 3.95 Td
(0)Tj
/T1_4 7.97 Tf
-0.39 -7.01 Td
(i)Tj
/T1_1 10.91 Tf
3.38 3.06 Td
[(;)-166(\277)]TJ
/T1_2 7.97 Tf
10.85 3.95 Td
(0)Tj
/T1_4 7.97 Tf
-1.24 -7.01 Td
(i)Tj
/T1_0 10.91 Tf
4.03 3.06 Td
[(\))-263(of)-263(the)-263(message)]TJ
/T1_3 10.91 Tf
77.95 0 Td
(U)Tj
/T1_4 7.97 Tf
5.73 -1.64 Td
(i)Tj
/T1_7 10.91 Tf
3.38 1.64 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(z)Tj
/T1_2 7.97 Tf
5.55 3.95 Td
(0)Tj
/T1_4 7.97 Tf
-0.48 -7.01 Td
(i)Tj
/T1_7 10.91 Tf
3.38 3.06 Td
(jj)Tj
/T1_0 10.91 Tf
9.18 2.75 Td
(^)Tj
/T1_1 10.91 Tf
-3.12 -2.75 Td
(X)Tj
/T1_2 7.97 Tf
9.89 3.95 Td
(0)Tj
/T1_4 7.97 Tf
-0.86 -7.01 Td
(i)Tj
/T1_7 10.91 Tf
3.65 3.06 Td
(jj)Tj
/T1_11 10.91 Tf
7.88 8.18 Td
(Q)Tj
/T1_4 7.97 Tf
10.3 -3.16 Td
(n)Tj
0 -8.25 TD
(j)Tj
/T1_12 7.97 Tf
3.88 0 Td
(=1)Tj
/T1_4 7.97 Tf
(;j)Tj
/T1_2 7.97 Tf
17.05 0 Td
(6)Tj
/T1_12 7.97 Tf
(=)Tj
/T1_4 7.97 Tf
6.59 0 Td
(l)Tj
/T1_1 10.91 Tf
4.94 3.23 Td
(z)Tj
/T1_2 7.97 Tf
5.55 3.95 Td
(0)Tj
/T1_4 7.97 Tf
-0.48 -7.01 Td
(j)Tj
/T1_0 10.91 Tf
7.25 3.06 Td
[(sen)27(t)-262(in)-263(Round)-263(2)-263(as)]TJ
/T1_7 10.91 Tf
-381.29 -21.92 Td
(A)Tj
/T1_0 10.91 Tf
12.03 0 Td
[(do)-27(es)-305(not)-304(kno)26(w)-303(the)-305(priv)55(ate)-304(k)27(ey)-304(\()-85(\271)]TJ
/T1_1 10.91 Tf
149.99 0 Td
(p)Tj
/T1_4 7.97 Tf
5.48 -1.64 Td
(i)Tj
/T1_1 10.91 Tf
3.38 1.64 Td
(;)Tj
/T1_0 10.91 Tf
5.66 0 Td
(\271)Tj
/T1_1 10.91 Tf
-0.81 0 Td
(q)Tj
/T1_4 7.97 Tf
4.87 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
3.38 1.64 Td
[(\))-304(of)]TJ
/T1_3 10.91 Tf
19.67 0 Td
(U)Tj
/T1_4 7.97 Tf
5.73 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
6.7 1.64 Td
[(and)-304(the)-304(Rabin)-305(signature)-305(sc)27(heme)-303(is)-305(secure.)-435(Therefore,)]TJ
-216.08 -21.92 Td
[(it)-428(is)-429(not)-429(p)-27(ossible)-429(for)-429(an)-428(adv)26(ersary)-427(to)-429(obtain)-429(the)-428(new)-429(group)-429(k)27(ey)-427(in)-429(this)-429(case.)-730(No)27(w,)-452(w)27(e)-428(consider)]TJ
0 -21.91 TD
[(the)-368(case)-369(\(b\))-368(as)-369(follo)27(ws:)-514(As)-369(an)-369(adv)27(ersary)]TJ
/T1_7 10.91 Tf
197.72 0 Td
(A)Tj
/T1_0 10.91 Tf
12.72 0 Td
[(is)-369(not)-368(a)-369(lea)27(ving)-368(user)]TJ
/T1_3 10.91 Tf
101.45 0 Td
(U)Tj
/T1_4 7.97 Tf
5.72 -1.78 Td
(l)Tj
/T1_0 10.91 Tf
3.12 1.78 Td
(,)Tj
/T1_7 10.91 Tf
7.15 0 Td
(A)Tj
/T1_0 10.91 Tf
12.73 0 Td
[(can)-368(only)-369(obtain)-368(the)-369(public)]TJ
-340.61 -21.92 Td
[(exc)27(hange)-313(information,)-318(that)-315(is,)]TJ
/T1_1 10.91 Tf
145.67 0 Td
(z)Tj
/T1_4 7.97 Tf
5.08 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
3.38 1.64 Td
(,)Tj
9.63 2.76 Td
(^)Tj
/T1_1 10.91 Tf
-3.13 -2.76 Td
(X)Tj
/T1_4 7.97 Tf
9.03 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
6.81 1.64 Td
[(for)-314(1)]TJ
/T1_7 10.91 Tf
24.97 0 Td
(\267)Tj
/T1_1 10.91 Tf
11.51 0 Td
(i)Tj
/T1_7 10.91 Tf
6.79 0 Td
(\267)Tj
/T1_1 10.91 Tf
11.51 0 Td
(n)Tj
/T1_0 10.91 Tf
9.98 0 Td
(and)Tj
/T1_1 10.91 Tf
21 0 Td
(z)Tj
/T1_2 7.97 Tf
5.55 3.96 Td
(0)Tj
/T1_4 7.97 Tf
-0.48 -7.01 Td
(j)Tj
/T1_0 10.91 Tf
4.38 3.05 Td
(,)Tj
9.63 2.76 Td
(^)Tj
/T1_1 10.91 Tf
-3.13 -2.76 Td
(X)Tj
/T1_2 7.97 Tf
9.9 3.96 Td
(0)Tj
/T1_4 7.97 Tf
-0.86 -7.01 Td
(j)Tj
/T1_0 10.91 Tf
7.81 3.05 Td
[(for)-314(1)]TJ
/T1_7 10.91 Tf
24.97 0 Td
(\267)Tj
/T1_1 10.91 Tf
11.51 0 Td
(j)Tj
/T1_7 10.91 Tf
8.15 0 Td
(6)Tj
/T1_0 10.91 Tf
(=)Tj
/T1_1 10.91 Tf
11.51 0 Td
(l)Tj
/T1_7 10.91 Tf
6.5 0 Td
(\267)Tj
/T1_1 10.91 Tf
11.51 0 Td
(n)Tj
/T1_0 10.91 Tf
9.97 0 Td
[(from)-314(IKA)-315(proto)-28(col)]TJ
-379.15 -21.92 Td
[(and)-345(the)-346(Lea)27(v)28(e)-345(proto)-27(col)-346(resp)-28(ectiv)27(ely)83(.)-480(It)-345(is)-346(noted)-345(that)]TJ
/T1_1 10.91 Tf
254.46 0 Td
(z)Tj
/T1_2 7.97 Tf
5.55 3.96 Td
(0)Tj
/T1_4 7.97 Tf
-0.48 -7.01 Td
(i)Tj
/T1_0 10.91 Tf
7.15 3.05 Td
(and)Tj
/T1_1 10.91 Tf
21.34 0 Td
(z)Tj
/T1_4 7.97 Tf
5.07 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
7.15 1.63 Td
[(are)-345(indep)-28(enden)27(t)-344(to)-346(eac)27(h)-345(other)-345(for)]TJ
/T1_1 10.91 Tf
163.87 0 Td
(i)Tj
/T1_0 10.91 Tf
-464.11 -21.91 Td
[(is)-373(o)-28(dd)-373(and)]TJ
/T1_1 10.91 Tf
54.99 0 Td
(i)Tj
/T1_7 10.91 Tf
7.51 0 Td
(6)Tj
/T1_0 10.91 Tf
(=)Tj
/T1_1 10.91 Tf
12.24 0 Td
(l)Tj
/T1_0 10.91 Tf
3.47 0 Td
[(,)-383(hence)]TJ
/T1_1 10.91 Tf
37.94 0 Td
(c)Tj
/T1_2 7.97 Tf
4.72 3.95 Td
(0)Tj
/T1_4 7.97 Tf
0 -7.01 TD
(i)Tj
/T1_0 10.91 Tf
7.13 3.06 Td
(=)Tj
/T1_8 10.91 Tf
12.24 0 Td
(H)Tj
/T1_0 10.91 Tf
(\()Tj
/T1_1 10.91 Tf
11.97 0 Td
(z)Tj
/T1_2 7.97 Tf
5.55 3.95 Td
(0)Tj
/T1_4 7.97 Tf
-0.48 -7.01 Td
(i)Tj
/T1_0 10.91 Tf
3.38 3.06 Td
[(\))-373(and)]TJ
/T1_1 10.91 Tf
29.95 0 Td
(c)Tj
/T1_4 7.97 Tf
4.72 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
7.14 1.64 Td
(=)Tj
/T1_8 10.91 Tf
12.24 0 Td
(H)Tj
/T1_0 10.91 Tf
(\()Tj
/T1_1 10.91 Tf
(z)Tj
/T1_4 7.97 Tf
17.03 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
3.38 1.64 Td
[(\))-373(are)-373(indep)-28(enden)27(t)-373(to)-373(eac)27(h)-372(other)-374(for)]TJ
/T1_1 10.91 Tf
174 0 Td
(i)Tj
/T1_0 10.91 Tf
7.83 0 Td
[(is)-373(o)-28(dd)-373(and)]TJ
/T1_1 10.91 Tf
-416.95 -21.92 Td
(i)Tj
/T1_7 10.91 Tf
6.79 0 Td
(6)Tj
/T1_0 10.91 Tf
(=)Tj
/T1_1 10.91 Tf
11.51 0 Td
(l)Tj
/T1_0 10.91 Tf
7.04 0 Td
[(as)-328(the)-327(output)-328(of)-328(the)-328(hash)-328(function)]TJ
/T1_8 10.91 Tf
166.93 0 Td
(H)Tj
/T1_0 10.91 Tf
11.3 0 Td
[(is)-328(indep)-27(enden)26(t,)-328(and)]TJ
99.97 2.76 Td
(^)Tj
/T1_1 10.91 Tf
-3.13 -2.76 Td
(X)Tj
/T1_2 7.97 Tf
9.89 3.96 Td
(0)Tj
/T1_4 7.97 Tf
-0.85 -7.01 Td
(i)Tj
/T1_0 10.91 Tf
7.22 3.05 Td
(and)Tj
24.28 2.76 Td
(^)Tj
/T1_1 10.91 Tf
-3.13 -2.76 Td
(X)Tj
/T1_4 7.97 Tf
9.03 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
6.96 1.64 Td
[(are)-327(indep)-28(enden)27(t)-327(to)-328(eac)27(h)]TJ
-353.81 -21.92 Td
[(other)-402(for)-403(1)]TJ
/T1_7 10.91 Tf
56.46 0 Td
(\267)Tj
/T1_1 10.91 Tf
12.78 0 Td
(i)Tj
/T1_7 10.91 Tf
8.05 0 Td
(\267)Tj
/T1_1 10.91 Tf
12.78 0 Td
(n)Tj
/T1_0 10.91 Tf
10.94 0 Td
[(suc)27(h)-402(that)]TJ
/T1_1 10.91 Tf
49.75 0 Td
(i)Tj
/T1_7 10.91 Tf
8.05 0 Td
(6)Tj
/T1_0 10.91 Tf
(=)Tj
/T1_1 10.91 Tf
12.78 0 Td
[(l)-19(;)-166(l)]TJ
/T1_7 10.91 Tf
14.71 0 Td
(\241)Tj
/T1_0 10.91 Tf
11.41 0 Td
(1)Tj
/T1_1 10.91 Tf
[(;)-166(l)]TJ
/T1_0 10.91 Tf
16.7 0 Td
[(+)-268(1.)-653(F)82(urthermore,)-419(the)-403(n)26(um)28(b)-27(er)-402(of)-403(terms)-403(of)-403(the)-403(form)]TJ
/T1_1 10.91 Tf
-214.41 -21.91 Td
(g)Tj
/T1_4 7.97 Tf
5.59 3.96 Td
(de)Tj
/T1_0 10.91 Tf
13.14 -3.96 Td
(in)Tj
/T1_1 10.91 Tf
13.44 0 Td
(K)Tj
/T1_0 10.91 Tf
14.39 0 Td
(and)Tj
/T1_1 10.91 Tf
21.92 0 Td
(K)Tj
/T1_2 7.97 Tf
10.04 3.96 Td
(0)Tj
/T1_0 10.91 Tf
7.15 -3.96 Td
[(are)-398(di\256eren)26(t)-398(b)27(y)-398(1.)-641(Therefore,)-415(the)-399(k)26(ey)]TJ
/T1_1 10.91 Tf
187.3 0 Td
(K)Tj
/T1_0 10.91 Tf
14.39 0 Td
(and)Tj
/T1_1 10.91 Tf
21.92 0 Td
(K)Tj
/T1_2 7.97 Tf
10.04 3.96 Td
(0)Tj
/T1_0 10.91 Tf
7.15 -3.96 Td
[(is)-398(indep)-28(enden)27(t)-398(to)-399(eac)26(h)-398(other.)]TJ
-326.47 -21.92 Td
[(Hence,)-402(the)-389(adv)26(ersary)]TJ
/T1_7 10.91 Tf
105.7 0 Td
(A)Tj
/T1_0 10.91 Tf
12.95 0 Td
[(can)-389(only)-389(deriv)27(e)-388(the)-389(k)27(ey)]TJ
/T1_1 10.91 Tf
117.59 0 Td
(K)Tj
/T1_2 7.97 Tf
10.04 3.96 Td
(0)Tj
/T1_0 10.91 Tf
7.03 -3.96 Td
[(from)-389(the)-389(public)-389(exc)27(hange)-388(information)-389(in)-389(the)]TJ
-253.31 -21.92 Td
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1.0003 0 0 1.0003 477.8636 340.3498 Tm
(n)Tj
/T1_0 10.91 Tf
8.97 0 Td
(+)Tj
1.0003 0 0 1.0003 72 769.82 Tm
425.619 -429.35 Td
(3)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 451.67 -433.41 cm
0 0 m
0 13.54 l
S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 453.66 -433.41 cm
0 0 m
0 13.54 l
S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 74.96 -433.61 cm
0 0 m
378.7 0 l
S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 14.21 -446.96 cm
0 0 m
0 13.55 l
S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 16.2 -446.96 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 101.0781 326.796 Tm
([BD95])Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 74.96 -446.96 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 154.113 326.796 Tm
(Lea)Tj
1.0003 0 0 1.0003 72 769.82 Tm
98.913 -442.9 Td
[(v)28(e)]TJ
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 116.33 -446.96 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 220.0314 326.796 Tm
(2)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 185.1 -446.96 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 274.5867 326.796 Tm
(2)Tj
/T1_1 10.91 Tf
(n)Tj
/T1_5 10.91 Tf
14.42 0 Td
(\241)Tj
/T1_0 10.91 Tf
10.91 0 Td
(2)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 250.74 -446.96 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 348.4274 326.796 Tm
(3)Tj
/T1_2 7.97 Tf
5.46 3.96 Td
(\244)Tj
/T1_4 7.97 Tf
(1)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 316.38 -446.96 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 420.1375 326.796 Tm
(2)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 385.15 -446.96 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_1 10.91 Tf
1.0003 0 0 1.0003 477.8636 326.796 Tm
(n)Tj
/T1_0 10.91 Tf
8.97 0 Td
(+)Tj
1.0003 0 0 1.0003 72 769.82 Tm
425.619 -442.9 Td
(1)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 451.67 -446.96 cm
0 0 m
0 13.55 l
S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 453.66 -446.96 cm
0 0 m
0 13.55 l
S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 74.96 -447.16 cm
0 0 m
378.7 0 l
S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 14.21 -460.5 cm
0 0 m
0 13.54 l
S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 16.2 -460.5 cm
0 0 m
0 13.54 l
S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 74.96 -460.5 cm
0 0 m
0 13.54 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 152.9627 313.2522 Tm
(Merge)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 116.33 -460.5 cm
0 0 m
0 13.54 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 220.0314 313.2522 Tm
(2)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 185.1 -460.5 cm
0 0 m
0 13.54 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 269.7954 313.2522 Tm
(2)Tj
/T1_1 10.91 Tf
(n)Tj
/T1_0 10.91 Tf
14.43 0 Td
(+)Tj
1.0003 0 0 1.0003 72 769.82 Tm
223.069 -456.44 Td
(2)Tj
/T1_1 10.91 Tf
5.461 0 Td
(m)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 250.74 -460.5 cm
0 0 m
0 13.54 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 348.4274 313.2522 Tm
(3)Tj
/T1_2 7.97 Tf
5.46 3.96 Td
(\244)Tj
/T1_4 7.97 Tf
(1)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 316.38 -460.5 cm
0 0 m
0 13.54 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 420.1375 313.2522 Tm
(2)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 385.15 -460.5 cm
0 0 m
0 13.54 l
S
Q
Q
BT
/T1_1 10.91 Tf
1.0003 0 0 1.0003 466.4004 313.2522 Tm
(n)Tj
/T1_0 10.91 Tf
8.97 0 Td
(+)Tj
/T1_1 10.91 Tf
10.91 0 Td
(m)Tj
/T1_0 10.91 Tf
12 0 Td
(+)Tj
1.0003 0 0 1.0003 72 769.82 Tm
437.08 -456.44 Td
(2)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 451.67 -460.5 cm
0 0 m
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 453.66 -460.5 cm
0 0 m
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 14.21 -460.7 cm
0 0 m
439.45 0 l
S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 14.21 -462.7 cm
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439.45 0 l
S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 14.21 -476.44 cm
0 0 m
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 16.2 -476.44 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 104.4791 297.3077 Tm
(Prop.)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 74.96 -476.44 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 157.594 297.3077 Tm
(Join)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 116.33 -476.44 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 220.0314 297.3077 Tm
(3)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 185.1 -476.44 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 287.2603 297.3077 Tm
(5)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 250.74 -476.44 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 348.4274 297.3077 Tm
(3)Tj
/T1_2 7.97 Tf
5.46 3.96 Td
(\244)Tj
/T1_4 7.97 Tf
(2)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 316.38 -476.44 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 420.1375 297.3077 Tm
(1)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 385.15 -476.44 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 487.7964 297.3077 Tm
(1)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 451.67 -476.44 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 453.66 -476.44 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 74.96 -476.64 cm
0 0 m
378.7 0 l
S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 14.21 -489.99 cm
0 0 m
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 16.2 -489.99 cm
0 0 m
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S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 107.75 283.7639 Tm
(Sc)Tj
1.0003 0 0 1.0003 72 769.82 Tm
46.345 -485.92 Td
(h.)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 74.96 -489.99 cm
0 0 m
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S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 154.113 283.7639 Tm
(Lea)Tj
1.0003 0 0 1.0003 72 769.82 Tm
98.913 -485.92 Td
[(v)28(e)]TJ
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 116.33 -489.99 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 220.0314 283.7639 Tm
(2)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 185.1 -489.99 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_1 10.91 Tf
1.0003 0 0 1.0003 267.8048 283.7639 Tm
(v)Tj
/T1_0 10.91 Tf
8.11 0 Td
(+)Tj
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10.9 0 Td
(n)Tj
/T1_5 10.91 Tf
8.97 0 Td
(\241)Tj
/T1_0 10.91 Tf
10.91 0 Td
(2)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 250.74 -489.99 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 348.4274 283.7639 Tm
(4)Tj
/T1_2 7.97 Tf
5.46 3.96 Td
(\244)Tj
/T1_4 7.97 Tf
(3)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 316.38 -489.99 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 420.1375 283.7639 Tm
(1)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 385.15 -489.99 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_1 10.91 Tf
1.0003 0 0 1.0003 477.8636 283.7639 Tm
(n)Tj
/T1_5 10.91 Tf
8.97 0 Td
(\241)Tj
/T1_0 10.91 Tf
10.9 0 Td
(1)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 451.67 -489.99 cm
0 0 m
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 453.66 -489.99 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 74.96 -490.18 cm
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378.7 0 l
S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 14.21 -503.53 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 16.2 -503.53 cm
0 0 m
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 74.96 -503.53 cm
0 0 m
0 13.54 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 152.9627 270.2101 Tm
(Merge)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 116.33 -503.53 cm
0 0 m
0 13.54 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 220.0314 270.2101 Tm
(3)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 185.1 -503.53 cm
0 0 m
0 13.54 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 270.6056 270.2101 Tm
(6\()Tj
/T1_1 10.91 Tf
(k)Tj
/T1_5 10.91 Tf
18.14 0 Td
(\241)Tj
/T1_0 10.91 Tf
10.91 0 Td
(1\))Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 250.74 -503.53 cm
0 0 m
0 13.54 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 348.4274 270.2101 Tm
(5)Tj
/T1_2 7.97 Tf
5.46 3.96 Td
(\244)Tj
/T1_4 7.97 Tf
(4)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 316.38 -503.53 cm
0 0 m
0 13.54 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 420.1375 270.2101 Tm
(1)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 385.15 -503.53 cm
0 0 m
0 13.54 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 487.7964 270.2101 Tm
(1)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 451.67 -503.53 cm
0 0 m
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 453.66 -503.53 cm
0 0 m
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 14.21 -503.73 cm
0 0 m
439.45 0 l
S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 14.21 -505.72 cm
0 0 m
439.45 0 l
S
Q
Q
BT
/T1_2 7.97 Tf
1.0003 0 0 1.0003 72 245.6733 Tm
(\244)Tj
/T1_4 7.97 Tf
(1)Tj
/T1_0 10.91 Tf
12.6 -3.96 Td
(:)Tj
1.0003 0 0 1.0003 72 769.82 Tm
20.477 -527.96 Td
[(F)82(or)-332(BD)-333(proto)-28(col,)-333(all)-334(users)-333(p)-28(erform)-333(3)-333(exp)-28(onen)27(tiations.)]TJ
/T1_2 7.97 Tf
-20.477 -9.59 Td
(\244)Tj
/T1_4 7.97 Tf
(2)Tj
/T1_0 10.91 Tf
12.6 -3.96 Td
[(:)-444(In)-333(our)-334(Join)-333(Proto)-28(col,)-333(only)]TJ
/T1_7 10.91 Tf
135.78 0 Td
(U)Tj
/T1_4 7.97 Tf
5.73 -1.63 Td
(1)Tj
/T1_0 10.91 Tf
8.36 1.63 Td
(and)Tj
/T1_7 10.91 Tf
21.21 0 Td
(U)Tj
/T1_6 7.97 Tf
5.72 -1.63 Td
(n)Tj
/T1_4 7.97 Tf
(+1)Tj
/T1_0 10.91 Tf
20.09 1.63 Td
[(p)-27(erform)-334(3)-333(exp)-28(onen)27(tiations)-332(eac)26(h.)]TJ
/T1_2 7.97 Tf
-209.49 -9.58 Td
(\244)Tj
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(3)Tj
/T1_0 10.91 Tf
11.76 -3.96 Td
[(:)-405(F)82(or)-255(our)-256(Lea)27(v)28(e)-256(Proto)-27(col,)-272(users)]TJ
/T1_7 10.91 Tf
147.71 0 Td
(U)Tj
/T1_6 7.97 Tf
5.72 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
6.17 1.64 Td
(for)Tj
/T1_1 10.91 Tf
15.86 0 Td
(i)Tj
/T1_0 10.91 Tf
6.55 0 Td
[(is)-255(o)-28(dd)-256(and)]TJ
/T1_7 10.91 Tf
51.15 0 Td
(U)Tj
/T1_6 7.97 Tf
5.73 -1.64 Td
(j)Tj
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7.17 1.64 Td
(for)Tj
/T1_1 10.91 Tf
15.85 0 Td
(j)Tj
/T1_0 10.91 Tf
7.91 0 Td
[(is)-256(ev)27(en)-255(p)-28(erform)-256(4)-256(and)-256(3)-256(exp)-28(onen)27(tiations)]TJ
-281.58 -13.55 Td
[(resp)-27(ectiv)27(ely)83(.)]TJ
/T1_2 7.97 Tf
0 -9.59 TD
(\244)Tj
/T1_4 7.97 Tf
(4)Tj
/T1_0 10.91 Tf
12.6 -3.95 Td
[(:)-444(In)-333(our)-334(Merge)-333(Proto)-28(col,)-333(only)]TJ
/T1_7 10.91 Tf
145.05 0 Td
(U)Tj
/T1_4 7.97 Tf
5.73 -1.64 Td
(1)Tj
/T1_0 10.91 Tf
8.36 1.64 Td
(and)Tj
/T1_7 10.91 Tf
21.21 0 Td
(U)Tj
/T1_6 7.97 Tf
5.72 -1.64 Td
(n)Tj
/T1_4 7.97 Tf
(+1)Tj
/T1_0 10.91 Tf
20.09 1.64 Td
[(p)-27(erforms)-334(5)-333(exp)-28(onen)27(tiations.)]TJ
-201.83 -34.22 Td
[(Our)-298(prop)-28(osed)-298(proto)-28(cols)-298(include)-298(the)-299(priv)55(ate)-297(k)26(eys)]TJ
/T1_1 10.91 Tf
230.29 0 Td
(x)Tj
/T1_6 7.97 Tf
6.24 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
6.63 1.63 Td
[(of)-298(all)-298(users)]TJ
/T1_7 10.91 Tf
53.84 0 Td
(U)Tj
/T1_6 7.97 Tf
5.72 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
6.64 1.63 Td
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T*
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T*
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/T1_3 10.91 Tf
130.14 0 Td
(p;)Tj
/T1_0 10.91 Tf
11.15 0 Td
(\271)Tj
/T1_3 10.91 Tf
-0.81 0 Td
[(q)-35(;)-167(d)]TJ
/T1_0 10.91 Tf
15.78 0 Td
(\).)Tj
-358.92 -21.92 Td
(Extract)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 0 -56.32 cm
0 0 m
36.23 0 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 113.6016 715.0147 Tm
(:)Tj
1.0003 0 0 1.0003 72 769.82 Tm
52.904 -54.79 Td
[(The)-492(PK)27(G)-490(v)27(eri\257es)]TJ
/T1_6 10.91 Tf
91.826 0 Td
(U)Tj
/T1_5 7.97 Tf
5.72 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
9.28 1.63 Td
(=)Tj
/T1_6 10.91 Tf
14.38 0 Td
(ID)Tj
/T1_5 7.97 Tf
11.45 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
8.74 1.63 Td
[(of)-491(user)]TJ
/T1_6 10.91 Tf
38.98 0 Td
(U)Tj
/T1_5 7.97 Tf
5.72 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
8.74 1.63 Td
[(and)-491(computes)-491(the)-491(secret)-491(k)27(ey)-491(for)]TJ
/T1_6 10.91 Tf
166.22 0 Td
(U)Tj
/T1_5 7.97 Tf
5.73 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
8.74 1.63 Td
(as)Tj
/T1_3 10.91 Tf
15.11 0 Td
(\271)Tj
/T1_5 7.97 Tf
6.57 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
9.28 1.63 Td
(=)Tj
/T1_1 10.91 Tf
-459.39 -21.92 Td
(H)Tj
/T1_0 10.91 Tf
7.73 0 Td
(\()Tj
/T1_6 10.91 Tf
(U)Tj
/T1_5 7.97 Tf
9.96 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
3.38 1.63 Td
(\))Tj
/T1_5 7.97 Tf
4.24 3.96 Td
(d)Tj
/T1_0 10.91 Tf
7.89 -3.96 Td
[(mo)-27(d)]TJ
/T1_3 10.91 Tf
23.93 0 Td
(N)Tj
/T1_0 10.91 Tf
9.95 0 Td
[(.)-444(The)-333(secret)-334(k)27(ey)]TJ
/T1_3 10.91 Tf
80.98 0 Td
(\271)Tj
/T1_5 7.97 Tf
6.57 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
7.02 1.63 Td
[(is)-333(then)-333(sen)27(t)-332(securely)-334(to)]TJ
/T1_6 10.91 Tf
113.51 0 Td
(U)Tj
/T1_5 7.97 Tf
5.73 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
3.38 1.63 Td
(.)Tj
-284.27 -21.91 Td
[(Round)-333(1)]TJ
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 0 -100.15 cm
0 0 m
40.75 0 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 115.8423 671.1724 Tm
(:)Tj
1.0003 0 0 1.0003 72 769.82 Tm
51.434 -98.62 Td
[(Eac)27(h)-283(user)]TJ
/T1_6 10.91 Tf
49.136 0 Td
(U)Tj
/T1_5 7.97 Tf
5.73 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
6.46 1.64 Td
[(for)-283(1)]TJ
/T1_2 10.91 Tf
24.63 0 Td
(\267)Tj
/T1_3 10.91 Tf
11.51 0 Td
(i)Tj
/T1_2 10.91 Tf
6.79 0 Td
(\267)Tj
/T1_3 10.91 Tf
11.51 0 Td
(n)Tj
/T1_0 10.91 Tf
9.64 0 Td
[(\257rst)-282(selects)]TJ
/T1_3 10.91 Tf
55.46 0 Td
(r)Tj
/T1_5 7.97 Tf
4.92 -1.64 Td
(i)Tj
/T1_2 10.91 Tf
6.41 1.64 Td
(2)Tj
/T1_3 10.91 Tf
10.3 0 Td
(Z)Tj
/T1_4 7.97 Tf
8.23 3.96 Td
(\244)Tj
/T1_5 7.97 Tf
-0.78 -6.66 Td
(q)Tj
/T1_0 10.91 Tf
8.6 2.7 Td
(and)Tj
/T1_3 10.91 Tf
20.66 0 Td
(\277)Tj
/T1_5 7.97 Tf
4.76 -1.64 Td
(i)Tj
/T1_2 10.91 Tf
6.41 1.64 Td
(2)Tj
/T1_3 10.91 Tf
10.3 0 Td
(Z)Tj
/T1_4 7.97 Tf
8.23 3.96 Td
(\244)Tj
/T1_5 7.97 Tf
-0.78 -7.19 Td
(N)Tj
/T1_0 10.91 Tf
11.15 3.23 Td
[(and)-283(computes)]TJ
/T1_3 10.91 Tf
68.65 0 Td
(z)Tj
/T1_5 7.97 Tf
5.07 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
6.41 1.64 Td
(=)Tj
/T1_3 10.91 Tf
11.51 0 Td
(g)Tj
/T1_5 7.97 Tf
5.59 3.96 Td
(r)Tj
/T1_7 5.98 Tf
3.82 -1.22 Td
(i)Tj
/T1_0 10.91 Tf
6.69 -2.74 Td
[(mo)-27(d)]TJ
/T1_3 10.91 Tf
23.93 0 Td
(p)Tj
/T1_0 10.91 Tf
-462.38 -21.92 Td
(and)Tj
/T1_3 10.91 Tf
21.21 0 Td
(t)Tj
/T1_5 7.97 Tf
3.93 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
6.41 1.63 Td
(=)Tj
/T1_3 10.91 Tf
11.52 0 Td
(\277)Tj
/T1_5 7.97 Tf
6 3.96 Td
(e)Tj
-1.24 -7.01 Td
(i)Tj
/T1_0 10.91 Tf
8.69 3.05 Td
[(mo)-28(d)]TJ
/T1_3 10.91 Tf
23.94 0 Td
(N)Tj
/T1_0 10.91 Tf
9.95 0 Td
(.)Tj
/T1_6 10.91 Tf
7.87 0 Td
(U)Tj
/T1_5 7.97 Tf
5.73 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
7.02 1.63 Td
[(then)-332(broadcast)]TJ
/T1_2 10.91 Tf
74.61 0 Td
(f)Tj
/T1_6 10.91 Tf
(U)Tj
/T1_5 7.97 Tf
11.18 -1.63 Td
(i)Tj
/T1_2 10.91 Tf
3.38 1.63 Td
(jj)Tj
/T1_3 10.91 Tf
6.06 0 Td
(z)Tj
/T1_5 7.97 Tf
5.07 -1.63 Td
(i)Tj
/T1_2 10.91 Tf
3.38 1.63 Td
(jj)Tj
/T1_3 10.91 Tf
6.06 0 Td
(t)Tj
/T1_5 7.97 Tf
3.94 -1.63 Td
(i)Tj
/T1_2 10.91 Tf
3.38 1.63 Td
(g)Tj
/T1_0 10.91 Tf
(.)Tj
-228.09 -21.91 Td
[(Round)-333(2)]TJ
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 0 -143.98 cm
0 0 m
40.75 0 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 116.3924 627.3301 Tm
(:)Tj
1.0003 0 0 1.0003 72 769.82 Tm
52.257 -142.45 Td
[(Eac)27(h)-333(user)]TJ
/T1_6 10.91 Tf
50.233 0 Td
(U)Tj
/T1_5 7.97 Tf
5.72 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
7.02 1.64 Td
[(for)-333(1)]TJ
/T1_2 10.91 Tf
25.17 0 Td
(\267)Tj
/T1_3 10.91 Tf
11.51 0 Td
(i)Tj
/T1_2 10.91 Tf
6.79 0 Td
(\267)Tj
/T1_3 10.91 Tf
11.51 0 Td
(n)Tj
/T1_0 10.91 Tf
10.19 0 Td
[(\257rst)-332(computes)-334(:)]TJ
/T1_3 10.91 Tf
-42.59 -39.65 Td
(X)Tj
/T1_5 7.97 Tf
9.03 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
13.34 1.63 Td
(=)Tj
/T1_8 10.91 Tf
18.45 15.38 Td
(\265)Tj
/T1_3 10.91 Tf
9.22 -8 Td
(z)Tj
/T1_5 7.97 Tf
5.07 -1.64 Td
(i)Tj
/T1_9 7.97 Tf
2.88 0 Td
(+1)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 187.85 -179.37 cm
0 0 m
19.27 0 l
S
Q
Q
BT
/T1_3 10.91 Tf
1.0003 0 0 1.0003 259.9026 580.1869 Tm
(z)Tj
/T1_5 7.97 Tf
5.07 -1.63 Td
(i)Tj
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2.88 0 Td
(\241)Tj
/T1_9 7.97 Tf
6.59 0 Td
(1)Tj
/T1_8 10.91 Tf
5.93 24.49 Td
(\266)Tj
/T1_5 7.97 Tf
8.02 -2.72 Td
(r)Tj
/T1_7 5.98 Tf
3.82 -1.21 Td
(i)Tj
/T1_0 10.91 Tf
6.69 -11.45 Td
(=)Tj
/T1_3 10.91 Tf
11.51 0 Td
(g)Tj
/T1_5 7.97 Tf
5.6 4.51 Td
(r)Tj
/T1_7 5.98 Tf
3.82 -1.22 Td
(i)Tj
/T1_5 7.97 Tf
3.16 1.22 Td
(r)Tj
/T1_7 5.98 Tf
3.82 -1.22 Td
(i)Tj
/T1_10 5.98 Tf
2.66 0 Td
(+1)Tj
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9.74 1.22 Td
(\241)Tj
/T1_5 7.97 Tf
(r)Tj
/T1_7 5.98 Tf
10.41 -1.22 Td
(i)Tj
/T1_11 5.98 Tf
2.66 0 Td
(\241)Tj
/T1_10 5.98 Tf
5.75 0 Td
(1)Tj
/T1_5 7.97 Tf
4.15 1.22 Td
(r)Tj
/T1_7 5.98 Tf
3.82 -1.22 Td
(i)Tj
/T1_0 10.91 Tf
6.69 -3.29 Td
(mo)Tj
1.0003 0 0 1.0003 72 769.82 Tm
315.478 -182.1 Td
(d)Tj
/T1_3 10.91 Tf
9.092 0 Td
(p)Tj
/T1_0 10.91 Tf
120.88 0 Td
(\(6.1\))Tj
-445.45 -39.64 Td
(Next,)Tj
/T1_6 10.91 Tf
30.17 0 Td
(U)Tj
/T1_5 7.97 Tf
5.72 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
7.4 1.64 Td
(computes)Tj
/T1_2 10.91 Tf
48.91 0 Td
(Z)Tj
/T1_0 10.91 Tf
12.44 0 Td
(=)Tj
/T1_8 10.91 Tf
12.15 8.18 Td
(Q)Tj
/T1_5 7.97 Tf
10.3 -3.16 Td
(n)Tj
0 -8.25 TD
(j)Tj
/T1_9 7.97 Tf
3.88 0 Td
(=1)Tj
/T1_3 10.91 Tf
13.13 3.23 Td
(z)Tj
/T1_5 7.97 Tf
5.08 -1.64 Td
(j)Tj
/T1_0 10.91 Tf
7.41 1.64 Td
[(mo)-27(d)]TJ
/T1_3 10.91 Tf
23.93 0 Td
(p)Tj
/T1_0 10.91 Tf
(,)Tj
/T1_2 10.91 Tf
12.63 0 Td
(T)Tj
/T1_0 10.91 Tf
12.38 0 Td
(=)Tj
/T1_8 10.91 Tf
12.15 8.18 Td
(Q)Tj
/T1_5 7.97 Tf
10.3 -3.16 Td
(n)Tj
T*
(j)Tj
/T1_9 7.97 Tf
3.88 0 Td
(=1)Tj
/T1_3 10.91 Tf
13.13 3.23 Td
(t)Tj
/T1_5 7.97 Tf
3.94 -1.64 Td
(j)Tj
/T1_0 10.91 Tf
7.41 1.64 Td
[(mo)-27(d)]TJ
/T1_3 10.91 Tf
23.93 0 Td
(N)Tj
/T1_0 10.91 Tf
13.97 0 Td
(and)Tj
/T1_3 10.91 Tf
21.59 0 Td
(\265)Tj
/T1_0 10.91 Tf
9.09 0 Td
(=)Tj
/T1_1 10.91 Tf
12.15 0 Td
(H)Tj
/T1_0 10.91 Tf
(\()Tj
/T1_2 10.91 Tf
(T)Tj
/T1_3 10.91 Tf
20.68 0 Td
(;)Tj
/T1_2 10.91 Tf
4.84 0 Td
(Z)Tj
/T1_0 10.91 Tf
8.77 0 Td
(\).)Tj
/T1_6 10.91 Tf
13.27 0 Td
(U)Tj
/T1_5 7.97 Tf
5.72 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
7.4 1.64 Td
[(then)-368(computes)]TJ
/T1_3 10.91 Tf
-397.75 -21.92 Td
(s)Tj
/T1_5 7.97 Tf
5.11 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
8.42 1.63 Td
(=)Tj
/T1_3 10.91 Tf
13.51 0 Td
(\277)Tj
/T1_5 7.97 Tf
4.77 -1.63 Td
(i)Tj
/T1_2 10.91 Tf
6.6 1.63 Td
(\242)Tj
/T1_3 10.91 Tf
6.26 0 Td
(\271)Tj
/T1_5 7.97 Tf
6.57 3.96 Td
(\265)Tj
0 -7.01 TD
(i)Tj
/T1_0 10.91 Tf
7.71 3.05 Td
[(mo)-27(d)]TJ
/T1_3 10.91 Tf
23.93 0 Td
(N)Tj
/T1_0 10.91 Tf
14.79 0 Td
[(and)-443(pro)-28(duces)-444(the)-443(signature)]TJ
/T1_3 10.91 Tf
137.99 0 Td
(\276)Tj
/T1_5 7.97 Tf
6.23 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
8.41 1.63 Td
[(=)-461(\()]TJ
/T1_3 10.91 Tf
(s)Tj
/T1_5 7.97 Tf
22.87 -1.63 Td
(i)Tj
/T1_3 10.91 Tf
3.38 1.63 Td
[(;)-166(\265)]TJ
/T1_0 10.91 Tf
10.27 0 Td
(\).)Tj
/T1_6 10.91 Tf
15.73 0 Td
(U)Tj
/T1_5 7.97 Tf
5.72 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
8.22 1.63 Td
(stores)Tj
/T1_2 10.91 Tf
32.25 0 Td
(Z)Tj
/T1_0 10.91 Tf
13.61 0 Td
(and)Tj
/T1_3 10.91 Tf
22.41 0 Td
(\265)Tj
/T1_0 10.91 Tf
10.26 0 Td
[(and)-443(broadcasts)]TJ
/T1_2 10.91 Tf
-395.02 -21.91 Td
(f)Tj
/T1_6 10.91 Tf
(U)Tj
/T1_5 7.97 Tf
11.18 -1.64 Td
(i)Tj
/T1_2 10.91 Tf
3.38 1.64 Td
(jj)Tj
/T1_3 10.91 Tf
6.06 0 Td
(X)Tj
/T1_5 7.97 Tf
9.03 -1.64 Td
(i)Tj
/T1_2 10.91 Tf
3.38 1.64 Td
(jj)Tj
/T1_3 10.91 Tf
6.06 0 Td
(s)Tj
/T1_5 7.97 Tf
5.11 -1.64 Td
(i)Tj
/T1_2 10.91 Tf
3.39 1.64 Td
(g)Tj
/T1_0 10.91 Tf
[(.)-498(It)-351(is)-351(noted)-352(that)]TJ
/T1_6 10.91 Tf
91.4 0 Td
(U)Tj
/T1_9 7.97 Tf
5.73 -1.64 Td
(1)Tj
/T1_0 10.91 Tf
8.56 1.64 Td
[(is)-351(assumed)-351(to)-352(b)-27(e)-352(a)-351(trusted)-351(con)26(troller)-350(suc)27(h)-350(that)]TJ
/T1_6 10.91 Tf
228.46 0 Td
(U)Tj
/T1_9 7.97 Tf
5.73 -1.64 Td
(1)Tj
/T1_0 10.91 Tf
8.56 1.64 Td
[(will)-351(b)-28(e)-351(the)-351(last)]TJ
-396.03 -21.92 Td
[(user)-333(to)-333(broadcast)-333(its)-334(message)-333(after)-333(all)-334(the)-333(other)-333(users)]TJ
/T1_6 10.91 Tf
258.99 0 Td
(U)Tj
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5.73 -1.64 Td
(j)Tj
/T1_2 10.91 Tf
7.41 1.64 Td
(6)Tj
/T1_0 10.91 Tf
(=)Tj
/T1_6 10.91 Tf
11.51 0 Td
(U)Tj
/T1_9 7.97 Tf
5.72 -1.64 Td
(1)Tj
/T1_0 10.91 Tf
8.37 1.64 Td
[(ha)27(v)28(e)-332(broadcast)-334(their)-333(messages.)]TJ
-297.73 -21.92 Td
[(Authen)27(tication)-332(and)-333(Key)-334(Computation)]TJ
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 0 -313.05 cm
0 0 m
182.07 0 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 254.121 460.3234 Tm
(:)Tj
1.0003 0 0 1.0003 72 769.82 Tm
190.034 -309.41 Td
[(Eac)27(h)]TJ
/T1_6 10.91 Tf
27.146 0 Td
(U)Tj
/T1_5 7.97 Tf
5.73 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
7.06 1.63 Td
[(v)28(eri\257es)-337(the)-337(receiv)27(ed)-336(signatures)-337(using)-337(the)-337(stored)]TJ
/T1_2 10.91 Tf
229.13 0 Td
(Z)Tj
/T1_0 10.91 Tf
-459.1 -21.91 Td
(and)Tj
/T1_3 10.91 Tf
21.21 0 Td
(\265)Tj
/T1_0 10.91 Tf
9.05 0 Td
[(to)-333(c)27(hec)27(k)-332(the)-333(equation:)]TJ
/T1_3 10.91 Tf
104.55 -46.48 Td
(\265)Tj
/T1_0 10.91 Tf
8.45 0 Td
(=)Tj
/T1_1 10.91 Tf
11.52 0 Td
(H)Tj
/T1_8 10.91 Tf
9.54 25.2 Td
(0)Tj
0 -19.2 TD
(B)Tj
0 -6.98 TD
(@)Tj
9.54 22.91 Td
(0)Tj
0 -19.64 TD
(@)Tj
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14.33 11.35 Td
(n)Tj
/T1_8 10.91 Tf
-4.4 -3.27 Td
(Y)Tj
/T1_5 7.97 Tf
-0.39 -23.45 Td
(j)Tj
/T1_9 7.97 Tf
3.89 0 Td
(=1)Tj
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12.63 13.08 Td
(s)Tj
/T1_5 7.97 Tf
5.11 -1.63 Td
(j)Tj
/T1_8 10.91 Tf
4.39 23.56 Td
(1)Tj
T*
(A)Tj
/T1_5 7.97 Tf
9.54 16.92 Td
(e)Tj
/T1_2 10.91 Tf
6.85 -19.21 Td
(\242)Tj
/T1_8 10.91 Tf
5.45 21.93 Td
(0)Tj
T*
(@)Tj
/T1_5 7.97 Tf
14.32 11.35 Td
(n)Tj
/T1_8 10.91 Tf
-4.39 -3.27 Td
(Y)Tj
/T1_5 7.97 Tf
-0.39 -23.45 Td
(j)Tj
/T1_9 7.97 Tf
3.89 0 Td
(=1)Tj
/T1_1 10.91 Tf
12.63 13.08 Td
(H)Tj
/T1_0 10.91 Tf
7.73 0 Td
(\()Tj
/T1_6 10.91 Tf
(U)Tj
/T1_5 7.97 Tf
9.96 -1.63 Td
(j)Tj
/T1_0 10.91 Tf
4.38 1.63 Td
(\))Tj
/T1_8 10.91 Tf
4.25 21.93 Td
(1)Tj
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q 1 0 0 1 0 -188.85 cm
0 0 m
40.75 0 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 112.7614 582.4476 Tm
(:)Tj
-40.75 -21.92 Td
(\()Tj
/T1_1 10.91 Tf
(i)Tj
/T1_0 10.91 Tf
(\))Tj
1.0003 0 0 1.0003 72 769.82 Tm
16.161 -209.24 Td
[(The)-359(new)-359(no)-28(de)]TJ
/T1_6 10.91 Tf
72.039 0 Td
(U)Tj
/T1_3 7.97 Tf
5.72 -1.63 Td
(n)Tj
/T1_2 7.97 Tf
(+1)Tj
/T1_0 10.91 Tf
20.37 1.63 Td
[(\257rst)-359(c)27(ho)-27(oses)-359(random)]TJ
/T1_1 10.91 Tf
102.28 0 Td
(r)Tj
/T1_3 7.97 Tf
4.92 -1.63 Td
(n)Tj
/T1_2 7.97 Tf
5.13 0 Td
(+1)Tj
/T1_5 10.91 Tf
14.82 1.63 Td
(2)Tj
/T1_1 10.91 Tf
10.77 0 Td
(Z)Tj
/T1_7 7.97 Tf
8.23 3.96 Td
(\244)Tj
/T1_3 7.97 Tf
-0.78 -6.65 Td
(q)Tj
/T1_0 10.91 Tf
9.42 2.69 Td
[(and)-359(computes)]TJ
/T1_1 10.91 Tf
70.31 0 Td
(z)Tj
/T1_3 7.97 Tf
5.07 -1.63 Td
(n)Tj
/T1_2 7.97 Tf
(+1)Tj
/T1_0 10.91 Tf
19.95 1.63 Td
(=)Tj
/T1_1 10.91 Tf
11.98 0 Td
(g)Tj
/T1_3 7.97 Tf
5.6 3.96 Td
(r)Tj
/T1_8 5.98 Tf
3.82 -1.11 Td
(n)Tj
/T1_9 5.98 Tf
4.6 0 Td
(+1)Tj
/T1_0 10.91 Tf
13.26 -2.85 Td
[(mo)-28(d)]TJ
/T1_1 10.91 Tf
23.94 0 Td
(p)Tj
/T1_0 10.91 Tf
5.48 0 Td
[(.)-522(Next,)]TJ
/T1_6 10.91 Tf
-433.09 -21.91 Td
(U)Tj
/T1_3 7.97 Tf
5.73 -1.64 Td
(n)Tj
/T1_2 7.97 Tf
5.13 0 Td
(+1)Tj
/T1_0 10.91 Tf
15.36 1.64 Td
(signs)Tj
/T1_6 10.91 Tf
27.18 0 Td
(U)Tj
/T1_3 7.97 Tf
5.73 -1.64 Td
(n)Tj
/T1_2 7.97 Tf
(+1)Tj
/T1_5 10.91 Tf
16.45 1.64 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(z)Tj
/T1_3 7.97 Tf
5.07 -1.64 Td
(n)Tj
/T1_2 7.97 Tf
(+1)Tj
/T1_0 10.91 Tf
20.49 1.64 Td
[(using)-370(the)-371(GQ)-370(ID-based)-371(signature)-370(sc)27(heme)-370(to)-370(obtain)-371(the)-370(signature)]TJ
/T1_1 10.91 Tf
316.38 0 Td
(\276)Tj
/T1_3 7.97 Tf
6.23 -1.64 Td
(n)Tj
/T1_2 7.97 Tf
5.13 0 Td
(+1)Tj
/T1_0 10.91 Tf
15.36 1.64 Td
(and)Tj
-450.3 -21.92 Td
(broadcasts)Tj
/T1_5 10.91 Tf
54.08 0 Td
(f)Tj
/T1_6 10.91 Tf
(U)Tj
/T1_3 7.97 Tf
11.17 -1.64 Td
(n)Tj
/T1_2 7.97 Tf
(+1)Tj
/T1_5 10.91 Tf
16.46 1.64 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(z)Tj
/T1_3 7.97 Tf
5.07 -1.64 Td
(n)Tj
/T1_2 7.97 Tf
5.13 0 Td
(+1)Tj
/T1_5 10.91 Tf
11.32 1.64 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(\276)Tj
/T1_3 7.97 Tf
6.23 -1.64 Td
(n)Tj
/T1_2 7.97 Tf
(+1)Tj
/T1_5 10.91 Tf
16.45 1.64 Td
(g)Tj
/T1_0 10.91 Tf
(.)Tj
-138.03 -21.92 Td
(\()Tj
/T1_1 10.91 Tf
(ii)Tj
/T1_0 10.91 Tf
(\))Tj
/T1_6 10.91 Tf
19.39 0 Td
(U)Tj
/T1_3 7.97 Tf
5.73 -1.63 Td
(n)Tj
/T1_0 10.91 Tf
9.03 1.63 Td
(signs)Tj
/T1_1 10.91 Tf
26.55 0 Td
(z)Tj
/T1_3 7.97 Tf
5.07 -1.63 Td
(n)Tj
/T1_0 10.91 Tf
9.03 1.63 Td
[(using)-311(the)-312(GQ)-311(ID-based)-312(signature)-311(sc)27(heme)-311(and)-312(obtains)-311(signature)]TJ
/T1_1 10.91 Tf
303.58 0 Td
(\276)Tj
/T1_7 7.97 Tf
6.62 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.39 -6.65 Td
(n)Tj
/T1_0 10.91 Tf
5.64 2.69 Td
[(.)-436(Next,)]TJ
/T1_6 10.91 Tf
37.29 0 Td
(U)Tj
/T1_3 7.97 Tf
5.73 -1.63 Td
(n)Tj
/T1_0 10.91 Tf
9.03 1.63 Td
(sends)Tj
/T1_5 10.91 Tf
-442.3 -21.91 Td
(f)Tj
/T1_6 10.91 Tf
(U)Tj
/T1_3 7.97 Tf
11.18 -1.64 Td
(n)Tj
/T1_5 10.91 Tf
5.63 1.64 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(z)Tj
/T1_3 7.97 Tf
5.07 -1.64 Td
(n)Tj
/T1_5 10.91 Tf
5.64 1.64 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(\276)Tj
/T1_7 7.97 Tf
6.62 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.39 -6.66 Td
(n)Tj
/T1_5 10.91 Tf
5.63 2.7 Td
(g)Tj
/T1_0 10.91 Tf
9.09 0 Td
(to)Tj
/T1_6 10.91 Tf
13.33 0 Td
(U)Tj
/T1_3 7.97 Tf
5.73 -1.64 Td
(n)Tj
/T1_2 7.97 Tf
(+1)Tj
/T1_0 10.91 Tf
16.45 1.64 Td
(.)Tj
-96.1 -21.92 Td
[(Round)-333(2)]TJ
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 0 -320.35 cm
0 0 m
40.75 0 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 112.7614 450.9107 Tm
(:)Tj
/T1_6 10.91 Tf
7.55 0 Td
(U)Tj
/T1_2 7.97 Tf
5.72 -1.63 Td
(1)Tj
/T1_0 10.91 Tf
7.72 1.63 Td
(v)Tj
1.0003 0 0 1.0003 72 769.82 Tm
67.195 -318.82 Td
[(eri\257es)-273(the)-273(signature)]TJ
/T1_1 10.91 Tf
95.165 0 Td
(\276)Tj
/T1_3 7.97 Tf
6.23 -1.63 Td
(n)Tj
/T1_2 7.97 Tf
(+1)Tj
/T1_0 10.91 Tf
16.45 1.63 Td
[(.)-424(If)-274(the)-273(signature)-274(is)-273(in)27(v)55(alid,)-284(then)]TJ
/T1_6 10.91 Tf
154.9 0 Td
(U)Tj
/T1_2 7.97 Tf
5.72 -1.63 Td
(1)Tj
/T1_0 10.91 Tf
7.72 1.63 Td
(rejects)Tj
/T1_6 10.91 Tf
33.67 0 Td
(U)Tj
/T1_3 7.97 Tf
5.72 -1.63 Td
(n)Tj
/T1_2 7.97 Tf
(+1)Tj
/T1_0 10.91 Tf
16.46 1.63 Td
[(.)-424(Otherwise,)]TJ
/T1_6 10.91 Tf
-409.23 -21.92 Td
(U)Tj
/T1_2 7.97 Tf
5.73 -1.63 Td
(1)Tj
/T1_0 10.91 Tf
8.36 1.63 Td
[(c)27(ho)-27(oses)-333(new)-333(random)]TJ
/T1_1 10.91 Tf
101.34 0 Td
(r)Tj
/T1_7 7.97 Tf
5.22 3.96 Td
(0)Tj
/T1_2 7.97 Tf
-0.3 -6.88 Td
(1)Tj
/T1_5 10.91 Tf
7.76 2.92 Td
(2)Tj
/T1_1 10.91 Tf
10.3 0 Td
(Z)Tj
/T1_7 7.97 Tf
8.22 3.96 Td
(\244)Tj
/T1_3 7.97 Tf
-0.78 -6.65 Td
(q)Tj
/T1_0 10.91 Tf
9.15 2.69 Td
[(and)-333(computes)]TJ
/T1_1 10.91 Tf
69.74 0 Td
(K)Tj
/T1_7 7.97 Tf
10.04 3.96 Td
(\244)Tj
/T1_0 10.91 Tf
8.37 -3.96 Td
[(as)-333(follo)27(ws:)]TJ
/T1_1 10.91 Tf
-113.96 -39.64 Td
(K)Tj
/T1_7 7.97 Tf
10.04 4.5 Td
(\244)Tj
/T1_0 10.91 Tf
14.69 -4.5 Td
(=)Tj
/T1_1 10.91 Tf
18.44 0 Td
(K)Tj
/T1_5 10.91 Tf
12.47 0 Td
(\242)Tj
/T1_0 10.91 Tf
5.45 0 Td
(\()Tj
/T1_1 10.91 Tf
(z)Tj
/T1_2 7.97 Tf
9.32 -1.63 Td
(2)Tj
/T1_5 10.91 Tf
7.15 1.63 Td
(\242)Tj
/T1_1 10.91 Tf
5.45 0 Td
(z)Tj
/T1_3 7.97 Tf
5.07 -1.63 Td
(n)Tj
/T1_0 10.91 Tf
5.64 1.63 Td
(\))Tj
/T1_7 7.97 Tf
4.24 4.5 Td
(\241)Tj
/T1_3 7.97 Tf
6.59 0 Td
(r)Tj
/T1_9 5.98 Tf
3.82 -1.1 Td
(1)Tj
/T1_5 10.91 Tf
7.07 -3.4 Td
(\242)Tj
/T1_0 10.91 Tf
5.45 0 Td
(\()Tj
/T1_1 10.91 Tf
(z)Tj
/T1_2 7.97 Tf
9.31 -1.63 Td
(2)Tj
/T1_5 10.91 Tf
7.16 1.63 Td
(\242)Tj
/T1_1 10.91 Tf
5.45 0 Td
(z)Tj
/T1_3 7.97 Tf
5.07 -1.63 Td
(n)Tj
/T1_2 7.97 Tf
(+1)Tj
/T1_0 10.91 Tf
16.45 1.63 Td
(\))Tj
/T1_3 7.97 Tf
4.25 4.5 Td
(r)Tj
/T1_10 5.98 Tf
4.05 2.82 Td
(0)Tj
/T1_9 5.98 Tf
-0.23 -5.29 Td
(1)Tj
/T1_0 10.91 Tf
7.67 -2.03 Td
[(mo)-28(d)]TJ
/T1_1 10.91 Tf
23.94 0 Td
(p)Tj
/T1_0 10.91 Tf
-179.28 -24.9 Td
(=)Tj
/T1_1 10.91 Tf
18.44 0 Td
(g)Tj
/T1_3 7.97 Tf
5.6 4.5 Td
(r)Tj
/T1_10 5.98 Tf
4.05 2.81 Td
(0)Tj
/T1_9 5.98 Tf
-0.23 -5.28 Td
(1)Tj
/T1_3 7.97 Tf
4.15 2.47 Td
(r)Tj
/T1_9 5.98 Tf
3.82 -1.11 Td
(2)Tj
/T1_2 7.97 Tf
4.15 1.11 Td
(+)Tj
/T1_3 7.97 Tf
(r)Tj
/T1_9 5.98 Tf
10.4 -1.11 Td
(2)Tj
/T1_3 7.97 Tf
4.15 1.11 Td
(r)Tj
/T1_9 5.98 Tf
3.82 -1.11 Td
(3)Tj
/T1_2 7.97 Tf
4.15 1.11 Td
(+)Tj
/T1_7 7.97 Tf
6.59 0 Td
(\242\242\242)Tj
/T1_2 7.97 Tf
(+)Tj
/T1_3 7.97 Tf
13.64 0 Td
(r)Tj
/T1_8 5.98 Tf
3.82 -1.11 Td
(n)Tj
/T1_10 5.98 Tf
4.6 0 Td
(\241)Tj
/T1_9 5.98 Tf
5.75 0 Td
(1)Tj
/T1_3 7.97 Tf
4.15 1.11 Td
(r)Tj
/T1_8 5.98 Tf
3.82 -1 Td
(n)Tj
/T1_2 7.97 Tf
5.1 1 Td
(+)Tj
/T1_3 7.97 Tf
(r)Tj
/T1_8 5.98 Tf
10.4 -1.11 Td
(n)Tj
/T1_9 5.98 Tf
4.6 0 Td
(+1)Tj
/T1_3 7.97 Tf
9.74 1.11 Td
(r)Tj
/T1_10 5.98 Tf
4.06 2.81 Td
(0)Tj
/T1_9 5.98 Tf
-0.24 -5.28 Td
(1)Tj
/T1_0 10.91 Tf
7.68 -2.03 Td
[(mo)-27(d)]TJ
/T1_1 10.91 Tf
23.93 0 Td
(p:)Tj
/T1_0 10.91 Tf
121.39 0 Td
(\(6.4\))Tj
/T1_6 10.91 Tf
-445.45 -39.65 Td
(U)Tj
/T1_2 7.97 Tf
5.73 -1.63 Td
(1)Tj
/T1_0 10.91 Tf
7.81 1.63 Td
[(then)-283(encrypts)]TJ
/T1_1 10.91 Tf
67.76 0 Td
(K)Tj
/T1_7 7.97 Tf
10.04 3.96 Td
(\244)Tj
/T1_5 10.91 Tf
4.73 -3.96 Td
(jj)Tj
/T1_6 10.91 Tf
6.06 0 Td
(U)Tj
/T1_2 7.97 Tf
5.73 -1.63 Td
(1)Tj
/T1_0 10.91 Tf
7.81 1.63 Td
[(using)-283(the)-283(previously)-283(established)-282(group)-283(k)26(ey)]TJ
/T1_1 10.91 Tf
202.71 0 Td
(K)Tj
/T1_0 10.91 Tf
13.12 0 Td
[(and)-283(a)-283(symmetric)-282(k)26(ey)-282(encryp-)]TJ
-331.5 -21.91 Td
(tion)Tj
/T1_11 10.91 Tf
22.42 0 Td
(SKE)Tj
/T1_0 10.91 Tf
23.78 0 Td
[(to)-333(obtain)]TJ
/T1_6 10.91 Tf
47.26 0 Td
(c)Tj
/T1_2 7.97 Tf
5.72 -1.64 Td
(1)Tj
/T1_0 10.91 Tf
7.77 1.64 Td
(=)Tj
/T1_5 10.91 Tf
11.51 0 Td
(E)Tj
/T1_3 7.97 Tf
5.75 -1.69 Td
(K)Tj
/T1_0 10.91 Tf
8.2 1.69 Td
(\()Tj
/T1_1 10.91 Tf
(K)Tj
/T1_7 7.97 Tf
14.29 3.96 Td
(\244)Tj
/T1_5 10.91 Tf
4.73 -3.96 Td
(jj)Tj
/T1_6 10.91 Tf
6.06 0 Td
(U)Tj
/T1_2 7.97 Tf
5.72 -1.64 Td
(1)Tj
/T1_0 10.91 Tf
4.73 1.64 Td
[(\))-333(and)-334(broadcasts)]TJ
/T1_5 10.91 Tf
83.16 0 Td
(f)Tj
/T1_6 10.91 Tf
(U)Tj
/T1_2 7.97 Tf
11.18 -1.64 Td
(1)Tj
/T1_5 10.91 Tf
4.73 1.64 Td
(jj)Tj
/T1_6 10.91 Tf
6.06 0 Td
(c)Tj
/T1_2 7.97 Tf
5.73 -1.64 Td
(1)Tj
/T1_5 10.91 Tf
4.73 1.64 Td
(g)Tj
/T1_0 10.91 Tf
9.09 0 Td
[(to)-333(existing)-333(group)]TJ
/T1_5 10.91 Tf
84.61 0 Td
(G)Tj
/T1_0 10.91 Tf
7.13 0 Td
(.)Tj
-384.36 -21.92 Td
[(Round)-333(3)]TJ
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 0 -490.29 cm
0 0 m
40.75 0 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 115.6622 280.9231 Tm
(:)Tj
/T1_6 10.91 Tf
7.51 0 Td
(U)Tj
/T1_3 7.97 Tf
5.72 -1.63 Td
(n)Tj
/T1_0 10.91 Tf
8.54 1.63 Td
(v)Tj
1.0003 0 0 1.0003 72 769.82 Tm
70.875 -488.76 Td
[(eri\257es)-265(signature)]TJ
/T1_1 10.91 Tf
76.865 0 Td
(\276)Tj
/T1_3 7.97 Tf
6.23 -1.63 Td
(n)Tj
/T1_2 7.97 Tf
(+1)Tj
/T1_0 10.91 Tf
16.46 1.63 Td
[(.)-421(If)-266(the)-266(signature)-266(is)-266(in)27(v)55(alid,)-278(then)]TJ
/T1_6 10.91 Tf
154.39 0 Td
(U)Tj
/T1_3 7.97 Tf
5.72 -1.63 Td
(n)Tj
/T1_0 10.91 Tf
8.54 1.63 Td
(rejects)Tj
/T1_6 10.91 Tf
33.59 0 Td
(U)Tj
/T1_3 7.97 Tf
5.72 -1.63 Td
(n)Tj
/T1_2 7.97 Tf
(+1)Tj
/T1_0 10.91 Tf
16.46 1.63 Td
[(.)-421(Otherwise,)]TJ
/T1_6 10.91 Tf
61.66 0 Td
(U)Tj
/T1_3 7.97 Tf
5.73 -1.63 Td
(n)Tj
/T1_0 10.91 Tf
-462.24 -20.29 Td
[(computes)-351(DH)-352(k)27(ey)]TJ
/T1_1 10.91 Tf
88.97 0 Td
(K)Tj
/T1_12 7.97 Tf
9.26 -1.63 Td
(U)Tj
/T1_8 5.98 Tf
4.23 -1 Td
(n)Tj
/T1_12 7.97 Tf
5.1 1 Td
(U)Tj
/T1_8 5.98 Tf
4.23 -1.11 Td
(n)Tj
/T1_9 5.98 Tf
4.6 0 Td
(+1)Tj
/T1_0 10.91 Tf
13.6 2.74 Td
(=)Tj
/T1_1 10.91 Tf
11.84 0 Td
(z)Tj
/T1_3 7.97 Tf
5.55 4.76 Td
(r)Tj
/T1_8 5.98 Tf
3.82 -1 Td
(n)Tj
/T1_3 7.97 Tf
-4.3 -6.88 Td
(n)Tj
/T1_2 7.97 Tf
(+1)Tj
/T1_0 10.91 Tf
19.82 3.12 Td
(=)Tj
/T1_1 10.91 Tf
11.84 0 Td
(g)Tj
/T1_3 7.97 Tf
5.59 3.96 Td
(r)Tj
/T1_8 5.98 Tf
3.82 -0.99 Td
(n)Tj
/T1_3 7.97 Tf
5.1 0.99 Td
(r)Tj
/T1_8 5.98 Tf
3.82 -1.1 Td
(n)Tj
/T1_9 5.98 Tf
4.6 0 Td
(+1)Tj
/T1_0 10.91 Tf
13.27 -2.86 Td
[(mo)-27(d)]TJ
/T1_1 10.91 Tf
23.93 0 Td
(p)Tj
/T1_0 10.91 Tf
[(,)-355(whic)27(h)-351(it)-352(shares)-351(with)]TJ
/T1_6 10.91 Tf
113.02 0 Td
(U)Tj
/T1_3 7.97 Tf
5.72 -1.63 Td
(n)Tj
/T1_2 7.97 Tf
(+1)Tj
/T1_0 10.91 Tf
16.45 1.63 Td
[(.)-499(Next,)]TJ
/T1_6 10.91 Tf
38.41 0 Td
(U)Tj
/T1_3 7.97 Tf
5.73 -1.63 Td
(n)Tj
/T1_0 10.91 Tf
9.47 1.63 Td
(encrypts)Tj
/T1_1 10.91 Tf
-427.49 -21.91 Td
(K)Tj
/T1_12 7.97 Tf
9.26 -1.64 Td
(U)Tj
/T1_8 5.98 Tf
4.24 -0.99 Td
(n)Tj
/T1_12 7.97 Tf
5.09 0.99 Td
(U)Tj
/T1_8 5.98 Tf
4.24 -1.1 Td
(n)Tj
/T1_9 5.98 Tf
4.6 0 Td
(+1)Tj
/T1_5 10.91 Tf
10.23 2.74 Td
(jj)Tj
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[(.)-494(If)-350(the)-350(iden)27(tit)28(y)]TJ
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(g)Tj
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[(Key)-333(Computation)]TJ
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 0 -623.9 cm
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85.73 0 l
S
Q
Q
BT
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1.0003 0 0 1.0003 161.395 149.3863 Tm
(:)Tj
136.39 -47.71 Td
(144)Tj
ET
q
1 0 0 1 -62.5 824 cm
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(\257rst)Tj
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[(v)26(eri\257es)-287(signature)]TJ
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[(.)-428(If)-288(the)-288(signature)-288(is)-288(in)26(v)56(alid,)-296(then)]TJ
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[(.)-428(Otherwise,)]TJ
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[(to)-362(obtain)]TJ
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(\244)Tj
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[(and)-361(the)-362(iden)27(tit)27(y)]TJ
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[(.)-530(If)]TJ
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[(the)-333(iden)27(tit)28(y)]TJ
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[(is)-333(not)-333(decrypted)-334(correctly)83(,)-333(then)]TJ
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[(1)-277(decrypts)]TJ
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[(using)-277(the)-278(previously)-277(established)-278(group)-277(k)27(ey)]TJ
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(K)Tj
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[(.)-438(If)-317(the)-317(iden)27(tit)27(y)]TJ
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[(is)-317(not)-317(decrypted)-317(correctly)82(,)-319(then)]TJ
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(\244)Tj
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4.73 -3.96 Td
[(.)-442(Next,)-328(users)]TJ
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(i)Tj
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6.94 1.63 Td
[(for)-326(1)]TJ
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(\241)Tj
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[(1)-326(decrypts)]TJ
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(K)Tj
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[(.)-444(If)-332(the)-332(iden)27(tit)28(y)]TJ
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[(is)-332(not)-332(decrypted)-332(correctly)83(,)-332(then)]TJ
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(U)Tj
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(i)Tj
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7.02 1.63 Td
[(for)-333(1)]TJ
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25.17 0 Td
(\267)Tj
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11.51 0 Td
(i)Tj
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(\267)Tj
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(n)Tj
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10.18 0 Td
(including)Tj
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(n)Tj
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(+1)Tj
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20.09 1.63 Td
[(compute)-333(the)-333(new)-333(group)-334(k)27(ey)]TJ
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136.05 0 Td
(K)Tj
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10.04 3.96 Td
(0)Tj
/T1_0 10.91 Tf
6.43 -3.96 Td
[(as)-333(follo)27(ws:)]TJ
/T1_1 10.91 Tf
-273.88 -39.64 Td
(K)Tj
/T1_5 7.97 Tf
10.04 4.5 Td
(0)Tj
/T1_0 10.91 Tf
12.75 -4.5 Td
(=)Tj
/T1_1 10.91 Tf
18.45 0 Td
(K)Tj
/T1_5 7.97 Tf
10.04 4.5 Td
(\244)Tj
/T1_9 10.91 Tf
7.15 -4.5 Td
(\242)Tj
/T1_1 10.91 Tf
5.46 0 Td
(K)Tj
/T1_6 7.97 Tf
9.26 -1.64 Td
(U)Tj
/T1_7 5.98 Tf
4.23 -0.99 Td
(n)Tj
/T1_6 7.97 Tf
5.1 0.99 Td
(U)Tj
/T1_7 5.98 Tf
4.23 -1.1 Td
(n)Tj
/T1_8 5.98 Tf
4.6 0 Td
(+1)Tj
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13.27 2.74 Td
[(mo)-27(d)]TJ
/T1_1 10.91 Tf
23.93 0 Td
(p)Tj
/T1_0 10.91 Tf
-105.72 -24.9 Td
(=)Tj
/T1_1 10.91 Tf
18.45 0 Td
(g)Tj
/T1_3 7.97 Tf
5.59 4.5 Td
(r)Tj
/T1_10 5.98 Tf
4.05 2.81 Td
(0)Tj
/T1_8 5.98 Tf
-0.23 -5.29 Td
(1)Tj
/T1_3 7.97 Tf
4.15 2.48 Td
(r)Tj
/T1_8 5.98 Tf
3.82 -1.11 Td
(2)Tj
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4.15 1.11 Td
(+)Tj
/T1_3 7.97 Tf
(r)Tj
/T1_8 5.98 Tf
10.4 -1.11 Td
(2)Tj
/T1_3 7.97 Tf
4.15 1.11 Td
(r)Tj
/T1_8 5.98 Tf
3.82 -1.11 Td
(3)Tj
/T1_4 7.97 Tf
4.15 1.11 Td
(+)Tj
/T1_5 7.97 Tf
6.59 0 Td
(\242\242\242)Tj
/T1_4 7.97 Tf
(+)Tj
/T1_3 7.97 Tf
13.64 0 Td
(r)Tj
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3.82 -1 Td
(n)Tj
/T1_3 7.97 Tf
5.1 1 Td
(r)Tj
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3.82 -1.11 Td
(n)Tj
/T1_8 5.98 Tf
4.6 0 Td
(+1)Tj
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9.73 1.11 Td
(+)Tj
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6.59 0 Td
(r)Tj
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3.82 -1.11 Td
(n)Tj
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4.6 0 Td
(+1)Tj
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9.74 1.11 Td
(r)Tj
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4.05 2.81 Td
(0)Tj
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-0.23 -5.29 Td
(1)Tj
/T1_0 10.91 Tf
7.67 -2.02 Td
[(mo)-28(d)]TJ
/T1_1 10.91 Tf
23.94 0 Td
(p)Tj
/T1_0 10.91 Tf
117.87 0 Td
(\(6.5\))Tj
/T1_11 11.95 Tf
-445.45 -40.29 Td
[(6.2.3)-1125(Merge)-375(Proto)-31(col)]TJ
/T1_0 10.91 Tf
0 -28.96 TD
[(A)-533(merge)-533(o)-28(ccurs)-533(when)-534(t)27(w)28(o)-532(or)-534(more)-533(subgroups)-533(are)-534(com)27(bined)-532(in)26(to)-532(a)-533(single)-534(group.)-1044(Let)]TJ
/T1_9 10.91 Tf
439.4 0 Td
(G)Tj
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6.48 -1.69 Td
(A)Tj
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13.51 1.69 Td
(=)Tj
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-459.39 -21.92 Td
(f)Tj
/T1_2 10.91 Tf
(U)Tj
/T1_4 7.97 Tf
11.18 -1.63 Td
(1)Tj
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4.73 1.63 Td
(;)Tj
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4.85 0 Td
(U)Tj
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5.72 -1.63 Td
(2)Tj
/T1_1 10.91 Tf
4.73 1.63 Td
(;)Tj
/T1_9 10.91 Tf
4.85 0 Td
[(\242)-166(\242)-167(\242)]TJ
/T1_1 10.91 Tf
16.36 0 Td
(;)Tj
/T1_2 10.91 Tf
4.85 0 Td
(U)Tj
/T1_3 7.97 Tf
5.72 -1.63 Td
(n)Tj
/T1_9 10.91 Tf
5.64 1.63 Td
(g)Tj
/T1_0 10.91 Tf
9.01 0 Td
[(denote)-326(all)-327(users)-327(in)-326(Group)]TJ
/T1_9 10.91 Tf
124.11 0 Td
(G)Tj
/T1_3 7.97 Tf
6.48 -1.69 Td
(A)Tj
/T1_0 10.91 Tf
10.4 1.69 Td
[(with)-327(previously)-326(established)-327(group)-327(k)27(ey)]TJ
/T1_1 10.91 Tf
183.17 0 Td
(K)Tj
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9.26 -1.69 Td
(A)Tj
/T1_0 10.91 Tf
10.4 1.69 Td
(and)Tj
/T1_9 10.91 Tf
21.14 0 Td
(G)Tj
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6.48 -1.69 Td
(B)Tj
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10.31 1.69 Td
(=)Tj
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-459.39 -21.92 Td
(f)Tj
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(U)Tj
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11.18 -1.63 Td
(n)Tj
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(+1)Tj
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16.45 1.63 Td
(;)Tj
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4.85 0 Td
(U)Tj
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5.72 -1.63 Td
(n)Tj
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(+2)Tj
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16.46 1.63 Td
(;)Tj
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4.84 0 Td
[(\242)-166(\242)-167(\242)]TJ
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16.36 0 Td
(;)Tj
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4.85 0 Td
(U)Tj
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5.73 -1.63 Td
(n)Tj
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5.13 0 Td
(+)Tj
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6.59 0 Td
(m)Tj
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7.98 1.63 Td
(g)Tj
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9.73 0 Td
[(denote)-392(all)-392(users)-392(in)-392(Group)]TJ
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127.67 0 Td
(G)Tj
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6.49 -1.68 Td
(B)Tj
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11.55 1.68 Td
[(with)-391(previously)-392(established)-392(group)-392(k)26(ey)]TJ
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186.72 0 Td
(K)Tj
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9.26 -1.68 Td
(B)Tj
/T1_0 10.91 Tf
7.28 1.68 Td
(.)Tj
-464.84 -21.91 Td
[(W)83(e)-250(divide)]TJ
/T1_9 10.91 Tf
49.39 0 Td
(G)Tj
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6.49 -1.69 Td
(A)Tj
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9.57 1.69 Td
[(in)28(to)]TJ
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21.21 0 Td
(f)Tj
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(U)Tj
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11.18 -1.64 Td
(1)Tj
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4.73 1.64 Td
(;)Tj
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4.84 0 Td
(U)Tj
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5.73 -1.64 Td
(n)Tj
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5.63 1.64 Td
(g)Tj
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8.19 0 Td
(and)Tj
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20.3 0 Td
(f)Tj
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(U)Tj
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11.18 -1.64 Td
(2)Tj
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4.73 1.64 Td
(;)Tj
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4.85 0 Td
[(\242)-166(\242)-167(\242)]TJ
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16.36 0 Td
(;)Tj
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7.57 0 Td
(U)Tj
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5.73 -1.64 Td
(n)Tj
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(\241)Tj
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(1)Tj
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16.45 1.64 Td
(g)Tj
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8.19 0 Td
(and)Tj
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20.3 0 Td
(G)Tj
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6.49 -1.69 Td
(B)Tj
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10 1.69 Td
[(in)27(to)]TJ
/T1_9 10.91 Tf
21.21 0 Td
(f)Tj
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(U)Tj
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11.18 -1.64 Td
(n)Tj
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(+1)Tj
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16.46 1.64 Td
(;)Tj
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4.84 0 Td
(U)Tj
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5.73 -1.64 Td
(n)Tj
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5.13 0 Td
(+)Tj
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6.59 0 Td
(m)Tj
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7.99 1.64 Td
(g)Tj
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8.18 0 Td
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20.3 0 Td
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(U)Tj
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11.18 -1.64 Td
(n)Tj
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16.45 1.64 Td
(;)Tj
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4.85 0 Td
[(\242)-166(\242)-167(\242)]TJ
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16.36 0 Td
(;)Tj
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7.58 0 Td
(U)Tj
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5.72 -1.64 Td
(n)Tj
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(+)Tj
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(m)Tj
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(\241)Tj
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25.8 0 Td
(1)Tj
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4.73 1.64 Td
(g)Tj
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(.)Tj
-459.39 -21.92 Td
[(W)83(e)-257(consider)-258(a)-258(so)-258(called)-258(ring)-258(structure)-258(for)-258(group)]TJ
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224.11 0 Td
(G)Tj
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6.49 -1.69 Td
(A)Tj
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6.84 1.69 Td
[(,)-273(group)]TJ
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36.12 0 Td
(G)Tj
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6.48 -1.69 Td
(B)Tj
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10.09 1.69 Td
[(and)-258(the)-258(merged)-258(group)]TJ
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105.84 0 Td
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7.13 3.96 Td
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5.83 -3.96 Td
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11.51 0 Td
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6.49 -1.69 Td
(A)Tj
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7.61 1.69 Td
[([)-71(G)]TJ
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14.54 -1.69 Td
(B)Tj
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(=)Tj
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4.73 1.64 Td
(;)Tj
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4.85 0 Td
[(\242)-166(\242)-167(\242)]TJ
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16.36 0 Td
(;)Tj
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4.84 0 Td
(U)Tj
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5.73 -1.64 Td
(n)Tj
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(+)Tj
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(m)Tj
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19.71 1.64 Td
(g)Tj
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[(.)-444(The)-333(Merge)-334(Proto)-27(col)-334(consists)-333(of)-333(three)-334(rounds)-333(and)-333(is)-334(describ)-27(ed)-334(as)-333(follo)27(ws:)]TJ
-67.4 -21.92 Td
[(Round)-333(1)]TJ
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 0 -453.11 cm
0 0 m
40.75 0 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 116.3924 318.1136 Tm
(:)Tj
-44.38 -21.92 Td
(\()Tj
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(i)Tj
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(\))Tj
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16.66 0 Td
(U)Tj
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5.73 -1.63 Td
(1)Tj
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9.15 1.63 Td
(\257rst)Tj
1.0003 0 0 1.0003 72 769.82 Tm
54.844 -473.5 Td
[(selects)-405(new)-405(random)]TJ
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98.836 0 Td
(r)Tj
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5.22 3.96 Td
(0)Tj
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-0.3 -6.88 Td
(1)Tj
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9.07 2.92 Td
(2)Tj
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11.61 0 Td
(Z)Tj
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8.22 3.96 Td
(\244)Tj
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-0.78 -6.65 Td
(q)Tj
/T1_0 10.91 Tf
9.94 2.69 Td
[(and)-404(computes)]TJ
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71.3 0 Td
(z)Tj
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5.56 3.96 Td
(0)Tj
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-0.48 -6.88 Td
(1)Tj
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9.07 2.92 Td
(=)Tj
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12.82 0 Td
(g)Tj
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5.59 3.96 Td
(r)Tj
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(0)Tj
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-0.24 -5.28 Td
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7.68 -1.49 Td
[(mo)-27(d)]TJ
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23.93 0 Td
(p)Tj
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[(.)-660(Next,)]TJ
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46.39 0 Td
(U)Tj
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5.73 -1.63 Td
(1)Tj
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9.15 1.63 Td
(signs)Tj
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27.57 0 Td
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4.73 1.63 Td
(jj)Tj
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6.06 0 Td
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(jj)Tj
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6.05 0 Td
(z)Tj
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5.08 -1.63 Td
(n)Tj
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-462.24 -20.28 Td
[(using)-333(GQ)-333(ID-based)-333(signature)-334(sc)27(heme)-332(to)-334(pro)-27(duce)-334(signature)]TJ
/T1_1 10.91 Tf
282.36 0 Td
(\276)Tj
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6.62 3.95 Td
(0)Tj
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-0.39 -6.88 Td
(1)Tj
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8.37 2.93 Td
[(and)-333(broadcasts)]TJ
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75.28 0 Td
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(U)Tj
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11.18 -1.64 Td
(1)Tj
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6.06 0 Td
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5.55 3.95 Td
(0)Tj
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(1)Tj
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4.73 2.93 Td
(jj)Tj
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6.06 0 Td
(z)Tj
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5.07 -1.64 Td
(n)Tj
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5.64 1.64 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(\276)Tj
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6.62 3.95 Td
(0)Tj
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-0.39 -6.88 Td
(1)Tj
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4.73 2.93 Td
(g)Tj
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(.)Tj
-437.8 -21.92 Td
(\()Tj
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(ii)Tj
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(\))Tj
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19.44 0 Td
(U)Tj
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5.72 -1.64 Td
(n)Tj
/T1_4 7.97 Tf
(+1)Tj
/T1_0 10.91 Tf
19.9 1.64 Td
[(selects)-315(new)-315(random)]TJ
/T1_1 10.91 Tf
95.9 0 Td
(r)Tj
/T1_5 7.97 Tf
5.23 3.96 Td
(0)Tj
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-0.31 -6.88 Td
(n)Tj
/T1_4 7.97 Tf
(+1)Tj
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19.48 2.92 Td
(2)Tj
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10.3 0 Td
(Z)Tj
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8.23 3.96 Td
(\244)Tj
/T1_3 7.97 Tf
-0.78 -6.66 Td
(q)Tj
/T1_0 10.91 Tf
5.51 2.7 Td
[(,)-319(computes)]TJ
/T1_1 10.91 Tf
54.85 0 Td
(z)Tj
/T1_5 7.97 Tf
5.55 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.48 -6.88 Td
(n)Tj
/T1_4 7.97 Tf
(+1)Tj
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19.48 2.92 Td
(=)Tj
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11.51 0 Td
(g)Tj
/T1_3 7.97 Tf
5.6 4.48 Td
(r)Tj
/T1_10 5.98 Tf
4.05 2.81 Td
(0)Tj
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-0.23 -5.29 Td
(n)Tj
/T1_8 5.98 Tf
4.6 0 Td
(+1)Tj
/T1_0 10.91 Tf
13.26 -2 Td
[(mo)-27(d)]TJ
/T1_1 10.91 Tf
23.93 0 Td
(p)Tj
/T1_0 10.91 Tf
8.93 0 Td
[(and)-315(signs)]TJ
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47.6 0 Td
(U)Tj
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5.73 -1.64 Td
(n)Tj
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5.13 0 Td
(+1)Tj
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11.32 1.64 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(z)Tj
/T1_5 7.97 Tf
5.55 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.48 -6.88 Td
(n)Tj
/T1_4 7.97 Tf
(+1)Tj
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16.45 2.92 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(z)Tj
/T1_3 7.97 Tf
5.07 -1.64 Td
(n)Tj
/T1_4 7.97 Tf
(+)Tj
/T1_3 7.97 Tf
(m)Tj
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(U)Tj
/T1_2 7.97 Tf
5.73 -1.63 Td
(n)Tj
/T1_5 7.97 Tf
5.13 0 Td
(+1)Tj
/T1_3 10.91 Tf
15.51 1.63 Td
(then)Tj
-446.66 -21.91 Td
(computes)Tj
/T1_0 10.91 Tf
48.53 0 Td
(K)Tj
/T1_1 7.97 Tf
10.04 3.96 Td
(\244)Tj
/T1_2 7.97 Tf
-0.78 -7.19 Td
(B)Tj
/T1_3 10.91 Tf
10.92 3.23 Td
[(as)-333(follo)27(ws:)]TJ
/T1_0 10.91 Tf
31.19 -39.65 Td
(K)Tj
/T1_1 7.97 Tf
10.04 4.51 Td
(\244)Tj
/T1_2 7.97 Tf
-0.78 -7.2 Td
(B)Tj
/T1_3 10.91 Tf
17.24 2.69 Td
(=)Tj
/T1_0 10.91 Tf
18.44 0 Td
(K)Tj
/T1_2 7.97 Tf
9.26 -1.68 Td
(B)Tj
/T1_4 10.91 Tf
9.7 1.68 Td
(\242)Tj
/T1_3 10.91 Tf
5.45 0 Td
(\()Tj
/T1_0 10.91 Tf
4.25 0 Td
(z)Tj
/T1_2 7.97 Tf
5.07 -1.63 Td
(n)Tj
/T1_4 10.91 Tf
8.06 1.63 Td
(\242)Tj
/T1_0 10.91 Tf
5.45 0 Td
(z)Tj
/T1_2 7.97 Tf
5.07 -1.63 Td
(n)Tj
/T1_5 7.97 Tf
(+2)Tj
/T1_3 10.91 Tf
16.45 1.63 Td
(\))Tj
/T1_2 7.97 Tf
4.24 4.51 Td
(r)Tj
/T1_7 5.98 Tf
4.06 2.81 Td
(0)Tj
/T1_8 5.98 Tf
-0.24 -5.29 Td
(n)Tj
/T1_6 5.98 Tf
4.6 0 Td
(+1)Tj
/T1_4 10.91 Tf
12.66 -2.03 Td
(\242)Tj
/T1_3 10.91 Tf
5.46 0 Td
(\()Tj
/T1_0 10.91 Tf
(z)Tj
/T1_2 7.97 Tf
9.31 -1.63 Td
(n)Tj
/T1_5 7.97 Tf
(+2)Tj
/T1_4 10.91 Tf
18.88 1.63 Td
(\242)Tj
/T1_0 10.91 Tf
5.45 0 Td
(z)Tj
/T1_2 7.97 Tf
5.07 -1.63 Td
(n)Tj
/T1_5 7.97 Tf
(+)Tj
/T1_2 7.97 Tf
(m)Tj
/T1_3 10.91 Tf
19.71 1.63 Td
(\))Tj
/T1_1 7.97 Tf
4.24 4.51 Td
(\241)Tj
/T1_2 7.97 Tf
(r)Tj
/T1_8 5.98 Tf
10.4 -1.11 Td
(n)Tj
/T1_6 5.98 Tf
4.6 0 Td
(+1)Tj
/T1_3 10.91 Tf
-195.64 -28.3 Td
(=)Tj
/T1_0 10.91 Tf
18.44 0 Td
(g)Tj
/T1_2 7.97 Tf
5.59 4.5 Td
(r)Tj
/T1_8 5.98 Tf
3.82 -0.99 Td
(n)Tj
/T1_2 7.97 Tf
5.1 0.99 Td
(r)Tj
/T1_7 5.98 Tf
4.05 2.82 Td
(0)Tj
/T1_8 5.98 Tf
-0.23 -5.29 Td
(n)Tj
/T1_6 5.98 Tf
4.6 0 Td
(+1)Tj
/T1_5 7.97 Tf
9.74 2.47 Td
(+)Tj
/T1_2 7.97 Tf
(r)Tj
/T1_7 5.98 Tf
10.64 2.82 Td
(0)Tj
/T1_8 5.98 Tf
-0.24 -5.29 Td
(n)Tj
/T1_6 5.98 Tf
4.6 0 Td
(+1)Tj
/T1_2 7.97 Tf
9.74 2.47 Td
(r)Tj
/T1_8 5.98 Tf
3.82 -1.1 Td
(n)Tj
/T1_6 5.98 Tf
4.6 0 Td
(+2)Tj
/T1_5 7.97 Tf
9.74 1.1 Td
(+)Tj
/T1_2 7.97 Tf
(r)Tj
/T1_8 5.98 Tf
10.4 -1.1 Td
(n)Tj
/T1_6 5.98 Tf
4.6 0 Td
(+2)Tj
/T1_2 7.97 Tf
9.74 1.1 Td
(r)Tj
/T1_8 5.98 Tf
3.82 -1.1 Td
(n)Tj
/T1_6 5.98 Tf
4.6 0 Td
(+3)Tj
/T1_5 7.97 Tf
9.74 1.1 Td
(+)Tj
/T1_1 7.97 Tf
(\242\242\242)Tj
/T1_5 7.97 Tf
13.64 0 Td
(+)Tj
/T1_2 7.97 Tf
(r)Tj
/T1_8 5.98 Tf
10.4 -1.1 Td
(n)Tj
/T1_6 5.98 Tf
4.6 0 Td
(+)Tj
/T1_8 5.98 Tf
(m)Tj
/T1_7 5.98 Tf
(\241)Tj
/T1_6 5.98 Tf
17.88 0 Td
(1)Tj
/T1_2 7.97 Tf
4.15 1.1 Td
(r)Tj
/T1_8 5.98 Tf
3.82 -1.07 Td
(n)Tj
/T1_6 5.98 Tf
4.6 0 Td
(+)Tj
/T1_8 5.98 Tf
(m)Tj
/T1_3 10.91 Tf
16.15 -3.43 Td
[(mo)-28(d)]TJ
/T1_0 10.91 Tf
23.94 0 Td
(p)Tj
/T1_3 10.91 Tf
82.96 0 Td
(\(6.7\))Tj
-445.45 -39.64 Td
(Next,)Tj
/T1_9 10.91 Tf
29.56 0 Td
(U)Tj
/T1_2 7.97 Tf
5.73 -1.64 Td
(n)Tj
/T1_5 7.97 Tf
5.13 0 Td
(+1)Tj
/T1_3 10.91 Tf
14.79 1.64 Td
(encrypts)Tj
/T1_0 10.91 Tf
43.86 0 Td
(K)Tj
/T1_1 7.97 Tf
10.04 3.96 Td
(\244)Tj
/T1_2 7.97 Tf
-0.78 -7.19 Td
(B)Tj
/T1_4 10.91 Tf
7.28 3.23 Td
(jj)Tj
/T1_9 10.91 Tf
6.06 0 Td
(U)Tj
/T1_2 7.97 Tf
5.72 -1.64 Td
(n)Tj
/T1_5 7.97 Tf
(+1)Tj
/T1_3 10.91 Tf
19.93 1.64 Td
[(using)-318(group)]TJ
/T1_4 10.91 Tf
59.15 0 Td
(G)Tj
/T1_2 7.97 Tf
6.48 -1.69 Td
(B)Tj
/T1_3 10.91 Tf
7.28 1.69 Td
[('s)-318(previously)-319(established)-318(k)26(ey)]TJ
/T1_0 10.91 Tf
138.08 0 Td
(K)Tj
/T1_2 7.97 Tf
9.26 -1.69 Td
(B)Tj
/T1_3 10.91 Tf
10.75 1.69 Td
(and)Tj
/T1_0 10.91 Tf
21.05 0 Td
(K)Tj
/T1_10 7.97 Tf
9.26 -1.64 Td
(U)Tj
/T1_6 5.98 Tf
4.23 -1.11 Td
(1)Tj
/T1_10 7.97 Tf
4.15 1.11 Td
(U)Tj
/T1_8 5.98 Tf
4.23 -1.11 Td
(n)Tj
/T1_6 5.98 Tf
4.6 0 Td
(+1)Tj
/T1_3 10.91 Tf
13.71 2.75 Td
[(to)-319(ob-)]TJ
-439.55 -21.92 Td
(tain)Tj
/T1_9 10.91 Tf
21.95 0 Td
(c)Tj
/T1_2 7.97 Tf
5.72 -1.63 Td
(n)Tj
/T1_5 7.97 Tf
(+1)Tj
/T1_3 10.91 Tf
19.49 1.63 Td
(=)Tj
/T1_4 10.91 Tf
11.51 0 Td
(E)Tj
/T1_2 7.97 Tf
5.75 -1.69 Td
(K)Tj
/T1_8 5.98 Tf
7.14 -1.34 Td
(B)Tj
/T1_3 10.91 Tf
6.82 3.03 Td
(\()Tj
/T1_0 10.91 Tf
(K)Tj
/T1_1 7.97 Tf
14.29 3.96 Td
(\244)Tj
/T1_2 7.97 Tf
-0.78 -7.19 Td
(B)Tj
/T1_4 10.91 Tf
7.27 3.23 Td
(jj)Tj
/T1_9 10.91 Tf
9.23 0 Td
(U)Tj
/T1_2 7.97 Tf
5.72 -1.63 Td
(n)Tj
/T1_5 7.97 Tf
(+1)Tj
/T1_3 10.91 Tf
16.46 1.63 Td
[(\))-290(and)]TJ
/T1_9 10.91 Tf
28.14 0 Td
(c)Tj
/T1_1 7.97 Tf
5.73 3.96 Td
(0)Tj
/T1_2 7.97 Tf
0 -6.88 TD
(n)Tj
/T1_5 7.97 Tf
5.13 0 Td
(+1)Tj
/T1_3 10.91 Tf
14.35 2.92 Td
(=)Tj
/T1_4 10.91 Tf
11.51 0 Td
(E)Tj
/T1_2 7.97 Tf
5.76 -1.69 Td
(K)Tj
/T1_10 5.98 Tf
7.14 -0.99 Td
(U)Tj
/T1_6 5.98 Tf
3.17 -1.8 Td
(1)Tj
/T1_10 5.98 Tf
4.15 1.8 Td
(U)Tj
/T1_8 5.98 Tf
3.18 -1.8 Td
(n)Tj
/T1_6 5.98 Tf
4.6 0 Td
(+1)Tj
/T1_3 10.91 Tf
10.73 4.48 Td
(\()Tj
/T1_0 10.91 Tf
(K)Tj
/T1_1 7.97 Tf
14.28 3.96 Td
(\244)Tj
/T1_2 7.97 Tf
-0.78 -7.19 Td
(B)Tj
/T1_4 10.91 Tf
7.28 3.23 Td
(jj)Tj
/T1_9 10.91 Tf
6.06 0 Td
(U)Tj
/T1_2 7.97 Tf
5.72 -1.63 Td
(n)Tj
/T1_5 7.97 Tf
(+1)Tj
/T1_3 10.91 Tf
16.46 1.63 Td
[(\))-290(resp)-27(ectiv)26(ely)84(.)-429(Finally)82(,)]TJ
/T1_9 10.91 Tf
108.91 0 Td
(U)Tj
/T1_2 7.97 Tf
5.72 -1.63 Td
(n)Tj
/T1_5 7.97 Tf
(+1)Tj
/T1_3 10.91 Tf
19.62 1.63 Td
(broadcasts)Tj
/T1_4 10.91 Tf
-417.43 -21.92 Td
(f)Tj
/T1_9 10.91 Tf
(U)Tj
/T1_2 7.97 Tf
11.18 -1.63 Td
(n)Tj
/T1_5 7.97 Tf
(+1)Tj
/T1_4 10.91 Tf
16.45 1.63 Td
(jj)Tj
/T1_9 10.91 Tf
6.06 0 Td
(c)Tj
/T1_2 7.97 Tf
5.73 -1.63 Td
(n)Tj
/T1_5 7.97 Tf
5.13 0 Td
(+1)Tj
/T1_4 10.91 Tf
11.32 1.63 Td
(jj)Tj
/T1_9 10.91 Tf
6.06 0 Td
(c)Tj
/T1_1 7.97 Tf
5.72 3.96 Td
(0)Tj
/T1_2 7.97 Tf
T*
(n)Tj
/T1_5 7.97 Tf
(+1)Tj
/T1_4 10.91 Tf
16.46 2.92 Td
(g)Tj
/T1_3 10.91 Tf
(.)Tj
-84.11 -21.91 Td
[(Round)-333(3)]TJ
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 0 -374.28 cm
0 0 m
40.75 0 l
S
Q
Q
BT
/T1_3 10.91 Tf
1.0003 0 0 1.0003 116.3924 396.9656 Tm
(:)Tj
-44.38 -21.92 Td
(\()Tj
/T1_0 10.91 Tf
(i)Tj
/T1_3 10.91 Tf
(\))Tj
/T1_9 10.91 Tf
16.78 0 Td
(U)Tj
/T1_5 7.97 Tf
5.72 -1.63 Td
(1)Tj
/T1_3 10.91 Tf
9.27 1.63 Td
(decrypts)Tj
/T1_9 10.91 Tf
44.93 0 Td
(c)Tj
/T1_1 7.97 Tf
5.72 3.96 Td
(0)Tj
/T1_2 7.97 Tf
T*
(n)Tj
/T1_5 7.97 Tf
(+1)Tj
/T1_3 10.91 Tf
20.99 2.92 Td
(to)Tj
1.0003 0 0 1.0003 72 769.82 Tm
117.648 -394.67 Td
(obtain)Tj
/T1_0 10.91 Tf
34.832 0 Td
(K)Tj
/T1_1 7.97 Tf
10.04 3.96 Td
(\244)Tj
/T1_2 7.97 Tf
-0.78 -7.19 Td
(B)Tj
/T1_3 10.91 Tf
11.82 3.23 Td
[(and)-415(the)-417(iden)27(tit)28(y)]TJ
/T1_9 10.91 Tf
82.99 0 Td
(U)Tj
/T1_2 7.97 Tf
5.72 -1.63 Td
(n)Tj
/T1_5 7.97 Tf
(+1)Tj
/T1_3 10.91 Tf
16.46 1.63 Td
[(.)-692(If)-416(the)-416(iden)26(tit)28(y)]TJ
/T1_9 10.91 Tf
83.27 0 Td
(U)Tj
/T1_2 7.97 Tf
5.73 -1.63 Td
(n)Tj
/T1_5 7.97 Tf
(+1)Tj
/T1_3 10.91 Tf
20.99 1.63 Td
[(is)-416(not)-416(decrypted)]TJ
-388.72 -21.91 Td
[(correctly)83(,)-397(then)]TJ
/T1_9 10.91 Tf
73.43 0 Td
(U)Tj
/T1_5 7.97 Tf
5.72 -1.64 Td
(1)Tj
/T1_3 10.91 Tf
8.93 1.64 Td
(rejects)Tj
/T1_9 10.91 Tf
34.89 0 Td
(c)Tj
/T1_1 7.97 Tf
5.72 3.95 Td
(0)Tj
/T1_2 7.97 Tf
T*
(n)Tj
/T1_5 7.97 Tf
(+1)Tj
/T1_3 10.91 Tf
16.46 2.93 Td
[(.)-598(Otherwise,)]TJ
/T1_9 10.91 Tf
64.88 0 Td
(U)Tj
/T1_5 7.97 Tf
5.73 -1.64 Td
(1)Tj
/T1_3 10.91 Tf
8.93 1.64 Td
(accepts)Tj
/T1_0 10.91 Tf
38.79 0 Td
(K)Tj
/T1_1 7.97 Tf
10.04 3.95 Td
(\244)Tj
/T1_2 7.97 Tf
-0.78 -7.19 Td
(B)Tj
/T1_3 10.91 Tf
7.28 3.24 Td
(.)Tj
/T1_9 10.91 Tf
9.56 0 Td
(U)Tj
/T1_5 7.97 Tf
5.73 -1.64 Td
(1)Tj
/T1_3 10.91 Tf
8.93 1.64 Td
[(then)-384(encrypts)]TJ
/T1_0 10.91 Tf
69.98 0 Td
(K)Tj
/T1_1 7.97 Tf
10.05 3.95 Td
(\244)Tj
/T1_2 7.97 Tf
-0.78 -7.19 Td
(B)Tj
/T1_4 10.91 Tf
7.27 3.24 Td
(jj)Tj
/T1_9 10.91 Tf
6.06 0 Td
(U)Tj
/T1_5 7.97 Tf
5.73 -1.64 Td
(1)Tj
/T1_3 10.91 Tf
8.93 1.64 Td
[(using)-384(group)]TJ
/T1_4 10.91 Tf
-411.48 -21.92 Td
(G)Tj
/T1_2 7.97 Tf
6.49 -1.69 Td
(A)Tj
/T1_3 10.91 Tf
6.84 1.69 Td
[('s)-443(previously)-443(established)-444(group)-444(k)27(ey)]TJ
/T1_0 10.91 Tf
175.66 0 Td
(K)Tj
/T1_2 7.97 Tf
9.26 -1.69 Td
(A)Tj
/T1_3 10.91 Tf
11.68 1.69 Td
[(to)-443(obtain)]TJ
/T1_9 10.91 Tf
49.67 0 Td
(c)Tj
/T1_1 7.97 Tf
5.72 3.96 Td
(00)Tj
/T1_5 7.97 Tf
T*
(1)Tj
/T1_3 10.91 Tf
10.13 2.92 Td
(=)Tj
/T1_4 10.91 Tf
13.51 0 Td
(E)Tj
/T1_2 7.97 Tf
5.76 -1.69 Td
(K)Tj
/T1_8 5.98 Tf
7.14 -1.34 Td
(A)Tj
/T1_3 10.91 Tf
6.52 3.03 Td
(\()Tj
/T1_0 10.91 Tf
(K)Tj
/T1_1 7.97 Tf
14.28 3.96 Td
(\244)Tj
/T1_2 7.97 Tf
-0.78 -7.19 Td
(B)Tj
/T1_4 10.91 Tf
7.28 3.23 Td
(jj)Tj
/T1_9 10.91 Tf
6.06 0 Td
(U)Tj
/T1_5 7.97 Tf
5.72 -1.64 Td
(1)Tj
/T1_3 10.91 Tf
4.73 1.64 Td
[(\).)-775(Finally)82(,)]TJ
/T1_9 10.91 Tf
56.47 0 Td
(U)Tj
/T1_5 7.97 Tf
5.72 -1.64 Td
(1)Tj
/T1_3 10.91 Tf
9.57 1.64 Td
(broadcasts)Tj
/T1_4 10.91 Tf
-417.43 -21.92 Td
(f)Tj
/T1_9 10.91 Tf
(U)Tj
/T1_5 7.97 Tf
11.18 -1.63 Td
(1)Tj
/T1_4 10.91 Tf
4.73 1.63 Td
(jj)Tj
/T1_9 10.91 Tf
6.06 0 Td
(c)Tj
/T1_1 7.97 Tf
5.72 3.96 Td
(00)Tj
/T1_5 7.97 Tf
T*
(1)Tj
/T1_4 10.91 Tf
5.09 2.92 Td
(g)Tj
/T1_3 10.91 Tf
9.09 0 Td
[(to)-333(group)]TJ
/T1_4 10.91 Tf
44.26 0 Td
(G)Tj
/T1_2 7.97 Tf
6.49 -1.69 Td
(A)Tj
/T1_3 10.91 Tf
6.84 1.69 Td
(.)Tj
-99.46 -21.91 Td
(\()Tj
/T1_0 10.91 Tf
(ii)Tj
/T1_3 10.91 Tf
(\))Tj
/T1_9 10.91 Tf
19.05 0 Td
(U)Tj
/T1_2 7.97 Tf
5.73 -1.64 Td
(n)Tj
/T1_5 7.97 Tf
(+1)Tj
/T1_3 10.91 Tf
19.51 1.64 Td
(decrypts)Tj
/T1_9 10.91 Tf
43.44 0 Td
(c)Tj
/T1_1 7.97 Tf
5.72 3.95 Td
(0)Tj
/T1_5 7.97 Tf
T*
(1)Tj
/T1_3 10.91 Tf
7.79 2.93 Td
[(to)-280(obtain)]TJ
/T1_0 10.91 Tf
46.1 0 Td
(K)Tj
/T1_1 7.97 Tf
10.05 3.95 Td
(\244)Tj
/T1_2 7.97 Tf
-0.78 -7.19 Td
(A)Tj
/T1_3 10.91 Tf
9.89 3.24 Td
[(and)-280(the)-280(iden)27(tit)27(y)]TJ
/T1_9 10.91 Tf
78.55 0 Td
(U)Tj
/T1_5 7.97 Tf
5.72 -1.64 Td
(1)Tj
/T1_3 10.91 Tf
4.73 1.64 Td
[(.)-427(If)-280(the)-280(iden)27(tit)27(y)]TJ
/T1_9 10.91 Tf
75.93 0 Td
(U)Tj
/T1_5 7.97 Tf
5.73 -1.64 Td
(1)Tj
/T1_3 10.91 Tf
7.78 1.64 Td
[(is)-280(not)-280(decrypted)-281(correctly)83(,)]TJ
-344.94 -21.92 Td
(then)Tj
/T1_9 10.91 Tf
24.74 0 Td
(U)Tj
/T1_2 7.97 Tf
5.72 -1.64 Td
(n)Tj
/T1_5 7.97 Tf
(+1)Tj
/T1_3 10.91 Tf
19.99 1.64 Td
(rejects)Tj
/T1_9 10.91 Tf
34.22 0 Td
(c)Tj
/T1_1 7.97 Tf
5.72 3.96 Td
(0)Tj
/T1_5 7.97 Tf
T*
(1)Tj
/T1_3 10.91 Tf
4.73 2.92 Td
[(.)-441(Otherwise,)]TJ
/T1_9 10.91 Tf
62.38 0 Td
(U)Tj
/T1_2 7.97 Tf
5.73 -1.64 Td
(n)Tj
/T1_5 7.97 Tf
(+1)Tj
/T1_3 10.91 Tf
19.98 1.64 Td
(accepts)Tj
/T1_0 10.91 Tf
38.13 0 Td
(K)Tj
/T1_1 7.97 Tf
10.04 3.96 Td
(\244)Tj
/T1_2 7.97 Tf
-0.78 -7.19 Td
(A)Tj
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4.05 2.82 Td
(0)Tj
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-0.23 -5.29 Td
(n)Tj
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4.6 0 Td
(+1)Tj
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9.74 2.47 Td
(+)Tj
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(r)Tj
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(0)Tj
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-0.24 -5.29 Td
(n)Tj
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4.6 0 Td
(+1)Tj
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9.74 2.47 Td
(r)Tj
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3.82 -1.1 Td
(n)Tj
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4.6 0 Td
(+2)Tj
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9.74 1.1 Td
(+)Tj
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(r)Tj
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10.4 -1.1 Td
(n)Tj
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4.6 0 Td
(+2)Tj
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9.74 1.1 Td
(r)Tj
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3.82 -1.1 Td
(n)Tj
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4.6 0 Td
(+3)Tj
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9.74 1.1 Td
(+)Tj
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(\242\242\242)Tj
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13.64 0 Td
(+)Tj
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(r)Tj
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10.4 -1.07 Td
(n)Tj
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4.6 0 Td
(+)Tj
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(m)Tj
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(r)Tj
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4.05 2.82 Td
(0)Tj
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-0.23 -5.29 Td
(1)Tj
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7.67 -2.03 Td
[(mo)-28(d)]TJ
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23.94 0 Td
(p:)Tj
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68.22 0 Td
(\(6.8\))Tj
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-445.45 -40.29 Td
[(6.2.4)-1125(Lea)31(v)31(e)-374(Proto)-31(col)]TJ
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0 -28.96 TD
(Let)Tj
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21.1 0 Td
(G)Tj
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12.75 0 Td
(=)Tj
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14.11 0 Td
(f)Tj
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(U)Tj
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11.18 -1.63 Td
(1)Tj
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4.73 1.63 Td
(;)Tj
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4.85 0 Td
[(\242)-166(\242)-166(\242)]TJ
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16.35 0 Td
(;)Tj
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4.85 0 Td
(U)Tj
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5.73 -1.63 Td
(n)Tj
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5.63 1.63 Td
(g)Tj
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10.65 0 Td
[(denote)-475(the)-476(previously)-476(established)-476(group,)]TJ
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204.11 0 Td
(U)Tj
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5.73 -1.77 Td
(l)Tj
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8.31 1.77 Td
[(denote)-475(the)-476(lea)27(ving)-475(user)-476(and)]TJ
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7.13 3.96 Td
(0)Tj
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7.02 -3.96 Td
(=)Tj
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12.7 0 Td
[(G)-325(n)-266(f)]TJ
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23.84 0 Td
(U)Tj
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5.73 -1.78 Td
(l)Tj
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3.12 1.78 Td
(g)Tj
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9.8 0 Td
[(denotes)-398(the)-399(new)-399(group.)-641(W)83(e)-398(consider)-399(a)-399(so)-399(called)-399(ring)-398(structure)-399(for)]TJ
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326.4 0 Td
(G)Tj
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11.48 0 Td
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21.92 0 Td
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(0)Tj
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0 -21.92 TD
[(Round)-333(1)]TJ
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 0 -365.44 cm
0 0 m
40.75 0 l
S
Q
Q
BT
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(\()Tj
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(i)Tj
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16.106 -385.83 Td
[(All)-355(remaining)]TJ
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69.264 0 Td
[(o)50(dd-indexe)51(d)]TJ
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60.23 0 Td
(users)Tj
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27.65 0 Td
(U)Tj
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5.72 -1.64 Td
(j)Tj
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7.8 1.64 Td
(6)Tj
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(=)Tj
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11.9 0 Td
(U)Tj
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5.73 -1.78 Td
(l)Tj
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6.99 1.78 Td
(for)Tj
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16.92 0 Td
(j)Tj
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8.99 0 Td
[(is)-354(o)-28(dd)-355(select)-354(new)-355(randoms)]TJ
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130.13 0 Td
(r)Tj
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5.22 3.96 Td
(0)Tj
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(j)Tj
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7.8 3.06 Td
(2)Tj
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10.69 0 Td
(Z)Tj
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8.22 3.96 Td
(\244)Tj
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(q)Tj
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9.38 2.7 Td
(and)Tj
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(\277)Tj
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6.01 3.96 Td
(0)Tj
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(j)Tj
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7.8 3.06 Td
(2)Tj
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10.69 0 Td
(Z)Tj
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8.22 3.96 Td
(\244)Tj
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(N)Tj
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[(and)-333(computes)]TJ
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69.74 0 Td
(z)Tj
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5.55 3.96 Td
(0)Tj
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(j)Tj
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7.41 3.05 Td
(=)Tj
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(g)Tj
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(r)Tj
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(0)Tj
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-0.23 -5.39 Td
(j)Tj
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7.43 -2.34 Td
[(mo)-27(d)]TJ
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23.93 0 Td
(p)Tj
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9.12 0 Td
(and)Tj
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21.21 0 Td
(t)Tj
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3.93 3.96 Td
(0)Tj
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0 -7.01 TD
(j)Tj
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7.42 3.05 Td
[(=)-277(\()]TJ
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(\277)Tj
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21.75 3.96 Td
(0)Tj
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-1.23 -7.01 Td
(j)Tj
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4.38 3.05 Td
(\))Tj
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(e)Tj
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7.45 -3.96 Td
[(mo)-28(d)]TJ
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23.94 0 Td
(N)Tj
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9.95 0 Td
(.)Tj
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7.87 0 Td
(U)Tj
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5.73 -1.63 Td
(j)Tj
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8.02 1.63 Td
[(then)-332(broadcasts)]TJ
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78.91 0 Td
(f)Tj
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(U)Tj
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11.18 -1.63 Td
(j)Tj
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4.38 1.63 Td
(jj)Tj
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6.06 0 Td
(z)Tj
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5.55 3.96 Td
(0)Tj
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-0.48 -7.01 Td
(j)Tj
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4.39 3.05 Td
(jj)Tj
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6.05 0 Td
(t)Tj
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3.94 3.96 Td
(0)Tj
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T*
(j)Tj
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4.38 3.05 Td
(g)Tj
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(.)Tj
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(\()Tj
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(ii)Tj
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[(\))-264(All)-264(remaining)]TJ
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86.18 0 Td
[(even-indexe)51(d)]TJ
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64.25 0 Td
(users)Tj
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26.67 0 Td
(U)Tj
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5.72 -1.64 Td
(j)Tj
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7.41 1.64 Td
(6)Tj
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(=)Tj
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11.51 0 Td
(U)Tj
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5.73 -1.78 Td
(l)Tj
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6 1.78 Td
(for)Tj
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15.94 0 Td
(j)Tj
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8 0 Td
[(is)-264(ev)27(en)-264(select)-264(new)-264(random)]TJ
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124.24 0 Td
(\277)Tj
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6 3.95 Td
(0)Tj
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-1.24 -7.01 Td
(j)Tj
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7.41 3.06 Td
(2)Tj
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10.31 0 Td
(Z)Tj
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8.22 3.95 Td
(\244)Tj
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-0.78 -7.19 Td
(N)Tj
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10.95 3.24 Td
[(and)-264(computes)]TJ
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-402.52 -21.92 Td
(t)Tj
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3.94 3.96 Td
(0)Tj
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0 -7.02 TD
(j)Tj
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7.41 3.06 Td
[(=)-277(\()]TJ
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(\277)Tj
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21.75 3.96 Td
(0)Tj
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-1.23 -7.02 Td
(j)Tj
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4.38 3.06 Td
(\))Tj
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4.24 3.96 Td
(e)Tj
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7.46 -3.96 Td
[(mo)-27(d)]TJ
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23.93 0 Td
(N)Tj
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9.95 0 Td
(.)Tj
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7.88 0 Td
(U)Tj
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5.72 -1.64 Td
(j)Tj
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8.02 1.64 Td
[(then)-333(broadcasts)]TJ
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78.92 0 Td
(f)Tj
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(U)Tj
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(j)Tj
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4.38 1.64 Td
(jj)Tj
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6.06 0 Td
(t)Tj
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3.93 3.96 Td
(0)Tj
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T*
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4.38 3.06 Td
(g)Tj
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(.)Tj
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[(Round)-333(2)]TJ
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 0 -475.02 cm
0 0 m
40.75 0 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 116.3924 296.1874 Tm
(:)Tj
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52.257 -473.5 Td
[(All)-333(remaining)-334(users)]TJ
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96.213 0 Td
(U)Tj
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5.73 -1.63 Td
(i)Tj
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6.41 1.63 Td
[(2)-277(G)]TJ
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17.43 3.96 Td
(0)Tj
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6.43 -3.96 Td
[(for)-333(1)]TJ
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25.18 0 Td
(\267)Tj
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11.51 0 Td
(i)Tj
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6.79 0 Td
(6)Tj
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(=)Tj
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11.51 0 Td
(l)Tj
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6.5 0 Td
(\267)Tj
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11.51 0 Td
(n)Tj
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10.18 0 Td
(compute)Tj
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44.23 0 Td
(X)Tj
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9.89 3.96 Td
(0)Tj
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-0.85 -7.01 Td
(i)Tj
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7.28 3.05 Td
[(as)-333(follo)27(ws:)]TJ
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-184.32 -61.63 Td
(X)Tj
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9.89 4.51 Td
(0)Tj
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-0.85 -7.2 Td
(i)Tj
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6.68 2.69 Td
(=)Tj
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11.51 38.72 Td
(8)Tj
0 -9.82 TD
(>)Tj
0 -3.27 TD
(>)Tj
T*
(>)Tj
T*
(>)Tj
T*
(>)Tj
T*
(<)Tj
0 -19.64 TD
(>)Tj
0 -3.27 TD
(>)Tj
T*
(>)Tj
T*
(>)Tj
T*
(>)Tj
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(:)Tj
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(\263)Tj
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(z)Tj
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(0)Tj
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-0.34 -5.39 Td
(i)Tj
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(+1)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 193.49 -510.13 cm
0 0 m
16.51 0 l
S
Q
Q
BT
/T1_3 7.97 Tf
1.0003 0 0 1.0003 265.5442 252.8253 Tm
(z)Tj
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4.28 2.74 Td
(0)Tj
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-0.34 -5.39 Td
(i)Tj
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2.66 0 Td
(\241)Tj
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(1)Tj
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11.1 18.74 Td
(\264)Tj
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6.52 -2.33 Td
(r)Tj
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(0)Tj
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-0.23 -5.39 Td
(i)Tj
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7.29 -7.19 Td
(if)Tj
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10 0 Td
(i)Tj
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6.78 0 Td
(6)Tj
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(=)Tj
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11.52 0 Td
(l)Tj
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260.578 -512.86 Td
[(;)-167(l)]TJ
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10.752 0 Td
(\241)Tj
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10.9 0 Td
(1)Tj
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[(;)-167(l)]TJ
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16.19 0 Td
[(+)-222(1)]TJ
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(;)Tj
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-112.64 -11.46 Td
(\263)Tj
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(z)Tj
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(0)Tj
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-0.34 -5.58 Td
(l)Tj
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2.4 0 Td
(+1)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 193.49 -533.7 cm
0 0 m
16.25 0 l
S
Q
Q
BT
/T1_3 7.97 Tf
1.0003 0 0 1.0003 265.5442 229.2487 Tm
(z)Tj
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4.28 2.75 Td
(0)Tj
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-0.34 -5.59 Td
(l)Tj
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2.4 0 Td
(\241)Tj
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(2)Tj
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11.1 18.94 Td
(\264)Tj
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6.51 -2.14 Td
(r)Tj
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4.06 2.81 Td
(0)Tj
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-0.24 -5.59 Td
(l)Tj
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2.4 0 Td
(\241)Tj
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(1)Tj
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14.04 -7.19 Td
(if)Tj
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10 0 Td
(i)Tj
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6.79 0 Td
(=)Tj
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11.51 0 Td
(l)Tj
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5.89 0 Td
(\241)Tj
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(1)Tj
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(;)Tj
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(\263)Tj
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7.8 -5.13 Td
(z)Tj
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(0)Tj
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-0.34 -5.58 Td
(l)Tj
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2.4 0 Td
(+2)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 193.49 -557.45 cm
0 0 m
16.25 0 l
S
Q
Q
BT
/T1_3 7.97 Tf
1.0003 0 0 1.0003 265.5442 205.492 Tm
(z)Tj
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4.28 2.74 Td
(0)Tj
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-0.34 -5.58 Td
(l)Tj
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2.4 0 Td
(\241)Tj
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(1)Tj
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(\264)Tj
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6.51 -2.15 Td
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[(and)-349(the)-350(GQ)-349(ID-based)]TJ
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[(signature)-321(sc)27(heme)-320(is)-321(assumed)-321(to)-321(b)-28(e)-321(secure,)-324(hence)]TJ
/T1_1 10.91 Tf
232.65 0 Td
(A)Tj
/T1_0 10.91 Tf
12.21 0 Td
[(is)-321(not)-321(able)-321(to)-321(pro)-28(duce)-321(the)-321(signature)]TJ
/T1_2 10.91 Tf
173.45 0 Td
(\276)Tj
/T1_5 7.97 Tf
6.62 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.39 -6.66 Td
(n)Tj
/T1_0 10.91 Tf
9.13 2.7 Td
(\()Tj
/T1_2 10.91 Tf
4.25 0 Td
(\276)Tj
/T1_3 7.97 Tf
6.23 -1.64 Td
(n)Tj
/T1_6 7.97 Tf
5.13 0 Td
(+1)Tj
/T1_0 10.91 Tf
11.32 1.64 Td
(\).)Tj
-460.6 -21.92 Td
[(Therefore,)-417(it)-400(is)-400(not)-401(p)-27(ossible)-401(for)-400(an)-400(adv)26(ersary)]TJ
/T1_1 10.91 Tf
222.12 0 Td
(A)Tj
/T1_0 10.91 Tf
13.08 0 Td
[(to)-399(obtain)-401(the)-400(new)-401(group)-400(k)27(ey)-399(in)-401(this)-400(case.)-646(No)27(w,)]TJ
-235.2 -21.92 Td
[(w)27(e)-333(consider)-334(the)-334(case)-335(\(b\))-334(as)-334(follo)27(ws:)-446(As)-334(an)-334(adv)27(ersary)]TJ
/T1_1 10.91 Tf
252.92 0 Td
(A)Tj
/T1_0 10.91 Tf
12.35 0 Td
[(is)-334(not)-334(a)-335(joining)-334(new)-334(user)]TJ
/T1_4 10.91 Tf
121.09 0 Td
(U)Tj
/T1_3 7.97 Tf
5.73 -1.63 Td
(n)Tj
/T1_6 7.97 Tf
5.13 0 Td
(+1)Tj
/T1_0 10.91 Tf
11.32 1.63 Td
(,)Tj
/T1_1 10.91 Tf
6.68 0 Td
(A)Tj
/T1_0 10.91 Tf
12.35 0 Td
[(can)-334(only)]TJ
-427.57 -21.91 Td
[(obtain)-394(the)-395(public)-395(exc)27(hange)-394(information,)-411(that)-395(is,)]TJ
/T1_2 10.91 Tf
236.88 0 Td
(z)Tj
/T1_3 7.97 Tf
5.07 -1.64 Td
(n)Tj
/T1_0 10.91 Tf
5.64 1.64 Td
(,)Tj
/T1_2 10.91 Tf
7.5 0 Td
(z)Tj
/T1_3 7.97 Tf
5.08 -1.64 Td
(n)Tj
/T1_6 7.97 Tf
5.13 0 Td
(+1)Tj
/T1_0 10.91 Tf
11.32 1.64 Td
(,)Tj
/T1_4 10.91 Tf
7.5 0 Td
(c)Tj
/T1_6 7.97 Tf
5.73 -1.64 Td
(1)Tj
/T1_0 10.91 Tf
4.73 1.64 Td
(,)Tj
/T1_4 10.91 Tf
7.5 0 Td
(c)Tj
/T1_3 7.97 Tf
5.73 -1.64 Td
(n)Tj
/T1_0 10.91 Tf
9.94 1.64 Td
(and)Tj
/T1_4 10.91 Tf
21.88 0 Td
(c)Tj
/T1_5 7.97 Tf
5.72 3.96 Td
(0)Tj
/T1_3 7.97 Tf
0 -6.66 TD
(n)Tj
/T1_0 10.91 Tf
5.64 2.7 Td
[(.)-629(As)-394(the)-395(new)-395(group)-395(k)27(ey)]TJ
/T1_2 10.91 Tf
-350.99 -21.92 Td
(K)Tj
/T1_5 7.97 Tf
10.04 3.96 Td
(0)Tj
/T1_0 10.91 Tf
6.66 -3.96 Td
(=)Tj
/T1_2 10.91 Tf
12.35 0 Td
(K)Tj
/T1_5 7.97 Tf
10.05 3.96 Td
(\244)Tj
/T1_1 10.91 Tf
7.49 -3.96 Td
(\242)Tj
/T1_2 10.91 Tf
5.79 0 Td
(g)Tj
/T1_3 7.97 Tf
5.59 3.96 Td
(r)Tj
/T1_7 5.98 Tf
3.82 -1 Td
(n)Tj
/T1_3 7.97 Tf
5.1 1 Td
(r)Tj
/T1_7 5.98 Tf
3.82 -1.11 Td
(n)Tj
/T1_8 5.98 Tf
4.6 0 Td
(+1)Tj
/T1_0 10.91 Tf
14.37 -2.85 Td
(where)Tj
/T1_2 10.91 Tf
32.04 0 Td
(K)Tj
/T1_5 7.97 Tf
10.04 3.96 Td
(\244)Tj
/T1_0 10.91 Tf
8.87 -3.96 Td
(and)Tj
/T1_2 10.91 Tf
21.71 0 Td
(g)Tj
/T1_3 7.97 Tf
5.59 3.96 Td
(r)Tj
/T1_7 5.98 Tf
3.82 -1 Td
(n)Tj
/T1_3 7.97 Tf
5.1 1 Td
(r)Tj
/T1_7 5.98 Tf
3.82 -1.11 Td
(n)Tj
/T1_8 5.98 Tf
4.6 0 Td
(+1)Tj
/T1_0 10.91 Tf
14.38 -2.85 Td
[(are)-379(the)-379(plain)27(text)-379(of)]TJ
/T1_4 10.91 Tf
97.47 0 Td
(c)Tj
/T1_6 7.97 Tf
5.72 -1.63 Td
(1)Tj
/T1_0 10.91 Tf
8.87 1.63 Td
(and)Tj
/T1_4 10.91 Tf
21.71 0 Td
(c)Tj
/T1_3 7.97 Tf
5.73 -1.63 Td
(n)Tj
/T1_0 10.91 Tf
9.77 1.63 Td
[(resp)-27(ectiv)27(ely)83(,)-390(therefore,)-391(it)]TJ
-348.92 -21.91 Td
[(is)-361(not)-362(p)-27(ossible)-362(for)]TJ
/T1_1 10.91 Tf
89.3 0 Td
(A)Tj
/T1_0 10.91 Tf
12.65 0 Td
[(to)-361(reco)27(v)28(er)]TJ
/T1_2 10.91 Tf
51.27 0 Td
(K)Tj
/T1_5 7.97 Tf
10.04 3.95 Td
(\244)Tj
/T1_0 10.91 Tf
8.67 -3.95 Td
(and)Tj
/T1_2 10.91 Tf
21.52 0 Td
(g)Tj
/T1_3 7.97 Tf
5.59 3.95 Td
(r)Tj
/T1_7 5.98 Tf
3.82 -0.99 Td
(n)Tj
/T1_3 7.97 Tf
5.1 0.99 Td
(r)Tj
/T1_7 5.98 Tf
3.82 -1.1 Td
(n)Tj
/T1_8 5.98 Tf
4.6 0 Td
(+1)Tj
/T1_0 10.91 Tf
14.18 -2.85 Td
(from)Tj
/T1_4 10.91 Tf
26.08 0 Td
(c)Tj
/T1_6 7.97 Tf
5.73 -1.64 Td
(1)Tj
/T1_0 10.91 Tf
8.67 1.64 Td
(and)Tj
/T1_4 10.91 Tf
21.52 0 Td
(c)Tj
/T1_3 7.97 Tf
5.72 -1.64 Td
(n)Tj
/T1_0 10.91 Tf
9.58 1.64 Td
[(resp)-27(ectiv)26(ely)-360(as)-362(it)-361(is)-362(assumed)-361(that)]TJ
-307.86 -21.92 Td
[(the)-384(symmetric)-384(k)26(ey)-383(encryption)-384(sc)26(heme)]TJ
/T1_9 10.91 Tf
185.95 0 Td
(SKE)Tj
/T1_0 10.91 Tf
24.33 0 Td
[(is)-384(secure.)-598(On)-384(the)-385(other)-384(hand,)-397(if)-385(the)-384(adv)27(ersary)]TJ
/T1_1 10.91 Tf
228.33 0 Td
(A)Tj
/T1_0 10.91 Tf
12.9 0 Td
(can)Tj
-451.51 -21.92 Td
(obtain)Tj
/T1_2 10.91 Tf
34.05 0 Td
(g)Tj
/T1_3 7.97 Tf
5.59 3.96 Td
(r)Tj
/T1_7 5.98 Tf
3.82 -1 Td
(n)Tj
/T1_3 7.97 Tf
5.1 1 Td
(r)Tj
/T1_7 5.98 Tf
3.82 -1.11 Td
(n)Tj
/T1_8 5.98 Tf
4.6 0 Td
(+1)Tj
/T1_0 10.91 Tf
13.98 -2.85 Td
(from)Tj
/T1_2 10.91 Tf
25.9 0 Td
(z)Tj
/T1_3 7.97 Tf
5.07 -1.63 Td
(n)Tj
/T1_0 10.91 Tf
9.39 1.63 Td
(and)Tj
/T1_2 10.91 Tf
21.32 0 Td
(z)Tj
/T1_3 7.97 Tf
5.07 -1.63 Td
(n)Tj
/T1_6 7.97 Tf
(+1)Tj
/T1_0 10.91 Tf
16.45 1.63 Td
[(,)-346(then)-344(the)-344(adv)26(ersary)]TJ
/T1_1 10.91 Tf
100.29 0 Td
(A)Tj
/T1_0 10.91 Tf
12.46 0 Td
[(can)-343(obtain)]TJ
/T1_2 10.91 Tf
54.15 0 Td
(K)Tj
/T1_5 7.97 Tf
10.04 3.96 Td
(\244)Tj
/T1_0 10.91 Tf
8.49 -3.96 Td
(from)Tj
/T1_4 10.91 Tf
25.89 0 Td
(c)Tj
/T1_5 7.97 Tf
5.73 3.96 Td
(0)Tj
/T1_3 7.97 Tf
0 -6.65 TD
(n)Tj
/T1_0 10.91 Tf
9.38 2.69 Td
(and)Tj
/T1_1 10.91 Tf
21.33 0 Td
(A)Tj
/T1_0 10.91 Tf
12.46 0 Td
[(obtains)-343(the)]TJ
-414.38 -21.91 Td
[(new)-325(group)-325(k)27(ey)]TJ
/T1_2 10.91 Tf
72.78 0 Td
(K)Tj
/T1_5 7.97 Tf
10.04 3.95 Td
(0)Tj
/T1_0 10.91 Tf
5.83 -3.95 Td
(=)Tj
/T1_2 10.91 Tf
11.51 0 Td
(K)Tj
/T1_5 7.97 Tf
10.04 3.95 Td
(\244)Tj
/T1_1 10.91 Tf
6.98 -3.95 Td
(\242)Tj
/T1_2 10.91 Tf
5.28 0 Td
(g)Tj
/T1_3 7.97 Tf
5.59 3.95 Td
(r)Tj
/T1_7 5.98 Tf
3.82 -0.99 Td
(n)Tj
/T1_3 7.97 Tf
5.1 0.99 Td
(r)Tj
/T1_7 5.98 Tf
3.82 -1.1 Td
(n)Tj
/T1_8 5.98 Tf
4.6 0 Td
(+1)Tj
/T1_0 10.91 Tf
10.24 -2.85 Td
[(.)-441(But)-325(this)-326(is)-325(not)-325(p)-28(ossible)-326(for)-325(the)-325(adv)26(ersary)]TJ
/T1_1 10.91 Tf
206.43 0 Td
(A)Tj
/T1_0 10.91 Tf
12.25 0 Td
[(to)-325(obtain)]TJ
/T1_2 10.91 Tf
47.09 0 Td
(g)Tj
/T1_3 7.97 Tf
5.59 3.95 Td
(r)Tj
/T1_7 5.98 Tf
3.82 -0.99 Td
(n)Tj
/T1_3 7.97 Tf
5.1 0.99 Td
(r)Tj
/T1_7 5.98 Tf
3.82 -1.1 Td
(n)Tj
/T1_8 5.98 Tf
4.6 0 Td
(+1)Tj
/T1_0 10.91 Tf
13.79 -2.85 Td
(as)Tj
-458.12 -21.92 Td
[(this)-327(is)-328(the)]TJ
/T1_9 10.91 Tf
50.84 0 Td
(CDH)Tj
/T1_0 10.91 Tf
26.14 0 Td
[(problem)-328(and)-328(is)-328(assumed)-328(to)-328(b)-27(e)-328(di\261cult.)-443(Therefore,)-329(the)-328(adv)27(ersary)]TJ
/T1_1 10.91 Tf
310.99 0 Td
(A)Tj
/T1_0 10.91 Tf
12.28 0 Td
[(is)-327(not)-328(p)-28(ossible)]TJ
-400.25 -21.92 Td
[(to)-333(obtain)-333(the)-333(new)-334(group)-333(k)27(ey)]TJ
/T1_2 10.91 Tf
139.08 0 Td
(K)Tj
/T1_5 7.97 Tf
10.05 3.96 Td
(0)Tj
/T1_0 10.91 Tf
2.79 -3.96 Td
(.)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
6.1 w
q 1 0 0 1 464.82 -252.04 cm
0 0 m
0 6.11 l
S
Q
Q
BT
/T1_10 11.95 Tf
1.0003 0 0 1.0003 72 480.529 Tm
(6.3.3)Tj
1.0003 0 0 1.0003 72 769.82 Tm
41.084 -289.21 Td
[(Securit)31(y)-374(Analysis)-375(of)-375(Merge)-375(Proto)-32(col)]TJ
/T1_0 10.91 Tf
-41.084 -28.96 Td
[(In)-348(this)-349(section,)-353(w)27(e)-348(\257rst)-349(sho)27(w)-348(that)-349(the)-349(Merge)-349(Proto)-28(col)-349(pro)27(vides)-348(bac)27(kw)28(ard)-348(secrecy)82(,)-352(that)-349(is,)-353(users)-348(in)]TJ
0 -21.91 TD
(group)Tj
/T1_1 10.91 Tf
31.28 0 Td
(G)Tj
/T1_3 7.97 Tf
6.49 -1.69 Td
(B)Tj
/T1_0 10.91 Tf
11.26 1.69 Td
[(cannot)-365(obtain)-365(group)]TJ
/T1_1 10.91 Tf
101.65 0 Td
(G)Tj
/T1_3 7.97 Tf
6.49 -1.69 Td
(A)Tj
/T1_0 10.91 Tf
6.84 1.69 Td
[('s)-365(previous)-365(group)-366(k)27(ey)]TJ
/T1_2 10.91 Tf
106.4 0 Td
(K)Tj
/T1_3 7.97 Tf
9.26 -1.69 Td
(A)Tj
/T1_0 10.91 Tf
10.82 1.69 Td
[(and)-365(users)-366(in)-365(group)]TJ
/T1_1 10.91 Tf
93.68 0 Td
(G)Tj
/T1_3 7.97 Tf
6.49 -1.69 Td
(A)Tj
/T1_0 10.91 Tf
10.82 1.69 Td
[(cannot)-365(obtain)]TJ
-401.48 -21.92 Td
(group)Tj
/T1_1 10.91 Tf
30.93 0 Td
(G)Tj
/T1_3 7.97 Tf
6.49 -1.69 Td
(B)Tj
/T1_0 10.91 Tf
7.27 1.69 Td
[('s)-333(previous)-334(k)27(ey)]TJ
/T1_2 10.91 Tf
74.08 0 Td
(K)Tj
/T1_3 7.97 Tf
9.26 -1.69 Td
(B)Tj
/T1_0 10.91 Tf
7.27 1.69 Td
(.)Tj
/T1_11 10.91 Tf
-135.3 -29.73 Td
[(Theorem)-383(20)]TJ
/T1_12 10.91 Tf
71.25 0 Td
[(The)-474(pr)50(op)51(ose)52(d)-473(Mer)50(ge)-473(pr)50(oto)51(c)51(ol)-473(achieves)-474(b)50(ackwar)51(d)-473(se)50(cr)51(e)51(cy)-473(pr)51(ovide)51(d)]TJ
/T1_9 10.91 Tf
318.98 0 Td
(CDH)Tj
/T1_12 10.91 Tf
27.74 0 Td
[(pr)51(oblem)-473(is)]TJ
-417.97 -21.92 Td
(di\261cult.)Tj
21.81 -29.72 Td
[(Pr)50(o)52(of:)]TJ
/T1_0 10.91 Tf
38.3 0 Td
[(In)-305(this)-306(theorem,)-312(w)27(e)-305(need)-306(to)-306(sho)27(w)-305(that)-306(an)27(y)-305(user)-306(in)-306(group)]TJ
/T1_1 10.91 Tf
269.7 0 Td
(G)Tj
/T1_3 7.97 Tf
6.49 -1.69 Td
(B)Tj
/T1_0 10.91 Tf
10.62 1.69 Td
(\()Tj
/T1_1 10.91 Tf
(G)Tj
/T1_3 7.97 Tf
10.72 -1.69 Td
(A)Tj
/T1_0 10.91 Tf
6.84 1.69 Td
[(\))-306(is)-306(not)-306(able)-306(to)-306(obtain)]TJ
-364.48 -21.92 Td
[(the)-387(previous)-388(group)-388(k)27(ey)]TJ
/T1_2 10.91 Tf
115.2 0 Td
(K)Tj
/T1_3 7.97 Tf
9.26 -1.69 Td
(A)Tj
/T1_0 10.91 Tf
11.07 1.69 Td
(\()Tj
/T1_2 10.91 Tf
(K)Tj
/T1_3 7.97 Tf
13.5 -1.69 Td
(B)Tj
/T1_0 10.91 Tf
7.28 1.69 Td
[(\))-387(of)-388(group)]TJ
/T1_1 10.91 Tf
53.01 0 Td
(G)Tj
/T1_3 7.97 Tf
6.49 -1.69 Td
(A)Tj
/T1_0 10.91 Tf
11.07 1.69 Td
(\()Tj
/T1_1 10.91 Tf
(G)Tj
/T1_3 7.97 Tf
10.73 -1.69 Td
(B)Tj
/T1_0 10.91 Tf
7.28 1.69 Td
[(\).)-607(Supp)-28(ose)-388(a)-388(user)]TJ
/T1_4 10.91 Tf
90.67 0 Td
(U)Tj
/T1_3 7.97 Tf
5.72 -1.78 Td
(k)Tj
/T1_0 10.91 Tf
9.35 1.78 Td
(\()Tj
/T1_2 10.91 Tf
(n)Tj
/T1_0 10.91 Tf
13.61 0 Td
[(+)-258(1)]TJ
/T1_1 10.91 Tf
20.78 0 Td
(\267)Tj
/T1_2 10.91 Tf
12.5 0 Td
(k)Tj
/T1_1 10.91 Tf
10.04 0 Td
(\267)Tj
/T1_2 10.91 Tf
12.51 0 Td
(n)Tj
/T1_0 10.91 Tf
9.36 0 Td
(+)Tj
/T1_2 10.91 Tf
11.3 0 Td
(m)Tj
/T1_0 10.91 Tf
[(\))-387(in)]TJ
-440.73 -21.92 Td
(group)Tj
/T1_1 10.91 Tf
31.11 0 Td
(G)Tj
/T1_3 7.97 Tf
6.49 -1.68 Td
(B)Tj
/T1_0 10.91 Tf
11.09 1.68 Td
[(tries)-349(to)-349(obtain)-350(the)-350(previous)-349(group)-350(k)27(ey)]TJ
/T1_2 10.91 Tf
185.64 0 Td
(K)Tj
/T1_3 7.97 Tf
9.27 -1.68 Td
(A)Tj
/T1_0 10.91 Tf
10.16 1.68 Td
(=)Tj
/T1_2 10.91 Tf
11.81 0 Td
(g)Tj
/T1_3 7.97 Tf
5.59 3.96 Td
(r)Tj
/T1_8 5.98 Tf
3.82 -1.11 Td
(1)Tj
/T1_3 7.97 Tf
4.15 1.11 Td
(r)Tj
/T1_8 5.98 Tf
3.82 -1.11 Td
(2)Tj
/T1_6 7.97 Tf
4.15 1.11 Td
(+)Tj
/T1_3 7.97 Tf
6.59 0 Td
(r)Tj
/T1_8 5.98 Tf
3.82 -1.11 Td
(2)Tj
/T1_3 7.97 Tf
4.15 1.11 Td
(r)Tj
/T1_8 5.98 Tf
3.82 -1.11 Td
(3)Tj
/T1_6 7.97 Tf
4.15 1.11 Td
(+)Tj
/T1_5 7.97 Tf
(\242\242\242)Tj
/T1_6 7.97 Tf
13.64 0 Td
(+)Tj
/T1_3 7.97 Tf
(r)Tj
/T1_7 5.98 Tf
10.4 -1.11 Td
(n)Tj
/T1_13 5.98 Tf
4.6 0 Td
(\241)Tj
/T1_8 5.98 Tf
(1)Tj
/T1_3 7.97 Tf
9.91 1.11 Td
(r)Tj
/T1_7 5.98 Tf
3.82 -0.99 Td
(n)Tj
/T1_6 7.97 Tf
5.09 0.99 Td
(+)Tj
/T1_3 7.97 Tf
6.59 0 Td
(r)Tj
/T1_7 5.98 Tf
3.82 -0.99 Td
(n)Tj
/T1_3 7.97 Tf
5.1 0.99 Td
(r)Tj
/T1_8 5.98 Tf
3.82 -1.11 Td
(1)Tj
/T1_0 10.91 Tf
8.46 -2.85 Td
[(of)-349(group)]TJ
/T1_1 10.91 Tf
43.71 0 Td
(G)Tj
/T1_3 7.97 Tf
6.48 -1.68 Td
(A)Tj
/T1_0 10.91 Tf
10.66 1.68 Td
(from)Tj
-445.73 -21.91 Td
[(the)-426(Merge)-426(proto)-28(col,)-449(then)]TJ
/T1_4 10.91 Tf
126.76 0 Td
(U)Tj
/T1_3 7.97 Tf
5.73 -1.64 Td
(n)Tj
/T1_6 7.97 Tf
5.13 0 Td
(+1)Tj
/T1_0 10.91 Tf
15.97 1.64 Td
[(\257rst)-426(obtained)]TJ
/T1_2 10.91 Tf
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[(is)-357(c)27(hec)27(k)28(ed)-357(b)27(y)]TJ
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[(resp)-28(ectiv)27(ely)83(,)-393(therefore,)-393(it)]TJ
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[(In)-280(this)-280(section,)-292(w)27(e)-279(\257rst)-281(sho)27(w)-279(that)-281(the)-280(prop)-28(osed)-281(Lea)27(v)28(e)-280(proto)-27(col)-281(ac)27(hiev)28(es)-280(forw)27(ard)-279(secrecy)82(,)-290(that)-281(is,)-291(the)]TJ
0 -21.91 TD
[(lea)27(ving)-250(user)]TJ
/T1_2 10.91 Tf
58.28 0 Td
(U)Tj
/T1_3 7.97 Tf
5.73 -1.78 Td
(l)Tj
/T1_1 10.91 Tf
5.85 1.78 Td
[(cannot)-251(obtain)-251(the)-251(previous)-251(group)-251(k)26(ey)]TJ
/T1_4 10.91 Tf
177.12 0 Td
(K)Tj
/T1_1 10.91 Tf
12.78 0 Td
[(from)-251(new)-251(group)-251(k)27(ey)]TJ
/T1_4 10.91 Tf
95.23 0 Td
(K)Tj
/T1_5 7.97 Tf
10.05 3.96 Td
(0)Tj
/T1_1 10.91 Tf
5.53 -3.96 Td
[(with)-251(the)-251(information)]TJ
-370.57 -21.92 Td
[(kno)27(wn)-298(b)27(y)-298(the)-298(lea)26(ving)-297(user)]TJ
/T1_2 10.91 Tf
126.66 0 Td
(U)Tj
/T1_3 7.97 Tf
5.72 -1.78 Td
(l)Tj
/T1_1 10.91 Tf
3.12 1.78 Td
[(.)-433(W)83(e)-298(then)-299(sho)27(w)-298(that)-299(an)-299(adv)27(ersary)]TJ
/T1_6 10.91 Tf
164.42 0 Td
(A)Tj
/T1_1 10.91 Tf
11.97 0 Td
[(cannot)-298(obtain)-299(the)-299(new)-299(group)-298(k)26(ey)]TJ
/T1_4 10.91 Tf
-311.89 -21.92 Td
(K)Tj
/T1_5 7.97 Tf
10.04 3.96 Td
(0)Tj
/T1_1 10.91 Tf
6.43 -3.96 Td
[(from)-333(the)-333(prop)-28(osed)-333(Lea)26(v)28(e)-332(proto)-28(col.)]TJ
/T1_7 10.91 Tf
-16.47 -33.86 Td
[(Theorem)-383(22)]TJ
/T1_8 10.91 Tf
71.25 0 Td
[(The)-388(pr)50(op)51(ose)52(d)-388(L)51(e)51(ave)-387(pr)50(oto)51(c)51(ol)-387(achieves)-388(forwar)50(d)-387(se)50(cr)51(e)51(cy)-387(pr)50(ovide)51(d)-387(the)]TJ
/T1_9 10.91 Tf
320.85 0 Td
(CDH)Tj
/T1_8 10.91 Tf
26.81 0 Td
[(pr)51(oblem)-387(is)]TJ
-418.91 -21.92 Td
[(di\261cult)-357(and)-358(the)-358(BD)-358(pr)51(oto)51(c)51(ol)-357(is)-358(se)50(cur)51(e.)]TJ
21.81 -33.87 Td
[(Pr)50(o)52(of:)]TJ
/T1_1 10.91 Tf
38.29 0 Td
[(As)-304(the)-305(lea)27(ving)-304(user)]TJ
/T1_2 10.91 Tf
93.72 0 Td
(U)Tj
/T1_3 7.97 Tf
5.73 -1.78 Td
(l)Tj
/T1_1 10.91 Tf
6.44 1.78 Td
[(kno)27(ws)-303(the)-305(previous)-305(group)-305(k)27(ey)]TJ
/T1_4 10.91 Tf
144.04 0 Td
(K)Tj
/T1_1 10.91 Tf
13.07 0 Td
(=)Tj
/T1_4 10.91 Tf
11.51 0 Td
(g)Tj
/T1_3 7.97 Tf
5.59 3.96 Td
(r)Tj
/T1_10 5.98 Tf
3.82 -1 Td
(n)Tj
/T1_3 7.97 Tf
5.1 1 Td
(r)Tj
/T1_11 5.98 Tf
3.82 -1.11 Td
(1)Tj
/T1_6 10.91 Tf
6.45 -2.85 Td
(\242)Tj
/T1_12 10.91 Tf
4.83 8.18 Td
(Q)Tj
/T1_3 7.97 Tf
10.3 -3.15 Td
(n)Tj
/T1_5 7.97 Tf
(\241)Tj
/T1_13 7.97 Tf
(1)Tj
/T1_3 7.97 Tf
0 -8.25 TD
(i)Tj
/T1_13 7.97 Tf
2.88 0 Td
(=1)Tj
/T1_4 10.91 Tf
15.39 3.22 Td
(g)Tj
/T1_3 7.97 Tf
5.59 3.96 Td
(r)Tj
/T1_10 5.98 Tf
3.82 -1.22 Td
(i)Tj
/T1_3 7.97 Tf
3.16 1.22 Td
(r)Tj
/T1_10 5.98 Tf
3.82 -1.22 Td
(i)Tj
/T1_11 5.98 Tf
(+1)Tj
/T1_1 10.91 Tf
16.23 -2.74 Td
[(\(whic)28(h)-304(is)]TJ
-425.41 -21.91 Td
(of)Tj
/T1_4 10.91 Tf
12.43 0 Td
(n)Tj
/T1_1 10.91 Tf
10.19 0 Td
[(terms)-334(of)-335(the)-334(form)]TJ
/T1_4 10.91 Tf
87.42 0 Td
(g)Tj
/T1_3 7.97 Tf
5.59 3.95 Td
[(r)-29(s)]TJ
/T1_1 10.91 Tf
8.47 -3.95 Td
[(\))-334(and)-334(all)]TJ
/T1_4 10.91 Tf
44.26 0 Td
(g)Tj
/T1_3 7.97 Tf
5.6 3.95 Td
(r)Tj
/T1_10 5.98 Tf
3.82 -1.21 Td
(i)Tj
/T1_3 7.97 Tf
3.16 1.21 Td
(r)Tj
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3.82 -1.21 Td
(i)Tj
/T1_11 5.98 Tf
2.66 0 Td
(+1)Tj
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13.88 -2.74 Td
[(for)-334(1)]TJ
/T1_6 10.91 Tf
25.21 0 Td
(\267)Tj
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11.53 0 Td
(i)Tj
/T1_6 10.91 Tf
6.8 0 Td
(\267)Tj
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11.53 0 Td
(n)Tj
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8.98 0 Td
(\241)Tj
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10.91 0 Td
[(1)-334(and)]TJ
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30.32 0 Td
(g)Tj
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5.59 3.95 Td
(r)Tj
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3.82 -0.99 Td
(n)Tj
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5.1 0.99 Td
(r)Tj
/T1_11 5.98 Tf
3.82 -1.1 Td
(1)Tj
/T1_1 10.91 Tf
4.65 -2.85 Td
[(,)-334(but)-334(the)-334(new)-335(group)-334(k)27(ey)-334(is)-334(of)]TJ
-329.56 -21.92 Td
[(the)-301(form)]TJ
/T1_4 10.91 Tf
43.87 0 Td
(K)Tj
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10.05 3.96 Td
(0)Tj
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5.82 -3.96 Td
(=)Tj
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11.51 0 Td
(g)Tj
/T1_3 7.97 Tf
5.59 4.77 Td
(r)Tj
/T1_14 5.98 Tf
4.06 2.82 Td
(0)Tj
/T1_11 5.98 Tf
-0.24 -5.29 Td
(1)Tj
/T1_3 7.97 Tf
4.15 2.47 Td
(r)Tj
/T1_14 5.98 Tf
4.06 2.82 Td
(0)Tj
/T1_11 5.98 Tf
-0.23 -5.29 Td
(2)Tj
/T1_13 7.97 Tf
4.14 2.47 Td
(+)Tj
/T1_3 7.97 Tf
6.59 0 Td
(r)Tj
/T1_14 5.98 Tf
4.06 2.82 Td
(0)Tj
/T1_11 5.98 Tf
-0.24 -5.29 Td
(2)Tj
/T1_3 7.97 Tf
4.15 2.47 Td
(r)Tj
/T1_14 5.98 Tf
4.06 2.82 Td
(0)Tj
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-0.24 -5.29 Td
(3)Tj
/T1_13 7.97 Tf
4.15 2.47 Td
(+)Tj
/T1_5 7.97 Tf
(\242\242\242)Tj
/T1_13 7.97 Tf
13.64 0 Td
(+)Tj
/T1_3 7.97 Tf
(r)Tj
/T1_14 5.98 Tf
10.64 2.82 Td
(0)Tj
/T1_10 5.98 Tf
-0.24 -5.59 Td
(l)Tj
/T1_14 5.98 Tf
2.4 0 Td
(\241)Tj
/T1_11 5.98 Tf
(2)Tj
/T1_3 7.97 Tf
9.91 2.77 Td
(r)Tj
/T1_14 5.98 Tf
4.05 2.82 Td
(0)Tj
/T1_10 5.98 Tf
-0.23 -5.59 Td
(l)Tj
/T1_14 5.98 Tf
2.4 0 Td
(\241)Tj
/T1_11 5.98 Tf
5.75 0 Td
(1)Tj
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4.15 2.77 Td
(+)Tj
/T1_3 7.97 Tf
6.59 0 Td
(r)Tj
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4.05 2.82 Td
(0)Tj
/T1_10 5.98 Tf
-0.23 -5.59 Td
(l)Tj
/T1_14 5.98 Tf
2.4 0 Td
(\241)Tj
/T1_11 5.98 Tf
5.75 0 Td
(1)Tj
/T1_3 7.97 Tf
4.15 2.77 Td
(r)Tj
/T1_14 5.98 Tf
4.06 2.82 Td
(0)Tj
/T1_10 5.98 Tf
-0.24 -5.59 Td
(l)Tj
/T1_11 5.98 Tf
2.4 0 Td
(+1)Tj
/T1_13 7.97 Tf
9.74 2.77 Td
(+)Tj
/T1_5 7.97 Tf
6.59 0 Td
(\242\242\242)Tj
/T1_13 7.97 Tf
(+)Tj
/T1_3 7.97 Tf
13.64 0 Td
(r)Tj
/T1_14 5.98 Tf
4.05 2.82 Td
(0)Tj
/T1_10 5.98 Tf
-0.23 -4.81 Td
(n)Tj
/T1_3 7.97 Tf
5.09 1.99 Td
(r)Tj
/T1_14 5.98 Tf
4.06 2.82 Td
(0)Tj
/T1_11 5.98 Tf
-0.24 -5.29 Td
(1)Tj
/T1_1 10.91 Tf
7.94 -2.3 Td
[(\(whic)27(h)-301(is)-301(of)]TJ
/T1_4 10.91 Tf
57.8 0 Td
(n)Tj
/T1_6 10.91 Tf
8.28 0 Td
(\241)Tj
/T1_1 10.91 Tf
10.21 0 Td
[(1)-302(terms)-301(of)-302(the)-302(form)]TJ
/T1_4 10.91 Tf
94.74 0 Td
(g)Tj
/T1_3 7.97 Tf
5.59 3.96 Td
[(r)-29(s)]TJ
/T1_1 10.91 Tf
8.47 -3.96 Td
[(\))-301(where)]TJ
/T1_4 10.91 Tf
-432.44 -21.92 Td
(r)Tj
/T1_5 7.97 Tf
5.22 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.3 -7.01 Td
(j)Tj
/T1_1 10.91 Tf
7.41 3.05 Td
(=)Tj
/T1_4 10.91 Tf
11.51 0 Td
(r)Tj
/T1_3 7.97 Tf
4.92 -1.63 Td
(j)Tj
/T1_1 10.91 Tf
7.58 1.63 Td
[(for)-292(1)]TJ
/T1_6 10.91 Tf
24.73 0 Td
(\267)Tj
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11.51 0 Td
(j)Tj
/T1_6 10.91 Tf
8.15 0 Td
(6)Tj
/T1_1 10.91 Tf
(=)Tj
/T1_4 10.91 Tf
11.51 0 Td
(l)Tj
/T1_6 10.91 Tf
6.5 0 Td
(\267)Tj
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11.51 0 Td
(n)Tj
/T1_1 10.91 Tf
9.74 0 Td
(and)Tj
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20.77 0 Td
(j)Tj
/T1_1 10.91 Tf
8.31 0 Td
[(is)-292(ev)27(en.)-430(F)82(urthermore,)-300(eac)27(h)]TJ
/T1_4 10.91 Tf
129.49 0 Td
(r)Tj
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5.22 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.3 -7.01 Td
(j)Tj
/T1_1 10.91 Tf
7.57 3.05 Td
[(is)-293(indep)-27(enden)26(t)-291(of)]TJ
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83.87 0 Td
(r)Tj
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4.92 -1.63 Td
(j)Tj
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7.57 1.63 Td
[(for)-293(1)]TJ
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24.74 0 Td
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11.51 0 Td
(j)Tj
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8.14 0 Td
(6)Tj
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(=)Tj
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11.51 0 Td
(l)Tj
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6.5 0 Td
(\267)Tj
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(n)Tj
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-461.32 -21.91 Td
(and)Tj
/T1_4 10.91 Tf
21.93 0 Td
(j)Tj
/T1_1 10.91 Tf
9.48 0 Td
[(is)-399(o)-28(dd,)-417(therefore,)]TJ
/T1_4 10.91 Tf
86.88 0 Td
(g)Tj
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5.59 4.91 Td
(r)Tj
/T1_14 5.98 Tf
4.06 2.82 Td
(0)Tj
/T1_10 5.98 Tf
-0.24 -5.4 Td
(j)Tj
/T1_3 7.97 Tf
3.91 2.58 Td
(r)Tj
/T1_10 5.98 Tf
3.82 -1.21 Td
(j)Tj
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3.4 0 Td
(+1)Tj
/T1_1 10.91 Tf
14.6 -3.7 Td
[(is)-399(indep)-28(enden)27(t)-399(of)]TJ
/T1_4 10.91 Tf
87.37 0 Td
(g)Tj
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5.59 3.95 Td
(r)Tj
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3.82 -1.21 Td
(j)Tj
/T1_3 7.97 Tf
3.9 1.21 Td
(r)Tj
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3.82 -1.21 Td
(j)Tj
/T1_11 5.98 Tf
3.4 0 Td
(+1)Tj
/T1_1 10.91 Tf
10.24 -2.74 Td
[(.)-644(On)-400(the)-400(other)-400(hand,)-416(if)-400(the)-400(lea)27(ving)-399(user)]TJ
/T1_2 10.91 Tf
-271.57 -21.92 Td
(U)Tj
/T1_3 7.97 Tf
5.73 -1.78 Td
(l)Tj
/T1_1 10.91 Tf
6.88 1.78 Td
[(can)-345(compute)]TJ
/T1_4 10.91 Tf
64.49 0 Td
(g)Tj
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5.59 4.92 Td
(r)Tj
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4.06 2.81 Td
(0)Tj
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-0.24 -5.39 Td
(j)Tj
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3.91 2.58 Td
(r)Tj
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3.82 -1.22 Td
(j)Tj
/T1_11 5.98 Tf
3.4 0 Td
(+1)Tj
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14 -3.7 Td
(from)Tj
/T1_4 10.91 Tf
25.92 0 Td
(g)Tj
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5.59 4.92 Td
(r)Tj
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4.06 2.81 Td
(0)Tj
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-0.24 -5.39 Td
(j)Tj
/T1_1 10.91 Tf
8.17 -2.34 Td
(and)Tj
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21.34 0 Td
(g)Tj
/T1_3 7.97 Tf
5.59 3.96 Td
(r)Tj
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3.82 -1.22 Td
(j)Tj
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3.4 0 Td
(+1)Tj
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14.01 -2.74 Td
[(whic)28(h)-345(is)-345(the)]TJ
/T1_9 10.91 Tf
61.35 0 Td
(CDH)Tj
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26.33 0 Td
[(problem,)-348(then)-346(this)-345(con)27(tradicts)-345(to)-345(the)]TJ
-290.98 -21.92 Td
[(fact)-289(that)-290(the)]TJ
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62.5 0 Td
(CDH)Tj
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25.73 0 Td
[(problem)-289(is)-290(di\261cult.)-430(F)83(urthermore,)-298(the)-289(t)26(w)28(o)-289(terms)]TJ
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230.77 0 Td
(g)Tj
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5.6 4.78 Td
(r)Tj
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4.05 2.81 Td
(0)Tj
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(l)Tj
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2.4 0 Td
(\241)Tj
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5.75 0 Td
(2)Tj
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4.15 2.77 Td
(r)Tj
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4.06 2.81 Td
(0)Tj
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-0.24 -5.58 Td
(l)Tj
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2.4 0 Td
(\241)Tj
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(1)Tj
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13.56 -2.01 Td
(and)Tj
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20.74 0 Td
(g)Tj
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5.59 4.78 Td
(r)Tj
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4.05 2.81 Td
(0)Tj
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-0.23 -5.58 Td
(l)Tj
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2.4 0 Td
(\241)Tj
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5.75 0 Td
(1)Tj
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(r)Tj
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4.06 2.81 Td
(0)Tj
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-0.24 -5.58 Td
(l)Tj
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2.4 0 Td
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13.4 -2.01 Td
[(whic)27(h)-289(are)]TJ
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[(only)-376(app)-28(eared)-376(in)]TJ
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85.06 0 Td
(K)Tj
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10.04 3.95 Td
(0)Tj
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2.8 -3.95 Td
[(,)-386(but)-377(not)-377(in)]TJ
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60.77 0 Td
(K)Tj
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10.04 0 Td
[(.)-574(Therefore,)]TJ
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62.35 0 Td
(K)Tj
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10.05 3.95 Td
(0)Tj
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6.9 -3.95 Td
[(is)-376(indep)-28(enden)27(t)-375(of)]TJ
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86.6 0 Td
(K)Tj
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10.04 0 Td
[(.)-574(Hence,)-387(ev)26(en)-375(the)-377(lea)27(ving)]TJ
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(user)Tj
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23.08 0 Td
(U)Tj
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5.72 -1.78 Td
(l)Tj
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6.72 1.78 Td
[(kno)28(ws)-329(all)]TJ
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47.84 0 Td
(g)Tj
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5.6 3.96 Td
(r)Tj
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3.82 -1.22 Td
(i)Tj
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3.16 1.22 Td
(r)Tj
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3.82 -1.22 Td
(i)Tj
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2.66 0 Td
(+1)Tj
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13.83 -2.74 Td
[(for)-330(1)]TJ
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25.14 0 Td
(\267)Tj
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11.51 0 Td
(i)Tj
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6.79 0 Td
(\267)Tj
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11.51 0 Td
(n)Tj
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8.89 0 Td
(\241)Tj
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10.83 0 Td
[(1)-329(and)]TJ
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30.22 0 Td
(g)Tj
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5.59 3.96 Td
(r)Tj
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0 -21.92 TD
[(the)-270(total)-270(n)27(um)27(b)-26(er)-271(of)-270(messages.)-423(F)82(or)-269(computational)-271(costs,)-283(w)27(e)-269(fo)-28(cus)-270(on)-270(the)-271(n)27(um)28(b)-27(er)-270(of)-271(exp)-27(onen)26(tiations,)]TJ
T*
[(signature)-333(generations,)-333(and)-333(signature)-334(v)27(eri\257cations)-332(to)-334(b)-27(e)-334(p)-28(erformed)-333(b)27(y)-332(eac)26(h)-332(user.)]TJ
105.23 -31.6 Td
[(T)83(able)-332(6.2:)-445(Complexit)27(y)-332(Analysis)-334(of)-333(Dynamic)-333(Proto)-28(cols)]TJ
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 40.26 -111.63 cm
0 0 m
387.35 0 l
S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 40.26 -113.62 cm
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387.35 0 l
S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 40.26 -127.36 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 42.25 -127.36 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 140.35 -127.36 cm
0 0 m
0 13.54 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 218.361 646.4855 Tm
(Comm)Tj
1.0003 0 0 1.0003 72 769.82 Tm
177.544 -123.3 Td
[(unication)-332(Costs)]TJ
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 257.54 -127.36 cm
0 0 m
0 13.54 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 363.0115 646.4855 Tm
(Computational)Tj
1.0003 0 0 1.0003 72 769.82 Tm
366.089 -123.3 Td
(Costs)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 425.62 -127.36 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 427.61 -127.36 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 140.35 -127.56 cm
0 0 m
287.26 0 l
S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 40.26 -140.91 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 42.25 -140.91 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 143.0799 632.9317 Tm
(Proto)Tj
1.0003 0 0 1.0003 72 769.82 Tm
98.204 -136.85 Td
(col)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 140.35 -140.91 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 218.361 632.9317 Tm
(Rounds)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 188.26 -140.91 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 273.2063 632.9317 Tm
(Messages)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 257.54 -140.91 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 335.5938 632.9317 Tm
(Mo)Tj
1.0003 0 0 1.0003 72 769.82 Tm
279.274 -136.85 Td
(d.)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 294.34 -140.91 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 376.0651 632.9317 Tm
(Signature)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 359.11 -140.91 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 441.7335 632.9317 Tm
(Signature)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 425.62 -140.91 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 427.61 -140.91 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 40.26 -154.45 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 42.25 -154.45 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 140.35 -154.45 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 188.26 -154.45 cm
0 0 m
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 257.54 -154.45 cm
0 0 m
0 13.54 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 336.8841 619.3879 Tm
(Exp.)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 294.34 -154.45 cm
0 0 m
0 13.54 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 372.3941 619.3879 Tm
(Generation)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 359.11 -154.45 cm
0 0 m
0 13.54 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 437.1822 619.3879 Tm
(V)Tj
1.0003 0 0 1.0003 72 769.82 Tm
372.357 -150.39 Td
(eri\257cation)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 425.62 -154.45 cm
0 0 m
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 427.61 -154.45 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 40.26 -154.65 cm
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387.35 0 l
S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 40.26 -156.65 cm
0 0 m
387.35 0 l
S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 40.26 -170.39 cm
0 0 m
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 42.25 -170.39 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 134.6075 603.4434 Tm
(BD)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 98.98 -170.39 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 181.6207 603.4434 Tm
(Join)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 140.35 -170.39 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 233.6252 603.4434 Tm
(2)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 188.26 -170.39 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 279.5681 603.4434 Tm
(2)Tj
/T1_1 10.91 Tf
(n)Tj
/T1_0 10.91 Tf
14.42 0 Td
(+)Tj
1.0003 0 0 1.0003 72 769.82 Tm
232.84 -166.33 Td
(2)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 257.54 -170.39 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 342.7958 603.4434 Tm
(3)Tj
/T1_2 7.97 Tf
5.45 3.96 Td
(a)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 294.34 -170.39 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 396.0807 603.4434 Tm
(2)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 359.11 -170.39 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_1 10.91 Tf
1.0003 0 0 1.0003 451.8063 603.4434 Tm
(n)Tj
/T1_0 10.91 Tf
8.97 0 Td
(+)Tj
1.0003 0 0 1.0003 72 769.82 Tm
399.58 -166.33 Td
(2)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 425.62 -170.39 cm
0 0 m
0 13.55 l
S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 427.61 -170.39 cm
0 0 m
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 98.98 -170.59 cm
0 0 m
328.63 0 l
S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 40.26 -183.94 cm
0 0 m
0 13.55 l
S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 42.25 -183.94 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 126.1151 589.8996 Tm
([BD95])Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 98.98 -183.94 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 178.1397 589.8996 Tm
(Lea)Tj
1.0003 0 0 1.0003 72 769.82 Tm
122.922 -179.87 Td
[(v)27(e)]TJ
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 140.35 -183.94 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 233.6252 589.8996 Tm
(2)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 188.26 -183.94 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 279.5681 589.8996 Tm
(2)Tj
/T1_1 10.91 Tf
(n)Tj
/T1_3 10.91 Tf
14.42 0 Td
(\241)Tj
/T1_0 10.91 Tf
10.91 0 Td
(2)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 257.54 -183.94 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 342.7958 589.8996 Tm
(3)Tj
/T1_2 7.97 Tf
5.45 3.96 Td
(a)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 294.34 -183.94 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 396.0807 589.8996 Tm
(2)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 359.11 -183.94 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_1 10.91 Tf
1.0003 0 0 1.0003 461.1989 589.8996 Tm
(n)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 425.62 -183.94 cm
0 0 m
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 427.61 -183.94 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 98.98 -184.13 cm
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328.63 0 l
S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 40.26 -197.48 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 42.25 -197.48 cm
0 0 m
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 98.98 -197.48 cm
0 0 m
0 13.54 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 176.9794 576.3458 Tm
(Merge)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 140.35 -197.48 cm
0 0 m
0 13.54 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 233.6252 576.3458 Tm
(2)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 188.26 -197.48 cm
0 0 m
0 13.54 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 274.7768 576.3458 Tm
(2)Tj
/T1_1 10.91 Tf
(n)Tj
/T1_0 10.91 Tf
14.42 0 Td
(+)Tj
1.0003 0 0 1.0003 72 769.82 Tm
228.05 -193.42 Td
(2)Tj
/T1_1 10.91 Tf
(m)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 257.54 -197.48 cm
0 0 m
0 13.54 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 342.7958 576.3458 Tm
(3)Tj
/T1_2 7.97 Tf
5.45 3.96 Td
(a)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 294.34 -197.48 cm
0 0 m
0 13.54 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 396.0807 576.3458 Tm
(2)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 359.11 -197.48 cm
0 0 m
0 13.54 l
S
Q
Q
BT
/T1_1 10.91 Tf
1.0003 0 0 1.0003 440.3531 576.3458 Tm
(n)Tj
/T1_0 10.91 Tf
8.97 0 Td
(+)Tj
/T1_1 10.91 Tf
10.9 0 Td
(m)Tj
/T1_0 10.91 Tf
12 0 Td
(+)Tj
1.0003 0 0 1.0003 72 769.82 Tm
411.03 -193.42 Td
(1)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 425.62 -197.48 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
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0 0 m
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 40.26 -197.68 cm
0 0 m
387.35 0 l
S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 40.26 -211.43 cm
0 0 m
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 42.25 -211.43 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 120.5436 562.3919 Tm
(Prop)Tj
1.0003 0 0 1.0003 72 769.82 Tm
72.041 -207.37 Td
(osed)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 98.98 -211.43 cm
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S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 181.6207 562.3919 Tm
(Join)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 140.35 -211.43 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 233.6252 562.3919 Tm
(3)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 188.26 -211.43 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 292.2316 562.3919 Tm
(5)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 257.54 -211.43 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 343.2259 562.3919 Tm
(2)Tj
/T1_2 7.97 Tf
5.46 3.96 Td
(b)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 294.34 -211.43 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 396.0807 562.3919 Tm
(1)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 359.11 -211.43 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 461.7491 562.3919 Tm
(1)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 425.62 -211.43 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 427.61 -211.43 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 98.98 -211.63 cm
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328.63 0 l
S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 42.25 -224.98 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 120.2435 548.8381 Tm
(Proto)Tj
1.0003 0 0 1.0003 72 769.82 Tm
75.374 -220.92 Td
(cols)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 98.98 -224.98 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 178.1397 548.8381 Tm
(Lea)Tj
1.0003 0 0 1.0003 72 769.82 Tm
122.922 -220.92 Td
[(v)27(e)]TJ
ET
q
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0 -21.91 TD
[(\(i\))-453(is)-454(again)-454(the)-454(most)-454(e\261cien)27(t)-453(follo)27(w)28(ed)-453(b)27(y)-453(the)-454(ID-based)-454(SSN)-453(sc)27(heme,)-483(BD)-454(with)-454(certi\257cate-based)]TJ
0 -21.92 TD
[(ECDSA)-291(signature)-291(sc)27(heme)-290(and)-291(BD)-292(with)-291(certi\257cate-based)-291(DSA)-291(signature)-291(sc)27(heme.)-430(Hence,)-299(the)-292(results)]TJ
T*
[(sho)27(w)-381(that)-382(our)-383(prop)-28(osed)-382(IKA)-382(proto)-28(col)-382(is)-383(the)-382(most)-382(energy-e\261cien)26(t)-381(when)-382(using)-383(either)-382(the)-382(100kbps)]TJ
0 -21.91 TD
[(transceiv)27(er)-332(mo)-28(dule)-333(or)-333(WLAN)-334(card.)]TJ
/T1_3 10.91 Tf
0 -21.92 TD
[(Energy)-383(Cost)-383(Results)-383(for)-384(Dynamic)-383(Proto)-32(cols)]TJ
/T1_0 10.91 Tf
16.93 -21.92 Td
[(In)-471(this)-471(section,)-505(w)27(e)-470(presen)27(t)-470(the)-471(energy)-471(cost)-471(analysis)-471(of)-471(our)-471(dynamic)-471(proto)-28(cols)-471(and)-471(compare)]TJ
-16.93 -21.91 Td
[(them)-403(with)-404(re-executing)-404(the)-404(authen)27(ticated)-403(BD)-403(proto)-28(col)-404(using)-404(the)-403(ECDSA)-404(signature)-404(sc)27(heme.)-655(W)82(e)]TJ
T*
[(assume)-391(that)-391(eac)27(h)-391(no)-27(de)-392(in)-391(the)-391(group)-391(is)-392(using)-391(the)-391(133MHz)-391(\\StrongARM")-392(micropro)-27(cessor)-392(and)-391(the)]TJ
T*
[(comm)27(unication)-425(mo)-27(dule)-426(used)-426(is)-426(the)-425(Sp)-28(ectrum24)-426(WLAN)-426(card)-426(as)-425(presen)26(ted)-424(in)-426(T)82(ables)-425(3.2)-425(and)-426(3.4)]TJ
0 -21.91 TD
[(resp)-27(ectiv)27(ely)83(.)-435(W)82(e)-306(also)-308(assume)-307(that)-308(the)-307(curren)26(t)-306(group)-308(size)]TJ
/T1_1 10.91 Tf
270.73 0 Td
(n)Tj
/T1_0 10.91 Tf
9.58 0 Td
[(=)-277(100)-308(and)-307(the)-308(n)27(um)28(b)-27(er)-307(of)-308(merging)-308(users)]TJ
/T1_1 10.91 Tf
-280.31 -21.92 Td
(m)Tj
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12.61 0 Td
[(=)-277(20.)-444(The)-334(energy)-333(cost)-333(results)-334(are)-333(sho)27(wn)-332(in)-334(T)83(able)-333(6.3.)]TJ
110.11 -31.61 Td
[(T)83(able)-333(6.3:)-444(Energy)-334(Cost)-333(for)-333(Dynamic)-334(Proto)-27(cols)]TJ
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(2)Tj
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(:)Tj
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ET
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[(Lea)27(v)28(e)]TJ
ET
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5.73 -1.63 Td
(i)Tj
/T1_2 10.91 Tf
8.06 1.63 Td
[(2)-428(G)]TJ
/T1_4 7.97 Tf
18.43 -1.63 Td
[(v)-35(;j)]TJ
/T1_0 10.91 Tf
15.76 1.63 Td
(for)Tj
/T1_1 10.91 Tf
17.68 0 Td
(i)Tj
/T1_0 10.91 Tf
8.44 0 Td
(=)Tj
/T1_1 10.91 Tf
-459.39 -21.91 Td
[(j)-57(c)]TJ
/T1_4 7.97 Tf
9.84 3.95 Td
(h)Tj
/T1_3 7.97 Tf
4.87 0 Td
(\241)Tj
/T1_4 7.97 Tf
6.59 0 Td
(v)Tj
/T1_1 10.91 Tf
4.9 -3.95 Td
[(;)-167(j)-57(c)]TJ
/T1_4 7.97 Tf
14.69 3.95 Td
(h)Tj
/T1_3 7.97 Tf
(\241)Tj
/T1_4 7.97 Tf
(v)Tj
/T1_0 10.91 Tf
18.79 -3.95 Td
(+)Tj
/T1_1 10.91 Tf
10.91 0 Td
(c)Tj
/T1_4 7.97 Tf
4.72 3.95 Td
(h)Tj
/T1_3 7.97 Tf
4.87 0 Td
(\241)Tj
/T1_4 7.97 Tf
6.59 0 Td
(v)Tj
/T1_3 7.97 Tf
4.41 0 Td
(\241)Tj
/T1_6 7.97 Tf
(1)Tj
/T1_1 10.91 Tf
11.31 -3.95 Td
[(;)-166(j)-58(c)]TJ
/T1_4 7.97 Tf
14.68 3.95 Td
(h)Tj
/T1_3 7.97 Tf
(\241)Tj
/T1_4 7.97 Tf
11.47 0 Td
(v)Tj
/T1_0 10.91 Tf
7.33 -3.95 Td
[(+)-222(2)]TJ
/T1_1 10.91 Tf
(c)Tj
/T1_4 7.97 Tf
21.08 3.95 Td
(h)Tj
/T1_3 7.97 Tf
(\241)Tj
/T1_4 7.97 Tf
(v)Tj
/T1_3 7.97 Tf
15.87 0 Td
(\241)Tj
/T1_6 7.97 Tf
(1)Tj
/T1_1 10.91 Tf
11.31 -3.95 Td
(;)Tj
/T1_2 10.91 Tf
4.85 0 Td
[(\242)-166(\242)-167(\242)]TJ
/T1_1 10.91 Tf
16.36 0 Td
[(;)-166(j)-57(c)]TJ
/T1_4 7.97 Tf
14.68 3.95 Td
(h)Tj
/T1_3 7.97 Tf
(\241)Tj
/T1_4 7.97 Tf
11.47 0 Td
(v)Tj
/T1_0 10.91 Tf
7.33 -3.95 Td
[(+)-221(\()]TJ
/T1_1 10.91 Tf
(c)Tj
/T1_2 10.91 Tf
22.29 0 Td
(\241)Tj
/T1_0 10.91 Tf
10.9 0 Td
(1\))Tj
/T1_1 10.91 Tf
(c)Tj
/T1_4 7.97 Tf
14.42 3.95 Td
(h)Tj
/T1_3 7.97 Tf
4.87 0 Td
(\241)Tj
/T1_4 7.97 Tf
6.59 0 Td
(v)Tj
/T1_3 7.97 Tf
4.41 0 Td
(\241)Tj
/T1_6 7.97 Tf
(1)Tj
/T1_0 10.91 Tf
14.94 -3.95 Td
[(computes)-333(and)-333(broadcasts)]TJ
/T1_1 10.91 Tf
123.81 0 Td
(z)Tj
/T1_4 7.97 Tf
5.07 -1.64 Td
[(v)-35(;i)]TJ
/T1_0 10.91 Tf
13.17 1.64 Td
(=)Tj
/T1_1 10.91 Tf
-459.39 -21.92 Td
(g)Tj
/T1_9 7.97 Tf
5.59 3.96 Td
(H)Tj
/T1_6 7.97 Tf
(\()Tj
/T1_4 7.97 Tf
(K)Tj
/T1_10 5.98 Tf
16.41 -1.41 Td
(v)Tj
/T1_11 5.98 Tf
3.95 0 Td
(+1)Tj
/T1_10 5.98 Tf
9.24 0 Td
(;k)Tj
/T1_6 7.97 Tf
6.84 1.41 Td
(\))Tj
/T1_0 10.91 Tf
6.82 -3.96 Td
[(mo)-27(d)]TJ
/T1_1 10.91 Tf
23.93 0 Td
(p)Tj
/T1_0 10.91 Tf
10.28 0 Td
[(in)-439(the)-439(\257rst)-439(round)-439(of)-439(the)-439(BD)-439(proto)-28(col)-439(run)-439(in)-439(subgroup)]TJ
/T1_2 10.91 Tf
271.98 0 Td
(G)Tj
/T1_4 7.97 Tf
6.48 -1.64 Td
[(v)-36(;j)]TJ
/T1_0 10.91 Tf
11.15 1.64 Td
[(,)-465(where)]TJ
/T1_1 10.91 Tf
40.79 0 Td
(k)Tj
/T1_0 10.91 Tf
10.97 0 Td
(=)Tj
/T1_4 7.97 Tf
27 4.29 Td
(i)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 439.06 -293.14 cm
0 0 m
27.62 0 l
S
Q
Q
BT
/T1_4 7.97 Tf
1.0003 0 0 1.0003 511.1829 469.5159 Tm
(c)Tj
/T1_10 5.98 Tf
3.67 2.27 Td
(h)Tj
/T1_12 5.98 Tf
(\241)Tj
/T1_10 5.98 Tf
10.09 0 Td
(v)Tj
/T1_12 5.98 Tf
3.95 0 Td
(\241)Tj
/T1_11 5.98 Tf
(1)Tj
/T1_0 10.91 Tf
-456.77 -19.84 Td
(and)Tj
/T1_1 10.91 Tf
22.02 0 Td
(K)Tj
/T1_4 7.97 Tf
9.26 -1.77 Td
(v)Tj
/T1_6 7.97 Tf
4.41 0 Td
(+1)Tj
/T1_4 7.97 Tf
(;k)Tj
/T1_0 10.91 Tf
22.73 1.77 Td
(is)Tj
1.0003 0 0 1.0003 72 769.82 Tm
70.192 -317.79 Td
[(the)-408(subgroup)-408(k)27(ey)-406(of)-408(subgroup)]TJ
/T1_2 10.91 Tf
149.658 0 Td
(G)Tj
/T1_4 7.97 Tf
6.48 -1.77 Td
(v)Tj
/T1_6 7.97 Tf
4.41 0 Td
(+1)Tj
/T1_4 7.97 Tf
(;k)Tj
/T1_0 10.91 Tf
22.74 1.77 Td
(that)Tj
/T1_8 10.91 Tf
24.44 0 Td
(U)Tj
/T1_4 7.97 Tf
5.72 -1.63 Td
(i)Tj
/T1_2 10.91 Tf
7.76 1.63 Td
[(2)-401(G)]TJ
/T1_4 7.97 Tf
18.14 -1.63 Td
[(v)-35(;j)]TJ
/T1_0 10.91 Tf
15.59 1.63 Td
[(con)28(trols)-407(at)-408(la)27(y)28(er)]TJ
/T1_2 10.91 Tf
83.13 0 Td
(L)Tj
/T1_4 7.97 Tf
7.53 -1.63 Td
(v)Tj
/T1_6 7.97 Tf
4.4 0 Td
(+1)Tj
/T1_0 10.91 Tf
11.32 1.63 Td
[(.)-667(Next,)]TJ
-431.51 -21.91 Td
[(the)-323(second)-323(round)-324(and)-323(k)26(ey)-322(computation)-323(round)-324(of)-323(the)-324(BD)-323(proto)-28(col)-323(are)-324(executed)-323(in)-324(subgroup)]TJ
/T1_2 10.91 Tf
437.02 0 Td
(G)Tj
/T1_4 7.97 Tf
6.49 -1.64 Td
[(v)-35(;j)]TJ
/T1_0 10.91 Tf
14.67 1.64 Td
(to)Tj
-458.18 -21.92 Td
[(obtain)-333(the)-333(subgroup)-333(k)26(ey)]TJ
/T1_1 10.91 Tf
119.75 0 Td
(K)Tj
/T1_4 7.97 Tf
9.27 -1.64 Td
[(v)-35(;j)]TJ
/T1_0 10.91 Tf
11.14 1.64 Td
(.)Tj
-140.16 -21.92 Td
[(This)-327(phase)-328(will)-328(complete)-328(when)-328(all)-328(subgroups)-328(at)-328(la)27(y)28(er)]TJ
/T1_2 10.91 Tf
256.36 0 Td
(L)Tj
/T1_6 7.97 Tf
7.53 -1.63 Td
(1)Tj
/T1_0 10.91 Tf
8.3 1.63 Td
[(ha)27(v)28(e)-327(computed)-328(their)-328(resp)-28(ectiv)27(e)-327(subgroup)]TJ
-272.19 -21.91 Td
[(k)27(eys)]TJ
/T1_1 10.91 Tf
23.99 0 Td
(K)Tj
/T1_6 7.97 Tf
9.27 -1.64 Td
(1)Tj
/T1_4 7.97 Tf
(;j)Tj
/T1_0 10.91 Tf
14.6 1.64 Td
[(for)-333(0)]TJ
/T1_2 10.91 Tf
25.17 0 Td
(\267)Tj
/T1_1 10.91 Tf
11.51 0 Td
(j)Tj
/T1_2 10.91 Tf
8.15 0 Td
(\267)Tj
/T1_1 10.91 Tf
11.51 0 Td
(c)Tj
/T1_2 10.91 Tf
7.14 0 Td
(\241)Tj
/T1_0 10.91 Tf
10.91 0 Td
(1.)Tj
/T1_7 10.91 Tf
-122.25 -21.92 Td
[(Phase)-468(3)-468(-)-468(Key)-469(Computation)]TJ
/T1_0 10.91 Tf
157.7 0 Td
[(.)-666(A)27(t)-406(the)-407(highest)-408(la)27(y)28(er)]TJ
/T1_2 10.91 Tf
112.07 0 Td
(L)Tj
/T1_6 7.97 Tf
7.52 -1.63 Td
(0)Tj
/T1_0 10.91 Tf
9.17 1.63 Td
[(and)-407(subgroup)]TJ
/T1_2 10.91 Tf
70.17 0 Td
(G)Tj
/T1_6 7.97 Tf
6.49 -1.63 Td
(0)Tj
/T1_4 7.97 Tf
(;)Tj
/T1_6 7.97 Tf
(0)Tj
/T1_0 10.91 Tf
11.31 1.63 Td
[(,)-425(eac)26(h)]TJ
/T1_8 10.91 Tf
33.02 0 Td
(U)Tj
/T1_4 7.97 Tf
5.72 -1.63 Td
(i)Tj
/T1_2 10.91 Tf
7.76 1.63 Td
[(2)-400(G)]TJ
/T1_6 7.97 Tf
18.13 -1.63 Td
(0)Tj
/T1_4 7.97 Tf
(;)Tj
/T1_6 7.97 Tf
(0)Tj
/T1_0 10.91 Tf
15.75 1.63 Td
(for)Tj
/T1_1 10.91 Tf
-454.81 -21.92 Td
(i)Tj
/T1_0 10.91 Tf
6.79 0 Td
[(=)-277(0)]TJ
/T1_1 10.91 Tf
[(;)-166(c)]TJ
/T1_4 7.97 Tf
26.53 3.96 Td
(h)Tj
/T1_3 7.97 Tf
(\241)Tj
/T1_6 7.97 Tf
(1)Tj
/T1_1 10.91 Tf
16.19 -3.96 Td
(;)Tj
/T1_0 10.91 Tf
4.85 0 Td
(2)Tj
/T1_1 10.91 Tf
(c)Tj
/T1_4 7.97 Tf
10.17 3.96 Td
(h)Tj
/T1_3 7.97 Tf
(\241)Tj
/T1_6 7.97 Tf
11.47 0 Td
(1)Tj
/T1_1 10.91 Tf
4.73 -3.96 Td
(;)Tj
/T1_2 10.91 Tf
4.84 0 Td
[(\242)-167(\242)-166(\242)]TJ
/T1_1 10.91 Tf
16.36 0 Td
(;)Tj
/T1_0 10.91 Tf
4.85 0 Td
(\()Tj
/T1_1 10.91 Tf
(c)Tj
/T1_2 10.91 Tf
10.86 0 Td
(\241)Tj
/T1_0 10.91 Tf
10.39 0 Td
(1\))Tj
/T1_1 10.91 Tf
9.69 0 Td
(c)Tj
/T1_4 7.97 Tf
4.72 3.96 Td
(h)Tj
/T1_3 7.97 Tf
(\241)Tj
/T1_6 7.97 Tf
11.47 0 Td
(1)Tj
/T1_0 10.91 Tf
8.1 -3.96 Td
[(computes)-309(and)-310(broadcasts)]TJ
/T1_1 10.91 Tf
123.04 0 Td
(z)Tj
/T1_6 7.97 Tf
5.07 -1.63 Td
(0)Tj
/T1_4 7.97 Tf
(;i)Tj
/T1_0 10.91 Tf
12.99 1.63 Td
(=)Tj
/T1_1 10.91 Tf
11.52 0 Td
(g)Tj
/T1_9 7.97 Tf
5.59 3.96 Td
(H)Tj
/T1_6 7.97 Tf
(\()Tj
/T1_4 7.97 Tf
(K)Tj
/T1_11 5.98 Tf
16.41 -1.4 Td
(1)Tj
/T1_10 5.98 Tf
3.65 0 Td
(;k)Tj
/T1_6 7.97 Tf
6.84 1.4 Td
(\))Tj
/T1_0 10.91 Tf
6.82 -3.96 Td
[(mo)-27(d)]TJ
/T1_1 10.91 Tf
23.93 0 Td
(p)Tj
/T1_0 10.91 Tf
8.86 0 Td
[(in)-309(the)-310(\257rst)-309(round)]TJ
-386.73 -21.91 Td
[(of)-305(the)-305(BD)-306(proto)-28(col)-305(run)-306(in)-305(subgroup)]TJ
/T1_2 10.91 Tf
171.61 0 Td
(G)Tj
/T1_6 7.97 Tf
6.49 -1.64 Td
(0)Tj
/T1_4 7.97 Tf
(;)Tj
/T1_6 7.97 Tf
6.59 0 Td
(0)Tj
/T1_0 10.91 Tf
4.73 1.64 Td
[(,)-310(where)]TJ
/T1_1 10.91 Tf
37.65 0 Td
(k)Tj
/T1_0 10.91 Tf
9.05 0 Td
(=)Tj
/T1_4 7.97 Tf
20.22 4.29 Td
(i)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 248.83 -468.48 cm
0 0 m
17.91 0 l
S
Q
Q
BT
/T1_4 7.97 Tf
1.0003 0 0 1.0003 320.8997 294.1368 Tm
(c)Tj
/T1_10 5.98 Tf
3.67 2.27 Td
(h)Tj
/T1_12 5.98 Tf
4.33 0 Td
(\241)Tj
/T1_11 5.98 Tf
(1)Tj
/T1_0 10.91 Tf
14.43 2.08 Td
(and)Tj
/T1_1 10.91 Tf
20.91 0 Td
(K)Tj
/T1_6 7.97 Tf
9.26 -1.78 Td
(1)Tj
/T1_4 7.97 Tf
(;k)Tj
/T1_0 10.91 Tf
15.03 1.78 Td
(is)Tj
1.0003 0 0 1.0003 72 769.82 Tm
327.119 -471.2 Td
[(the)-306(subgroup)-305(k)27(ey)-305(of)-305(subgroup)]TJ
/T1_2 10.91 Tf
-327.119 -21.92 Td
(G)Tj
/T1_6 7.97 Tf
6.49 -1.77 Td
(1)Tj
/T1_4 7.97 Tf
(;k)Tj
/T1_0 10.91 Tf
15.55 1.77 Td
(that)Tj
/T1_8 10.91 Tf
23.85 0 Td
(U)Tj
/T1_4 7.97 Tf
5.73 -1.63 Td
(i)Tj
/T1_2 10.91 Tf
6.77 1.63 Td
[(2)-310(G)]TJ
/T1_6 7.97 Tf
17.15 -1.63 Td
(0)Tj
/T1_4 7.97 Tf
(;)Tj
/T1_6 7.97 Tf
(0)Tj
/T1_0 10.91 Tf
15.17 1.63 Td
[(con)28(trols)-353(at)-353(La)27(y)28(er)]TJ
/T1_2 10.91 Tf
85.14 0 Td
(L)Tj
/T1_6 7.97 Tf
7.52 -1.63 Td
(1)Tj
/T1_0 10.91 Tf
4.73 1.63 Td
[(.)-504(After)-353(completing)-354(the)-353(BD)-353(proto)-28(col,)-358(eac)27(h)]TJ
/T1_8 10.91 Tf
202.93 0 Td
(U)Tj
/T1_4 7.97 Tf
5.72 -1.63 Td
(i)Tj
/T1_2 10.91 Tf
6.78 1.63 Td
[(2)-310(G)]TJ
/T1_6 7.97 Tf
17.15 -1.63 Td
(0)Tj
/T1_4 7.97 Tf
(;)Tj
/T1_6 7.97 Tf
(0)Tj
/T1_0 10.91 Tf
15.16 1.63 Td
[(will)-353(b)-28(e)]TJ
-435.84 -21.91 Td
[(able)-413(to)-413(compute)-413(the)-414(subgroup)-413(k)27(ey)]TJ
/T1_1 10.91 Tf
171.64 0 Td
(K)Tj
/T1_6 7.97 Tf
9.26 -1.64 Td
(0)Tj
/T1_4 7.97 Tf
4.24 0 Td
(;)Tj
/T1_6 7.97 Tf
(0)Tj
/T1_0 10.91 Tf
11.58 1.64 Td
[(that)-413(is)-413(also)-414(the)-413(\257nal)-413(group)-414(k)27(ey)]TJ
/T1_1 10.91 Tf
156.22 0 Td
(K)Tj
/T1_0 10.91 Tf
14.55 0 Td
[(\(for)-413(easier)-413(notations,)]TJ
-367.49 -21.92 Td
[(w)27(e)-480(denote)]TJ
/T1_1 10.91 Tf
54.42 0 Td
(K)Tj
/T1_6 7.97 Tf
9.26 -1.64 Td
(0)Tj
/T1_4 7.97 Tf
(;)Tj
/T1_6 7.97 Tf
(0)Tj
/T1_0 10.91 Tf
16.56 1.64 Td
(as)Tj
/T1_1 10.91 Tf
15 0 Td
(K)Tj
/T1_0 10.91 Tf
10.04 0 Td
[(\).)-887(Eac)27(h)]TJ
/T1_8 10.91 Tf
45.67 0 Td
(U)Tj
/T1_4 7.97 Tf
5.73 -1.64 Td
(i)Tj
/T1_2 10.91 Tf
9.09 1.64 Td
[(2)-523(G)]TJ
/T1_6 7.97 Tf
19.47 -1.64 Td
(0)Tj
/T1_4 7.97 Tf
(;)Tj
/T1_6 7.97 Tf
6.59 0 Td
(0)Tj
/T1_0 10.91 Tf
9.97 1.64 Td
[(then)-481(uses)-481(the)-480(subgroup)-481(k)26(ey)]TJ
/T1_1 10.91 Tf
141.86 0 Td
(K)Tj
/T1_6 7.97 Tf
9.26 -1.78 Td
(1)Tj
/T1_4 7.97 Tf
4.24 0 Td
(;k)Tj
/T1_0 10.91 Tf
12.71 1.78 Td
[(of)-481(its)-481(subgroup)]TJ
/T1_2 10.91 Tf
79.81 0 Td
(G)Tj
/T1_6 7.97 Tf
6.49 -1.78 Td
(1)Tj
/T1_4 7.97 Tf
(;k)Tj
/T1_0 10.91 Tf
-456.17 -20.14 Td
[(and)-346(a)-346(symmetric)-346(k)27(ey)-345(encryption)-346(sc)27(heme)]TJ
/T1_5 10.91 Tf
195.51 0 Td
(SKE)Tj
/T1_0 10.91 Tf
23.92 0 Td
[(to)-345(pro)-28(duce)-346(and)-346(broadcast)]TJ
/T1_2 10.91 Tf
126.39 0 Td
(E)Tj
/T1_4 7.97 Tf
5.76 -1.69 Td
(K)Tj
/T1_11 5.98 Tf
7.14 -1.4 Td
(1)Tj
/T1_10 5.98 Tf
3.65 0 Td
(;k)Tj
/T1_0 10.91 Tf
7.34 3.09 Td
(\()Tj
/T1_1 10.91 Tf
(K)Tj
/T1_0 10.91 Tf
14.28 0 Td
[(\))-346(to)-346(its)-346(resp)-28(ectiv)27(e)]TJ
-383.99 -21.91 Td
(subgroup)Tj
/T1_2 10.91 Tf
47.35 0 Td
(G)Tj
/T1_6 7.97 Tf
6.49 -1.78 Td
(1)Tj
/T1_4 7.97 Tf
(;k)Tj
/T1_0 10.91 Tf
11.7 1.78 Td
(.)Tj
/T1_7 10.91 Tf
-65.54 -21.92 Td
[(Phase)-383(4)-383(-)-383(Key)-384(Distribution)]TJ
/T1_0 10.91 Tf
T*
(\()Tj
/T1_1 10.91 Tf
(i)Tj
/T1_0 10.91 Tf
[(\))-419(This)-419(phase)-419(starts)-419(from)-420(second)-419(highest)-419(la)27(y)28(er)]TJ
/T1_2 10.91 Tf
234.07 0 Td
(L)Tj
/T1_6 7.97 Tf
7.52 -1.63 Td
(1)Tj
/T1_0 10.91 Tf
9.31 1.63 Td
[(do)28(wn)-418(to)-420(second)-419(lo)27(w)28(est)-419(la)27(y)28(er)]TJ
/T1_2 10.91 Tf
141.16 0 Td
(L)Tj
/T1_4 7.97 Tf
7.52 -1.77 Td
(h)Tj
/T1_3 7.97 Tf
(\241)Tj
/T1_6 7.97 Tf
(2)Tj
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Q
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q
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BT
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ET
q
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BT
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BT
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ET
q
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BT
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BT
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BT
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ET
q
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BT
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ET
q
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BT
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q
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Q
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q
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Q
Q
BT
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ET
q
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Q
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Q
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BT
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ET
q
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Q
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BT
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BT
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ET
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BT
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ET
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Q
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BT
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BT
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BT
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ET
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BT
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ET
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Q
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BT
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ET
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Q
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Q
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Q
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S
Q
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[(As)-267(sho)27(wn)-266(in)-268(T)83(able)-267(7.1,)-280(the)-267(BD)-268(requires)-267(eac)27(h)-267(user)-267(to)-267(p)-28(erform)-267(three)-267(mo)-28(dular)-267(exp)-28(onen)27(tiations)-267(and)]TJ
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23.93 0 Td
(p)Tj
/T1_0 10.91 Tf
(.)Tj
/T1_5 10.91 Tf
14.98 0 Td
(S)Tj
/T1_2 7.97 Tf
5.72 -1.78 Td
(h)Tj
/T1_3 7.97 Tf
(\241)Tj
/T1_4 7.97 Tf
(1)Tj
/T1_2 7.97 Tf
15.7 0 Td
(;j)Tj
/T1_0 10.91 Tf
10.9 1.78 Td
[(then)-382(signs)]TJ
/T1_5 10.91 Tf
52.7 0 Td
(S)Tj
/T1_2 7.97 Tf
5.72 -1.78 Td
(h)Tj
/T1_3 7.97 Tf
(\241)Tj
/T1_4 7.97 Tf
11.47 0 Td
(1)Tj
/T1_2 7.97 Tf
(;j)Tj
/T1_1 10.91 Tf
10.96 1.78 Td
(jj)Tj
/T1_6 10.91 Tf
6.06 0 Td
(z)Tj
/T1_2 7.97 Tf
5.07 -1.78 Td
(h)Tj
/T1_3 7.97 Tf
(\241)Tj
/T1_4 7.97 Tf
11.47 0 Td
(1)Tj
/T1_2 7.97 Tf
(;j)Tj
/T1_0 10.91 Tf
-456.91 -20.14 Td
[(and)-409(obtains)-410(signature)]TJ
/T1_6 10.91 Tf
109.29 0 Td
(\276)Tj
/T1_2 7.97 Tf
6.23 -1.77 Td
(h)Tj
/T1_3 7.97 Tf
(\241)Tj
/T1_4 7.97 Tf
11.47 0 Td
(1)Tj
/T1_2 7.97 Tf
(;j)Tj
/T1_0 10.91 Tf
15.43 1.77 Td
[(and)-410(sends)]TJ
/T1_1 10.91 Tf
52.08 0 Td
(f)Tj
/T1_5 10.91 Tf
(S)Tj
/T1_2 7.97 Tf
11.18 -1.77 Td
(h)Tj
/T1_3 7.97 Tf
(\241)Tj
/T1_4 7.97 Tf
(1)Tj
/T1_2 7.97 Tf
15.7 0 Td
(;j)Tj
/T1_1 10.91 Tf
6.73 1.77 Td
(jj)Tj
/T1_6 10.91 Tf
6.06 0 Td
(z)Tj
/T1_2 7.97 Tf
5.07 -1.77 Td
(h)Tj
/T1_3 7.97 Tf
(\241)Tj
/T1_4 7.97 Tf
(1)Tj
/T1_2 7.97 Tf
15.7 0 Td
(;j)Tj
/T1_1 10.91 Tf
6.73 1.77 Td
(jj)Tj
/T1_6 10.91 Tf
6.06 0 Td
(\276)Tj
/T1_2 7.97 Tf
6.23 -1.77 Td
(h)Tj
/T1_3 7.97 Tf
(\241)Tj
/T1_4 7.97 Tf
(1)Tj
/T1_2 7.97 Tf
15.7 0 Td
(;j)Tj
/T1_1 10.91 Tf
6.73 1.77 Td
(jj)Tj
/T1_5 10.91 Tf
6.06 0 Td
(cert)Tj
/T1_0 10.91 Tf
22.9 0 Td
([)Tj
/T1_5 10.91 Tf
(S)Tj
/T1_2 7.97 Tf
8.75 -1.77 Td
(h)Tj
/T1_3 7.97 Tf
(\241)Tj
/T1_4 7.97 Tf
11.47 0 Td
(1)Tj
/T1_2 7.97 Tf
(;j)Tj
/T1_0 10.91 Tf
10.96 1.77 Td
(])Tj
/T1_1 10.91 Tf
(g)Tj
/T1_0 10.91 Tf
12.96 0 Td
[(to)-409(its)-410(subgroup)-410(con-)]TJ
-369.49 -21.91 Td
(troller)Tj
/T1_5 10.91 Tf
32.78 0 Td
(S)Tj
/T1_2 7.97 Tf
5.72 -1.78 Td
(h)Tj
/T1_3 7.97 Tf
(\241)Tj
/T1_4 7.97 Tf
11.47 0 Td
(2)Tj
/T1_2 7.97 Tf
(;i)Tj
/T1_0 10.91 Tf
13.6 1.78 Td
[(at)-333(la)27(y)28(er)]TJ
/T1_1 10.91 Tf
39.71 0 Td
(L)Tj
/T1_2 7.97 Tf
7.53 -1.78 Td
(h)Tj
/T1_3 7.97 Tf
(\241)Tj
/T1_4 7.97 Tf
(2)Tj
/T1_0 10.91 Tf
19.83 1.78 Td
(where)Tj
/T1_6 10.91 Tf
31.53 0 Td
(i)Tj
/T1_0 10.91 Tf
6.79 0 Td
(=)Tj
/T1_1 10.91 Tf
11.51 0 Td
(b)Tj
/T1_2 7.97 Tf
6.04 4.93 Td
(j)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 186.51 -95.9 cm
0 0 m
3.89 0 l
S
Q
Q
BT
/T1_2 7.97 Tf
1.0003 0 0 1.0003 258.6723 667.4113 Tm
(c)Tj
/T1_1 10.91 Tf
4.97 3.76 Td
(c)Tj
/T1_0 10.91 Tf
4.85 0 Td
(.)Tj
-196.44 -21.92 Td
(Phase)Tj
1.0003 0 0 1.0003 72 769.82 Tm
31.726 -120.54 Td
(2a)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 0 -122.06 cm
0 0 m
42.62 0 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 118.273 649.2462 Tm
(:)Tj
-46.26 -21.91 Td
(\()Tj
/T1_6 10.91 Tf
(i)Tj
/T1_0 10.91 Tf
(\))Tj
1.0003 0 0 1.0003 72 769.82 Tm
17.535 -142.45 Td
[(This)-486(phase)-485(starts)-486(from)-485(second)-486(lo)27(w)28(est)-485(la)27(y)28(er)]TJ
/T1_1 10.91 Tf
217.475 0 Td
(L)Tj
/T1_2 7.97 Tf
7.52 -1.78 Td
(h)Tj
/T1_3 7.97 Tf
(\241)Tj
/T1_4 7.97 Tf
11.47 0 Td
(2)Tj
/T1_0 10.91 Tf
10.02 1.78 Td
[(up)-485(to)-486(second)-486(highest)-485(la)27(y)27(er)]TJ
/T1_1 10.91 Tf
136.61 0 Td
(L)Tj
/T1_4 7.97 Tf
7.52 -1.64 Td
(1)Tj
/T1_0 10.91 Tf
4.73 1.64 Td
[(.)-901(F)83(or)-485(eac)27(h)]TJ
-412.88 -21.92 Td
[(la)27(y)28(er)]TJ
/T1_1 10.91 Tf
27.86 0 Td
(L)Tj
/T1_2 7.97 Tf
7.52 -1.64 Td
(v)Tj
/T1_0 10.91 Tf
10.02 1.64 Td
[(for)-468(1)]TJ
/T1_1 10.91 Tf
29.11 0 Td
(\267)Tj
/T1_6 10.91 Tf
13.97 0 Td
(v)Tj
/T1_1 10.91 Tf
11.17 0 Td
(\267)Tj
/T1_6 10.91 Tf
13.97 0 Td
(h)Tj
/T1_1 10.91 Tf
9.69 0 Td
(\241)Tj
/T1_0 10.91 Tf
11.89 0 Td
[(2,)-502(eac)26(h)-467(subgroup)-469(con)27(troller)]TJ
/T1_5 10.91 Tf
139.12 0 Td
(S)Tj
/T1_2 7.97 Tf
5.72 -1.64 Td
[(v)-36(;j)]TJ
/T1_0 10.91 Tf
16.26 1.64 Td
[(for)-468(0)]TJ
/T1_1 10.91 Tf
29.11 0 Td
(\267)Tj
/T1_6 10.91 Tf
13.97 0 Td
(j)Tj
/T1_1 10.91 Tf
10.6 0 Td
(\267)Tj
/T1_6 10.91 Tf
13.97 0 Td
(c)Tj
/T1_2 7.97 Tf
4.72 3.96 Td
(v)Tj
/T1_4 7.97 Tf
4.41 0 Td
(+1)Tj
/T1_1 10.91 Tf
14.72 -3.96 Td
(\241)Tj
/T1_0 10.91 Tf
11.89 0 Td
[(1)-469(of)-468(subgroup)]TJ
/T1_1 10.91 Tf
-399.69 -21.92 Td
(G)Tj
/T1_2 7.97 Tf
6.49 -1.63 Td
(v)Tj
/T1_4 7.97 Tf
4.41 0 Td
(+1)Tj
/T1_2 7.97 Tf
10.81 0 Td
(;j)Tj
/T1_0 10.91 Tf
9.91 1.63 Td
(=)Tj
/T1_1 10.91 Tf
11.65 0 Td
(f)Tj
/T1_5 10.91 Tf
(S)Tj
/T1_2 7.97 Tf
11.18 -1.63 Td
(v)Tj
/T1_4 7.97 Tf
4.41 0 Td
(+1)Tj
/T1_2 7.97 Tf
[(;j)-57(c)]TJ
/T1_6 10.91 Tf
21.21 1.63 Td
(;)Tj
/T1_5 10.91 Tf
4.85 0 Td
(S)Tj
/T1_2 7.97 Tf
5.73 -1.63 Td
(v)Tj
/T1_4 7.97 Tf
4.41 0 Td
(+1)Tj
/T1_2 7.97 Tf
10.81 0 Td
[(;j)-58(c)]TJ
/T1_4 7.97 Tf
9.9 0 Td
(+1)Tj
/T1_6 10.91 Tf
11.32 1.63 Td
(;)Tj
/T1_5 10.91 Tf
4.85 0 Td
(S)Tj
/T1_2 7.97 Tf
5.72 -1.63 Td
(v)Tj
/T1_4 7.97 Tf
4.41 0 Td
(+1)Tj
/T1_2 7.97 Tf
[(;j)-57(c)]TJ
/T1_4 7.97 Tf
(+2)Tj
/T1_6 10.91 Tf
32.04 1.63 Td
(;)Tj
/T1_1 10.91 Tf
4.84 0 Td
[(\242)-166(\242)-167(\242)]TJ
/T1_6 10.91 Tf
16.36 0 Td
(;)Tj
/T1_5 10.91 Tf
6.75 0 Td
(S)Tj
/T1_2 7.97 Tf
5.73 -1.63 Td
(v)Tj
/T1_4 7.97 Tf
4.41 0 Td
(+1)Tj
/T1_2 7.97 Tf
10.81 0 Td
[(;j)-58(c)]TJ
/T1_4 7.97 Tf
(+)Tj
/T1_2 7.97 Tf
(c)Tj
/T1_3 7.97 Tf
(\241)Tj
/T1_4 7.97 Tf
(1)Tj
/T1_1 10.91 Tf
31.47 1.63 Td
(g)Tj
/T1_0 10.91 Tf
9.18 0 Td
[(\257rst)-340(v)27(eri\257es)-341(the)-341(certi\257cates)]TJ
/T1_5 10.91 Tf
132.69 0 Td
(cert)Tj
/T1_0 10.91 Tf
([)Tj
/T1_5 10.91 Tf
(S)Tj
/T1_2 7.97 Tf
31.66 -1.77 Td
(v)Tj
/T1_4 7.97 Tf
4.41 0 Td
(+1)Tj
/T1_2 7.97 Tf
[(;j)-57(c)]TJ
/T1_4 7.97 Tf
(+)Tj
/T1_2 7.97 Tf
(k)Tj
/T1_0 10.91 Tf
32.42 1.77 Td
(])Tj
-464.84 -21.91 Td
[(and)-400(signatures)]TJ
/T1_6 10.91 Tf
74.32 0 Td
(\276)Tj
/T1_2 7.97 Tf
6.24 -1.78 Td
(v)Tj
/T1_4 7.97 Tf
4.4 0 Td
(+1)Tj
/T1_2 7.97 Tf
[(;j)-57(c)]TJ
/T1_4 7.97 Tf
(+)Tj
/T1_2 7.97 Tf
27.31 0 Td
(k)Tj
/T1_0 10.91 Tf
9.48 1.78 Td
[(sen)27(t)-400(b)27(y)-399(its)-401(subgroup)-400(mem)27(b)-27(ers)]TJ
/T1_5 10.91 Tf
150.29 0 Td
(S)Tj
/T1_2 7.97 Tf
5.73 -1.78 Td
(v)Tj
/T1_4 7.97 Tf
4.41 0 Td
(+1)Tj
/T1_2 7.97 Tf
10.81 0 Td
[(;j)-58(c)]TJ
/T1_4 7.97 Tf
(+)Tj
/T1_2 7.97 Tf
(k)Tj
/T1_1 10.91 Tf
25.86 1.78 Td
[(2)-389(G)]TJ
/T1_2 7.97 Tf
18.01 -1.64 Td
(v)Tj
/T1_4 7.97 Tf
4.4 0 Td
(+1)Tj
/T1_2 7.97 Tf
(;j)Tj
/T1_0 10.91 Tf
21.92 1.64 Td
[(for)-400(0)]TJ
/T1_1 10.91 Tf
27.13 0 Td
(\267)Tj
/T1_6 10.91 Tf
12.73 0 Td
(k)Tj
/T1_1 10.91 Tf
10.27 0 Td
(\267)Tj
/T1_6 10.91 Tf
12.74 0 Td
(c)Tj
/T1_1 10.91 Tf
7.63 0 Td
(\241)Tj
/T1_0 10.91 Tf
11.39 0 Td
[(1.)-646(If)]TJ
-445.07 -21.92 Td
[(the)-394(v)26(eri\257cations)-393(are)-395(not)-395(correct,)-410(then)-395(eac)27(h)-394(subgroup)-395(con)27(troller)]TJ
/T1_5 10.91 Tf
308.27 0 Td
(S)Tj
/T1_2 7.97 Tf
5.73 -1.64 Td
[(v)-35(;j)]TJ
/T1_0 10.91 Tf
15.45 1.64 Td
(rejects)Tj
/T1_5 10.91 Tf
34.99 0 Td
(S)Tj
/T1_2 7.97 Tf
5.73 -1.78 Td
(v)Tj
/T1_4 7.97 Tf
4.4 0 Td
(+1)Tj
/T1_2 7.97 Tf
[(;j)-57(c)]TJ
/T1_4 7.97 Tf
(+)Tj
/T1_2 7.97 Tf
27.31 0 Td
(k)Tj
/T1_0 10.91 Tf
5.12 1.78 Td
[(.)-628(Otherwise,)]TJ
/T1_5 10.91 Tf
-407 -21.92 Td
(S)Tj
/T1_2 7.97 Tf
5.73 -1.63 Td
[(v)-35(;j)]TJ
/T1_0 10.91 Tf
16.47 1.63 Td
[(selects)-488(random)]TJ
/T1_6 10.91 Tf
77.46 0 Td
(r)Tj
/T1_2 7.97 Tf
4.92 -1.63 Td
[(v)-35(;j)]TJ
/T1_1 10.91 Tf
17 1.63 Td
(2)Tj
/T1_6 10.91 Tf
13.12 0 Td
(Z)Tj
/T1_3 7.97 Tf
8.23 3.96 Td
(\244)Tj
/T1_2 7.97 Tf
-0.78 -6.65 Td
(q)Tj
/T1_0 10.91 Tf
10.84 2.69 Td
[(and)-488(computes)-549(\271)]TJ
/T1_6 10.91 Tf
73.13 0 Td
(z)Tj
/T1_2 7.97 Tf
5.07 -1.63 Td
[(v)-36(;j)]TJ
/T1_0 10.91 Tf
17 1.63 Td
(=)Tj
/T1_6 10.91 Tf
14.34 0 Td
(g)Tj
/T1_2 7.97 Tf
5.59 3.96 Td
(r)Tj
/T1_7 5.98 Tf
3.82 -1.21 Td
[(v)-36(;j)]TJ
/T1_0 10.91 Tf
13.65 -2.75 Td
[(mo)-27(d)]TJ
/T1_6 10.91 Tf
23.93 0 Td
(p)Tj
/T1_0 10.91 Tf
10.82 0 Td
[(and)-488(Di\261e-Hellman)-489(\(DH\))-489(k)27(eys)]TJ
/T1_6 10.91 Tf
-320.34 -21.91 Td
(T)Tj
/T1_2 7.97 Tf
6.37 -1.78 Td
(v)Tj
/T1_4 7.97 Tf
4.41 0 Td
(+1)Tj
/T1_2 7.97 Tf
[(;j)-57(c)]TJ
/T1_4 7.97 Tf
(+)Tj
/T1_2 7.97 Tf
27.31 0 Td
(k)Tj
/T1_0 10.91 Tf
8.85 1.78 Td
(=)Tj
/T1_6 10.91 Tf
12.22 0 Td
(z)Tj
/T1_2 7.97 Tf
5.55 6.13 Td
(r)Tj
/T1_7 5.98 Tf
3.82 -1.21 Td
[(v)-35(;j)]TJ
/T1_2 7.97 Tf
-4.3 -8.45 Td
(v)Tj
/T1_4 7.97 Tf
4.41 0 Td
(+1)Tj
/T1_2 7.97 Tf
10.81 0 Td
[(;j)-58(c)]TJ
/T1_4 7.97 Tf
9.9 0 Td
(+)Tj
/T1_2 7.97 Tf
6.59 0 Td
(k)Tj
/T1_0 10.91 Tf
8.15 3.53 Td
[(mo)-27(d)]TJ
/T1_6 10.91 Tf
23.93 0 Td
(p)Tj
/T1_0 10.91 Tf
9.55 0 Td
[(that)-371(it)-372(shares)-372(with)-373(eac)27(h)-371(subgroup)-372(mem)27(b)-27(er)]TJ
/T1_5 10.91 Tf
208.93 0 Td
(S)Tj
/T1_2 7.97 Tf
5.73 -1.78 Td
(v)Tj
/T1_4 7.97 Tf
4.4 0 Td
(+1)Tj
/T1_2 7.97 Tf
[(;j)-57(c)]TJ
/T1_4 7.97 Tf
(+)Tj
/T1_2 7.97 Tf
27.31 0 Td
(k)Tj
/T1_0 10.91 Tf
5.12 1.78 Td
[(.)-560(Eac)27(h)]TJ
/T1_5 10.91 Tf
36.68 0 Td
(S)Tj
/T1_2 7.97 Tf
5.73 -1.64 Td
[(v)-35(;j)]TJ
/T1_0 10.91 Tf
15.19 1.64 Td
(then)Tj
-446.66 -21.92 Td
[(computes)-332(the)-333(subgroup)-333(k)27(ey)]TJ
/T1_6 10.91 Tf
134.34 0 Td
(K)Tj
/T1_2 7.97 Tf
9.26 -1.64 Td
(v)Tj
/T1_4 7.97 Tf
4.41 0 Td
(+1)Tj
/T1_2 7.97 Tf
(;j)Tj
/T1_0 10.91 Tf
20.58 1.64 Td
[(=)-337(\271)]TJ
/T1_6 10.91 Tf
11.51 0 Td
(z)Tj
/T1_2 7.97 Tf
5.55 6.13 Td
(r)Tj
/T1_7 5.98 Tf
3.82 -1.21 Td
[(v)-36(;j)]TJ
/T1_2 7.97 Tf
-4.3 -8.18 Td
[(v)-36(;j)]TJ
/T1_1 10.91 Tf
17.33 3.26 Td
(\242)Tj
/T1_10 10.91 Tf
5.45 8.18 Td
(Q)Tj
/T1_2 7.97 Tf
10.3 -3.15 Td
(c)Tj
/T1_3 7.97 Tf
3.66 0 Td
(\241)Tj
/T1_4 7.97 Tf
6.59 0 Td
(1)Tj
/T1_2 7.97 Tf
-10.25 -8.25 Td
(k)Tj
/T1_4 7.97 Tf
4.62 0 Td
(=0)Tj
/T1_6 10.91 Tf
13.13 3.22 Td
(T)Tj
/T1_2 7.97 Tf
6.37 -1.78 Td
(v)Tj
/T1_4 7.97 Tf
4.41 0 Td
(+1)Tj
/T1_2 7.97 Tf
[(;j)-57(c)]TJ
/T1_4 7.97 Tf
(+)Tj
/T1_2 7.97 Tf
27.31 0 Td
(k)Tj
/T1_0 10.91 Tf
8.14 1.78 Td
[(mo)-28(d)]TJ
/T1_6 10.91 Tf
23.94 0 Td
(p)Tj
/T1_0 10.91 Tf
5.48 0 Td
[(.)-444(Next,)]TJ
/T1_5 10.91 Tf
37.56 0 Td
(S)Tj
/T1_2 7.97 Tf
5.73 -1.64 Td
[(v)-35(;j)]TJ
/T1_0 10.91 Tf
14.77 1.64 Td
(encrypts)Tj
/T1_6 10.91 Tf
44.01 0 Td
(K)Tj
/T1_2 7.97 Tf
9.27 -1.64 Td
(v)Tj
/T1_4 7.97 Tf
4.4 0 Td
(+1)Tj
/T1_2 7.97 Tf
(;j)Tj
/T1_1 10.91 Tf
17.56 1.64 Td
(jj)Tj
/T1_5 10.91 Tf
6.05 0 Td
(S)Tj
/T1_2 7.97 Tf
5.73 -1.64 Td
[(v)-35(;j)]TJ
/T1_0 10.91 Tf
-456.73 -20.28 Td
(using)Tj
/T1_6 10.91 Tf
28.6 0 Td
(T)Tj
/T1_2 7.97 Tf
6.37 -1.77 Td
(v)Tj
/T1_4 7.97 Tf
4.41 0 Td
(+1)Tj
/T1_2 7.97 Tf
[(;j)-57(c)]TJ
/T1_4 7.97 Tf
(+)Tj
/T1_2 7.97 Tf
27.31 0 Td
(k)Tj
/T1_0 10.91 Tf
8.81 1.77 Td
[(and)-339(a)-339(symmetric)-339(k)27(ey)-338(encryption)]TJ
/T1_11 10.91 Tf
157.66 0 Td
(SKE)Tj
/T1_0 10.91 Tf
23.85 0 Td
[(to)-338(obtain)]TJ
/T1_5 10.91 Tf
47.38 0 Td
(c)Tj
/T1_2 7.97 Tf
5.73 -1.77 Td
(v)Tj
/T1_4 7.97 Tf
4.4 0 Td
(+1)Tj
/T1_2 7.97 Tf
[(;j)-57(c)]TJ
/T1_4 7.97 Tf
(+)Tj
/T1_2 7.97 Tf
27.31 0 Td
(k)Tj
/T1_0 10.91 Tf
8.25 1.77 Td
(=)Tj
/T1_1 10.91 Tf
11.61 0 Td
(E)Tj
/T1_2 7.97 Tf
5.76 -1.68 Td
(T)Tj
/T1_7 5.98 Tf
4.93 -1.41 Td
(v)Tj
/T1_9 5.98 Tf
3.95 0 Td
(+1)Tj
/T1_7 5.98 Tf
9.24 0 Td
[(;j)-57(c)]TJ
/T1_9 5.98 Tf
(+)Tj
/T1_7 5.98 Tf
(k)Tj
/T1_0 10.91 Tf
19.67 3.09 Td
(\()Tj
/T1_6 10.91 Tf
(K)Tj
/T1_2 7.97 Tf
13.51 -1.63 Td
(v)Tj
/T1_4 7.97 Tf
4.4 0 Td
(+1)Tj
/T1_2 7.97 Tf
(;j)Tj
/T1_1 10.91 Tf
17.55 1.63 Td
(jj)Tj
/T1_5 10.91 Tf
6.06 0 Td
(S)Tj
/T1_2 7.97 Tf
5.73 -1.63 Td
[(v)-35(;j)]TJ
/T1_0 10.91 Tf
11.14 1.63 Td
(\))Tj
-463.63 -21.91 Td
[(for)-338(0)]TJ
/T1_1 10.91 Tf
25.31 0 Td
(\267)Tj
/T1_6 10.91 Tf
11.6 0 Td
(k)Tj
/T1_1 10.91 Tf
9.14 0 Td
(\267)Tj
/T1_6 10.91 Tf
11.6 0 Td
(c)Tj
/T1_1 10.91 Tf
7.17 0 Td
(\241)Tj
/T1_0 10.91 Tf
10.94 0 Td
[(1.)-458(Eac)26(h)]TJ
/T1_5 10.91 Tf
40.65 0 Td
(S)Tj
/T1_2 7.97 Tf
5.73 -1.64 Td
[(v)-35(;j)]TJ
/T1_0 10.91 Tf
14.83 1.64 Td
[(then)-337(computes)]TJ
/T1_6 10.91 Tf
73.47 0 Td
(z)Tj
/T1_2 7.97 Tf
5.08 -1.64 Td
[(v)-35(;j)]TJ
/T1_0 10.91 Tf
14.25 1.64 Td
(=)Tj
/T1_6 10.91 Tf
11.6 0 Td
(g)Tj
/T1_12 7.97 Tf
5.59 3.95 Td
(H)Tj
/T1_4 7.97 Tf
(\()Tj
/T1_2 7.97 Tf
(K)Tj
/T1_7 5.98 Tf
16.41 -1.21 Td
(v)Tj
/T1_9 5.98 Tf
3.95 0 Td
(+1)Tj
/T1_7 5.98 Tf
9.24 0 Td
(;j)Tj
/T1_4 7.97 Tf
6.17 1.21 Td
(\))Tj
/T1_0 10.91 Tf
6.82 -3.95 Td
[(mo)-27(d)]TJ
/T1_6 10.91 Tf
23.93 0 Td
(p)Tj
/T1_0 10.91 Tf
[(.)-458(Next,)-340(eac)27(h)]TJ
/T1_5 10.91 Tf
67.87 0 Td
(S)Tj
/T1_2 7.97 Tf
5.72 -1.64 Td
[(v)-36(;j)]TJ
/T1_0 10.91 Tf
14.83 1.64 Td
(signs)Tj
/T1_5 10.91 Tf
26.83 0 Td
(S)Tj
/T1_2 7.97 Tf
5.73 -1.64 Td
[(v)-35(;j)]TJ
/T1_1 10.91 Tf
11.14 1.64 Td
(jj)Tj
/T1_6 10.91 Tf
6.06 0 Td
(z)Tj
/T1_2 7.97 Tf
5.07 -1.64 Td
[(v)-35(;j)]TJ
/T1_0 10.91 Tf
-456.73 -20.28 Td
(and)Tj
/T1_5 10.91 Tf
21.08 0 Td
(S)Tj
/T1_2 7.97 Tf
5.72 -1.64 Td
[(v)-36(;j)]TJ
/T1_1 10.91 Tf
11.15 1.64 Td
(jj)Tj
/T1_0 10.91 Tf
6.71 0 Td
(\271)Tj
/T1_6 10.91 Tf
-0.66 0 Td
(z)Tj
/T1_2 7.97 Tf
5.08 -1.64 Td
[(v)-35(;j)]TJ
/T1_1 10.91 Tf
11.14 1.64 Td
(jj)Tj
/T1_5 10.91 Tf
6.06 0 Td
(c)Tj
/T1_2 7.97 Tf
5.72 -1.78 Td
(v)Tj
/T1_4 7.97 Tf
4.41 0 Td
(+1)Tj
/T1_2 7.97 Tf
[(;j)-57(c)]TJ
/T1_4 7.97 Tf
(+)Tj
/T1_2 7.97 Tf
(k)Tj
/T1_0 10.91 Tf
35.93 1.78 Td
[(for)-321(0)]TJ
/T1_1 10.91 Tf
25.05 0 Td
(\267)Tj
/T1_6 10.91 Tf
11.51 0 Td
(k)Tj
/T1_1 10.91 Tf
9.05 0 Td
(\267)Tj
/T1_6 10.91 Tf
11.51 0 Td
(c)Tj
/T1_1 10.91 Tf
6.89 0 Td
(\241)Tj
/T1_0 10.91 Tf
10.65 0 Td
[(1)-322(and)-321(obtains)-322(signatures)]TJ
/T1_6 10.91 Tf
119.67 0 Td
(\276)Tj
/T1_2 7.97 Tf
6.24 -1.64 Td
[(v)-35(;j)]TJ
/T1_0 10.91 Tf
14.65 1.64 Td
[(and)-374(\271)]TJ
/T1_6 10.91 Tf
21.07 0 Td
(\276)Tj
/T1_2 7.97 Tf
6.24 -1.64 Td
[(v)-35(;j)]TJ
/T1_0 10.91 Tf
14.65 1.64 Td
[(resp)-27(ectiv)27(ely)83(.)-439(Finally)82(,)]TJ
/T1_5 10.91 Tf
-369.52 -21.92 Td
(S)Tj
/T1_2 7.97 Tf
5.73 -1.63 Td
[(v)-35(;j)]TJ
/T1_0 10.91 Tf
16.11 1.63 Td
(broadcasts)Tj
/T1_1 10.91 Tf
55.42 0 Td
(f)Tj
/T1_5 10.91 Tf
(S)Tj
/T1_2 7.97 Tf
11.18 -1.63 Td
[(v)-35(;j)]TJ
/T1_1 10.91 Tf
11.14 1.63 Td
(jj)Tj
/T1_6 10.91 Tf
6.06 0 Td
(z)Tj
/T1_2 7.97 Tf
5.07 -1.63 Td
[(v)-35(;j)]TJ
/T1_1 10.91 Tf
11.14 1.63 Td
(jj)Tj
/T1_6 10.91 Tf
6.06 0 Td
(\276)Tj
/T1_2 7.97 Tf
6.23 -1.63 Td
[(v)-36(;j)]TJ
/T1_1 10.91 Tf
11.14 1.63 Td
(jj)Tj
/T1_5 10.91 Tf
6.06 0 Td
(cert)Tj
/T1_0 10.91 Tf
22.9 0 Td
([)Tj
/T1_5 10.91 Tf
(S)Tj
/T1_2 7.97 Tf
8.76 -1.63 Td
[(v)-35(;j)]TJ
/T1_0 10.91 Tf
11.14 1.63 Td
(])Tj
/T1_1 10.91 Tf
(g)Tj
/T1_0 10.91 Tf
13.46 0 Td
[(to)-456(its)-456(subgroup)-456(con)26(troller)]TJ
/T1_5 10.91 Tf
130.09 0 Td
(S)Tj
/T1_2 7.97 Tf
5.72 -1.63 Td
(v)Tj
/T1_3 7.97 Tf
4.41 0 Td
(\241)Tj
/T1_4 7.97 Tf
6.59 0 Td
(1)Tj
/T1_2 7.97 Tf
(;i)Tj
/T1_0 10.91 Tf
14.94 1.63 Td
[(at)-456(la)27(y)28(er)]TJ
/T1_1 10.91 Tf
42.4 0 Td
(L)Tj
/T1_2 7.97 Tf
7.52 -1.63 Td
(v)Tj
/T1_3 7.97 Tf
4.41 0 Td
(\241)Tj
/T1_4 7.97 Tf
(1)Tj
/T1_0 10.91 Tf
16.29 1.63 Td
(where)Tj
/T1_6 10.91 Tf
-439.97 -21.91 Td
(i)Tj
/T1_0 10.91 Tf
7 0 Td
(=)Tj
/T1_1 10.91 Tf
11.72 0 Td
(b)Tj
/T1_2 7.97 Tf
6.04 4.93 Td
(j)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 24.76 -402.73 cm
0 0 m
3.89 0 l
S
Q
Q
BT
/T1_2 7.97 Tf
1.0003 0 0 1.0003 96.877 360.4954 Tm
(c)Tj
/T1_1 10.91 Tf
4.97 3.76 Td
(c)Tj
/T1_0 10.91 Tf
8.61 0 Td
(and)Tj
/T1_1 10.91 Tf
21.34 0 Td
(f)Tj
/T1_5 10.91 Tf
(S)Tj
/T1_2 7.97 Tf
11.17 -1.64 Td
(v)Tj
1.0003 0 0 1.0003 72 769.82 Tm
75.367 -407.09 Td
(;j)Tj
/T1_1 10.91 Tf
6.743 1.64 Td
(jj)Tj
/T1_0 10.91 Tf
6.71 0 Td
(\271)Tj
/T1_6 10.91 Tf
-0.66 0 Td
(z)Tj
/T1_2 7.97 Tf
5.08 -1.64 Td
[(v)-35(;j)]TJ
/T1_1 10.91 Tf
11.14 1.64 Td
(jj)Tj
/T1_5 10.91 Tf
6.06 0 Td
(c)Tj
/T1_2 7.97 Tf
5.72 -1.78 Td
(v)Tj
/T1_4 7.97 Tf
4.41 0 Td
(+1)Tj
/T1_2 7.97 Tf
[(;j)-57(c)]TJ
/T1_4 7.97 Tf
(+)Tj
/T1_2 7.97 Tf
(k)Tj
/T1_1 10.91 Tf
32.42 1.78 Td
(jj)Tj
/T1_0 10.91 Tf
6.65 0 Td
(\271)Tj
/T1_6 10.91 Tf
-0.59 0 Td
(\276)Tj
/T1_2 7.97 Tf
6.23 -1.64 Td
[(v)-36(;j)]TJ
/T1_1 10.91 Tf
11.14 1.64 Td
(jj)Tj
/T1_5 10.91 Tf
6.06 0 Td
(cert)Tj
/T1_0 10.91 Tf
([)Tj
/T1_5 10.91 Tf
25.93 0 Td
(S)Tj
/T1_2 7.97 Tf
5.73 -1.64 Td
[(v)-35(;j)]TJ
/T1_0 10.91 Tf
11.14 1.64 Td
(])Tj
/T1_1 10.91 Tf
(g)Tj
/T1_0 10.91 Tf
12.25 0 Td
[(for)-344(0)]TJ
/T1_1 10.91 Tf
25.51 0 Td
(\267)Tj
/T1_6 10.91 Tf
11.72 0 Td
(k)Tj
/T1_1 10.91 Tf
9.27 0 Td
(\267)Tj
/T1_6 10.91 Tf
11.72 0 Td
(c)Tj
/T1_1 10.91 Tf
7.23 0 Td
(\241)Tj
/T1_0 10.91 Tf
10.99 0 Td
[(1)-344(to)-345(its)-345(subgroup)]TJ
/T1_1 10.91 Tf
85.48 0 Td
(G)Tj
/T1_2 7.97 Tf
6.49 -1.64 Td
(v)Tj
/T1_4 7.97 Tf
4.41 0 Td
(+1)Tj
/T1_2 7.97 Tf
(;j)Tj
/T1_0 10.91 Tf
21.31 1.64 Td
[(at)-345(la)27(y)28(er)]TJ
/T1_1 10.91 Tf
-431.66 -21.92 Td
(L)Tj
/T1_2 7.97 Tf
7.52 -1.63 Td
(v)Tj
/T1_4 7.97 Tf
4.41 0 Td
(+1)Tj
/T1_0 10.91 Tf
11.32 1.63 Td
(.)Tj
-23.25 -21.92 Td
(\()Tj
/T1_6 10.91 Tf
(ii)Tj
/T1_0 10.91 Tf
[(\))-257(F)82(or)-257(La)27(y)28(er)]TJ
/T1_1 10.91 Tf
66.91 0 Td
(L)Tj
/T1_4 7.97 Tf
7.53 -1.63 Td
(0)Tj
/T1_0 10.91 Tf
4.73 1.63 Td
[(,)-272(eac)26(h)]TJ
/T1_5 10.91 Tf
29.72 0 Td
(S)Tj
/T1_4 7.97 Tf
5.73 -1.63 Td
(0)Tj
/T1_2 7.97 Tf
(;j)Tj
/T1_0 10.91 Tf
13.78 1.63 Td
[(for)-258(0)]TJ
/T1_1 10.91 Tf
24.35 0 Td
(\267)Tj
/T1_6 10.91 Tf
11.52 0 Td
(j)Tj
/T1_1 10.91 Tf
8.14 0 Td
(\267)Tj
/T1_6 10.91 Tf
11.51 0 Td
(c)Tj
/T1_1 10.91 Tf
5.5 0 Td
(\241)Tj
/T1_0 10.91 Tf
9.27 0 Td
[(1)-257(of)-258(subgroup)]TJ
/T1_1 10.91 Tf
66.4 0 Td
(G)Tj
/T1_4 7.97 Tf
6.48 -1.63 Td
(1)Tj
/T1_2 7.97 Tf
4.24 0 Td
(;j)Tj
/T1_0 10.91 Tf
9.76 1.63 Td
(=)Tj
/T1_1 10.91 Tf
11.51 0 Td
(f)Tj
/T1_5 10.91 Tf
(S)Tj
/T1_4 7.97 Tf
11.18 -1.63 Td
(1)Tj
/T1_2 7.97 Tf
[(;j)-57(c)]TJ
/T1_6 10.91 Tf
14.63 1.63 Td
(;)Tj
/T1_5 10.91 Tf
4.85 0 Td
(S)Tj
/T1_4 7.97 Tf
5.72 -1.63 Td
(1)Tj
/T1_2 7.97 Tf
4.24 0 Td
[(;j)-57(c)]TJ
/T1_4 7.97 Tf
(+1)Tj
/T1_6 10.91 Tf
21.21 1.63 Td
(;)Tj
/T1_5 10.91 Tf
4.85 0 Td
(S)Tj
/T1_4 7.97 Tf
5.73 -1.63 Td
(1)Tj
/T1_2 7.97 Tf
[(;j)-57(c)]TJ
/T1_4 7.97 Tf
(+2)Tj
/T1_6 10.91 Tf
25.45 1.63 Td
(;)Tj
/T1_1 10.91 Tf
4.84 0 Td
[(\242)-167(\242)-166(\242)]TJ
/T1_6 10.91 Tf
16.36 0 Td
(;)Tj
/T1_5 10.91 Tf
4.85 0 Td
(S)Tj
/T1_4 7.97 Tf
5.73 -1.63 Td
(1)Tj
/T1_2 7.97 Tf
[(;j)-57(c)]TJ
/T1_4 7.97 Tf
(+)Tj
/T1_2 7.97 Tf
20.72 0 Td
(c)Tj
/T1_3 7.97 Tf
3.66 0 Td
(\241)Tj
/T1_4 7.97 Tf
6.59 0 Td
(1)Tj
/T1_1 10.91 Tf
4.73 1.63 Td
(g)Tj
/T1_0 10.91 Tf
-462.42 -21.91 Td
[(\257rst)-484(v)27(eri\257es)-484(the)-485(certi\257cates)]TJ
/T1_5 10.91 Tf
138.96 0 Td
(cert)Tj
/T1_0 10.91 Tf
22.9 0 Td
([)Tj
/T1_5 10.91 Tf
(S)Tj
/T1_4 7.97 Tf
8.75 -1.78 Td
(1)Tj
/T1_2 7.97 Tf
4.24 0 Td
[(;j)-57(c)]TJ
/T1_4 7.97 Tf
(+)Tj
/T1_2 7.97 Tf
(k)Tj
/T1_0 10.91 Tf
21.6 1.78 Td
[(])-484(and)-485(signatures)]TJ
/T1_6 10.91 Tf
84.48 0 Td
(\276)Tj
/T1_4 7.97 Tf
6.23 -1.78 Td
(1)Tj
/T1_2 7.97 Tf
[(;j)-57(c)]TJ
/T1_4 7.97 Tf
(+)Tj
/T1_2 7.97 Tf
20.72 0 Td
(k)Tj
/T1_0 10.91 Tf
10.4 1.78 Td
[(sen)27(t)-483(b)26(y)-483(its)-485(subgroup)-484(mem)26(b)-26(ers)]TJ
/T1_5 10.91 Tf
-318.28 -21.92 Td
(S)Tj
/T1_4 7.97 Tf
5.73 -1.77 Td
(1)Tj
/T1_2 7.97 Tf
[(;j)-57(c)]TJ
/T1_4 7.97 Tf
(+)Tj
/T1_2 7.97 Tf
(k)Tj
/T1_1 10.91 Tf
31.82 1.77 Td
[(2)-549(G)]TJ
/T1_4 7.97 Tf
19.75 -1.63 Td
(1)Tj
/T1_2 7.97 Tf
4.24 0 Td
(;j)Tj
/T1_0 10.91 Tf
12.14 1.63 Td
[(for)-496(0)]TJ
/T1_1 10.91 Tf
29.91 0 Td
(\267)Tj
/T1_6 10.91 Tf
14.48 0 Td
(k)Tj
/T1_1 10.91 Tf
12.01 0 Td
(\267)Tj
/T1_6 10.91 Tf
14.47 0 Td
(c)Tj
/T1_1 10.91 Tf
8.33 0 Td
(\241)Tj
/T1_0 10.91 Tf
12.09 0 Td
[(1.)-933(If)-496(the)-496(v)26(eri\257cations)-495(are)-496(not)-496(correct,)-537(then)-497(eac)27(h)]TJ
/T1_5 10.91 Tf
250.11 0 Td
(S)Tj
/T1_4 7.97 Tf
5.72 -1.63 Td
(0)Tj
/T1_2 7.97 Tf
4.24 0 Td
(;j)Tj
/T1_0 10.91 Tf
12.14 1.63 Td
(rejects)Tj
/T1_5 10.91 Tf
-437.18 -21.91 Td
(S)Tj
/T1_4 7.97 Tf
5.73 -1.78 Td
(1)Tj
/T1_2 7.97 Tf
[(;j)-57(c)]TJ
/T1_4 7.97 Tf
(+)Tj
/T1_2 7.97 Tf
(k)Tj
/T1_0 10.91 Tf
25.83 1.78 Td
[(.)-662(Otherwise,)]TJ
/T1_5 10.91 Tf
65.86 0 Td
(S)Tj
/T1_4 7.97 Tf
5.73 -1.64 Td
(0)Tj
/T1_2 7.97 Tf
(;j)Tj
/T1_0 10.91 Tf
15.39 1.64 Td
[(selects)-406(random)]TJ
/T1_6 10.91 Tf
75.66 0 Td
(r)Tj
/T1_4 7.97 Tf
4.92 -1.64 Td
(0)Tj
/T1_2 7.97 Tf
(;j)Tj
/T1_1 10.91 Tf
15.31 1.64 Td
(2)Tj
/T1_6 10.91 Tf
11.62 0 Td
(Z)Tj
/T1_3 7.97 Tf
8.22 3.95 Td
(\244)Tj
/T1_2 7.97 Tf
-0.78 -6.65 Td
(q)Tj
/T1_0 10.91 Tf
9.94 2.7 Td
[(and)-406(computes)-465(\271)]TJ
/T1_6 10.91 Tf
71.32 0 Td
(z)Tj
/T1_4 7.97 Tf
5.07 -1.64 Td
(0)Tj
/T1_2 7.97 Tf
4.24 0 Td
(;j)Tj
/T1_0 10.91 Tf
11.08 1.64 Td
(=)Tj
/T1_6 10.91 Tf
12.83 0 Td
(g)Tj
/T1_2 7.97 Tf
5.59 3.95 Td
(r)Tj
/T1_9 5.98 Tf
3.82 -1.21 Td
(0)Tj
/T1_7 5.98 Tf
3.65 0 Td
(;j)Tj
/T1_0 10.91 Tf
9.7 -2.74 Td
[(mo)-27(d)]TJ
/T1_6 10.91 Tf
23.93 0 Td
(p)Tj
/T1_0 10.91 Tf
9.92 0 Td
[(and)-405(DH)-406(k)27(eys)]TJ
/T1_6 10.91 Tf
-404.58 -21.92 Td
(T)Tj
/T1_4 7.97 Tf
6.37 -1.78 Td
(1)Tj
/T1_2 7.97 Tf
4.24 0 Td
[(;j)-57(c)]TJ
/T1_4 7.97 Tf
(+)Tj
/T1_2 7.97 Tf
(k)Tj
/T1_0 10.91 Tf
24.63 1.78 Td
(=)Tj
/T1_6 10.91 Tf
11.51 0 Td
(z)Tj
/T1_2 7.97 Tf
5.55 6.13 Td
(r)Tj
/T1_9 5.98 Tf
3.82 -1.21 Td
(0)Tj
/T1_7 5.98 Tf
3.66 0 Td
(;j)Tj
/T1_4 7.97 Tf
-7.96 -8.44 Td
(1)Tj
/T1_2 7.97 Tf
4.24 0 Td
[(;j)-57(c)]TJ
/T1_4 7.97 Tf
(+)Tj
/T1_2 7.97 Tf
(k)Tj
/T1_0 10.91 Tf
24.63 3.52 Td
[(mo)-27(d)]TJ
/T1_6 10.91 Tf
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(;i)Tj
/T1_0 10.91 Tf
9.96 1.64 Td
[(.)-484(If)]TJ
-452.29 -21.92 Td
[(the)-315(v)26(eri\257cations)-315(are)-315(not)-316(correct,)-320(then)]TJ
/T1_3 10.91 Tf
180.24 0 Td
(S)Tj
/T1_4 7.97 Tf
5.73 -1.63 Td
[(v)-35(;j)]TJ
/T1_0 10.91 Tf
14.58 1.63 Td
(rejects)Tj
/T1_3 10.91 Tf
34.14 0 Td
(S)Tj
/T1_4 7.97 Tf
5.72 -1.63 Td
(v)Tj
/T1_6 7.97 Tf
4.41 0 Td
(\241)Tj
/T1_2 7.97 Tf
6.59 0 Td
(1)Tj
/T1_4 7.97 Tf
(;i)Tj
/T1_0 10.91 Tf
9.96 1.63 Td
[(.)-438(Otherwise,)]TJ
/T1_3 10.91 Tf
62.28 0 Td
(S)Tj
/T1_4 7.97 Tf
5.73 -1.63 Td
[(v)-35(;j)]TJ
/T1_0 10.91 Tf
14.58 1.63 Td
[(computes)-316(the)-316(DH)-316(k)27(ey)]TJ
/T1_5 10.91 Tf
106.4 0 Td
(T)Tj
/T1_4 7.97 Tf
6.37 -1.63 Td
[(v)-35(;j)]TJ
/T1_0 10.91 Tf
-456.73 -20.28 Td
[(that)-333(it)-333(shares)-333(with)-334(its)-333(subgroup)-333(con)26(troller)]TJ
/T1_3 10.91 Tf
203.64 0 Td
(S)Tj
/T1_4 7.97 Tf
5.73 -1.64 Td
(v)Tj
/T1_6 7.97 Tf
4.4 0 Td
(\241)Tj
/T1_2 7.97 Tf
6.59 0 Td
(1)Tj
/T1_4 7.97 Tf
(;i)Tj
/T1_0 10.91 Tf
13.6 1.64 Td
[(as)-333(follo)27(ws:)]TJ
/T1_5 10.91 Tf
-114.56 -48.55 Td
(T)Tj
/T1_4 7.97 Tf
6.38 -1.63 Td
[(v)-35(;j)]TJ
/T1_0 10.91 Tf
14.17 1.63 Td
(=)Tj
/T1_7 10.91 Tf
11.51 25.63 Td
(8)Tj
0 -9.81 TD
(>)Tj
0 -3.27 TD
(<)Tj
0 -19.64 TD
(>)Tj
0 -3.27 TD
(:)Tj
/T1_0 10.91 Tf
15.33 19.67 Td
(\271)Tj
/T1_5 10.91 Tf
-0.66 -0.01 Td
(z)Tj
/T1_8 7.97 Tf
5.56 6.14 Td
(H)Tj
/T1_2 7.97 Tf
5.97 0 Td
(\()Tj
/T1_4 7.97 Tf
(K)Tj
/T1_9 5.98 Tf
10.43 -1.22 Td
(v)Tj
/T1_10 5.98 Tf
3.95 0 Td
(+1)Tj
/T1_9 5.98 Tf
9.24 0 Td
(;j)Tj
/T1_2 7.97 Tf
6.17 1.22 Td
(\))Tj
/T1_4 7.97 Tf
-36.24 -9.39 Td
(v)Tj
/T1_6 7.97 Tf
4.4 0 Td
(\241)Tj
/T1_2 7.97 Tf
6.59 0 Td
(1)Tj
/T1_4 7.97 Tf
(;i)Tj
/T1_0 10.91 Tf
32.07 3.26 Td
[(mo)-28(d)]TJ
/T1_5 10.91 Tf
23.94 -0.01 Td
(p)Tj
/T1_0 10.91 Tf
19.08 0.01 Td
[(for)-333(1)]TJ
/T1_1 10.91 Tf
25.17 -0.01 Td
(\267)Tj
/T1_5 10.91 Tf
11.52 0.01 Td
(v)Tj
/T1_1 10.91 Tf
8.7 -0.01 Td
(\267)Tj
/T1_5 10.91 Tf
11.51 0.01 Td
(h)Tj
/T1_1 10.91 Tf
8.71 -0.01 Td
(\241)Tj
/T1_0 10.91 Tf
10.91 0.01 Td
(2)Tj
/T1_5 10.91 Tf
5.45 -0.01 Td
(;)Tj
/T1_0 10.91 Tf
-172.47 -21.91 Td
(\271)Tj
/T1_5 10.91 Tf
-0.66 0 Td
(z)Tj
/T1_4 7.97 Tf
5.56 6.13 Td
(r)Tj
/T1_9 5.98 Tf
3.82 -1.21 Td
[(v)-35(;j)]TJ
/T1_4 7.97 Tf
-4.3 -8.18 Td
(v)Tj
/T1_6 7.97 Tf
4.4 0 Td
(\241)Tj
/T1_2 7.97 Tf
6.59 0 Td
(1)Tj
/T1_4 7.97 Tf
(;i)Tj
/T1_0 10.91 Tf
12.99 3.26 Td
[(mo)-28(d)]TJ
/T1_5 10.91 Tf
23.94 0 Td
(p)Tj
/T1_0 10.91 Tf
38.16 0 Td
(for)Tj
/T1_5 10.91 Tf
16.69 0 Td
(v)Tj
/T1_0 10.91 Tf
8.71 0 Td
(=)Tj
/T1_5 10.91 Tf
11.51 0 Td
(h)Tj
/T1_1 10.91 Tf
8.71 0 Td
(\241)Tj
/T1_0 10.91 Tf
10.9 0 Td
(1)Tj
/T1_5 10.91 Tf
(:)Tj
/T1_0 10.91 Tf
-313.81 -26.61 Td
[(Next,)-355(eac)27(h)]TJ
/T1_3 10.91 Tf
54.66 0 Td
(S)Tj
/T1_4 7.97 Tf
5.72 -1.63 Td
[(v)-36(;j)]TJ
/T1_0 10.91 Tf
14.97 1.63 Td
(uses)Tj
/T1_5 10.91 Tf
23.33 0 Td
(T)Tj
/T1_4 7.97 Tf
6.38 -1.63 Td
[(v)-35(;j)]TJ
/T1_0 10.91 Tf
14.96 1.63 Td
[(to)-351(decrypt)]TJ
/T1_3 10.91 Tf
53.43 0 Td
(c)Tj
/T1_4 7.97 Tf
5.73 -1.63 Td
[(v)-35(;j)]TJ
/T1_0 10.91 Tf
14.96 1.63 Td
[(and)-351(obtains)-350(the)-351(subgroup)-351(k)27(ey)]TJ
/T1_5 10.91 Tf
146.22 0 Td
(K)Tj
/T1_4 7.97 Tf
9.26 -1.63 Td
[(v)-36(;i)]TJ
/T1_0 10.91 Tf
13.97 1.63 Td
[(and)-350(iden)27(tit)27(y)]TJ
/T1_3 10.91 Tf
61.88 0 Td
(S)Tj
/T1_4 7.97 Tf
5.72 -1.63 Td
(v)Tj
/T1_6 7.97 Tf
4.41 0 Td
(\241)Tj
/T1_2 7.97 Tf
6.59 0 Td
(1)Tj
/T1_4 7.97 Tf
(;i)Tj
/T1_0 10.91 Tf
9.96 1.63 Td
[(.)-497(If)]TJ
-452.15 -21.91 Td
[(the)-253(iden)27(tit)28(y)]TJ
/T1_3 10.91 Tf
57.33 0 Td
(S)Tj
/T1_4 7.97 Tf
5.72 -1.64 Td
(v)Tj
/T1_6 7.97 Tf
4.41 0 Td
(\241)Tj
/T1_2 7.97 Tf
6.59 0 Td
(1)Tj
/T1_4 7.97 Tf
(;i)Tj
/T1_0 10.91 Tf
12.72 1.64 Td
[(is)-253(not)-253(decrypted)-253(correctly)82(,)-268(then)]TJ
/T1_3 10.91 Tf
148.95 0 Td
(S)Tj
/T1_4 7.97 Tf
5.72 -1.64 Td
[(v)-36(;j)]TJ
/T1_0 10.91 Tf
13.91 1.64 Td
(rejects)Tj
/T1_3 10.91 Tf
33.45 0 Td
(c)Tj
/T1_4 7.97 Tf
5.72 -1.64 Td
[(v)-36(;j)]TJ
/T1_0 10.91 Tf
11.14 1.64 Td
[(.)-417(Otherwise,)]TJ
/T1_3 10.91 Tf
61.51 0 Td
(S)Tj
/T1_4 7.97 Tf
5.73 -1.64 Td
[(v)-35(;j)]TJ
/T1_0 10.91 Tf
13.9 1.64 Td
[(accepts)-252(subgroup)]TJ
-386.8 -21.92 Td
[(k)27(ey)]TJ
/T1_5 10.91 Tf
19.69 0 Td
(K)Tj
/T1_4 7.97 Tf
9.26 -1.64 Td
[(v)-36(;i)]TJ
/T1_0 10.91 Tf
13.78 1.64 Td
(.)Tj
-42.73 -21.92 Td
[(Phase)-333(3)]TJ
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 0 -297.49 cm
0 0 m
37.17 0 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 112.6814 473.7671 Tm
(:)Tj
1.0003 0 0 1.0003 72 769.82 Tm
48.471 -295.97 Td
[(F)82(or)-319(the)-320(Con)26(trol)-319(Group)-320(\()]TJ
/T1_11 10.91 Tf
115.779 0 Td
(CG)Tj
/T1_0 10.91 Tf
14.24 0 Td
[(\))-320(at)-320(La)27(y)27(er)]TJ
/T1_1 10.91 Tf
50.95 0 Td
(L)Tj
/T1_2 7.97 Tf
7.53 -1.63 Td
(0)Tj
/T1_0 10.91 Tf
4.73 1.63 Td
[(,)-322(eac)27(h)-320(subgroup)-320(con)27(troller)]TJ
/T1_3 10.91 Tf
126.85 0 Td
(S)Tj
/T1_2 7.97 Tf
5.72 -1.63 Td
(0)Tj
/T1_4 7.97 Tf
4.24 0 Td
(;j)Tj
/T1_0 10.91 Tf
10.22 1.63 Td
[(for)-320(0)]TJ
/T1_1 10.91 Tf
25.04 0 Td
(\267)Tj
/T1_5 10.91 Tf
11.51 0 Td
(j)Tj
/T1_1 10.91 Tf
8.14 0 Td
(\267)Tj
/T1_5 10.91 Tf
11.52 0 Td
(c)Tj
/T1_1 10.91 Tf
6.86 0 Td
(\241)Tj
/T1_0 10.91 Tf
10.62 0 Td
(1)Tj
-462.42 -21.91 Td
[(\257rst)-381(v)26(eri\257es)-381(the)-382(certi\257cates)]TJ
/T1_3 10.91 Tf
134.48 0 Td
(cert)Tj
/T1_0 10.91 Tf
22.9 0 Td
([)Tj
/T1_3 10.91 Tf
(S)Tj
/T1_2 7.97 Tf
8.76 -1.78 Td
(0)Tj
/T1_4 7.97 Tf
(;k)Tj
/T1_0 10.91 Tf
11.7 1.78 Td
[(])-381(for)-382(0)]TJ
/T1_1 10.91 Tf
33.78 0 Td
(\267)Tj
/T1_5 10.91 Tf
12.4 0 Td
(k)Tj
/T1_1 10.91 Tf
9.93 0 Td
(6)Tj
/T1_0 10.91 Tf
(=)Tj
/T1_5 10.91 Tf
12.4 0 Td
(j)Tj
/T1_1 10.91 Tf
9.03 0 Td
(\267)Tj
/T1_5 10.91 Tf
12.39 0 Td
(c)Tj
/T1_1 10.91 Tf
7.5 0 Td
(\241)Tj
/T1_0 10.91 Tf
11.26 0 Td
[(1.)-589(If)-382(the)-382(v)26(eri\257cations)-381(are)-381(not)-382(correct,)]TJ
-286.53 -21.92 Td
[(then)-333(eac)27(h)]TJ
/T1_3 10.91 Tf
49.38 0 Td
(S)Tj
/T1_2 7.97 Tf
5.73 -1.64 Td
(0)Tj
/T1_4 7.97 Tf
(;j)Tj
/T1_0 10.91 Tf
14.6 1.64 Td
(rejects)Tj
/T1_3 10.91 Tf
34.32 0 Td
(S)Tj
/T1_2 7.97 Tf
5.73 -1.78 Td
(0)Tj
/T1_4 7.97 Tf
(;k)Tj
/T1_0 10.91 Tf
11.7 1.78 Td
[(.)-444(Otherwise,)]TJ
/T1_3 10.91 Tf
62.5 0 Td
(S)Tj
/T1_2 7.97 Tf
5.73 -1.64 Td
(0)Tj
/T1_4 7.97 Tf
(;j)Tj
/T1_0 10.91 Tf
14.6 1.64 Td
[(v)27(eri\257es)-332(signatures)]TJ
/T1_5 10.91 Tf
88.1 0 Td
(\276)Tj
/T1_2 7.97 Tf
6.23 -1.64 Td
(0)Tj
/T1_4 7.97 Tf
(;j)Tj
/T1_6 7.97 Tf
10.47 0 Td
(\241)Tj
/T1_2 7.97 Tf
(1)Tj
/T1_0 10.91 Tf
14.95 1.64 Td
(and)Tj
/T1_5 10.91 Tf
21.2 0 Td
(\276)Tj
/T1_2 7.97 Tf
6.24 -1.64 Td
(0)Tj
/T1_4 7.97 Tf
(;j)Tj
/T1_2 7.97 Tf
10.46 0 Td
(+1)Tj
/T1_0 10.91 Tf
11.32 1.64 Td
[(.)-444(If)-333(the)-334(v)27(eri\257cations)]TJ
-373.26 -21.92 Td
[(are)-333(not)-333(correct,)-333(then)-334(eac)27(h)]TJ
/T1_3 10.91 Tf
126.42 0 Td
(S)Tj
/T1_2 7.97 Tf
5.73 -1.63 Td
(0)Tj
/T1_4 7.97 Tf
(;j)Tj
/T1_0 10.91 Tf
14.6 1.63 Td
(rejects)Tj
/T1_3 10.91 Tf
34.32 0 Td
(S)Tj
/T1_2 7.97 Tf
5.73 -1.63 Td
(0)Tj
/T1_4 7.97 Tf
(;j)Tj
/T1_6 7.97 Tf
10.46 0 Td
(\241)Tj
/T1_2 7.97 Tf
6.59 0 Td
(1)Tj
/T1_0 10.91 Tf
8.36 1.63 Td
(and)Tj
/T1_3 10.91 Tf
21.21 0 Td
(S)Tj
/T1_2 7.97 Tf
5.73 -1.63 Td
(0)Tj
/T1_4 7.97 Tf
(;j)Tj
/T1_2 7.97 Tf
10.46 0 Td
(+1)Tj
/T1_0 10.91 Tf
11.32 1.63 Td
[(.)-444(Otherwise,)]TJ
/T1_3 10.91 Tf
62.5 0 Td
(S)Tj
/T1_2 7.97 Tf
5.72 -1.63 Td
(0)Tj
/T1_4 7.97 Tf
4.24 0 Td
(;j)Tj
/T1_0 10.91 Tf
10.36 1.63 Td
(computes)Tj
/T1_5 10.91 Tf
-224.95 -39.64 Td
(X)Tj
/T1_2 7.97 Tf
9.04 -1.64 Td
(0)Tj
/T1_4 7.97 Tf
(;j)Tj
/T1_0 10.91 Tf
20.92 1.64 Td
(=)Tj
/T1_7 10.91 Tf
18.45 15.38 Td
(\265)Tj
/T1_5 10.91 Tf
9.22 -7.94 Td
(z)Tj
/T1_2 7.97 Tf
5.07 -1.64 Td
(0)Tj
/T1_4 7.97 Tf
(;j)Tj
/T1_2 7.97 Tf
10.47 0 Td
(+1)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 176.43 -398.63 cm
0 0 m
26.85 0 l
S
Q
Q
BT
/T1_5 10.91 Tf
1.0003 0 0 1.0003 248.4794 360.8655 Tm
(z)Tj
/T1_2 7.97 Tf
5.07 -1.64 Td
(0)Tj
/T1_4 7.97 Tf
(;j)Tj
/T1_6 7.97 Tf
10.47 0 Td
(\241)Tj
/T1_2 7.97 Tf
(1)Tj
/T1_7 10.91 Tf
12.51 24.5 Td
(\266)Tj
/T1_8 7.97 Tf
8.03 -2.72 Td
(H)Tj
/T1_2 7.97 Tf
5.97 0 Td
(\()Tj
/T1_4 7.97 Tf
3.3 0 Td
(K)Tj
/T1_10 5.98 Tf
7.14 -1.21 Td
(1)Tj
/T1_9 5.98 Tf
3.65 0 Td
(;j)Tj
/T1_2 7.97 Tf
6.17 1.21 Td
(\))Tj
/T1_0 10.91 Tf
206.71 -12.66 Td
(\(8.1\))Tj
-296.69 -24.9 Td
(=)Tj
/T1_5 10.91 Tf
18.45 0 Td
(g)Tj
/T1_8 7.97 Tf
5.59 4.5 Td
(H)Tj
/T1_2 7.97 Tf
(\()Tj
/T1_4 7.97 Tf
(K)Tj
/T1_10 5.98 Tf
16.41 -1.22 Td
(1)Tj
/T1_9 5.98 Tf
3.65 0 Td
(;j)Tj
/T1_2 7.97 Tf
6.17 1.22 Td
(\))Tj
/T1_8 7.97 Tf
(H)Tj
/T1_2 7.97 Tf
(\()Tj
/T1_4 7.97 Tf
(K)Tj
/T1_10 5.98 Tf
19.7 -1.22 Td
(1)Tj
/T1_9 5.98 Tf
3.65 0 Td
(;j)Tj
/T1_10 5.98 Tf
5.67 0 Td
(+1)Tj
/T1_2 7.97 Tf
9.74 1.22 Td
(\))Tj
/T1_6 7.97 Tf
(\241)Tj
/T1_8 7.97 Tf
9.88 0 Td
(H)Tj
/T1_2 7.97 Tf
(\()Tj
/T1_4 7.97 Tf
(K)Tj
/T1_10 5.98 Tf
16.41 -1.22 Td
(1)Tj
/T1_9 5.98 Tf
3.65 0 Td
(;j)Tj
/T1_12 5.98 Tf
5.67 0 Td
(\241)Tj
/T1_10 5.98 Tf
(1)Tj
/T1_2 7.97 Tf
9.91 1.22 Td
(\))Tj
/T1_8 7.97 Tf
(H)Tj
/T1_2 7.97 Tf
9.26 0 Td
(\()Tj
/T1_4 7.97 Tf
3.3 0 Td
(K)Tj
/T1_10 5.98 Tf
7.14 -1.22 Td
(1)Tj
/T1_9 5.98 Tf
3.65 0 Td
(;j)Tj
/T1_2 7.97 Tf
6.17 1.22 Td
(\))Tj
/T1_0 10.91 Tf
6.82 -4.5 Td
(mo)Tj
1.0003 0 0 1.0003 72 769.82 Tm
334.488 -426.26 Td
(d)Tj
/T1_5 10.91 Tf
9.092 0 Td
(p)Tj
/T1_0 10.91 Tf
-343.58 -39.65 Td
(where)Tj
/T1_5 10.91 Tf
32.2 0 Td
(z)Tj
/T1_2 7.97 Tf
5.07 -1.63 Td
(0)Tj
/T1_4 7.97 Tf
(;)Tj
/T1_6 7.97 Tf
6.59 0 Td
(\241)Tj
/T1_2 7.97 Tf
(1)Tj
/T1_0 10.91 Tf
15.45 1.63 Td
(=)Tj
/T1_5 10.91 Tf
12.61 0 Td
(z)Tj
/T1_2 7.97 Tf
5.08 -1.63 Td
(0)Tj
/T1_4 7.97 Tf
(;c)Tj
/T1_6 7.97 Tf
(\241)Tj
/T1_2 7.97 Tf
(1)Tj
/T1_0 10.91 Tf
21.56 1.63 Td
(,)Tj
/T1_5 10.91 Tf
7.5 0 Td
(z)Tj
/T1_2 7.97 Tf
5.07 -1.63 Td
(0)Tj
/T1_4 7.97 Tf
(;c)Tj
/T1_0 10.91 Tf
14.88 1.63 Td
(=)Tj
/T1_5 10.91 Tf
12.62 0 Td
(z)Tj
/T1_2 7.97 Tf
5.07 -1.63 Td
(0)Tj
/T1_4 7.97 Tf
(;)Tj
/T1_2 7.97 Tf
6.59 0 Td
(0)Tj
/T1_0 10.91 Tf
4.73 1.63 Td
(,)Tj
/T1_11 10.91 Tf
7.49 0 Td
(H)Tj
/T1_0 10.91 Tf
7.73 0 Td
(\()Tj
/T1_5 10.91 Tf
(K)Tj
/T1_2 7.97 Tf
13.5 -1.63 Td
(1)Tj
/T1_4 7.97 Tf
(;)Tj
/T1_6 7.97 Tf
(\241)Tj
/T1_2 7.97 Tf
13.17 0 Td
(1)Tj
/T1_0 10.91 Tf
4.73 1.63 Td
[(\))-379(=)]TJ
/T1_11 10.91 Tf
20.99 0 Td
(H)Tj
/T1_0 10.91 Tf
7.73 0 Td
(\()Tj
/T1_5 10.91 Tf
(K)Tj
/T1_2 7.97 Tf
13.5 -1.63 Td
(1)Tj
/T1_4 7.97 Tf
(;c)Tj
/T1_6 7.97 Tf
(\241)Tj
/T1_2 7.97 Tf
16.84 0 Td
(1)Tj
/T1_0 10.91 Tf
4.73 1.63 Td
[(\))-393(and)]TJ
/T1_11 10.91 Tf
30.41 0 Td
(H)Tj
/T1_0 10.91 Tf
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[(do)28(wn)-418(to)-420(second)-419(lo)27(w)28(est)-419(la)27(y)28(er)]TJ
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141.16 0 Td
(L)Tj
/T1_3 7.97 Tf
7.52 -1.78 Td
(h)Tj
/T1_4 7.97 Tf
(\241)Tj
/T1_2 7.97 Tf
(2)Tj
/T1_0 10.91 Tf
16.19 1.78 Td
[(.)-702(F)82(or)-418(eac)27(h)]TJ
-415.77 -21.92 Td
[(la)27(y)28(er)]TJ
/T1_6 10.91 Tf
27.9 0 Td
(L)Tj
/T1_3 7.97 Tf
7.52 -1.63 Td
(v)Tj
/T1_0 10.91 Tf
10.06 1.63 Td
[(for)-471(1)]TJ
/T1_6 10.91 Tf
29.21 0 Td
(\267)Tj
/T1_1 10.91 Tf
14.03 0 Td
(v)Tj
/T1_6 10.91 Tf
11.23 0 Td
(\267)Tj
/T1_1 10.91 Tf
14.04 0 Td
(h)Tj
/T1_6 10.91 Tf
9.72 0 Td
(\241)Tj
/T1_0 10.91 Tf
11.91 0 Td
[(2,)-506(eac)26(h)-471(subgroup)-472(mem)27(b)-27(er)]TJ
/T1_5 10.91 Tf
132.28 0 Td
(S)Tj
/T1_3 7.97 Tf
5.72 -1.63 Td
[(v)-36(;j)]TJ
/T1_0 10.91 Tf
16.29 1.63 Td
[(for)-472(0)]TJ
/T1_6 10.91 Tf
29.22 0 Td
(\267)Tj
/T1_1 10.91 Tf
14.03 0 Td
(j)Tj
/T1_6 10.91 Tf
10.67 0 Td
(\267)Tj
/T1_1 10.91 Tf
14.03 0 Td
(c)Tj
/T1_3 7.97 Tf
4.72 3.96 Td
(v)Tj
/T1_2 7.97 Tf
4.41 0 Td
(+1)Tj
/T1_6 10.91 Tf
14.75 -3.96 Td
(\241)Tj
/T1_0 10.91 Tf
11.92 0 Td
[(1)-471(of)]TJ
/T1_6 10.91 Tf
24.53 0 Td
(G)Tj
/T1_3 7.97 Tf
6.49 -1.63 Td
[(v)-35(;i)]TJ
/T1_0 10.91 Tf
15.29 1.63 Td
(where)Tj
/T1_1 10.91 Tf
-439.97 -21.91 Td
(i)Tj
/T1_0 10.91 Tf
8.91 0 Td
(=)Tj
/T1_6 10.91 Tf
13.64 0 Td
(b)Tj
/T1_3 7.97 Tf
6.04 4.93 Td
(j)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 28.59 -139.73 cm
0 0 m
3.88 0 l
S
Q
Q
BT
/T1_3 7.97 Tf
1.0003 0 0 1.0003 100.708 623.5591 Tm
(c)Tj
/T1_6 10.91 Tf
4.97 3.77 Td
(c)Tj
/T1_0 10.91 Tf
9.76 0 Td
(\257rst)Tj
1.0003 0 0 1.0003 72 769.82 Tm
67.214 -142.45 Td
(decrypts)Tj
/T1_5 10.91 Tf
45.286 0 Td
(c)Tj
/T1_4 7.97 Tf
5.73 3.95 Td
(0)Tj
/T1_3 7.97 Tf
T*
(v)Tj
/T1_4 7.97 Tf
4.41 0 Td
(\241)Tj
/T1_2 7.97 Tf
(1)Tj
/T1_3 7.97 Tf
(;i)Tj
/T1_0 10.91 Tf
21.7 3.06 Td
(=)Tj
/T1_6 10.91 Tf
13.64 0 Td
(E)Tj
/T1_3 7.97 Tf
5.75 -1.69 Td
(K)Tj
/T1_9 5.98 Tf
7.14 -1.22 Td
[(v)-36(;i)]TJ
/T1_0 10.91 Tf
9.88 2.91 Td
(\()Tj
/T1_1 10.91 Tf
(K)Tj
/T1_6 10.91 Tf
14.28 0 Td
(jj)Tj
/T1_5 10.91 Tf
6.06 0 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.64 Td
(v)Tj
/T1_4 7.97 Tf
4.41 0 Td
(\241)Tj
/T1_2 7.97 Tf
(1)Tj
/T1_3 7.97 Tf
(;i)Tj
/T1_0 10.91 Tf
16.54 1.64 Td
[(\))-450(from)-450(its)-451(subgroup)-450(con)27(troller)]TJ
/T1_5 10.91 Tf
151.43 0 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.64 Td
(v)Tj
/T1_4 7.97 Tf
4.4 0 Td
(\241)Tj
/T1_2 7.97 Tf
6.59 0 Td
(1)Tj
/T1_3 7.97 Tf
(;i)Tj
/T1_0 10.91 Tf
14.87 1.64 Td
[(and)-450(obtains)]TJ
/T1_1 10.91 Tf
-410.79 -21.92 Td
(K)Tj
/T1_0 10.91 Tf
14.27 0 Td
[(and)-387(iden)27(tit)28(y)]TJ
/T1_5 10.91 Tf
62.67 0 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.64 Td
(v)Tj
/T1_4 7.97 Tf
4.41 0 Td
(\241)Tj
/T1_2 7.97 Tf
(1)Tj
/T1_3 7.97 Tf
(;i)Tj
/T1_0 10.91 Tf
16.55 1.64 Td
[(.)-606(If)-387(the)-387(iden)26(tit)28(y)]TJ
/T1_5 10.91 Tf
81.39 0 Td
(S)Tj
/T1_3 7.97 Tf
5.72 -1.64 Td
(v)Tj
/T1_4 7.97 Tf
4.41 0 Td
(\241)Tj
/T1_2 7.97 Tf
6.59 0 Td
(1)Tj
/T1_3 7.97 Tf
(;i)Tj
/T1_0 10.91 Tf
14.19 1.64 Td
[(w)28(as)-387(not)-387(decrypted)-387(correctly)82(,)-400(then)]TJ
/T1_5 10.91 Tf
166.22 0 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.64 Td
[(v)-35(;j)]TJ
/T1_0 10.91 Tf
15.36 1.64 Td
(rejects)Tj
/T1_5 10.91 Tf
34.92 0 Td
(c)Tj
/T1_4 7.97 Tf
5.72 3.96 Td
(0)Tj
/T1_3 7.97 Tf
0 -7.02 TD
(v)Tj
/T1_4 7.97 Tf
4.41 0 Td
(\241)Tj
/T1_2 7.97 Tf
6.59 0 Td
(1)Tj
/T1_3 7.97 Tf
(;i)Tj
/T1_0 10.91 Tf
9.96 3.06 Td
(.)Tj
-464.84 -21.92 Td
(Otherwise,)Tj
/T1_5 10.91 Tf
54.09 0 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.63 Td
[(v)-35(;j)]TJ
/T1_0 10.91 Tf
14.11 1.63 Td
[(accepts)-273(the)-272(group)-273(k)27(ey)]TJ
/T1_1 10.91 Tf
105 0 Td
(K)Tj
/T1_0 10.91 Tf
10.04 0 Td
[(.)-424(Next,)]TJ
/T1_5 10.91 Tf
36.82 0 Td
(S)Tj
/T1_3 7.97 Tf
5.72 -1.63 Td
[(v)-36(;j)]TJ
/T1_0 10.91 Tf
14.12 1.63 Td
(encrypts)Tj
/T1_1 10.91 Tf
43.36 0 Td
(K)Tj
/T1_6 10.91 Tf
10.04 0 Td
(jj)Tj
/T1_5 10.91 Tf
6.06 0 Td
(S)Tj
/T1_3 7.97 Tf
5.72 -1.63 Td
[(v)-36(;j)]TJ
/T1_0 10.91 Tf
14.12 1.63 Td
[(using)-272(the)-273(subgroup)-273(k)27(ey)]TJ
/T1_1 10.91 Tf
111.72 0 Td
(K)Tj
/T1_3 7.97 Tf
9.26 -1.63 Td
(v)Tj
/T1_2 7.97 Tf
4.41 0 Td
(+1)Tj
/T1_3 7.97 Tf
(;j)Tj
/T1_0 10.91 Tf
-450.32 -20.28 Td
[(of)-370(subgroup)]TJ
/T1_6 10.91 Tf
60.58 0 Td
(G)Tj
/T1_3 7.97 Tf
6.49 -1.64 Td
(v)Tj
/T1_2 7.97 Tf
4.4 0 Td
(+1)Tj
/T1_3 7.97 Tf
(;j)Tj
/T1_0 10.91 Tf
21.59 1.64 Td
[(that)-370(it)-370(con)26(trols)-369(at)-370(la)27(y)27(er)]TJ
/T1_6 10.91 Tf
117.26 0 Td
(L)Tj
/T1_3 7.97 Tf
7.52 -1.64 Td
(v)Tj
/T1_2 7.97 Tf
4.41 0 Td
(+1)Tj
/T1_0 10.91 Tf
15.35 1.64 Td
[(and)-370(symmetric)-371(k)27(ey)-369(encryption)]TJ
/T1_7 10.91 Tf
149.88 0 Td
(SKE)Tj
/T1_0 10.91 Tf
24.18 0 Td
[(and)-370(obtains)]TJ
/T1_5 10.91 Tf
-411.66 -21.92 Td
(c)Tj
/T1_4 7.97 Tf
5.73 3.96 Td
(0)Tj
/T1_3 7.97 Tf
T*
[(v)-35(;j)]TJ
/T1_0 10.91 Tf
14.17 3.06 Td
(=)Tj
/T1_6 10.91 Tf
11.51 0 Td
(E)Tj
/T1_3 7.97 Tf
5.75 -1.69 Td
(K)Tj
/T1_9 5.98 Tf
7.14 -1.21 Td
(v)Tj
/T1_8 5.98 Tf
3.95 0 Td
(+1)Tj
/T1_9 5.98 Tf
9.24 0 Td
(;j)Tj
/T1_0 10.91 Tf
6.67 2.9 Td
(\()Tj
/T1_1 10.91 Tf
(K)Tj
/T1_6 10.91 Tf
14.29 0 Td
(jj)Tj
/T1_5 10.91 Tf
6.05 0 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.64 Td
[(v)-35(;j)]TJ
/T1_0 10.91 Tf
11.14 1.64 Td
(\).)Tj
/T1_5 10.91 Tf
12.12 0 Td
(S)Tj
/T1_3 7.97 Tf
5.72 -1.64 Td
[(v)-36(;j)]TJ
/T1_0 10.91 Tf
14.78 1.64 Td
[(then)-333(broadcast)]TJ
/T1_6 10.91 Tf
74.62 0 Td
(f)Tj
/T1_5 10.91 Tf
(S)Tj
/T1_3 7.97 Tf
11.17 -1.64 Td
[(v)-36(;j)]TJ
/T1_6 10.91 Tf
11.15 1.64 Td
(jj)Tj
/T1_5 10.91 Tf
6.05 0 Td
(c)Tj
/T1_4 7.97 Tf
5.73 3.96 Td
(0)Tj
/T1_3 7.97 Tf
T*
[(v)-35(;j)]TJ
/T1_6 10.91 Tf
11.14 3.06 Td
(g)Tj
/T1_0 10.91 Tf
9.09 0 Td
[(to)-333(its)-333(subgroup)]TJ
/T1_6 10.91 Tf
75.89 0 Td
(G)Tj
/T1_3 7.97 Tf
6.49 -1.64 Td
(v)Tj
/T1_2 7.97 Tf
4.4 0 Td
(+1)Tj
/T1_3 7.97 Tf
(;j)Tj
/T1_0 10.91 Tf
21.19 1.64 Td
[(at)-333(la)27(y)28(er)]TJ
/T1_6 10.91 Tf
39.72 0 Td
(L)Tj
/T1_3 7.97 Tf
7.52 -1.64 Td
(v)Tj
/T1_2 7.97 Tf
4.41 0 Td
(+1)Tj
/T1_0 10.91 Tf
11.31 1.64 Td
(.)Tj
-433.87 -21.92 Td
(\()Tj
/T1_1 10.91 Tf
(ii)Tj
/T1_0 10.91 Tf
[(\))-303(A)27(t)-303(lo)27(w)28(est)-303(la)27(y)28(er)]TJ
/T1_6 10.91 Tf
93.26 0 Td
(L)Tj
/T1_3 7.97 Tf
7.52 -1.77 Td
(h)Tj
/T1_4 7.97 Tf
(\241)Tj
/T1_2 7.97 Tf
11.47 0 Td
(1)Tj
/T1_0 10.91 Tf
4.73 1.77 Td
[(,)-309(eac)27(h)]TJ
/T1_5 10.91 Tf
30.62 0 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.77 Td
(h)Tj
/T1_4 7.97 Tf
4.87 0 Td
(\241)Tj
/T1_2 7.97 Tf
6.59 0 Td
(1)Tj
/T1_3 7.97 Tf
(;j)Tj
/T1_0 10.91 Tf
14.28 1.77 Td
[(for)-303(0)]TJ
/T1_6 10.91 Tf
24.85 0 Td
(\267)Tj
/T1_1 10.91 Tf
11.51 0 Td
(j)Tj
/T1_6 10.91 Tf
8.15 0 Td
(\267)Tj
/T1_1 10.91 Tf
11.51 0 Td
(c)Tj
/T1_3 7.97 Tf
4.72 3.96 Td
(h)Tj
/T1_6 10.91 Tf
7.15 -3.96 Td
(\241)Tj
/T1_0 10.91 Tf
10.26 0 Td
[(1)-304(who)-303(is)-304(a)-304(subgroup)-304(mem)27(b)-27(er)-303(of)]TJ
/T1_6 10.91 Tf
151.52 0 Td
(G)Tj
/T1_3 7.97 Tf
6.49 -1.77 Td
(h)Tj
/T1_4 7.97 Tf
(\241)Tj
/T1_2 7.97 Tf
(1)Tj
/T1_3 7.97 Tf
(;i)Tj
/T1_0 10.91 Tf
24.74 1.77 Td
(where)Tj
/T1_1 10.91 Tf
-439.97 -21.91 Td
(i)Tj
/T1_0 10.91 Tf
6.79 0 Td
(=)Tj
/T1_6 10.91 Tf
11.51 0 Td
(b)Tj
/T1_3 7.97 Tf
6.04 4.93 Td
(j)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 24.34 -271.23 cm
0 0 m
3.88 0 l
S
Q
Q
BT
/T1_3 7.97 Tf
1.0003 0 0 1.0003 96.4568 492.0322 Tm
(c)Tj
/T1_6 10.91 Tf
4.97 3.76 Td
(c)Tj
/T1_0 10.91 Tf
8.02 0 Td
(\257rst)Tj
1.0003 0 0 1.0003 72 769.82 Tm
59.5 -273.95 Td
(decrypts)Tj
/T1_5 10.91 Tf
43.55 0 Td
(c)Tj
/T1_4 7.97 Tf
5.73 3.95 Td
(0)Tj
/T1_3 7.97 Tf
0 -7.27 TD
(h)Tj
/T1_4 7.97 Tf
(\241)Tj
/T1_2 7.97 Tf
(2)Tj
/T1_3 7.97 Tf
(;i)Tj
/T1_0 10.91 Tf
24.46 3.32 Td
(=)Tj
/T1_6 10.91 Tf
11.51 0 Td
(E)Tj
/T1_3 7.97 Tf
5.75 -1.69 Td
(K)Tj
/T1_9 5.98 Tf
7.14 -1.41 Td
(h)Tj
/T1_10 5.98 Tf
(\241)Tj
/T1_8 5.98 Tf
10.09 0 Td
(1)Tj
/T1_9 5.98 Tf
3.66 0 Td
(;i)Tj
/T1_0 10.91 Tf
5.92 3.1 Td
(\()Tj
/T1_1 10.91 Tf
(K)Tj
/T1_6 10.91 Tf
14.29 0 Td
(jj)Tj
/T1_5 10.91 Tf
6.06 0 Td
(S)Tj
/T1_3 7.97 Tf
5.72 -1.78 Td
(h)Tj
/T1_4 7.97 Tf
(\241)Tj
/T1_2 7.97 Tf
(2)Tj
/T1_3 7.97 Tf
15.7 0 Td
(;i)Tj
/T1_0 10.91 Tf
5.73 1.78 Td
[(\))-291(from)-291(its)-291(subgroup)-291(con)26(troller)]TJ
/T1_5 10.91 Tf
142.76 0 Td
(S)Tj
/T1_3 7.97 Tf
5.72 -1.78 Td
(h)Tj
/T1_4 7.97 Tf
(\241)Tj
/T1_2 7.97 Tf
(2)Tj
/T1_3 7.97 Tf
15.7 0 Td
(;i)Tj
/T1_0 10.91 Tf
5.73 1.78 Td
[(.)-430(If)-291(the)-291(iden)26(tit)28(y)]TJ
/T1_5 10.91 Tf
-394.72 -21.92 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.78 Td
(h)Tj
/T1_4 7.97 Tf
4.87 0 Td
(\241)Tj
/T1_2 7.97 Tf
6.59 0 Td
(2)Tj
/T1_3 7.97 Tf
(;i)Tj
/T1_0 10.91 Tf
13.73 1.78 Td
[(w)27(as)-345(not)-345(decrypted)-346(correctly)82(,)-347(then)]TJ
/T1_5 10.91 Tf
163.84 0 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.78 Td
(h)Tj
/T1_4 7.97 Tf
(\241)Tj
/T1_2 7.97 Tf
(1)Tj
/T1_3 7.97 Tf
15.7 0 Td
(;j)Tj
/T1_0 10.91 Tf
10.5 1.78 Td
(rejects)Tj
/T1_5 10.91 Tf
34.46 0 Td
(c)Tj
/T1_4 7.97 Tf
5.72 3.96 Td
(0)Tj
/T1_3 7.97 Tf
0 -7.28 TD
(h)Tj
/T1_4 7.97 Tf
(\241)Tj
/T1_2 7.97 Tf
11.47 0 Td
(2)Tj
/T1_3 7.97 Tf
(;i)Tj
/T1_0 10.91 Tf
9.96 3.32 Td
[(.)-481(Otherwise,)]TJ
/T1_5 10.91 Tf
63.07 0 Td
(S)Tj
/T1_3 7.97 Tf
5.72 -1.78 Td
(h)Tj
/T1_4 7.97 Tf
(\241)Tj
/T1_2 7.97 Tf
11.47 0 Td
(1)Tj
/T1_3 7.97 Tf
(;j)Tj
/T1_0 10.91 Tf
14.73 1.78 Td
[(accepts)-345(the)-346(group)]TJ
-383.29 -21.92 Td
[(k)27(ey)]TJ
/T1_1 10.91 Tf
19.69 0 Td
(K)Tj
/T1_0 10.91 Tf
10.04 0 Td
(.)Tj
/T1_11 14.34 Tf
-29.73 -45.44 Td
[(8.3)-1124(Securit)30(y)-374(Analysis)]TJ
/T1_0 10.91 Tf
0 -32.71 TD
[(In)-369(this)-370(section,)-379(w)27(e)-369(analyze)-370(the)-370(securit)27(y)-369(of)-370(our)-369(prop)-28(osed)-370(proto)-28(col.)-554(W)83(e)-369(consider)-370(t)27(w)28(o)-369(cases,)-379(that)-370(is,)]TJ
0 -21.92 TD
[(the)-341(up)-341(\260o)27(w)-340(information)-341(\(Phase)-342(1,)-343(2a,)-343(3)-341(and)-341(4\))-342(and)-341(do)27(wn)-340(\260o)27(w)-341(information)-341(\(Phase)-341(2b)-341(and)-341(5\).)-468(The)]TJ
T*
[(up)-351(\260o)26(w)-351(information)-351(is)-352(the)-352(information)-352(sen)27(t)-351(from)-352(the)-352(lo)27(w)27(est)-350(la)26(y)28(er)]TJ
/T1_6 10.91 Tf
315.17 0 Td
(L)Tj
/T1_3 7.97 Tf
7.52 -1.77 Td
(h)Tj
/T1_4 7.97 Tf
(\241)Tj
/T1_2 7.97 Tf
11.47 0 Td
(1)Tj
/T1_0 10.91 Tf
8.57 1.77 Td
[(up)-351(to)-352(the)-352(highest)-352(la)27(y)28(er)]TJ
/T1_6 10.91 Tf
112.89 0 Td
(L)Tj
/T1_2 7.97 Tf
7.52 -1.63 Td
(0)Tj
/T1_0 10.91 Tf
-463.14 -20.28 Td
[(to)-424(form)-425(the)-425(subgroup)-425(k)26(eys)]TJ
/T1_1 10.91 Tf
134.23 0 Td
(K)Tj
/T1_3 7.97 Tf
9.27 -1.64 Td
[(v)-35(;j)]TJ
/T1_0 10.91 Tf
15.77 1.64 Td
[(for)-425(1)]TJ
/T1_6 10.91 Tf
27.84 0 Td
(\267)Tj
/T1_1 10.91 Tf
13.18 0 Td
(v)Tj
/T1_6 10.91 Tf
10.37 0 Td
(\267)Tj
/T1_1 10.91 Tf
13.18 0 Td
(h)Tj
/T1_6 10.91 Tf
9.37 0 Td
(\241)Tj
/T1_0 10.91 Tf
11.57 0 Td
[(1)-425(and)-425(0)]TJ
/T1_6 10.91 Tf
42.45 0 Td
(\267)Tj
/T1_1 10.91 Tf
13.17 0 Td
(j)Tj
/T1_6 10.91 Tf
9.81 0 Td
(\267)Tj
/T1_1 10.91 Tf
13.18 0 Td
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[(do)-27(es)-362(not)-361(kno)27(w)-361(the)-362(priv)55(ate)-361(k)27(ey)-361(of)]TJ
/T1_3 10.91 Tf
162.21 0 Td
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5.72 -1.77 Td
(h)Tj
/T1_5 7.97 Tf
(\241)Tj
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(1)Tj
/T1_4 7.97 Tf
15.7 0 Td
(;j)Tj
/T1_1 10.91 Tf
10.67 1.77 Td
[(and)-362(the)-361(DSA)]TJ
-404.69 -21.91 Td
[(signature)-243(sc)26(heme)-242(is)-244(assumed)-244(to)-244(b)-27(e)-244(secure,)-262(therefore)]TJ
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241.59 0 Td
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11.36 0 Td
[(is)-244(not)-243(able)-244(to)-244(pro)-28(duce)-244(a)-243(v)54(alid)-243(signature)]TJ
/T1_7 10.91 Tf
183.23 0 Td
(\276)Tj
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6.23 -1.78 Td
(h)Tj
/T1_5 7.97 Tf
(\241)Tj
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11.47 0 Td
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-464.84 -21.92 Td
(Hence)Tj
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32.89 0 Td
(A)Tj
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12.81 0 Td
[(is)-376(not)-377(able)-377(to)-376(imp)-28(ersonate)-377(user)]TJ
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154.25 0 Td
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5.73 -1.78 Td
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4.87 0 Td
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6.59 0 Td
(1)Tj
/T1_4 7.97 Tf
(;j)Tj
/T1_1 10.91 Tf
15.07 1.78 Td
[(for)-376(0)]TJ
/T1_2 10.91 Tf
26.44 0 Td
(\267)Tj
/T1_7 10.91 Tf
12.3 0 Td
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8.93 0 Td
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12.3 0 Td
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4.72 3.96 Td
(h)Tj
/T1_2 10.91 Tf
8.11 -3.96 Td
(\241)Tj
/T1_1 10.91 Tf
11.22 0 Td
[(1.)-574(Next,)-388(supp)-27(ose)-377(the)-377(adv)27(ersary)]TJ
/T1_2 10.91 Tf
-316.23 -21.92 Td
(A)Tj
/T1_1 10.91 Tf
12.65 0 Td
[(tries)-361(to)-361(imp)-28(ersonate)-362(a)-361(subgroup)-361(con)26(troller)]TJ
/T1_3 10.91 Tf
206.36 0 Td
(S)Tj
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5.72 -1.63 Td
[(v)-36(;j)]TJ
/T1_1 10.91 Tf
15.09 1.63 Td
(\(0)Tj
/T1_2 10.91 Tf
13.23 0 Td
(\267)Tj
/T1_7 10.91 Tf
12.02 0 Td
(v)Tj
/T1_2 10.91 Tf
9.22 0 Td
(\267)Tj
/T1_7 10.91 Tf
12.03 0 Td
(h)Tj
/T1_2 10.91 Tf
8.91 0 Td
(\241)Tj
/T1_1 10.91 Tf
11.11 0 Td
[(2)-361(and)-361(0)]TJ
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39.9 0 Td
(\267)Tj
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12.02 0 Td
(j)Tj
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8.66 0 Td
(\267)Tj
/T1_7 10.91 Tf
12.02 0 Td
(c)Tj
/T1_4 7.97 Tf
4.72 3.96 Td
(v)Tj
/T1_6 7.97 Tf
4.41 0 Td
(+1)Tj
/T1_2 10.91 Tf
13.94 -3.96 Td
(\241)Tj
/T1_1 10.91 Tf
11.11 0 Td
[(1\))-361(in)-361(Phase)]TJ
-413.12 -21.91 Td
[(2a,)-385(then)]TJ
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43.44 0 Td
(A)Tj
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12.8 0 Td
[(computes)-435(\271)]TJ
/T1_7 10.91 Tf
48.99 0 Td
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5.07 -1.64 Td
[(v)-35(;j)]TJ
/T1_1 10.91 Tf
14.93 1.64 Td
(=)Tj
/T1_7 10.91 Tf
12.27 0 Td
(g)Tj
/T1_4 7.97 Tf
5.6 3.96 Td
(r)Tj
/T1_8 5.98 Tf
3.82 -1.22 Td
[(v)-35(;j)]TJ
/T1_1 10.91 Tf
13.64 -2.74 Td
[(mo)-28(d)]TJ
/T1_7 10.91 Tf
23.94 0 Td
(p)Tj
/T1_1 10.91 Tf
5.48 0 Td
[(,)-386(DH)-375(k)27(eys)]TJ
/T1_7 10.91 Tf
52.29 0 Td
(T)Tj
/T1_4 7.97 Tf
6.37 -1.78 Td
(v)Tj
/T1_6 7.97 Tf
4.41 0 Td
(+1)Tj
/T1_4 7.97 Tf
[(;j)-57(c)]TJ
/T1_6 7.97 Tf
(+)Tj
/T1_4 7.97 Tf
27.31 0 Td
(k)Tj
/T1_1 10.91 Tf
8.91 1.78 Td
(=)Tj
/T1_7 10.91 Tf
12.27 0 Td
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/T1_4 7.97 Tf
5.55 6.13 Td
(r)Tj
/T1_8 5.98 Tf
3.82 -1.21 Td
[(v)-35(;j)]TJ
/T1_4 7.97 Tf
-4.3 -8.44 Td
(v)Tj
/T1_6 7.97 Tf
4.41 0 Td
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/T1_4 7.97 Tf
[(;j)-57(c)]TJ
/T1_6 7.97 Tf
(+)Tj
/T1_4 7.97 Tf
(k)Tj
/T1_1 10.91 Tf
35.45 3.52 Td
[(mo)-27(d)]TJ
/T1_7 10.91 Tf
23.93 0 Td
(p)Tj
/T1_1 10.91 Tf
9.58 0 Td
[(for)-375(0)]TJ
/T1_2 10.91 Tf
26.39 0 Td
(\267)Tj
/T1_7 10.91 Tf
12.28 0 Td
(k)Tj
/T1_2 10.91 Tf
9.81 0 Td
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/T1_7 10.91 Tf
12.27 0 Td
(c)Tj
/T1_2 10.91 Tf
7.45 0 Td
(\241)Tj
/T1_1 10.91 Tf
11.21 0 Td
(1,)Tj
-459.39 -21.92 Td
[(subgroup)-302(k)26(ey)]TJ
/T1_7 10.91 Tf
66.38 0 Td
(K)Tj
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9.26 -1.63 Td
(v)Tj
/T1_6 7.97 Tf
4.41 0 Td
(+1)Tj
/T1_4 7.97 Tf
(;j)Tj
/T1_1 10.91 Tf
20.58 1.63 Td
[(=)-337(\271)]TJ
/T1_7 10.91 Tf
11.51 0 Td
(z)Tj
/T1_4 7.97 Tf
5.55 6.14 Td
(r)Tj
/T1_8 5.98 Tf
3.82 -1.22 Td
[(v)-36(;j)]TJ
/T1_4 7.97 Tf
-4.3 -8.17 Td
[(v)-36(;j)]TJ
/T1_2 10.91 Tf
16.68 3.25 Td
(\242)Tj
/T1_11 10.91 Tf
4.8 8.18 Td
(Q)Tj
/T1_4 7.97 Tf
10.3 -3.15 Td
(c)Tj
/T1_5 7.97 Tf
3.66 0 Td
(\241)Tj
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6.59 0 Td
(1)Tj
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-10.25 -8.25 Td
(k)Tj
/T1_6 7.97 Tf
4.62 0 Td
(=0)Tj
/T1_7 10.91 Tf
13.13 3.22 Td
(T)Tj
/T1_4 7.97 Tf
6.37 -1.77 Td
(v)Tj
/T1_6 7.97 Tf
4.41 0 Td
(+1)Tj
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[(;j)-57(c)]TJ
/T1_6 7.97 Tf
(+)Tj
/T1_4 7.97 Tf
(k)Tj
/T1_1 10.91 Tf
35.45 1.77 Td
[(mo)-27(d)]TJ
/T1_7 10.91 Tf
23.93 0 Td
(p)Tj
/T1_1 10.91 Tf
[(,)-309(ciphertexts)]TJ
/T1_3 10.91 Tf
67.7 0 Td
(c)Tj
/T1_4 7.97 Tf
5.72 -1.77 Td
(v)Tj
/T1_6 7.97 Tf
4.41 0 Td
(+1)Tj
/T1_4 7.97 Tf
[(;j)-57(c)]TJ
/T1_6 7.97 Tf
(+)Tj
/T1_4 7.97 Tf
27.31 0 Td
(k)Tj
/T1_1 10.91 Tf
8.14 1.77 Td
(=)Tj
/T1_2 10.91 Tf
11.51 0 Td
(E)Tj
/T1_4 7.97 Tf
5.76 -1.69 Td
(T)Tj
/T1_8 5.98 Tf
4.93 -1.4 Td
(v)Tj
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3.95 0 Td
(+1)Tj
/T1_8 5.98 Tf
9.24 0 Td
[(;j)-57(c)]TJ
/T1_10 5.98 Tf
(+)Tj
/T1_8 5.98 Tf
(k)Tj
/T1_1 10.91 Tf
19.67 3.09 Td
(\()Tj
/T1_7 10.91 Tf
(K)Tj
/T1_4 7.97 Tf
13.51 -1.63 Td
(v)Tj
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4.4 0 Td
(+1)Tj
/T1_4 7.97 Tf
(;j)Tj
/T1_2 10.91 Tf
17.55 1.63 Td
(jj)Tj
/T1_3 10.91 Tf
6.06 0 Td
(S)Tj
/T1_4 7.97 Tf
5.73 -1.63 Td
[(v)-35(;j)]TJ
/T1_1 10.91 Tf
11.14 1.63 Td
(\))Tj
-463.63 -21.91 Td
[(for)-397(0)]TJ
/T1_2 10.91 Tf
27.05 0 Td
(\267)Tj
/T1_7 10.91 Tf
12.68 0 Td
(k)Tj
/T1_2 10.91 Tf
10.23 0 Td
(\267)Tj
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12.68 0 Td
(c)Tj
/T1_2 10.91 Tf
7.61 0 Td
(\241)Tj
/T1_1 10.91 Tf
11.38 0 Td
[(1)-397(and)]TJ
/T1_7 10.91 Tf
31.7 0 Td
(z)Tj
/T1_4 7.97 Tf
5.07 -1.64 Td
[(v)-35(;j)]TJ
/T1_1 10.91 Tf
15.34 1.64 Td
(=)Tj
/T1_7 10.91 Tf
12.69 0 Td
(g)Tj
/T1_12 7.97 Tf
5.59 3.95 Td
(H)Tj
/T1_6 7.97 Tf
(\()Tj
/T1_4 7.97 Tf
(K)Tj
/T1_8 5.98 Tf
16.41 -1.21 Td
(v)Tj
/T1_10 5.98 Tf
3.95 0 Td
(+1)Tj
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9.24 0 Td
(;j)Tj
/T1_6 7.97 Tf
6.17 1.21 Td
(\))Tj
/T1_1 10.91 Tf
6.82 -3.95 Td
[(mo)-27(d)]TJ
/T1_7 10.91 Tf
23.93 0 Td
(p)Tj
/T1_1 10.91 Tf
[(.)-637(Next,)]TJ
/T1_2 10.91 Tf
46.04 0 Td
(A)Tj
/T1_1 10.91 Tf
13.05 0 Td
[(has)-397(to)-398(compute)-398(the)-398(signatures)]TJ
/T1_7 10.91 Tf
150.96 0 Td
(\276)Tj
/T1_4 7.97 Tf
6.23 -1.64 Td
[(v)-35(;j)]TJ
/T1_1 10.91 Tf
15.48 1.64 Td
(and)Tj
-449.71 -21.92 Td
(\271)Tj
/T1_7 10.91 Tf
-0.59 0 Td
(\276)Tj
/T1_4 7.97 Tf
6.23 -1.64 Td
[(v)-36(;j)]TJ
/T1_1 10.91 Tf
15.66 1.64 Td
(of)Tj
/T1_3 10.91 Tf
13.3 0 Td
(S)Tj
/T1_4 7.97 Tf
5.73 -1.64 Td
[(v)-35(;j)]TJ
/T1_2 10.91 Tf
11.14 1.64 Td
(jj)Tj
/T1_7 10.91 Tf
6.06 0 Td
(z)Tj
/T1_4 7.97 Tf
5.07 -1.64 Td
[(v)-35(;j)]TJ
/T1_1 10.91 Tf
15.66 1.64 Td
(and)Tj
/T1_3 10.91 Tf
22.08 0 Td
(S)Tj
/T1_4 7.97 Tf
5.73 -1.64 Td
[(v)-35(;j)]TJ
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11.14 1.64 Td
(jj)Tj
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6.71 0 Td
(\271)Tj
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-0.65 0 Td
(z)Tj
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5.07 -1.64 Td
[(v)-36(;j)]TJ
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11.14 1.64 Td
(jj)Tj
/T1_3 10.91 Tf
6.06 0 Td
(c)Tj
/T1_4 7.97 Tf
5.73 -1.78 Td
(v)Tj
/T1_6 7.97 Tf
4.4 0 Td
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[(;j)-57(c)]TJ
/T1_6 7.97 Tf
(+)Tj
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27.31 0 Td
(k)Tj
/T1_1 10.91 Tf
9.63 1.78 Td
[(for)-414(0)]TJ
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27.53 0 Td
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12.98 0 Td
(k)Tj
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10.52 0 Td
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12.98 0 Td
(c)Tj
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7.73 0 Td
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11.49 0 Td
[(1)-414(resp)-28(ectiv)27(ely)83(.)-685(The)-415(v)55(alidit)28(y)-413(of)]TJ
/T1_7 10.91 Tf
151.98 0 Td
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6.23 -1.64 Td
[(v)-36(;j)]TJ
/T1_1 10.91 Tf
15.66 1.64 Td
(and)Tj
-449.71 -21.92 Td
(\271)Tj
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-0.59 0 Td
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/T1_4 7.97 Tf
6.23 -1.63 Td
[(v)-36(;j)]TJ
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15.4 1.63 Td
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13.76 0 Td
(\267)Tj
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12.54 0 Td
(v)Tj
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9.74 0 Td
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12.55 0 Td
(h)Tj
/T1_2 10.91 Tf
9.12 0 Td
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11.32 0 Td
[(2)-389(and)-391(0)]TJ
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41.05 0 Td
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12.54 0 Td
(j)Tj
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9.18 0 Td
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12.55 0 Td
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4.72 3.96 Td
(v)Tj
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4.41 0 Td
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14.15 -3.96 Td
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11.32 0 Td
[(1\))-389(is)-391(c)27(hec)28(k)28(ed)-390(b)27(y)]TJ
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81.91 0 Td
(S)Tj
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5.73 -1.63 Td
(v)Tj
/T1_5 7.97 Tf
4.4 0 Td
(\241)Tj
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6.59 0 Td
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(;i)Tj
/T1_1 10.91 Tf
14.22 1.63 Td
(where)Tj
/T1_7 10.91 Tf
32.16 0 Td
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7.82 0 Td
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12.54 0 Td
(b)Tj
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6.04 4.93 Td
(j)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 371.99 -392.76 cm
0 0 m
3.89 0 l
S
Q
Q
BT
/T1_4 7.97 Tf
1.0003 0 0 1.0003 444.2042 370.4582 Tm
(c)Tj
/T1_2 10.91 Tf
4.97 3.76 Td
(c)Tj
/T1_1 10.91 Tf
9.11 0 Td
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21.82 0 Td
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5.73 -1.77 Td
(v)Tj
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4.41 0 Td
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10.81 0 Td
(;j)Tj
1.0003 0 0 1.0003 72 769.82 Tm
435.191 -397.26 Td
(c)Tj
/T1_6 7.97 Tf
(+)Tj
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(k)Tj
/T1_1 10.91 Tf
19.619 1.77 Td
(for)Tj
-454.81 -21.91 Td
(0)Tj
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8.48 0 Td
(\267)Tj
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11.51 0 Td
(k)Tj
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9.05 0 Td
(\267)Tj
/T1_7 10.91 Tf
11.52 0 Td
(c)Tj
/T1_2 10.91 Tf
6.53 0 Td
(\241)Tj
/T1_1 10.91 Tf
10.3 0 Td
[(1)-305(resp)-28(ectiv)27(ely)83(.)-434(If)-306(the)-305(signatures)]TJ
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151.92 0 Td
(\276)Tj
/T1_4 7.97 Tf
6.23 -1.64 Td
[(v)-36(;j)]TJ
/T1_1 10.91 Tf
14.48 1.64 Td
[(and)-358(\271)]TJ
/T1_7 10.91 Tf
20.9 0 Td
(\276)Tj
/T1_4 7.97 Tf
6.23 -1.64 Td
[(v)-36(;j)]TJ
/T1_1 10.91 Tf
14.48 1.64 Td
[(are)-305(not)-305(correct,)-311(then)]TJ
/T1_3 10.91 Tf
100.72 0 Td
(S)Tj
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5.73 -1.64 Td
(v)Tj
/T1_5 7.97 Tf
4.41 0 Td
(\241)Tj
/T1_6 7.97 Tf
(1)Tj
/T1_4 7.97 Tf
10.82 0 Td
(;i)Tj
/T1_1 10.91 Tf
9.06 1.64 Td
(where)Tj
/T1_7 10.91 Tf
31.23 0 Td
(i)Tj
/T1_1 10.91 Tf
6.79 0 Td
(=)Tj
/T1_2 10.91 Tf
11.51 0 Td
(b)Tj
/T1_4 7.97 Tf
6.05 4.93 Td
(j)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 457.95 -414.68 cm
0 0 m
3.88 0 l
S
Q
Q
BT
/T1_4 7.97 Tf
1.0003 0 0 1.0003 530.1783 348.5421 Tm
(c)Tj
/T1_2 10.91 Tf
4.97 3.76 Td
(c)Tj
/T1_1 10.91 Tf
-463.02 -21.92 Td
(and)Tj
/T1_3 10.91 Tf
21.1 0 Td
(S)Tj
/T1_4 7.97 Tf
5.72 -1.78 Td
(v)Tj
/T1_6 7.97 Tf
4.41 0 Td
(+1)Tj
/T1_4 7.97 Tf
(;j)Tj
1.0003 0 0 1.0003 72 769.82 Tm
48.283 -441.1 Td
(c)Tj
/T1_6 7.97 Tf
(+)Tj
/T1_4 7.97 Tf
(k)Tj
/T1_1 10.91 Tf
18.897 1.78 Td
[(for)-322(0)]TJ
/T1_2 10.91 Tf
25.06 0 Td
(\267)Tj
/T1_7 10.91 Tf
11.51 0 Td
(k)Tj
/T1_2 10.91 Tf
9.05 0 Td
(\267)Tj
/T1_7 10.91 Tf
11.51 0 Td
(c)Tj
/T1_2 10.91 Tf
6.93 0 Td
(\241)Tj
/T1_1 10.91 Tf
10.68 0 Td
[(1)-323(rejects)]TJ
/T1_3 10.91 Tf
43.19 0 Td
(S)Tj
/T1_4 7.97 Tf
5.73 -1.64 Td
[(v)-35(;j)]TJ
/T1_1 10.91 Tf
11.14 1.64 Td
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10.06 0 Td
[(1)-294(or)-294(subgroup)]TJ
-402.56 -21.92 Td
[(con)27(troller)]TJ
/T1_1 10.91 Tf
49.68 0 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.63 Td
[(v)-35(;j)]TJ
/T1_0 10.91 Tf
15.62 1.63 Td
[(for)-410(0)]TJ
/T1_4 10.91 Tf
27.43 0 Td
(\267)Tj
/T1_5 10.91 Tf
12.92 0 Td
(v)Tj
/T1_4 10.91 Tf
10.12 0 Td
(\267)Tj
/T1_5 10.91 Tf
12.92 0 Td
(h)Tj
/T1_4 10.91 Tf
9.28 0 Td
(\241)Tj
/T1_0 10.91 Tf
11.47 0 Td
[(2)-410(and)-411(0)]TJ
/T1_4 10.91 Tf
41.88 0 Td
(\267)Tj
/T1_5 10.91 Tf
12.92 0 Td
(j)Tj
/T1_4 10.91 Tf
9.55 0 Td
(\267)Tj
/T1_5 10.91 Tf
12.93 0 Td
(c)Tj
/T1_3 7.97 Tf
4.72 3.96 Td
(v)Tj
/T1_2 7.97 Tf
4.4 0 Td
(+1)Tj
/T1_4 10.91 Tf
14.31 -3.96 Td
(\241)Tj
/T1_0 10.91 Tf
11.47 0 Td
[(1)-410(to)-411(establish)-411(the)-411(subgroup)-411(k)27(eys)]TJ
/T1_5 10.91 Tf
162.58 0 Td
(K)Tj
/T1_3 7.97 Tf
9.26 -1.63 Td
[(v)-36(;j)]TJ
/T1_0 10.91 Tf
15.62 1.63 Td
(for)Tj
-454.81 -21.91 Td
(1)Tj
/T1_4 10.91 Tf
9.32 0 Td
(\267)Tj
/T1_5 10.91 Tf
12.35 0 Td
(v)Tj
/T1_4 10.91 Tf
9.55 0 Td
(\267)Tj
/T1_5 10.91 Tf
12.35 0 Td
(h)Tj
/T1_4 10.91 Tf
9.04 0 Td
(\241)Tj
/T1_0 10.91 Tf
11.24 0 Td
[(1)-379(and)-379(0)]TJ
/T1_4 10.91 Tf
40.62 0 Td
(\267)Tj
/T1_5 10.91 Tf
12.35 0 Td
(j)Tj
/T1_4 10.91 Tf
8.98 0 Td
(\267)Tj
/T1_5 10.91 Tf
12.35 0 Td
(c)Tj
/T1_3 7.97 Tf
4.72 3.96 Td
(v)Tj
/T1_4 10.91 Tf
7.67 -3.96 Td
(\241)Tj
/T1_0 10.91 Tf
11.24 0 Td
[(1)-379(and)-379(the)-380(\257nal)-379(group)-379(k)26(ey)]TJ
/T1_5 10.91 Tf
126.95 0 Td
(K)Tj
/T1_0 10.91 Tf
10.04 0 Td
[(.)-583(No)27(w)-378(consider)-380(case)-379(\(b\))-379(as)-380(follo)27(ws:)]TJ
-298.77 -21.92 Td
[(Supp)-27(ose)-266(the)-266(adv)27(ersary)]TJ
/T1_4 10.91 Tf
108.86 0 Td
(A)Tj
/T1_0 10.91 Tf
11.61 0 Td
[(tries)-265(to)-266(obtain)-266(the)-266(subgroup)-266(k)27(eys)]TJ
/T1_5 10.91 Tf
157.3 0 Td
(K)Tj
/T1_3 7.97 Tf
9.26 -1.63 Td
[(v)-36(;j)]TJ
/T1_0 10.91 Tf
14.05 1.63 Td
[(for)-265(1)]TJ
/T1_4 10.91 Tf
24.44 0 Td
(\267)Tj
/T1_5 10.91 Tf
11.51 0 Td
(v)Tj
/T1_4 10.91 Tf
8.71 0 Td
(\267)Tj
/T1_5 10.91 Tf
11.51 0 Td
(h)Tj
/T1_4 10.91 Tf
7.24 0 Td
(\241)Tj
/T1_0 10.91 Tf
9.43 0 Td
[(1)-266(and)-266(0)]TJ
/T1_4 10.91 Tf
37.31 0 Td
(\267)Tj
/T1_5 10.91 Tf
11.51 0 Td
(j)Tj
/T1_4 10.91 Tf
8.15 0 Td
(\267)Tj
/T1_5 10.91 Tf
11.51 0 Td
(c)Tj
/T1_3 7.97 Tf
4.72 3.96 Td
(v)Tj
/T1_4 10.91 Tf
5.86 -3.96 Td
(\241)Tj
/T1_0 10.91 Tf
9.44 0 Td
(1)Tj
-462.42 -21.91 Td
[(from)-304(the)-305(up)-304(\260o)26(w)-303(information)-305(sen)27(t.)-434(Then)-305(Phase)-304(1)-305(and)-305(Phase)-304(2a)-305(\(without)-305(the)-304(signature)-305(information)]TJ
0 -21.92 TD
[(sen)27(t\))-391(is)-392(just)-392(the)-393(NLKW)-392(proto)-28(col)-392(for)-392(eac)27(h)-391(subgroup)]TJ
/T1_4 10.91 Tf
253.77 0 Td
(G)Tj
/T1_3 7.97 Tf
6.49 -1.64 Td
[(v)-35(;j)]TJ
/T1_0 10.91 Tf
15.42 1.64 Td
(\(1)Tj
/T1_4 10.91 Tf
13.79 0 Td
(\267)Tj
/T1_5 10.91 Tf
12.58 0 Td
(v)Tj
/T1_4 10.91 Tf
9.78 0 Td
(\267)Tj
/T1_5 10.91 Tf
12.58 0 Td
(h)Tj
/T1_4 10.91 Tf
9.14 0 Td
(\241)Tj
/T1_0 10.91 Tf
11.33 0 Td
[(1)-392(and)-392(0)]TJ
/T1_4 10.91 Tf
41.13 0 Td
(\267)Tj
/T1_5 10.91 Tf
12.59 0 Td
(j)Tj
/T1_4 10.91 Tf
9.21 0 Td
(\267)Tj
/T1_5 10.91 Tf
12.58 0 Td
(c)Tj
/T1_3 7.97 Tf
4.72 3.96 Td
(v)Tj
/T1_4 10.91 Tf
7.76 -3.96 Td
(\241)Tj
/T1_0 10.91 Tf
11.33 0 Td
[(1\))-392(to)]TJ
-444.2 -21.92 Td
[(establish)-370(the)-370(subgroup)-370(k)27(ey)]TJ
/T1_5 10.91 Tf
132.39 0 Td
(K)Tj
/T1_3 7.97 Tf
9.26 -1.63 Td
[(v)-36(;j)]TJ
/T1_0 10.91 Tf
11.14 1.63 Td
[(.)-555(As)-370(the)-370(NLKW)-370(proto)-28(col)-370(is)-370(pro)26(v)56(ably)-369(secure,)-380(hence)-370(the)-370(adv)27(ersary)]TJ
/T1_4 10.91 Tf
-152.79 -21.91 Td
(A)Tj
/T1_0 10.91 Tf
12.56 0 Td
[(is)-354(not)-353(able)-354(to)-353(obtain)-354(the)-354(subgroup)-353(k)27(ey)]TJ
/T1_5 10.91 Tf
188.24 0 Td
(K)Tj
/T1_3 7.97 Tf
9.26 -1.64 Td
[(v)-35(;j)]TJ
/T1_0 10.91 Tf
15 1.64 Td
[(for)-353(1)]TJ
/T1_4 10.91 Tf
25.76 0 Td
(\267)Tj
/T1_5 10.91 Tf
11.88 0 Td
(v)Tj
/T1_4 10.91 Tf
9.08 0 Td
(\267)Tj
/T1_5 10.91 Tf
11.88 0 Td
(h)Tj
/T1_4 10.91 Tf
8.85 0 Td
(\241)Tj
/T1_0 10.91 Tf
11.06 0 Td
[(1)-353(and)-353(0)]TJ
/T1_4 10.91 Tf
39.59 0 Td
(\267)Tj
/T1_5 10.91 Tf
11.88 0 Td
(j)Tj
/T1_4 10.91 Tf
8.51 0 Td
(\267)Tj
/T1_5 10.91 Tf
11.88 0 Td
(c)Tj
/T1_3 7.97 Tf
4.72 3.95 Td
(v)Tj
/T1_4 10.91 Tf
7.48 -3.95 Td
(\241)Tj
/T1_0 10.91 Tf
11.05 0 Td
[(1)-353(using)-354(the)-353(up)]TJ
-398.68 -21.92 Td
[(\260o)27(w)-303(information.)-435(Next,)-310(supp)-28(ose)-304(the)-304(adv)27(ersary)]TJ
/T1_4 10.91 Tf
223.43 0 Td
(A)Tj
/T1_0 10.91 Tf
12.03 0 Td
[(tries)-303(to)-305(obtain)-304(the)-304(\257nal)-304(group)-305(k)27(ey)]TJ
/T1_5 10.91 Tf
163 0 Td
(K)Tj
/T1_0 10.91 Tf
13.36 0 Td
[(from)-304(the)-304(up)]TJ
-411.82 -21.92 Td
[(\260o)27(w)-306(information)-308(sen)27(t.)-435(Then)-308(Phase)-308(2a\(ii\),)-312(Phase)-308(3)-308(and)-307(Phase)-308(4)-308(is)-307(just)-308(the)-308(BD)-307(proto)-28(col)-308(to)-308(establish)]TJ
0 -21.91 TD
[(the)-301(\257nal)-301(group)-301(k)27(ey)]TJ
/T1_5 10.91 Tf
92.23 0 Td
(K)Tj
/T1_0 10.91 Tf
10.04 0 Td
[(.)-434(As)-301(the)-301(BD)-301(proto)-27(col)-301(is)-301(pro)26(v)56(ably)-300(secure,)-308(hence)-301(the)-301(adv)27(ersary)]TJ
/T1_4 10.91 Tf
291.59 0 Td
(A)Tj
/T1_0 10.91 Tf
11.99 0 Td
[(is)-301(not)-301(able)-301(to)]TJ
-405.85 -21.92 Td
[(obtain)-360(the)-360(\257nal)-360(group)-360(k)27(ey)]TJ
/T1_5 10.91 Tf
129.03 0 Td
(K)Tj
/T1_0 10.91 Tf
13.97 0 Td
[(from)-360(the)-360(up)-360(\260o)27(w)-359(information.)-525(Therefore,)-367(w)27(e)-359(conclude)-360(that)-360(it)-360(is)-360(not)]TJ
-143 -21.92 Td
[(p)-27(ossible)-305(for)-306(the)-305(adv)27(ersary)]TJ
/T1_4 10.91 Tf
124.77 0 Td
(A)Tj
/T1_0 10.91 Tf
12.03 0 Td
[(to)-305(obtain)-305(the)-305(subgroup)-305(k)27(eys)]TJ
/T1_5 10.91 Tf
135.85 0 Td
(K)Tj
/T1_3 7.97 Tf
9.26 -1.63 Td
[(v)-36(;j)]TJ
/T1_0 10.91 Tf
14.47 1.63 Td
[(for)-305(1)]TJ
/T1_4 10.91 Tf
24.87 0 Td
(\267)Tj
/T1_5 10.91 Tf
11.51 0 Td
(v)Tj
/T1_4 10.91 Tf
8.71 0 Td
(\267)Tj
/T1_5 10.91 Tf
11.51 0 Td
(h)Tj
/T1_4 10.91 Tf
8.09 0 Td
(\241)Tj
/T1_0 10.91 Tf
10.29 0 Td
[(1)-305(and)-305(0)]TJ
/T1_4 10.91 Tf
38.16 0 Td
(\267)Tj
/T1_5 10.91 Tf
11.52 0 Td
(j)Tj
/T1_4 10.91 Tf
8.14 0 Td
(\267)Tj
/T1_5 10.91 Tf
11.51 0 Td
(c)Tj
/T1_3 7.97 Tf
4.72 3.96 Td
(v)Tj
/T1_4 10.91 Tf
6.72 -3.96 Td
(\241)Tj
/T1_0 10.91 Tf
10.29 0 Td
(1)Tj
-462.42 -21.91 Td
[(and)-333(the)-333(\257nal)-333(group)-334(k)27(ey)]TJ
/T1_5 10.91 Tf
114.85 0 Td
(K)Tj
/T1_0 10.91 Tf
13.68 0 Td
[(from)-332(the)-334(up)-333(\260o)27(w)-333(information)-333(sen)27(t)-333(\(Phase)-333(1,)-333(2a,)-334(3)-333(and)-333(4\).)]TJ
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
6.1 w
q 1 0 0 1 464.82 -339.7 cm
0 0 m
0 6.1 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 88.9347 408.0987 Tm
(Next,)Tj
1.0003 0 0 1.0003 72 769.82 Tm
46.649 -361.62 Td
[(w)27(e)-333(shall)-335(examine)-335(the)-334(securit)26(y)-333(of)-335(the)-335(subgroup)-334(k)27(eys)]TJ
/T1_5 10.91 Tf
246.411 0 Td
(K)Tj
/T1_3 7.97 Tf
9.26 -1.64 Td
[(v)-36(;j)]TJ
/T1_0 10.91 Tf
14.79 1.64 Td
[(and)-335(\257nal)-334(group)-335(k)27(ey)]TJ
/T1_5 10.91 Tf
96.13 0 Td
(K)Tj
/T1_0 10.91 Tf
13.69 0 Td
[(from)-334(the)]TJ
-426.93 -21.92 Td
[(do)27(wn)-332(\260o)27(w)-333(information)-333(\(Phase)-333(2b)-334(and)-333(5\).)]TJ
/T1_7 10.91 Tf
0 -29.91 TD
[(Theorem)-383(26)]TJ
/T1_8 10.91 Tf
71.25 0 Td
[(Given)-390(the)-391(down)-390(\260ow)-391(information)-390(\(Phase)-390(2b)-391(and)-390(5\),)-399(an)-390(adversary)]TJ
/T1_4 10.91 Tf
320.15 0 Td
(A)Tj
/T1_8 10.91 Tf
12.97 0 Td
[(is)-390(not)-390(able)-391(to)]TJ
-404.37 -21.92 Td
[(obtain)-342(the)-342(sub)50(gr)52(oup)-341(keys)]TJ
/T1_5 10.91 Tf
119.02 0 Td
(K)Tj
/T1_3 7.97 Tf
9.26 -1.64 Td
[(v)-36(;j)]TJ
/T1_8 10.91 Tf
14.87 1.64 Td
(for)Tj
/T1_0 10.91 Tf
17.25 0 Td
(1)Tj
/T1_4 10.91 Tf
8.48 0 Td
(\267)Tj
/T1_5 10.91 Tf
11.52 0 Td
(v)Tj
/T1_4 10.91 Tf
8.7 0 Td
(\267)Tj
/T1_5 10.91 Tf
11.52 0 Td
(h)Tj
/T1_4 10.91 Tf
8.33 0 Td
(\241)Tj
/T1_0 10.91 Tf
10.53 0 Td
(1)Tj
/T1_8 10.91 Tf
9.19 0 Td
(and)Tj
/T1_0 10.91 Tf
21.01 0 Td
(0)Tj
/T1_4 10.91 Tf
8.48 0 Td
(\267)Tj
/T1_5 10.91 Tf
11.51 0 Td
(j)Tj
/T1_4 10.91 Tf
8.15 0 Td
(\267)Tj
/T1_5 10.91 Tf
11.51 0 Td
(c)Tj
/T1_3 7.97 Tf
4.72 3.96 Td
(v)Tj
/T1_4 10.91 Tf
6.96 -3.96 Td
(\241)Tj
/T1_0 10.91 Tf
10.53 0 Td
(1)Tj
/T1_8 10.91 Tf
9.18 0 Td
[(and)-342(\257nal)-342(gr)50(oup)-341(key)]TJ
/T1_5 10.91 Tf
94.22 0 Td
(K)Tj
/T1_8 10.91 Tf
13.77 0 Td
[(pr)50(ovide)52(d)]TJ
-428.71 -21.92 Td
[(the)-357(symmetric)-358(key)-358(encryption)-358(scheme)]TJ
/T1_9 10.91 Tf
182.55 0 Td
(SKE)Tj
/T1_8 10.91 Tf
24.05 0 Td
[(is)-357(se)50(cur)51(e)-357(and)-358(the)]TJ
/T1_9 10.91 Tf
83.75 0 Td
(CDH)Tj
/T1_8 10.91 Tf
26.48 0 Td
[(pr)51(oblem)-357(is)-358(di\261cult.)]TJ
-295.02 -29.92 Td
[(Pr)50(o)52(of:)]TJ
/T1_0 10.91 Tf
38.34 0 Td
[(As)-309(it)-310(is)-310(already)-309(sho)26(wn)-308(in)-310(Theorem)-310(25)-309(that)-310(the)-310(adv)27(ersary)]TJ
/T1_4 10.91 Tf
272 0 Td
(A)Tj
/T1_0 10.91 Tf
12.09 0 Td
[(is)-309(not)-310(able)-309(to)-310(imp)-28(ersonate)]TJ
-344.24 -21.91 Td
[(an)27(y)-244(user)]TJ
/T1_1 10.91 Tf
41.79 0 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.78 Td
(h)Tj
/T1_6 7.97 Tf
4.87 0 Td
(\241)Tj
/T1_2 7.97 Tf
6.59 0 Td
(1)Tj
/T1_3 7.97 Tf
(;j)Tj
/T1_0 10.91 Tf
13.64 1.78 Td
[(for)-244(0)]TJ
/T1_4 10.91 Tf
24.21 0 Td
(\267)Tj
/T1_5 10.91 Tf
11.51 0 Td
(j)Tj
/T1_4 10.91 Tf
8.15 0 Td
(\267)Tj
/T1_5 10.91 Tf
11.51 0 Td
(c)Tj
/T1_3 7.97 Tf
4.72 3.95 Td
(h)Tj
/T1_4 10.91 Tf
5.87 -3.95 Td
(\241)Tj
/T1_0 10.91 Tf
8.98 0 Td
[(1)-245(and)-245(subgroup)-245(con)27(troller)]TJ
/T1_1 10.91 Tf
122.63 0 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.64 Td
[(v)-35(;j)]TJ
/T1_0 10.91 Tf
13.81 1.64 Td
[(for)-245(0)]TJ
/T1_4 10.91 Tf
24.21 0 Td
(\267)Tj
/T1_5 10.91 Tf
11.51 0 Td
(v)Tj
/T1_4 10.91 Tf
8.71 0 Td
(\267)Tj
/T1_5 10.91 Tf
11.51 0 Td
(h)Tj
/T1_4 10.91 Tf
6.79 0 Td
(\241)Tj
/T1_0 10.91 Tf
8.98 0 Td
[(2)-244(and)-245(0)]TJ
/T1_4 10.91 Tf
36.85 0 Td
(\267)Tj
/T1_5 10.91 Tf
11.51 0 Td
(j)Tj
/T1_4 10.91 Tf
8.14 0 Td
(\267)Tj
/T1_5 10.91 Tf
11.52 0 Td
(c)Tj
/T1_3 7.97 Tf
4.72 3.95 Td
(v)Tj
/T1_2 7.97 Tf
4.4 0 Td
(+1)Tj
/T1_4 10.91 Tf
11.82 -3.95 Td
(\241)Tj
/T1_0 10.91 Tf
8.98 0 Td
(1,)Tj
-459.39 -21.92 Td
[(hence)-370(the)-371(adv)27(ersary)-370(only)-371(has)-370(the)-371(do)27(wn)-370(\260o)27(w)-370(information)-371(in)-370(Phase)-371(2b)-371(and)-370(5.)-557(First,)-380(w)27(e)-370(consider)-371(if)]TJ
0 -21.92 TD
[(the)-331(adv)27(ersary)]TJ
/T1_4 10.91 Tf
68.24 0 Td
(A)Tj
/T1_0 10.91 Tf
12.32 0 Td
[(is)-331(able)-331(to)-332(obtain)-331(the)-332(subgroup)-331(k)27(eys)]TJ
/T1_5 10.91 Tf
171.23 0 Td
(K)Tj
/T1_3 7.97 Tf
9.26 -1.63 Td
[(v)-36(;j)]TJ
/T1_0 10.91 Tf
14.76 1.63 Td
[(from)-331(the)-331(do)27(wn)-330(\260o)26(w)-330(information,)-332(that)-331(is,)]TJ
-275.15 -21.91 Td
(\271)Tj
/T1_5 10.91 Tf
-0.66 0 Td
(z)Tj
/T1_3 7.97 Tf
5.07 -1.64 Td
(v)Tj
/T1_6 7.97 Tf
4.41 0 Td
(\241)Tj
/T1_2 7.97 Tf
(1)Tj
/T1_3 7.97 Tf
10.82 0 Td
(;j)Tj
/T1_0 10.91 Tf
6.73 1.64 Td
(,)Tj
/T1_5 10.91 Tf
6.04 0 Td
(z)Tj
/T1_3 7.97 Tf
5.08 -1.78 Td
[(v)-35(;k)]TJ
/T1_0 10.91 Tf
14.73 1.78 Td
(and)Tj
/T1_1 10.91 Tf
20.43 0 Td
(c)Tj
/T1_3 7.97 Tf
5.73 -1.78 Td
[(v)-35(;k)]TJ
/T1_0 10.91 Tf
14.74 1.78 Td
[(for)-261(1)]TJ
/T1_4 10.91 Tf
24.39 0 Td
(\267)Tj
/T1_5 10.91 Tf
11.52 0 Td
(v)Tj
/T1_4 10.91 Tf
8.7 0 Td
(\267)Tj
/T1_5 10.91 Tf
11.52 0 Td
(h)Tj
/T1_4 10.91 Tf
7.15 0 Td
(\241)Tj
/T1_0 10.91 Tf
9.35 0 Td
[(1,)-276(0)]TJ
/T1_4 10.91 Tf
19.98 0 Td
(\267)Tj
/T1_5 10.91 Tf
11.51 0 Td
(k)Tj
/T1_4 10.91 Tf
9.05 0 Td
(\267)Tj
/T1_5 10.91 Tf
11.52 0 Td
(c)Tj
/T1_3 7.97 Tf
4.72 3.96 Td
(v)Tj
/T1_2 7.97 Tf
4.4 0 Td
(+1)Tj
/T1_4 10.91 Tf
12.19 -3.96 Td
(\241)Tj
/T1_0 10.91 Tf
9.35 0 Td
[(1)-262(and)]TJ
/T1_5 10.91 Tf
28.75 0 Td
(j)Tj
/T1_0 10.91 Tf
8.14 0 Td
(=)Tj
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/T1_5 7.97 Tf
(;)Tj
/T1_4 7.97 Tf
(0)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 106.52 -195.11 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 108.51 -195.11 cm
0 0 m
0 13.54 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 194.8344 578.7165 Tm
(3)Tj
/T1_1 10.91 Tf
(h)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 148.82 -195.11 cm
0 0 m
0 13.54 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 233.2051 578.7165 Tm
(2)Tj
/T1_1 10.91 Tf
(h)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 185.23 -195.11 cm
0 0 m
0 13.54 l
S
Q
Q
BT
/T1_1 10.91 Tf
1.0003 0 0 1.0003 263.2635 578.7165 Tm
(h)Tj
/T1_0 10.91 Tf
(\()Tj
/T1_1 10.91 Tf
(c)Tj
/T1_0 10.91 Tf
17.67 0 Td
(+)Tj
1.0003 0 0 1.0003 72 769.82 Tm
219.779 -191.05 Td
(1\))Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 235.45 -195.11 cm
0 0 m
0 13.54 l
S
Q
Q
BT
/T1_1 10.91 Tf
1.0003 0 0 1.0003 323.0003 578.7165 Tm
(h)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 272.69 -195.11 cm
0 0 m
0 13.54 l
S
Q
Q
BT
/T1_1 10.91 Tf
1.0003 0 0 1.0003 350.748 578.7165 Tm
(h)Tj
/T1_0 10.91 Tf
(\()Tj
/T1_1 10.91 Tf
10.53 0 Td
(c)Tj
/T1_2 10.91 Tf
7.14 0 Td
(\241)Tj
/T1_0 10.91 Tf
10.9 0 Td
(1\))Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 322.91 -195.11 cm
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0 13.54 l
S
Q
Q
BT
/T1_1 10.91 Tf
1.0003 0 0 1.0003 400.9821 578.7165 Tm
(h)Tj
/T1_0 10.91 Tf
(\()Tj
/T1_1 10.91 Tf
10.53 0 Td
(c)Tj
/T1_2 10.91 Tf
7.14 0 Td
(\241)Tj
/T1_0 10.91 Tf
10.9 0 Td
(1\))Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 373.13 -195.11 cm
0 0 m
0 13.54 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 451.2162 578.7165 Tm
(3)Tj
/T1_1 10.91 Tf
(h)Tj
/T1_2 10.91 Tf
14.16 0 Td
(\241)Tj
/T1_0 10.91 Tf
10.91 0 Td
(1)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 415.61 -195.11 cm
0 0 m
0 13.54 l
S
Q
Q
BT
/T1_1 10.91 Tf
1.0003 0 0 1.0003 493.698 578.7165 Tm
(h)Tj
/T1_0 10.91 Tf
6.29 0 Td
(\()Tj
/T1_1 10.91 Tf
(c)Tj
/T1_0 10.91 Tf
11.38 0 Td
(+)Tj
1.0003 0 0 1.0003 72 769.82 Tm
450.16 -191.05 Td
(1\))Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 465.83 -195.11 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
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q 1 0 0 1 467.82 -195.11 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 65.65 -195.31 cm
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402.17 0 l
S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
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q 1 0 0 1 0.05 -208.66 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 2.04 -208.66 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 86.154 565.1627 Tm
(BD-)Tj
1.0003 0 0 1.0003 72 769.82 Tm
37.486 -204.6 Td
(BD)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 65.65 -208.66 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_2 10.91 Tf
1.0003 0 0 1.0003 149.2916 565.1627 Tm
(G)Tj
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6.49 -1.63 Td
(v)Tj
1.0003 0 0 1.0003 72 769.82 Tm
88.159 -206.23 Td
(;j)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 106.52 -208.66 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 108.51 -208.66 cm
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0 13.55 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 188.4626 565.1627 Tm
(3\()Tj
/T1_1 10.91 Tf
(h)Tj
/T1_2 10.91 Tf
(\241)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 148.82 -208.66 cm
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S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 226.8333 565.1627 Tm
(2\()Tj
/T1_1 10.91 Tf
(h)Tj
/T1_2 10.91 Tf
(\241)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 185.23 -208.66 cm
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S
Q
Q
BT
/T1_1 10.91 Tf
1.0003 0 0 1.0003 277.9877 565.1627 Tm
(B)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 235.45 -208.66 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_1 10.91 Tf
1.0003 0 0 1.0003 313.4976 565.1627 Tm
(h)Tj
/T1_2 10.91 Tf
8.7 0 Td
(\241)Tj
/T1_1 10.91 Tf
10.91 0 Td
(v)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 272.69 -208.66 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_1 10.91 Tf
1.0003 0 0 1.0003 365.6022 565.1627 Tm
(C)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 322.91 -208.66 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_1 10.91 Tf
1.0003 0 0 1.0003 415.8362 565.1627 Tm
(C)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 373.13 -208.66 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_1 10.91 Tf
1.0003 0 0 1.0003 462.3893 565.1627 Tm
(A)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 415.61 -208.66 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_1 10.91 Tf
1.0003 0 0 1.0003 499.0295 565.1627 Tm
(B)Tj
/T1_0 10.91 Tf
11.25 0 Td
(+)Tj
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449.07 -204.6 Td
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ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 465.83 -208.66 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 2.04 -222.2 cm
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0 13.54 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 90.4052 551.6189 Tm
(\(Ch.7\))Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 65.65 -222.2 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 108.51 -222.2 cm
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S
Q
Q
BT
/T1_1 10.91 Tf
1.0003 0 0 1.0003 195.7346 551.6189 Tm
(v)Tj
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5.68 0 Td
(\))Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 148.82 -222.2 cm
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S
Q
Q
BT
/T1_1 10.91 Tf
1.0003 0 0 1.0003 234.1154 551.6189 Tm
(v)Tj
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ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
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q 1 0 0 1 272.69 -222.2 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
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S
Q
Q
q
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S
Q
Q
q
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 65.65 -235.75 cm
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S
Q
Q
BT
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1.0003 0 0 1.0003 143.6401 538.0651 Tm
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6.49 -1.77 Td
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(\241)Tj
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11.47 0 Td
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(;j)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
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S
Q
Q
BT
/T1_0 10.91 Tf
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(6)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 148.82 -235.75 cm
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S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 236.346 538.0651 Tm
(4)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 185.23 -235.75 cm
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S
Q
Q
BT
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1.0003 0 0 1.0003 263.6737 538.0651 Tm
(2\()Tj
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(c)Tj
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16.84 0 Td
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ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 235.45 -235.75 cm
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S
Q
Q
BT
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1.0003 0 0 1.0003 323.4204 538.0651 Tm
(2)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 272.69 -235.75 cm
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0 13.55 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 351.1681 538.0651 Tm
(2\()Tj
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(c)Tj
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(\241)Tj
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ET
q
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0.4 w
q 1 0 0 1 322.91 -235.75 cm
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S
Q
Q
BT
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1.0003 0 0 1.0003 401.4022 538.0651 Tm
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ET
q
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0.4 w
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S
Q
Q
BT
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(5)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 415.61 -235.75 cm
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S
Q
Q
BT
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1.0003 0 0 1.0003 498.3593 538.0651 Tm
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12.59 0 Td
(+)Tj
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ET
q
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0.4 w
q 1 0 0 1 465.83 -235.75 cm
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S
Q
Q
q
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0.4 w
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S
Q
Q
q
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S
Q
Q
q
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S
Q
Q
q
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S
Q
Q
q
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0.4 w
q 1 0 0 1 65.65 -249.3 cm
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S
Q
Q
BT
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ET
q
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0.4 w
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S
Q
Q
q
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0 13.55 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 197.9753 524.5213 Tm
(3)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 148.82 -249.3 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 236.346 524.5213 Tm
(2)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 185.23 -249.3 cm
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0 13.55 l
S
Q
Q
BT
/T1_1 10.91 Tf
1.0003 0 0 1.0003 270.6456 524.5213 Tm
(c)Tj
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7.14 0 Td
(+)Tj
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ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 235.45 -249.3 cm
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S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 323.4204 524.5213 Tm
(1)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 272.69 -249.3 cm
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0 13.55 l
S
Q
Q
BT
/T1_1 10.91 Tf
1.0003 0 0 1.0003 358.1301 524.5213 Tm
(c)Tj
/T1_2 10.91 Tf
7.15 0 Td
(\241)Tj
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10.9 0 Td
(1)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
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S
Q
Q
BT
/T1_1 10.91 Tf
1.0003 0 0 1.0003 408.3642 524.5213 Tm
(c)Tj
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7.15 0 Td
(\241)Tj
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10.9 0 Td
(1)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
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0 13.55 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 463.7497 524.5213 Tm
(2)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 415.61 -249.3 cm
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0 13.55 l
S
Q
Q
BT
/T1_1 10.91 Tf
1.0003 0 0 1.0003 501.0801 524.5213 Tm
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7.15 0 Td
(+)Tj
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447.02 -245.23 Td
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ET
q
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0.4 w
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S
Q
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q
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
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467.77 0 l
S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 2.04 -263.24 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 92.7358 510.5674 Tm
(Prop.)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 65.65 -263.24 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_3 10.91 Tf
1.0003 0 0 1.0003 149.7618 510.5674 Tm
(S)Tj
/T1_4 7.97 Tf
5.72 -1.63 Td
(0)Tj
/T1_5 7.97 Tf
4.24 0 Td
(;j)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 106.52 -263.24 cm
0 0 m
0 13.55 l
S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 108.51 -263.24 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_1 10.91 Tf
1.0003 0 0 1.0003 194.0942 510.5674 Tm
(c)Tj
/T1_0 10.91 Tf
(+)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 148.82 -263.24 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 236.346 510.5674 Tm
(3)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 185.23 -263.24 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 273.0663 510.5674 Tm
(2)Tj
/T1_1 10.91 Tf
(c)Tj
/T1_0 10.91 Tf
(+)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 235.45 -263.24 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 323.4204 510.5674 Tm
(2)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 272.69 -263.24 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 360.5608 510.5674 Tm
(2)Tj
/T1_1 10.91 Tf
(c)Tj
/T1_2 10.91 Tf
(\241)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 322.91 -263.24 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 410.7948 510.5674 Tm
(2)Tj
/T1_1 10.91 Tf
(c)Tj
/T1_2 10.91 Tf
(\241)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 373.13 -263.24 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 463.7497 510.5674 Tm
(4)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 415.61 -263.24 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 503.5108 510.5674 Tm
(2)Tj
/T1_1 10.91 Tf
(c)Tj
/T1_0 10.91 Tf
(+)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 465.83 -263.24 cm
0 0 m
0 13.55 l
S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 467.82 -263.24 cm
0 0 m
0 13.55 l
S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 0.05 -276.78 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 2.04 -276.78 cm
0 0 m
0 13.54 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 93.6461 497.0236 Tm
(Prot.)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 65.65 -276.78 cm
0 0 m
0 13.54 l
S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 106.52 -276.78 cm
0 0 m
0 13.54 l
S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 108.51 -276.78 cm
0 0 m
0 13.54 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 197.9753 497.0236 Tm
(5)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 148.82 -276.78 cm
0 0 m
0 13.54 l
S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 185.23 -276.78 cm
0 0 m
0 13.54 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 279.6681 497.0236 Tm
(1)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 235.45 -276.78 cm
0 0 m
0 13.54 l
S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 272.69 -276.78 cm
0 0 m
0 13.54 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 367.1626 497.0236 Tm
(1)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 322.91 -276.78 cm
0 0 m
0 13.54 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 417.3967 497.0236 Tm
(1)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 373.13 -276.78 cm
0 0 m
0 13.54 l
S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 415.61 -276.78 cm
0 0 m
0 13.54 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 510.1126 497.0236 Tm
(1)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 465.83 -276.78 cm
0 0 m
0 13.54 l
S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 467.82 -276.78 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 65.65 -276.98 cm
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402.17 0 l
S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 0.05 -290.33 cm
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0 13.55 l
S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 2.04 -290.33 cm
0 0 m
0 13.55 l
S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 65.65 -290.33 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_3 10.91 Tf
1.0003 0 0 1.0003 149.6717 483.4698 Tm
(S)Tj
/T1_5 7.97 Tf
5.73 -1.63 Td
(v)Tj
1.0003 0 0 1.0003 72 769.82 Tm
87.779 -287.9 Td
(;j)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 106.52 -290.33 cm
0 0 m
0 13.55 l
S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 108.51 -290.33 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_1 10.91 Tf
1.0003 0 0 1.0003 194.0942 483.4698 Tm
(c)Tj
/T1_0 10.91 Tf
(+)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 148.82 -290.33 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 236.346 483.4698 Tm
(2)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 185.23 -290.33 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_1 10.91 Tf
1.0003 0 0 1.0003 275.797 483.4698 Tm
(c)Tj
/T1_0 10.91 Tf
(+)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 235.45 -290.33 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 323.4204 483.4698 Tm
(2)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 272.69 -290.33 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_1 10.91 Tf
1.0003 0 0 1.0003 363.2815 483.4698 Tm
(c)Tj
/T1_0 10.91 Tf
(+)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 322.91 -290.33 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_1 10.91 Tf
1.0003 0 0 1.0003 413.5156 483.4698 Tm
(c)Tj
/T1_0 10.91 Tf
(+)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 373.13 -290.33 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 463.7497 483.4698 Tm
(3)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 415.61 -290.33 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_1 10.91 Tf
1.0003 0 0 1.0003 506.2316 483.4698 Tm
(c)Tj
/T1_0 10.91 Tf
(+)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 465.83 -290.33 cm
0 0 m
0 13.55 l
S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 467.82 -290.33 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 0.05 -303.88 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 2.04 -303.88 cm
0 0 m
0 13.55 l
S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 65.65 -303.88 cm
0 0 m
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 106.52 -303.88 cm
0 0 m
0 13.55 l
S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 108.51 -303.88 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 197.9753 469.9261 Tm
(4)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 148.82 -303.88 cm
0 0 m
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 185.23 -303.88 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 279.6681 469.9261 Tm
(1)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 235.45 -303.88 cm
0 0 m
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 272.69 -303.88 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 367.1626 469.9261 Tm
(1)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 322.91 -303.88 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 417.3967 469.9261 Tm
(1)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 373.13 -303.88 cm
0 0 m
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 415.61 -303.88 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 510.1126 469.9261 Tm
(2)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 465.83 -303.88 cm
0 0 m
0 13.55 l
S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 467.82 -303.88 cm
0 0 m
0 13.55 l
S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 65.65 -304.07 cm
0 0 m
402.17 0 l
S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 0.05 -317.42 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 2.04 -317.42 cm
0 0 m
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 65.65 -317.42 cm
0 0 m
0 13.54 l
S
Q
Q
BT
/T1_3 10.91 Tf
1.0003 0 0 1.0003 144.5303 456.3723 Tm
(S)Tj
/T1_5 7.97 Tf
5.72 -1.77 Td
(h)Tj
/T1_6 7.97 Tf
(\241)Tj
/T1_4 7.97 Tf
(1)Tj
/T1_5 7.97 Tf
15.7 0 Td
(;i)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 106.52 -317.42 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 108.51 -317.42 cm
0 0 m
0 13.54 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 197.9753 456.3723 Tm
(2)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 148.82 -317.42 cm
0 0 m
0 13.54 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 236.346 456.3723 Tm
(1)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 185.23 -317.42 cm
0 0 m
0 13.54 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 279.6681 456.3723 Tm
(1)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 235.45 -317.42 cm
0 0 m
0 13.54 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 323.4204 456.3723 Tm
(1)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 272.69 -317.42 cm
0 0 m
0 13.54 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 367.1626 456.3723 Tm
(1)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 322.91 -317.42 cm
0 0 m
0 13.54 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 417.3967 456.3723 Tm
(1)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 373.13 -317.42 cm
0 0 m
0 13.54 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 463.7497 456.3723 Tm
(1)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 415.61 -317.42 cm
0 0 m
0 13.54 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 510.1126 456.3723 Tm
(2)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 465.83 -317.42 cm
0 0 m
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 467.82 -317.42 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 0.05 -317.62 cm
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467.77 0 l
S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 0.05 -319.61 cm
0 0 m
467.77 0 l
S
Q
Q
BT
/T1_1 10.91 Tf
1.0003 0 0 1.0003 72 428.7845 Tm
(A)Tj
/T1_0 10.91 Tf
11.81 0 Td
(:)Tj
1.0003 0 0 1.0003 72 769.82 Tm
19.687 -340.94 Td
(2\()Tj
/T1_1 10.91 Tf
(h)Tj
/T1_2 10.91 Tf
18.403 0 Td
(\241)Tj
/T1_1 10.91 Tf
10.91 0 Td
(v)Tj
/T1_0 10.91 Tf
5.68 0 Td
[(\))-221(+)-223(\()]TJ
/T1_1 10.91 Tf
21.81 0 Td
(h)Tj
/T1_2 10.91 Tf
8.71 0 Td
(\241)Tj
/T1_1 10.91 Tf
10.9 0 Td
(v)Tj
/T1_0 10.91 Tf
8.1 0 Td
[(+)-222(1\))]TJ
/T1_1 10.91 Tf
63.86 0 Td
(B)Tj
/T1_0 10.91 Tf
12.46 0 Td
[(:)-444(\(\()]TJ
/T1_1 10.91 Tf
(h)Tj
/T1_2 10.91 Tf
25.07 0 Td
(\241)Tj
/T1_1 10.91 Tf
10.9 0 Td
(v)Tj
/T1_0 10.91 Tf
5.68 0 Td
(\)\()Tj
/T1_1 10.91 Tf
8.48 0 Td
(c)Tj
/T1_0 10.91 Tf
7.15 0 Td
[(+)-221(1\)\))]TJ
/T1_1 10.91 Tf
68.1 0 Td
(C)Tj
/T1_0 10.91 Tf
12.21 0 Td
[(:)-444(\(\()]TJ
/T1_1 10.91 Tf
(h)Tj
/T1_2 10.91 Tf
25.06 0 Td
(\241)Tj
/T1_1 10.91 Tf
10.91 0 Td
(v)Tj
/T1_0 10.91 Tf
5.68 0 Td
(\)\()Tj
/T1_1 10.91 Tf
8.48 0 Td
(c)Tj
/T1_2 10.91 Tf
7.14 0 Td
(\241)Tj
/T1_0 10.91 Tf
10.91 0 Td
(1\)\))Tj
-386.29 -13.54 Td
[(F)83(or)-332(NLKW)-334([NLKW05],)]TJ
/T1_3 10.91 Tf
116.21 0 Td
(C)Tj
/T1_0 10.91 Tf
9.36 0 Td
[(refers)-333(to)-333(the)-334(con)27(troller)-332(no)-28(de.)]TJ
-125.57 -13.55 Td
[(F)83(or)-332(NHS)-334([NKW05],)]TJ
/T1_3 10.91 Tf
97.12 0 Td
(C)Tj
/T1_0 10.91 Tf
9.37 0 Td
(and)Tj
/T1_3 10.91 Tf
21.2 0 Td
(S)Tj
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T*
[(is)-314(imp)-28(ortan)27(t)-314(for)-315(GKA)-314(proto)-28(cols)-315(to)-314(pro)26(vide)-313(protection)-315(against)-315(DoS)-314(attac)27(ks.)-438(Ho)27(w)28(ev)28(er,)-318(most)-314(curren)26(t)]TJ
0 -21.91 TD
[(GKA)-333(proto)-28(cols)-333(in)-333(literature)-334(do)-333(not)-333(discuss)-334(on)-333(protection)-333(against)-334(DoS)-333(attac)27(ks.)]TJ
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[(can)-310(also)-310(launc)27(h)-309(insider)-310(attac)27(ks)-309(in)-310(whic)26(h)-309(they)-310(send)-310(\\bad")-310(or)-310(\\wrong")-310(proto)-28(col)-310(messages)-310(to)-310(halt)-310(the)]TJ
T*
[(GKA)-266(proto)-28(col.)-422(This)-266(will)-266(cause)-266(all)-267(group)-266(mem)27(b)-27(ers)-266(to)-267(rep)-27(eatedly)-267(re-start)-266(the)-266(GKA)-267(proto)-27(col,)-280(thereb)27(y)]TJ
0 -21.92 TD
[(depleting)-378(system)-379(resources)-379(without)-378(establish)-379(an)27(y)-378(group)-379(k)27(ey)83(.)-579(Kim)-379(et)-378(al)-379([KLL04])-379(brie\260y)-379(describ)-27(ed)]TJ
T*
[(in)-375(their)-375(pap)-28(er)-375(that)-375(it)-376(is)-375(not)-375(easy)-376(to)-375(detect)-375(insider)-375(adv)26(ersaries)-374(but)-375(did)-376(not)-375(go)-375(in)27(to)-375(details)-375(on)-375(ho)27(w)]TJ
0 -21.91 TD
[(to)-377(reco)27(v)28(er)-376(from)-378(suc)27(h)-376(an)-377(insider)-378(attac)27(k.)-575(In)-377(fact,)-388(most)-377(curren)26(t)-376(GKA)-377(proto)-28(cols,)-388(with)-377(the)-378(exception)]TJ
0 -21.92 TD
[(of)-391([DPSW06],)-405(fo)-28(cus)-391(mainly)-391(on)-391(protection)-392(against)-391(malicious)-391(adv)27(ersaries)-390(\(also)-391(kno)26(wn)-390(as)-391(malicious)]TJ
T*
[(outsider)-333(adv)27(ersaries\))-332(and)-334(do)-333(not)-333(consider)-334(malicious)-333(group)-333(mem)26(b)-26(ers.)]TJ
16.93 -21.91 Td
[(In)-444(this)-445(c)27(hapter,)-471(w)27(e)-444(prop)-28(ose)-444(three)-444(GKA)-445(proto)-28(cols,)-472(namely)-444(the)-445(Initial)-444(GKA,)-445(Join)-444(and)-445(Lea)27(v)28(e)]TJ
208.83 -47.37 Td
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[(lea)27(ving)-491(and)-493(the)-492(\257nal)-492(group)-493(k)27(ey)-491(when)-493(dynamic)-492(group)-493(mem)27(b)-27(ership)-492(ev)27(en)28(ts)-492(suc)27(h)-491(as)-493(user)-492(join)-493(or)]TJ
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[(user)-459(lea)27(v)28(e)-458(o)-28(ccur.)-822(The)-459(prop)-28(osed)-459(proto)-28(cols)-459(pro)27(vide)-458(b)-28(oth)-459(protection)-459(against)-459(insider)-459(and)-459(outsider)]TJ
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[(DoS)-466(attac)27(ks)-466(and)-467(k)27(ey)-466(con\257rmation,)-500(whic)27(h)-466(are)-467(not)-467(pro)27(vided)-466(b)27(y)-466(most)-466(GKA)-467(proto)-28(cols)-467(in)-466(curren)26(t)]TJ
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T*
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[(group)-404(mem)27(b)-27(ers.)-657(Both)-404(the)-404(complexit)27(y)-403(and)-404(energy)-405(analysis)-404(sho)27(w)-403(that)-404(the)-405(prop)-27(osed)-404(Initial)-405(GKA,)]TJ
T*
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[(our)-320(comm)27(unication)-319(energy)-321(analysis)-320(separates)-321(p)-27(oin)26(t-to-p)-26(oin)26(t)-319(\(P2P\))-320(and)-321(broadcast)-320(comm)27(unications)]TJ
T*
[(\(transmission)-389(and)-390(reception\))-390(to)-390(pro)26(vide)-388(a)-390(more)-390(detailed)-390(study)-390(of)-390(comm)27(unication)-389(energy)-390(costs)-390(as)]TJ
0 -21.91 TD
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0 -21.92 TD
[(and)-451(broadcast)-451(transmission)-451(and)-452(reception)-451(energy)-451(costs.)-799(W)83(e)-451(also)-451(state)-451(the)-451(assumptions)-452(for)-451(the)]TJ
T*
[(Certi\257cation)-333(Authorit)27(y)-332(and)-334(Heterogeneous)-333(Net)27(w)28(ork)-333(no)-28(des)-333(b)-28(elo)27(w.)]TJ
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[(9.1.1)-1125(Certi\257cation)-375(Authorit)31(y)]TJ
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0 -21.92 TD
[(its)-285(public)-286(k)27(ey)-285(with)-286(the)-285(Certi\257cation)-286(Authorit)27(y)-285(\(CA\))-286(to)-286(obtain)-285(a)-286(RSA)-286(public)-286(k)27(ey)-284(certi\257cate)-286(through)]TJ
T*
[(a)-333(secure)-333(c)27(hannel)-333(during)-333(the)-333(Initialization)-334(Phase.)]TJ
/T1_3 11.95 Tf
0 -37.82 TD
[(9.1.2)-1125(Heterogeneous)-375(Net)31(w)31(ork)-374(no)-31(des)]TJ
/T1_0 10.91 Tf
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[(W)83(e)-394(assume)-394(that)-394(the)-395(asymmetric)-394(heterogenous)-395(net)27(w)28(ork)-394(consists)-394(of)-395(high)-394(p)-28(o)27(w)28(er)-394(no)-27(des)-395(\(e.g.)-628(access)]TJ
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(190)Tj
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T*
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[(net)27(w)28(ork.)-592(Therefore,)-395(attac)27(ks)-382(suc)27(h)-382(as)-383(tamp)-28(ering,)-395(capture)-382(or)-383(replication)-383(of)-383(these)-383(high)-382(p)-28(o)27(w)27(er)-381(no)-28(des)]TJ
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[(9.2)-1124(Prop)-32(osed)-375(Group)-375(Key)-375(Agreemen)31(t)-374(Proto)-32(cols)-375(for)-375(the)]TJ
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[(Group)-436(Key)-437(Agreemen)26(t)-435(\(GKA\))-437(\(Group)-437(F)82(ormation\))-436(Proto)-28(col,)-462(Join)-437(Proto)-28(col)-437(and)-437(Lea)27(v)28(e)-436(Proto)-28(col,)]TJ
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T*
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T*
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/T1_0 10.91 Tf
10.04 0 Td
[(.)-432(Note)-295(that)-296(coun)27(ter)]TJ
/T1_1 10.91 Tf
95.61 0 Td
(v)Tj
/T1_0 10.91 Tf
8.71 0 Td
[(=)-277(0)-296(for)-296(the)-295(Initial)-296(GKA)-296(proto)-28(col.)-432(The)-295(coun)26(ter)]TJ
/T1_1 10.91 Tf
-248.24 -21.92 Td
(v)Tj
/T1_0 10.91 Tf
9.08 0 Td
[(is)-312(used)-313(to)-312(k)27(eep)-312(trac)27(k)-311(of)-313(the)-312(n)27(um)28(b)-27(er)-313(of)-312(proto)-28(col)-312(executions)-312(and)-313(also)-312(to)-313(b)-27(e)-313(used)-312(as)-313(an)-312(input)-312(to)-313(the)]TJ
-9.08 -21.91 Td
[(hash)-333(functions)-333(to)-333(prev)26(en)28(t)-332(repla)27(y)-333(attac)27(ks.)-443(The)-334(Initial)-333(GKA)-333(proto)-28(col)-334(is)-333(as)-333(follo)27(ws:)]TJ
/T1_4 10.91 Tf
0 -27.89 TD
[(Phase)-383(1:)-511(Subgroup)-383(Key)-384(Generation)]TJ
/T1_0 10.91 Tf
0 -27.9 TD
[(Round)-333(1)]TJ
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 0 -155.93 cm
0 0 m
40.75 0 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 117.7328 615.3668 Tm
(:)Tj
1.0003 0 0 1.0003 72 769.82 Tm
56.259 -154.41 Td
[(Eac)27(h)-455(subgroup)-455(con)26(troller)]TJ
/T1_2 10.91 Tf
127.301 0 Td
(S)Tj
/T1_3 7.97 Tf
5.72 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
8.64 1.63 Td
(=)Tj
/T1_2 10.91 Tf
13.73 0 Td
(U)Tj
/T1_3 7.97 Tf
5.73 -1.63 Td
(i;)Tj
/T1_5 7.97 Tf
5.23 0 Td
(1)Tj
/T1_0 10.91 Tf
9.7 1.63 Td
[(for)-455(1)]TJ
/T1_6 10.91 Tf
28.73 0 Td
(\267)Tj
/T1_1 10.91 Tf
13.74 0 Td
(i)Tj
/T1_6 10.91 Tf
9 0 Td
(\267)Tj
/T1_1 10.91 Tf
13.74 0 Td
(n)Tj
/T1_3 7.97 Tf
6.55 -1.63 Td
(c)Tj
/T1_0 10.91 Tf
9.13 1.63 Td
[(randomly)-455(selects)]TJ
/T1_1 10.91 Tf
85.52 0 Td
(\267)Tj
/T1_3 7.97 Tf
6.29 -1.63 Td
(i;)Tj
/T1_5 7.97 Tf
5.23 0 Td
(1)Tj
/T1_6 10.91 Tf
9.98 1.63 Td
[(2)-481(f)]TJ
/T1_0 10.91 Tf
(0)Tj
/T1_1 10.91 Tf
(;)Tj
/T1_0 10.91 Tf
28.28 0 Td
(1)Tj
/T1_6 10.91 Tf
(g)Tj
/T1_3 7.97 Tf
10.9 3.96 Td
(\270)Tj
/T1_0 10.91 Tf
5.44 -3.96 Td
(,)Tj
-464.84 -21.91 Td
(computes)Tj
/T1_1 10.91 Tf
48.32 0 Td
(\277)Tj
/T1_3 7.97 Tf
4.76 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
6.41 1.64 Td
(=)Tj
/T1_7 10.91 Tf
11.52 0 Td
(H)Tj
/T1_0 10.91 Tf
(\()Tj
/T1_1 10.91 Tf
(\267)Tj
/T1_3 7.97 Tf
18.25 -1.64 Td
(i;)Tj
/T1_5 7.97 Tf
5.23 0 Td
(1)Tj
/T1_6 10.91 Tf
4.73 1.64 Td
(jj)Tj
/T1_0 10.91 Tf
6.06 0 Td
[(0\))-313(and)-313(broadcasts)]TJ
/T1_6 10.91 Tf
87.96 0 Td
(f)Tj
/T1_2 10.91 Tf
(S)Tj
/T1_3 7.97 Tf
11.18 -1.64 Td
(i)Tj
/T1_6 10.91 Tf
3.38 1.64 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(\277)Tj
/T1_3 7.97 Tf
4.77 -1.64 Td
(i)Tj
/T1_6 10.91 Tf
3.38 1.64 Td
(g)Tj
/T1_0 10.91 Tf
8.87 0 Td
[(to)-313(subgroup)-313(mem)26(b)-26(ers)-314(of)]TJ
/T1_6 10.91 Tf
118.37 0 Td
(G)Tj
/T1_3 7.97 Tf
6.49 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
3.38 1.64 Td
[(,)-317(where)]TJ
/T1_1 10.91 Tf
37.81 0 Td
(\270)Tj
/T1_0 10.91 Tf
9.78 0 Td
[(is)-313(an)-314(in)27(teger.)]TJ
-406.71 -21.92 Td
[(Round)-333(2)]TJ
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 0 -199.77 cm
0 0 m
40.75 0 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 116.8325 571.5245 Tm
(:)Tj
1.0003 0 0 1.0003 72 769.82 Tm
53.559 -198.24 Td
[(Eac)26(h)-372(subgroup)-373(mem)27(b)-27(er)]TJ
/T1_2 10.91 Tf
117.611 0 Td
(U)Tj
/T1_3 7.97 Tf
5.73 -1.64 Td
(i;j)Tj
/T1_0 10.91 Tf
13.68 1.64 Td
[(for)-373(1)]TJ
/T1_6 10.91 Tf
26.34 0 Td
(\267)Tj
/T1_1 10.91 Tf
12.23 0 Td
(i)Tj
/T1_6 10.91 Tf
7.51 0 Td
(\267)Tj
/T1_1 10.91 Tf
12.24 0 Td
(n)Tj
/T1_3 7.97 Tf
6.55 -1.64 Td
(c)Tj
/T1_0 10.91 Tf
8.23 1.64 Td
[(and)-373(2)]TJ
/T1_6 10.91 Tf
30.85 0 Td
(\267)Tj
/T1_1 10.91 Tf
12.24 0 Td
(j)Tj
/T1_6 10.91 Tf
8.87 0 Td
(\267)Tj
/T1_1 10.91 Tf
12.24 0 Td
(n)Tj
/T1_3 7.97 Tf
6.54 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
7.45 1.64 Td
[(randomly)-373(selects)]TJ
/T1_1 10.91 Tf
83.73 0 Td
(r)Tj
/T1_3 7.97 Tf
4.92 -1.64 Td
(i;j)Tj
/T1_6 10.91 Tf
13.37 1.64 Td
(2)Tj
/T1_1 10.91 Tf
11.02 0 Td
(Z)Tj
/T1_8 7.97 Tf
8.23 3.96 Td
(\244)Tj
/T1_3 7.97 Tf
-0.78 -6.66 Td
(q)Tj
/T1_0 10.91 Tf
-462.36 -19.22 Td
[(and)-465(computes)]TJ
/T1_1 10.91 Tf
72.61 0 Td
(z)Tj
/T1_3 7.97 Tf
5.07 -1.63 Td
(i;j)Tj
/T1_0 10.91 Tf
15.04 1.63 Td
(=)Tj
/T1_1 10.91 Tf
13.91 0 Td
(g)Tj
/T1_3 7.97 Tf
5.59 3.96 Td
(r)Tj
/T1_9 5.98 Tf
3.82 -1.21 Td
(i;j)Tj
/T1_0 10.91 Tf
12.36 -2.75 Td
[(mo)-28(d)]TJ
/T1_1 10.91 Tf
23.94 0 Td
(p)Tj
/T1_0 10.91 Tf
5.48 0 Td
[(.)-840(Next,)]TJ
/T1_2 10.91 Tf
43.68 0 Td
(U)Tj
/T1_3 7.97 Tf
5.72 -1.63 Td
(i;j)Tj
/T1_0 10.91 Tf
14.69 1.63 Td
(broadcasts)Tj
/T1_6 10.91 Tf
55.51 0 Td
(f)Tj
/T1_2 10.91 Tf
(U)Tj
/T1_3 7.97 Tf
11.18 -1.63 Td
(i;j)Tj
/T1_6 10.91 Tf
9.62 1.63 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(z)Tj
/T1_3 7.97 Tf
5.07 -1.63 Td
(i;j)Tj
/T1_6 10.91 Tf
9.61 1.63 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(\276)Tj
/T1_3 7.97 Tf
6.23 -1.63 Td
(i;j)Tj
/T1_6 10.91 Tf
9.62 1.63 Td
(jj)Tj
/T1_2 10.91 Tf
6.06 0 Td
(cert)Tj
/T1_0 10.91 Tf
22.9 0 Td
([)Tj
/T1_2 10.91 Tf
(U)Tj
/T1_3 7.97 Tf
8.75 -1.63 Td
(i;j)Tj
/T1_0 10.91 Tf
9.62 1.63 Td
(])Tj
/T1_6 10.91 Tf
(g)Tj
/T1_0 10.91 Tf
[(,)-498(where)]TJ
/T1_1 10.91 Tf
49.92 0 Td
(\276)Tj
/T1_3 7.97 Tf
6.23 -1.63 Td
(i;j)Tj
/T1_0 10.91 Tf
15.04 1.63 Td
(=)Tj
/T1_6 10.91 Tf
-459.39 -21.91 Td
(S)Tj
/T1_0 10.91 Tf
7.42 0 Td
(\()Tj
/T1_2 10.91 Tf
(U)Tj
/T1_3 7.97 Tf
9.97 -1.64 Td
(i;j)Tj
/T1_6 10.91 Tf
9.61 1.64 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(z)Tj
/T1_3 7.97 Tf
5.07 -1.64 Td
(i;j)Tj
/T1_6 10.91 Tf
9.62 1.64 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(\277)Tj
/T1_3 7.97 Tf
4.77 -1.64 Td
(i)Tj
/T1_6 10.91 Tf
3.38 1.64 Td
(jj)Tj
/T1_0 10.91 Tf
6.06 0 Td
[(0\))-332(and)-334(stores)]TJ
/T1_1 10.91 Tf
65.58 0 Td
(\277)Tj
/T1_3 7.97 Tf
4.77 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
3.38 1.64 Td
(.)Tj
-141.75 -21.92 Td
[(Round)-333(3)]TJ
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 0 -265.52 cm
0 0 m
40.75 0 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 116.9726 505.7561 Tm
(:)Tj
1.0003 0 0 1.0003 72 769.82 Tm
54.004 -263.99 Td
[(Eac)26(h)]TJ
/T1_2 10.91 Tf
27.696 0 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
7.6 1.63 Td
[(for)-386(1)]TJ
/T1_6 10.91 Tf
26.73 0 Td
(\267)Tj
/T1_1 10.91 Tf
12.48 0 Td
(i)Tj
/T1_6 10.91 Tf
7.76 0 Td
(\267)Tj
/T1_1 10.91 Tf
12.49 0 Td
(n)Tj
/T1_3 7.97 Tf
6.54 -1.63 Td
(c)Tj
/T1_0 10.91 Tf
8.39 1.63 Td
[(\257rst)-386(c)27(hec)28(ks)-386(the)-387(receiv)27(ed)-386(signatures)]TJ
/T1_1 10.91 Tf
171.38 0 Td
(\276)Tj
/T1_3 7.97 Tf
6.23 -1.63 Td
(i;j)Tj
/T1_0 10.91 Tf
13.84 1.63 Td
[(for)-386(2)]TJ
/T1_6 10.91 Tf
26.73 0 Td
(\267)Tj
/T1_1 10.91 Tf
12.48 0 Td
(j)Tj
/T1_6 10.91 Tf
9.12 0 Td
(\267)Tj
/T1_1 10.91 Tf
12.48 0 Td
(n)Tj
/T1_3 7.97 Tf
6.55 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
3.38 1.63 Td
[(.)-604(If)-387(the)]TJ
-431.61 -21.92 Td
[(signature)-321(v)27(eri\257cations)-321(are)-321(correct,)]TJ
/T1_2 10.91 Tf
165.19 0 Td
(S)Tj
/T1_3 7.97 Tf
5.72 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
6.89 1.63 Td
[(c)27(hec)28(ks)-320(the)-322(receiv)27(ed)-320(certi\257cates)]TJ
/T1_2 10.91 Tf
148.41 0 Td
(cert)Tj
/T1_0 10.91 Tf
22.9 0 Td
([)Tj
/T1_2 10.91 Tf
(U)Tj
/T1_3 7.97 Tf
8.76 -1.63 Td
(i;j)Tj
/T1_0 10.91 Tf
9.61 1.63 Td
[(])-321(for)-321(2)]TJ
/T1_6 10.91 Tf
31.58 0 Td
(\267)Tj
/T1_1 10.91 Tf
11.51 0 Td
(j)Tj
/T1_6 10.91 Tf
8.15 0 Td
(\267)Tj
/T1_1 10.91 Tf
11.51 0 Td
(n)Tj
/T1_3 7.97 Tf
6.55 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
3.38 1.63 Td
[(.)-440(If)]TJ
/T1_2 10.91 Tf
18.6 0 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
-464.49 -20.28 Td
[(detects)-333(in)26(v)56(alid)-333(certi\257cates)-334(and/or)-333(signatures)-334(sen)27(t)-333(b)27(y)-333(certain)-334(malicious)-334(no)-27(des,)-334(then)-334(these)-334(malicious)]TJ
0 -21.92 TD
[(no)-27(des)-355(will)-354(b)-28(e)-355(placed)-354(in)27(to)-354(a)-354(list)]TJ
/T1_2 10.91 Tf
151.09 0 Td
(BL)Tj
/T1_10 7.97 Tf
11.45 -1.63 Td
(Z)Tj
/T1_0 10.91 Tf
4.73 1.63 Td
(.)Tj
/T1_2 10.91 Tf
8.57 0 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
7.25 1.63 Td
[(then)-354(selects)-354(random)]TJ
/T1_1 10.91 Tf
99.6 0 Td
(r)Tj
/T1_3 7.97 Tf
4.92 -1.63 Td
(i;)Tj
/T1_5 7.97 Tf
(1)Tj
/T1_6 10.91 Tf
13.38 1.63 Td
(2)Tj
/T1_1 10.91 Tf
10.69 0 Td
(Z)Tj
/T1_8 7.97 Tf
8.22 3.96 Td
(\244)Tj
/T1_3 7.97 Tf
-0.78 -6.65 Td
(q)Tj
/T1_0 10.91 Tf
5.51 2.69 Td
[(,)-360(computes)]TJ
/T1_1 10.91 Tf
55.72 0 Td
(z)Tj
/T1_3 7.97 Tf
5.07 -1.63 Td
(i;)Tj
/T1_5 7.97 Tf
(1)Tj
/T1_0 10.91 Tf
13.38 1.63 Td
(=)Tj
/T1_1 10.91 Tf
11.9 0 Td
(g)Tj
/T1_3 7.97 Tf
5.59 3.96 Td
(r)Tj
/T1_9 5.98 Tf
3.82 -1.22 Td
(i;)Tj
/T1_11 5.98 Tf
4.93 0 Td
(1)Tj
/T1_0 10.91 Tf
7.68 -2.74 Td
[(mo)-27(d)]TJ
/T1_1 10.91 Tf
23.93 0 Td
(p)Tj
/T1_0 10.91 Tf
-462.38 -21.91 Td
[(and)-333(broadcasts)]TJ
/T1_6 10.91 Tf
75.28 0 Td
(f)Tj
/T1_2 10.91 Tf
(S)Tj
/T1_3 7.97 Tf
11.18 -1.64 Td
(i)Tj
/T1_6 10.91 Tf
3.38 1.64 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(z)Tj
/T1_3 7.97 Tf
5.07 -1.64 Td
(i;)Tj
/T1_5 7.97 Tf
(1)Tj
/T1_6 10.91 Tf
9.97 1.64 Td
(jj)Tj
/T1_2 10.91 Tf
6.06 0 Td
(BL)Tj
/T1_10 7.97 Tf
11.45 -1.64 Td
(Z)Tj
/T1_6 10.91 Tf
4.73 1.64 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(\276)Tj
/T1_3 7.97 Tf
6.23 -1.64 Td
(i;)Tj
/T1_5 7.97 Tf
5.23 0 Td
(1)Tj
/T1_6 10.91 Tf
4.73 1.64 Td
(jj)Tj
/T1_2 10.91 Tf
6.06 0 Td
(cert)Tj
/T1_0 10.91 Tf
([)Tj
/T1_2 10.91 Tf
(S)Tj
/T1_3 7.97 Tf
31.66 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
3.38 1.64 Td
(])Tj
/T1_6 10.91 Tf
(g)Tj
/T1_0 10.91 Tf
[(,)-333(where)]TJ
/T1_1 10.91 Tf
46.69 0 Td
(\276)Tj
/T1_3 7.97 Tf
6.23 -1.64 Td
(i;)Tj
/T1_5 7.97 Tf
5.23 0 Td
(1)Tj
/T1_0 10.91 Tf
7.76 1.64 Td
(=)Tj
/T1_6 10.91 Tf
11.51 0 Td
(S)Tj
/T1_0 10.91 Tf
7.43 0 Td
(\()Tj
/T1_2 10.91 Tf
(S)Tj
/T1_3 7.97 Tf
9.96 -1.64 Td
(i)Tj
/T1_6 10.91 Tf
3.38 1.64 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(\277)Tj
/T1_3 7.97 Tf
4.77 -1.64 Td
(i)Tj
/T1_6 10.91 Tf
3.38 1.64 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(z)Tj
/T1_3 7.97 Tf
5.07 -1.64 Td
(i;)Tj
/T1_5 7.97 Tf
5.23 0 Td
(1)Tj
/T1_6 10.91 Tf
4.74 1.64 Td
(jj)Tj
/T1_2 10.91 Tf
6.05 0 Td
(BL)Tj
/T1_10 7.97 Tf
11.46 -1.64 Td
(Z)Tj
/T1_6 10.91 Tf
4.73 1.64 Td
(jj)Tj
/T1_0 10.91 Tf
6.06 0 Td
(0\).)Tj
-358.33 -21.92 Td
[(Round)-333(4)]TJ
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 0 -375.1 cm
0 0 m
40.75 0 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 118.0529 396.1454 Tm
(:)Tj
1.0003 0 0 1.0003 72 769.82 Tm
57.245 -373.57 Td
[(Eac)27(h)]TJ
/T1_2 10.91 Tf
28.775 0 Td
(U)Tj
/T1_3 7.97 Tf
5.72 -1.64 Td
(i;j)Tj
/T1_0 10.91 Tf
14.91 1.64 Td
[(for)-486(1)]TJ
/T1_6 10.91 Tf
29.61 0 Td
(\267)Tj
/T1_1 10.91 Tf
14.28 0 Td
(i)Tj
/T1_6 10.91 Tf
9.56 0 Td
(\267)Tj
/T1_1 10.91 Tf
14.28 0 Td
(n)Tj
/T1_3 7.97 Tf
6.54 -1.64 Td
(c)Tj
/T1_0 10.91 Tf
9.46 1.64 Td
[(and)-485(2)]TJ
/T1_6 10.91 Tf
34.12 0 Td
(\267)Tj
/T1_1 10.91 Tf
14.28 0 Td
(j)Tj
/T1_6 10.91 Tf
10.92 0 Td
(\267)Tj
/T1_1 10.91 Tf
14.28 0 Td
(n)Tj
/T1_3 7.97 Tf
6.54 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
8.68 1.64 Td
[(\257rst)-485(c)27(hec)27(ks)-484(the)-486(receiv)27(ed)-485(signature)]TJ
/T1_1 10.91 Tf
172.47 0 Td
(\276)Tj
/T1_3 7.97 Tf
6.24 -1.64 Td
(i;)Tj
/T1_5 7.97 Tf
5.23 0 Td
(1)Tj
/T1_0 10.91 Tf
-463.14 -20.28 Td
[(and)-422(certi\257cate)]TJ
/T1_2 10.91 Tf
73.46 0 Td
(cert)Tj
/T1_0 10.91 Tf
22.9 0 Td
([)Tj
/T1_2 10.91 Tf
(S)Tj
/T1_3 7.97 Tf
8.76 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
3.38 1.63 Td
[(].)-710(If)-422(the)-422(v)26(eri\257cations)-421(are)-422(not)-422(correct,)-444(then)]TJ
/T1_2 10.91 Tf
213.08 0 Td
(U)Tj
/T1_3 7.97 Tf
5.72 -1.63 Td
(i;j)Tj
/T1_0 10.91 Tf
14.22 1.63 Td
(rejects)Tj
/T1_2 10.91 Tf
35.29 0 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
3.38 1.63 Td
[(.)-710(Otherwise,)]TJ
/T1_2 10.91 Tf
66.61 0 Td
(U)Tj
/T1_3 7.97 Tf
5.73 -1.63 Td
(i;j)Tj
/T1_0 10.91 Tf
-458.26 -20.28 Td
[(c)27(hec)28(ks)-506(the)-508(list)]TJ
/T1_2 10.91 Tf
76.4 0 Td
(BL)Tj
/T1_10 7.97 Tf
11.45 -1.64 Td
(Z)Tj
/T1_0 10.91 Tf
10.27 1.64 Td
[(to)-507(iden)27(tify)-506(the)-507(malicious)-508(no)-28(des)-507(to)-507(b)-28(e)-507(blo)-28(c)27(k)27(ed)-506(from)-507(the)-508(GKA.)-507(\(F)82(or)-506(exam-)]TJ
-98.12 -21.92 Td
[(ple,)-505(if)]TJ
/T1_2 10.91 Tf
33.98 0 Td
(U)Tj
/T1_3 7.97 Tf
5.73 -1.64 Td
(i;j)Tj
/T1_0 10.91 Tf
14.75 1.64 Td
[(disco)27(v)28(ers)-470(that)-471(its)-472(neigh)27(b)-27(or)]TJ
/T1_2 10.91 Tf
135.62 0 Td
(U)Tj
/T1_3 7.97 Tf
5.72 -1.64 Td
(i;j)Tj
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9.12 0 Td
(\241)Tj
/T1_5 7.97 Tf
(1)Tj
/T1_0 10.91 Tf
16.45 1.64 Td
[(is)-471(in)-471(the)-471(list)]TJ
/T1_2 10.91 Tf
66.73 0 Td
(BL)Tj
/T1_10 7.97 Tf
11.45 -1.64 Td
(Z)Tj
/T1_0 10.91 Tf
4.73 1.64 Td
[(,)-505(then)]TJ
/T1_2 10.91 Tf
34.89 0 Td
(U)Tj
/T1_3 7.97 Tf
5.73 -1.64 Td
(i;j)Tj
/T1_0 10.91 Tf
14.75 1.64 Td
[(will)-471(excludes)-471(neigh)27(b)-27(or)]TJ
/T1_2 10.91 Tf
-359.65 -21.92 Td
(U)Tj
/T1_3 7.97 Tf
5.73 -1.63 Td
(i;j)Tj
/T1_8 7.97 Tf
9.11 0 Td
(\241)Tj
/T1_5 7.97 Tf
6.59 0 Td
(1)Tj
/T1_0 10.91 Tf
8.76 1.63 Td
[(from)-368(GKA)-370(and)-369(set)]TJ
/T1_2 10.91 Tf
94.43 0 Td
(U)Tj
/T1_3 7.97 Tf
5.73 -1.63 Td
(i;j)Tj
/T1_8 7.97 Tf
9.11 0 Td
(\241)Tj
/T1_5 7.97 Tf
6.59 0 Td
(2)Tj
/T1_0 10.91 Tf
8.76 1.63 Td
[(as)-368(its)-370(neigh)27(b)-27(or)-369(i.e.)]TJ
/T1_2 10.91 Tf
94.59 0 Td
(U)Tj
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5.73 -1.63 Td
(i;j)Tj
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9.12 0 Td
(\241)Tj
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(2)Tj
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14.99 1.63 Td
(=)Tj
/T1_2 10.91 Tf
12.17 0 Td
(U)Tj
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5.72 -1.63 Td
(i;j)Tj
/T1_8 7.97 Tf
9.12 0 Td
(\241)Tj
/T1_5 7.97 Tf
(1)Tj
/T1_0 10.91 Tf
11.32 1.63 Td
[(,)-377(pro)26(vided)]TJ
/T1_2 10.91 Tf
52.41 0 Td
(U)Tj
/T1_3 7.97 Tf
5.72 -1.63 Td
(i;j)Tj
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9.12 0 Td
(\241)Tj
/T1_5 7.97 Tf
6.59 0 Td
(2)Tj
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8.75 1.63 Td
[(is)-369(not)-369(in)]TJ
/T1_2 10.91 Tf
44.26 0 Td
(BL)Tj
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11.45 -1.63 Td
(Z)Tj
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4.73 1.63 Td
(\).)Tj
-460.6 -21.91 Td
(Next,)Tj
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30.29 0 Td
(U)Tj
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5.73 -1.64 Td
(i;j)Tj
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13.73 1.64 Td
(computes)Tj
/T1_1 10.91 Tf
49.01 0 Td
(L)Tj
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7.43 -1.64 Td
(i;j)Tj
/T1_0 10.91 Tf
13.44 1.64 Td
(=)Tj
/T1_7 10.91 Tf
12.32 0 Td
(H)Tj
/T1_0 10.91 Tf
7.73 0 Td
(\()Tj
/T1_1 10.91 Tf
(z)Tj
/T1_3 7.97 Tf
9.79 6.13 Td
(r)Tj
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3.82 -1.21 Td
(i;j)Tj
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-4.3 -8.18 Td
(i;j)Tj
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9.12 0 Td
(\241)Tj
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(1)Tj
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11.31 3.26 Td
(jj)Tj
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6.06 0 Td
(SID)Tj
/T1_3 7.97 Tf
17.18 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
3.38 1.64 Td
(\),)Tj
/T1_1 10.91 Tf
11.51 0 Td
(R)Tj
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8.28 -1.64 Td
(i;j)Tj
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13.45 1.64 Td
(=)Tj
/T1_7 10.91 Tf
12.31 0 Td
(H)Tj
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7.73 0 Td
(\()Tj
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(z)Tj
/T1_3 7.97 Tf
9.79 6.13 Td
(r)Tj
/T1_9 5.98 Tf
3.82 -1.21 Td
(i;j)Tj
/T1_3 7.97 Tf
-4.3 -8.18 Td
(i;j)Tj
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9.12 0 Td
(+1)Tj
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11.31 3.26 Td
(jj)Tj
/T1_2 10.91 Tf
6.06 0 Td
(SID)Tj
/T1_3 7.97 Tf
17.18 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
3.38 1.64 Td
[(\))-377(and)-378(generates)]TJ
/T1_1 10.91 Tf
78.49 0 Td
(X)Tj
/T1_3 7.97 Tf
9.03 -1.64 Td
(i;j)Tj
/T1_0 10.91 Tf
13.45 1.64 Td
(=)Tj
/T1_1 10.91 Tf
12.31 0 Td
(L)Tj
/T1_3 7.97 Tf
7.43 -1.64 Td
(i;j)Tj
/T1_6 10.91 Tf
12.36 1.64 Td
(\251)Tj
/T1_1 10.91 Tf
11.22 0 Td
(R)Tj
/T1_3 7.97 Tf
8.29 -1.64 Td
(i;j)Tj
/T1_0 10.91 Tf
-458.26 -20.28 Td
(where)Tj
/T1_2 10.91 Tf
31.48 0 Td
(SID)Tj
/T1_3 7.97 Tf
17.18 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
6.41 1.64 Td
(=)Tj
/T1_7 10.91 Tf
11.51 0 Td
(H)Tj
/T1_0 10.91 Tf
(\()Tj
/T1_1 10.91 Tf
11.97 0 Td
(\277)Tj
/T1_3 7.97 Tf
4.76 -1.64 Td
(i)Tj
/T1_6 10.91 Tf
3.38 1.64 Td
(jj)Tj
/T1_2 10.91 Tf
6.06 0 Td
(U)Tj
/T1_3 7.97 Tf
5.73 -1.64 Td
(i;)Tj
/T1_5 7.97 Tf
5.23 0 Td
(1)Tj
/T1_6 10.91 Tf
4.73 1.64 Td
(jj)Tj
/T1_2 10.91 Tf
6.06 0 Td
(U)Tj
/T1_3 7.97 Tf
5.73 -1.64 Td
(i;)Tj
/T1_5 7.97 Tf
5.23 0 Td
(2)Tj
/T1_6 10.91 Tf
4.73 1.64 Td
[(jj)-166(\242)-167(\242)-167(\242)-166(jj)]TJ
/T1_2 10.91 Tf
28.48 0 Td
(U)Tj
/T1_3 7.97 Tf
5.73 -1.64 Td
(i;n)Tj
/T1_9 5.98 Tf
10.37 -1.21 Td
(i)Tj
/T1_0 10.91 Tf
3.66 2.85 Td
[(\).)-442(Finally)83(,)]TJ
/T1_2 10.91 Tf
51.28 0 Td
(U)Tj
/T1_3 7.97 Tf
5.73 -1.64 Td
(i;j)Tj
/T1_0 10.91 Tf
13.19 1.64 Td
[(randomly)-328(selects)]TJ
/T1_1 10.91 Tf
82.75 0 Td
(\267)Tj
/T1_3 7.97 Tf
6.28 -1.64 Td
(i;j)Tj
/T1_6 10.91 Tf
12.64 1.64 Td
[(2)-278(f)]TJ
/T1_0 10.91 Tf
(0)Tj
/T1_1 10.91 Tf
(;)Tj
/T1_0 10.91 Tf
26.06 0 Td
(1)Tj
/T1_6 10.91 Tf
(g)Tj
/T1_3 7.97 Tf
10.9 3.96 Td
(\270)Tj
/T1_0 10.91 Tf
9.02 -3.96 Td
[(and)-328(broadcasts)]TJ
/T1_6 10.91 Tf
-396.28 -21.92 Td
(f)Tj
/T1_2 10.91 Tf
(U)Tj
/T1_3 7.97 Tf
11.18 -1.63 Td
(i;j)Tj
/T1_6 10.91 Tf
9.61 1.63 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(\267)Tj
/T1_3 7.97 Tf
6.29 -1.63 Td
(i;j)Tj
/T1_6 10.91 Tf
9.61 1.63 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(X)Tj
/T1_3 7.97 Tf
9.04 -1.63 Td
(i;j)Tj
/T1_6 10.91 Tf
9.61 1.63 Td
(jj)Tj
/T1_0 10.91 Tf
6.64 0 Td
(\271)Tj
/T1_1 10.91 Tf
-0.58 0 Td
(\276)Tj
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6.23 -1.63 Td
(i;j)Tj
/T1_6 10.91 Tf
9.62 1.63 Td
(g)Tj
/T1_0 10.91 Tf
[(,)-333(where)-387(\271)]TJ
/T1_1 10.91 Tf
43.65 0 Td
(\276)Tj
/T1_3 7.97 Tf
6.23 -1.63 Td
(i;j)Tj
/T1_0 10.91 Tf
12.65 1.63 Td
(=)Tj
/T1_6 10.91 Tf
11.51 0 Td
(S)Tj
/T1_0 10.91 Tf
7.42 0 Td
(\()Tj
/T1_2 10.91 Tf
(U)Tj
/T1_3 7.97 Tf
9.97 -1.63 Td
(i;j)Tj
/T1_6 10.91 Tf
9.61 1.63 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(\267)Tj
/T1_3 7.97 Tf
6.29 -1.63 Td
(i;j)Tj
/T1_6 10.91 Tf
9.61 1.63 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(X)Tj
/T1_3 7.97 Tf
9.03 -1.63 Td
(i;j)Tj
/T1_6 10.91 Tf
9.62 1.63 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(\277)Tj
/T1_3 7.97 Tf
4.77 -1.63 Td
(i)Tj
/T1_6 10.91 Tf
3.38 1.63 Td
(jj)Tj
/T1_0 10.91 Tf
6.06 0 Td
(0\).)Tj
-257.35 -21.91 Td
[(Round)-333(5)]TJ
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 0 -550.43 cm
0 0 m
40.75 0 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 115.7823 220.7663 Tm
(:)Tj
1.0003 0 0 1.0003 72 769.82 Tm
51.342 -548.9 Td
[(Eac)27(h)]TJ
/T1_2 10.91 Tf
26.508 0 Td
(S)Tj
/T1_3 7.97 Tf
5.72 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
6.41 1.64 Td
[(for)-277(1)]TJ
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24.56 0 Td
(\267)Tj
/T1_1 10.91 Tf
11.51 0 Td
(i)Tj
/T1_6 10.91 Tf
6.79 0 Td
(\267)Tj
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11.51 0 Td
(n)Tj
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6.55 -1.64 Td
(c)Tj
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7.19 1.64 Td
[(\257rst)-277(c)27(hec)28(ks)-277(the)-277(receiv)27(ed)-277(signatures)-331(\271)]TJ
/T1_1 10.91 Tf
165.42 0 Td
(\276)Tj
/T1_3 7.97 Tf
6.23 -1.64 Td
(i;j)Tj
/T1_0 10.91 Tf
12.64 1.64 Td
[(for)-277(2)]TJ
/T1_6 10.91 Tf
24.56 0 Td
(\267)Tj
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11.52 0 Td
(j)Tj
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8.14 0 Td
(\267)Tj
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11.51 0 Td
(n)Tj
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6.55 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
3.38 1.64 Td
[(.)-425(If)-278(there)-277(are)]TJ
-408.04 -21.92 Td
[(in)27(v)56(alid)-246(signatures,)]TJ
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88.13 0 Td
(S)Tj
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5.73 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
6.07 1.64 Td
[(will)-247(place)-247(the)-247(iden)26(tities)-246(of)-247(in)27(v)55(alid)-246(users)]TJ
/T1_12 10.91 Tf
182.51 1.97 Td
(e)Tj
/T1_2 10.91 Tf
0.17 -1.97 Td
(U)Tj
/T1_3 7.97 Tf
5.72 -1.64 Td
(i;j)Tj
/T1_0 10.91 Tf
12.32 1.64 Td
[(that)-246(generated)-247(the)-248(in)27(v)56(alid)-247(signature)]TJ
-300.65 -21.92 Td
[(to)-387(a)-387(list)]TJ
/T1_2 10.91 Tf
42.41 0 Td
(BL)Tj
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11.45 -1.63 Td
(X)Tj
/T1_0 10.91 Tf
8.96 1.63 Td
[(and)-386(broadcast)]TJ
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72.15 0 Td
(f)Tj
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(S)Tj
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11.18 -1.63 Td
(i)Tj
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3.38 1.63 Td
(jj)Tj
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6.06 0 Td
(BL)Tj
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11.45 -1.63 Td
(X)Tj
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4.73 1.63 Td
(jj)Tj
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6.64 0 Td
(\271)Tj
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-0.58 0 Td
(\276)Tj
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6.23 -1.63 Td
(i;)Tj
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5.23 0 Td
(1)Tj
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4.73 1.63 Td
(g)Tj
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[(,)-400(where)-440(\271)]TJ
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44.98 0 Td
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6.23 -1.63 Td
(i;)Tj
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5.23 0 Td
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8.74 1.63 Td
(=)Tj
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12.49 0 Td
(S)Tj
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7.42 0 Td
(\()Tj
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(S)Tj
/T1_3 7.97 Tf
9.97 -1.63 Td
(i)Tj
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3.38 1.63 Td
(jj)Tj
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6.06 0 Td
(\277)Tj
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4.76 -1.63 Td
(i)Tj
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3.38 1.63 Td
(jj)Tj
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6.06 0 Td
(BL)Tj
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11.45 -1.63 Td
(X)Tj
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4.74 1.63 Td
(jj)Tj
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6.05 0 Td
[(0\).)-606(Otherwise,)]TJ
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74.69 0 Td
(S)Tj
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5.72 -1.63 Td
(i)Tj
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7.6 1.63 Td
(computes)Tj
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-422.97 -21.91 Td
(L)Tj
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7.42 -1.64 Td
(i;)Tj
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(1)Tj
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13.23 1.64 Td
(=)Tj
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11.75 0 Td
(H)Tj
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(\()Tj
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11.97 0 Td
(z)Tj
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5.55 6.13 Td
(r)Tj
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3.82 -1.21 Td
(i;)Tj
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4.93 0 Td
(1)Tj
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-9.23 -8.18 Td
(i;n)Tj
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10.37 -1.21 Td
(i)Tj
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3.66 4.47 Td
(jj)Tj
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6.06 0 Td
(SID)Tj
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17.17 -1.64 Td
(i)Tj
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3.38 1.64 Td
(\),)Tj
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11.09 0 Td
(R)Tj
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8.28 -1.64 Td
(i;)Tj
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5.23 0 Td
(1)Tj
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8 1.64 Td
(=)Tj
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11.74 0 Td
(H)Tj
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7.73 0 Td
(\()Tj
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(z)Tj
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9.79 6.13 Td
(r)Tj
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3.82 -1.21 Td
(i;)Tj
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4.93 0 Td
(1)Tj
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-9.23 -8.18 Td
(i;)Tj
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(2)Tj
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13.88 3.26 Td
(jj)Tj
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6.06 0 Td
(SID)Tj
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17.18 -1.64 Td
(i)Tj
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3.38 1.64 Td
(\),)Tj
/T1_1 10.91 Tf
11.08 0 Td
(X)Tj
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9.04 -1.64 Td
(i;)Tj
/T1_5 7.97 Tf
5.23 0 Td
(1)Tj
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8 1.64 Td
(=)Tj
/T1_1 10.91 Tf
11.74 0 Td
(L)Tj
/T1_3 7.97 Tf
7.43 -1.64 Td
(i;)Tj
/T1_5 7.97 Tf
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/T1_3 7.97 Tf
17.52 6.13 Td
(r)Tj
/T1_8 5.98 Tf
3.82 -1.21 Td
(i;j)Tj
/T1_9 5.98 Tf
8.33 0 Td
(\241)Tj
/T1_10 5.98 Tf
(1)Tj
/T1_3 7.97 Tf
-12.63 -8.18 Td
(i;j)Tj
/T1_5 7.97 Tf
9.11 0 Td
(+1)Tj
/T1_11 10.91 Tf
13.92 3.26 Td
(jj)Tj
/T1_1 10.91 Tf
8.46 1.97 Td
(g)Tj
/T1_2 10.91 Tf
-2.4 -1.97 Td
(SID)Tj
/T1_3 7.97 Tf
17.18 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
3.38 1.64 Td
(\),)Tj
/T1_6 10.91 Tf
-460.6 -21.92 Td
(X)Tj
/T1_3 7.97 Tf
9.04 -1.63 Td
(i;j)Tj
/T1_4 7.97 Tf
9.11 0 Td
(\241)Tj
/T1_5 7.97 Tf
6.59 0 Td
(1)Tj
/T1_0 10.91 Tf
7.76 1.63 Td
(=)Tj
/T1_6 10.91 Tf
11.51 0 Td
(L)Tj
/T1_3 7.97 Tf
7.42 -1.63 Td
(i;j)Tj
/T1_4 7.97 Tf
9.12 0 Td
(\241)Tj
/T1_5 7.97 Tf
(1)Tj
/T1_11 10.91 Tf
13.53 1.63 Td
(\251)Tj
/T1_6 10.91 Tf
10.69 0 Td
(R)Tj
/T1_3 7.97 Tf
8.28 -1.63 Td
(i;j)Tj
/T1_4 7.97 Tf
9.12 0 Td
(\241)Tj
/T1_5 7.97 Tf
6.59 0 Td
(1)Tj
/T1_0 10.91 Tf
8.26 1.63 Td
[(and)-323(transmit)]TJ
/T1_6 10.91 Tf
65.31 0 Td
(X)Tj
/T1_3 7.97 Tf
9.04 -1.63 Td
(i;j)Tj
/T1_4 7.97 Tf
9.12 0 Td
(\241)Tj
/T1_5 7.97 Tf
(1)Tj
/T1_0 10.91 Tf
14.84 1.63 Td
[(with)-323(signature,)-326(where)]TJ
/T1_1 10.91 Tf
108.87 1.97 Td
(g)Tj
/T1_2 10.91 Tf
-2.4 -1.97 Td
(SID)Tj
/T1_3 7.97 Tf
17.17 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
6.91 1.63 Td
[(is)-324(equal)-323(to)]TJ
/T1_2 10.91 Tf
52.76 0 Td
(SID)Tj
/T1_3 7.97 Tf
17.18 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
6.91 1.63 Td
(excluding)Tj
-422.73 -21.91 Td
[(the)-496(iden)27(tities)-495(of)-496(the)-496(discarded)-496(users)-496(in)]TJ
/T1_2 10.91 Tf
198.13 0 Td
(BL)Tj
/T1_12 7.97 Tf
11.45 -1.64 Td
(X)Tj
/T1_0 10.91 Tf
4.73 1.64 Td
[(.)-932(The)-496(honest)-496(righ)27(t)-495(neigh)26(b)-26(or)]TJ
/T1_2 10.91 Tf
148.56 0 Td
(U)Tj
/T1_3 7.97 Tf
5.73 -1.64 Td
(i;j)Tj
/T1_5 7.97 Tf
9.12 0 Td
(+1)Tj
/T1_0 10.91 Tf
11.31 1.64 Td
[(,)-537(whic)27(h)-495(has)-496(not)]TJ
-389.03 -21.92 Td
[(b)-27(een)-383(blo)-28(c)27(k)28(ed,)-395(of)]TJ
/T1_1 10.91 Tf
82.17 1.97 Td
(e)Tj
/T1_2 10.91 Tf
0.17 -1.97 Td
(U)Tj
/T1_3 7.97 Tf
5.73 -1.64 Td
(i;j)Tj
/T1_0 10.91 Tf
13.79 1.64 Td
[(will)-382(re-compute)]TJ
/T1_6 10.91 Tf
78.66 0 Td
(L)Tj
/T1_3 7.97 Tf
7.42 -1.64 Td
(i;j)Tj
/T1_5 7.97 Tf
9.12 0 Td
(+1)Tj
/T1_0 10.91 Tf
15.25 1.64 Td
(=)Tj
/T1_7 10.91 Tf
12.41 0 Td
(H)Tj
/T1_0 10.91 Tf
(\()Tj
/T1_6 10.91 Tf
11.97 0 Td
(z)Tj
/T1_3 7.97 Tf
5.55 6.13 Td
(r)Tj
/T1_8 5.98 Tf
3.82 -1.21 Td
(i;j)Tj
/T1_10 5.98 Tf
8.33 0 Td
(+1)Tj
/T1_3 7.97 Tf
-12.63 -8.18 Td
(i;j)Tj
/T1_4 7.97 Tf
9.11 0 Td
(\241)Tj
/T1_5 7.97 Tf
6.59 0 Td
(1)Tj
/T1_11 10.91 Tf
7.17 3.26 Td
(jj)Tj
/T1_1 10.91 Tf
8.46 1.97 Td
(g)Tj
/T1_2 10.91 Tf
-2.4 -1.97 Td
(SID)Tj
/T1_3 7.97 Tf
17.17 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
3.39 1.64 Td
(\),)Tj
/T1_6 10.91 Tf
11.58 0 Td
(R)Tj
/T1_3 7.97 Tf
8.28 -1.64 Td
(i;j)Tj
/T1_5 7.97 Tf
9.11 0 Td
(+1)Tj
/T1_0 10.91 Tf
15.25 1.64 Td
(=)Tj
/T1_7 10.91 Tf
12.41 0 Td
(H)Tj
/T1_0 10.91 Tf
7.73 0 Td
(\()Tj
/T1_6 10.91 Tf
(z)Tj
/T1_3 7.97 Tf
9.79 6.13 Td
(r)Tj
/T1_8 5.98 Tf
3.82 -1.21 Td
(i;j)Tj
/T1_10 5.98 Tf
8.34 0 Td
(+1)Tj
/T1_3 7.97 Tf
-12.64 -8.18 Td
(i;j)Tj
/T1_5 7.97 Tf
9.12 0 Td
(+2)Tj
/T1_11 10.91 Tf
13.75 3.26 Td
(jj)Tj
/T1_1 10.91 Tf
8.46 1.97 Td
(g)Tj
/T1_2 10.91 Tf
-2.4 -1.97 Td
(SID)Tj
/T1_3 7.97 Tf
17.18 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
3.38 1.64 Td
(\),)Tj
/T1_6 10.91 Tf
11.58 0 Td
(X)Tj
/T1_3 7.97 Tf
9.04 -1.64 Td
(i;j)Tj
/T1_5 7.97 Tf
9.11 0 Td
(+1)Tj
/T1_0 10.91 Tf
15.25 1.64 Td
(=)Tj
/T1_6 10.91 Tf
-459.39 -21.92 Td
(L)Tj
/T1_3 7.97 Tf
7.42 -1.63 Td
(i;j)Tj
/T1_5 7.97 Tf
9.12 0 Td
(+1)Tj
/T1_11 10.91 Tf
13.89 1.63 Td
(\251)Tj
/T1_6 10.91 Tf
11.06 0 Td
(R)Tj
/T1_3 7.97 Tf
8.28 -1.63 Td
(i;j)Tj
/T1_5 7.97 Tf
9.12 0 Td
(+1)Tj
/T1_0 10.91 Tf
15.18 1.63 Td
[(and)-354(transmit)]TJ
/T1_6 10.91 Tf
65.99 0 Td
(X)Tj
/T1_3 7.97 Tf
9.03 -1.63 Td
(i;j)Tj
/T1_5 7.97 Tf
9.12 0 Td
(+1)Tj
/T1_0 10.91 Tf
15.18 1.63 Td
[(with)-354(signature.)-508(It)-354(should)-354(b)-28(e)-355(noted)-354(that)-354(if)-355(left)-354(neigh)26(b)-26(or)]TJ
/T1_2 10.91 Tf
268.32 0 Td
(U)Tj
/T1_3 7.97 Tf
5.73 -1.63 Td
(i;j)Tj
/T1_4 7.97 Tf
9.12 0 Td
(\241)Tj
/T1_5 7.97 Tf
(1)Tj
/T1_0 10.91 Tf
-456.56 -20.28 Td
(of)Tj
/T1_1 10.91 Tf
14.03 1.97 Td
(e)Tj
/T1_2 10.91 Tf
0.17 -1.97 Td
(U)Tj
/T1_3 7.97 Tf
5.72 -1.64 Td
(i;j)Tj
/T1_0 10.91 Tf
15.03 1.64 Td
[(is)-496(also)-496(an)-496(in)27(v)55(alid)-495(user)-496(or)-497(malicious)-496(group)-496(mem)27(b)-27(er)-496(that)-496(has)-497(b)-28(een)-496(blo)-28(c)27(k)28(ed,)-536(then)-496(w)27(e)-496(set)]TJ
/T1_2 10.91 Tf
-34.95 -21.92 Td
(U)Tj
/T1_3 7.97 Tf
5.73 -1.63 Td
(i;j)Tj
/T1_4 7.97 Tf
9.11 0 Td
(\241)Tj
/T1_5 7.97 Tf
6.59 0 Td
(2)Tj
/T1_0 10.91 Tf
8.35 1.63 Td
(=)Tj
/T1_2 10.91 Tf
12.11 0 Td
(U)Tj
/T1_3 7.97 Tf
5.73 -1.63 Td
(i;j)Tj
/T1_4 7.97 Tf
9.12 0 Td
(\241)Tj
/T1_5 7.97 Tf
(1)Tj
/T1_0 10.91 Tf
11.31 1.63 Td
[(.)-543(Similarly)83(,)-374(if)-366(righ)27(t)-365(neigh)27(b)-27(or)]TJ
/T1_2 10.91 Tf
140.23 0 Td
(U)Tj
/T1_3 7.97 Tf
5.72 -1.63 Td
(i;j)Tj
/T1_5 7.97 Tf
9.12 0 Td
(+1)Tj
/T1_0 10.91 Tf
15.31 1.63 Td
(of)Tj
/T1_1 10.91 Tf
12.61 1.97 Td
(e)Tj
/T1_2 10.91 Tf
0.17 -1.97 Td
(U)Tj
/T1_3 7.97 Tf
5.72 -1.63 Td
(i;j)Tj
/T1_0 10.91 Tf
13.61 1.63 Td
[(is)-366(also)-366(an)-366(in)27(v)55(alid)-365(user)-366(or)-366(malicious)-366(group)]TJ
-270.54 -21.92 Td
[(mem)27(b)-26(er)-386(that)-386(has)-386(b)-28(een)-385(blo)-28(c)27(k)27(ed,)-398(then)-385(w)26(e)-384(set)]TJ
/T1_2 10.91 Tf
215.72 0 Td
(U)Tj
/T1_3 7.97 Tf
5.73 -1.63 Td
(i;j)Tj
/T1_5 7.97 Tf
9.12 0 Td
(+2)Tj
/T1_0 10.91 Tf
15.29 1.63 Td
(=)Tj
/T1_2 10.91 Tf
12.47 0 Td
(U)Tj
/T1_3 7.97 Tf
5.73 -1.63 Td
(i;j)Tj
/T1_5 7.97 Tf
9.11 0 Td
(+1)Tj
/T1_0 10.91 Tf
11.32 1.63 Td
[(.)-601(All)-386(other)-386(users)]TJ
/T1_2 10.91 Tf
85.11 0 Td
(U)Tj
/T1_3 7.97 Tf
5.72 -1.63 Td
(i;j)Tj
/T1_0 10.91 Tf
13.82 1.63 Td
[(will)-386(use)-386(the)-385(new)]TJ
-389.14 -21.91 Td
[(session)-313(iden)26(tit)28(y)]TJ
/T1_1 10.91 Tf
78.2 1.97 Td
(g)Tj
/T1_2 10.91 Tf
-2.4 -1.97 Td
(SID)Tj
/T1_3 7.97 Tf
17.18 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
6.8 1.64 Td
[(to)-313(re-compute)]TJ
/T1_6 10.91 Tf
69.89 0 Td
(L)Tj
/T1_3 7.97 Tf
7.42 -1.64 Td
(i;j)Tj
/T1_0 10.91 Tf
9.62 1.64 Td
(,)Tj
/T1_6 10.91 Tf
6.49 0 Td
(R)Tj
/T1_3 7.97 Tf
8.28 -1.64 Td
(i;j)Tj
/T1_0 10.91 Tf
9.62 1.64 Td
(,)Tj
/T1_6 10.91 Tf
6.49 0 Td
(X)Tj
/T1_3 7.97 Tf
9.04 -1.64 Td
(i;j)Tj
/T1_0 10.91 Tf
13.04 1.64 Td
[(as)-313(in)-314(Round)-314(4)-314(and)-314(transmit)]TJ
/T1_6 10.91 Tf
134.75 0 Td
(X)Tj
/T1_3 7.97 Tf
9.04 -1.64 Td
(i;j)Tj
/T1_0 10.91 Tf
13.04 1.64 Td
[(with)-313(signature.)]TJ
-396.5 -21.92 Td
[(Next,)-394(Round)-383(5)-382(and)-383(Round)-382(6)-383(can)-382(con)27(tin)28(ue)-382(without)-382(in)26(v)56(alid)-381(signatures)-383(and)-382(in)26(v)56(alid)-381(X)26(OR)-381(equations)]TJ
0 -21.91 TD
[(detected)-340(in)-340(Round)-340(5)-340(as)-341(all)-340(the)-340(in)27(v)55(alid)-339(users)-340(and)-340(malicious)-340(group)-341(mem)27(b)-27(ers)]TJ
/T1_1 10.91 Tf
357.62 1.96 Td
(e)Tj
/T1_2 10.91 Tf
0.17 -1.96 Td
(U)Tj
/T1_3 7.97 Tf
5.72 -1.64 Td
(i;j)Tj
/T1_0 10.91 Tf
13.33 1.64 Td
[(ha)28(v)27(e)-339(b)-28(een)-340(detected)]TJ
-376.84 -21.92 Td
[(and)-333(blo)-28(c)27(k)28(ed.)]TJ
/T1_13 10.91 Tf
0 -27.89 TD
[(Phase)-383(2:)-511(Final)-383(Group)-384(Key)-383(Generation)]TJ
/T1_0 10.91 Tf
0 -27.9 TD
[(Round)-333(1)]TJ
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 0 -430.88 cm
0 0 m
40.75 0 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 116.0923 340.3398 Tm
(:)Tj
1.0003 0 0 1.0003 72 769.82 Tm
51.804 -429.36 Td
[(Eac)26(h)]TJ
/T1_2 10.91 Tf
26.816 0 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
6.71 1.63 Td
[(for)-306(1)]TJ
/T1_11 10.91 Tf
24.88 0 Td
(\267)Tj
/T1_6 10.91 Tf
11.51 0 Td
(i)Tj
/T1_11 10.91 Tf
6.79 0 Td
(\267)Tj
/T1_6 10.91 Tf
11.51 0 Td
(n)Tj
/T1_3 7.97 Tf
6.54 -1.63 Td
(c)Tj
/T1_0 10.91 Tf
7.5 1.63 Td
(computes)Tj
/T1_6 10.91 Tf
48.24 0 Td
(y)Tj
/T1_3 7.97 Tf
5.34 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
6.41 1.63 Td
(=)Tj
/T1_6 10.91 Tf
11.51 0 Td
(g)Tj
/T1_3 7.97 Tf
5.6 3.96 Td
(K)Tj
/T1_8 5.98 Tf
7.14 -1.21 Td
(i)Tj
/T1_0 10.91 Tf
6.69 -2.75 Td
[(mo)-27(d)]TJ
/T1_6 10.91 Tf
23.93 0 Td
(p)Tj
/T1_0 10.91 Tf
8.82 0 Td
[(and)-305(sends)]TJ
/T1_11 10.91 Tf
49.81 0 Td
(f)Tj
/T1_2 10.91 Tf
(S)Tj
/T1_3 7.97 Tf
11.18 -1.63 Td
(i)Tj
/T1_11 10.91 Tf
3.38 1.63 Td
(jj)Tj
/T1_6 10.91 Tf
6.06 0 Td
(y)Tj
/T1_3 7.97 Tf
5.35 -1.63 Td
(i)Tj
/T1_11 10.91 Tf
3.38 1.63 Td
(jj)Tj
/T1_6 10.91 Tf
6.05 0 Td
(\276)Tj
/T1_3 7.97 Tf
6.24 -1.63 Td
(i)Tj
/T1_11 10.91 Tf
3.38 1.63 Td
(jj)Tj
/T1_2 10.91 Tf
6.06 0 Td
(cert)Tj
/T1_0 10.91 Tf
22.9 0 Td
([)Tj
/T1_2 10.91 Tf
(S)Tj
/T1_3 7.97 Tf
8.75 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
3.38 1.63 Td
(])Tj
/T1_11 10.91 Tf
(g)Tj
/T1_0 10.91 Tf
11.82 0 Td
[(to)-305(main)]TJ
-431.21 -21.91 Td
[(con)27(troller)]TJ
/T1_2 10.91 Tf
48.84 0 Td
(C)Tj
/T1_0 10.91 Tf
5.72 0 Td
[(,)-333(where)]TJ
/T1_6 10.91 Tf
38.2 0 Td
(\276)Tj
/T1_3 7.97 Tf
6.23 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
6.41 1.64 Td
(=)Tj
/T1_11 10.91 Tf
11.52 0 Td
(S)Tj
/T1_0 10.91 Tf
7.42 0 Td
(\()Tj
/T1_2 10.91 Tf
(S)Tj
/T1_3 7.97 Tf
9.96 -1.64 Td
(i)Tj
/T1_11 10.91 Tf
3.39 1.64 Td
(jj)Tj
/T1_6 10.91 Tf
6.05 0 Td
(y)Tj
/T1_3 7.97 Tf
5.35 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
3.38 1.64 Td
(\).)Tj
-152.47 -21.92 Td
[(Round)-333(2)]TJ
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 0 -474.72 cm
0 0 m
40.75 0 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 117.3427 296.4975 Tm
(:)Tj
1.0003 0 0 1.0003 72 769.82 Tm
55.094 -473.19 Td
[(Main)-420(con)27(troller)]TJ
/T1_2 10.91 Tf
78.896 0 Td
(C)Tj
/T1_0 10.91 Tf
10.31 0 Td
[(\257rst)-420(v)27(eri\257es)-419(the)-420(receiv)27(ed)-419(signatures)]TJ
/T1_6 10.91 Tf
175.95 0 Td
(\276)Tj
/T1_3 7.97 Tf
6.24 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
7.96 1.63 Td
[(and)-419(certi\257cates)]TJ
/T1_2 10.91 Tf
77.72 0 Td
(cert)Tj
/T1_0 10.91 Tf
22.9 0 Td
([)Tj
/T1_2 10.91 Tf
(S)Tj
/T1_3 7.97 Tf
8.75 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
3.38 1.63 Td
[(])-420(for)]TJ
-447.2 -21.92 Td
(1)Tj
/T1_11 10.91 Tf
8.48 0 Td
(\267)Tj
/T1_6 10.91 Tf
11.51 0 Td
(i)Tj
/T1_11 10.91 Tf
6.79 0 Td
(\267)Tj
/T1_6 10.91 Tf
11.51 0 Td
(n)Tj
/T1_3 7.97 Tf
6.55 -1.63 Td
(c)Tj
/T1_0 10.91 Tf
4.16 1.63 Td
[(.)-408(If)-223(the)-223(v)26(eri\257cations)-222(are)-223(not)-223(correct,)-246(then)]TJ
/T1_2 10.91 Tf
191.57 0 Td
(C)Tj
/T1_0 10.91 Tf
8.16 0 Td
(rejects)Tj
/T1_2 10.91 Tf
33.13 0 Td
(S)Tj
/T1_3 7.97 Tf
5.72 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
3.38 1.63 Td
[(.)-408(Otherwise,)]TJ
/T1_2 10.91 Tf
61.14 0 Td
(C)Tj
/T1_0 10.91 Tf
8.16 0 Td
[(selects)-223(random)]TJ
/T1_6 10.91 Tf
71.67 0 Td
(r)Tj
/T1_12 7.97 Tf
4.92 -1.63 Td
(C)Tj
/T1_11 10.91 Tf
7.76 1.63 Td
(2)Tj
/T1_6 10.91 Tf
10.3 0 Td
(Z)Tj
/T1_4 7.97 Tf
8.23 3.96 Td
(\244)Tj
/T1_3 7.97 Tf
-0.78 -6.65 Td
(q)Tj
/T1_0 10.91 Tf
-462.36 -19.22 Td
[(and)-420(computes)]TJ
/T1_6 10.91 Tf
71.63 0 Td
(y)Tj
/T1_12 7.97 Tf
5.35 -1.64 Td
(C)Tj
/T1_0 10.91 Tf
9.33 1.64 Td
(=)Tj
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[(Eac)27(h)]TJ
/T1_1 10.91 Tf
27.601 0 Td
(U)Tj
/T1_2 7.97 Tf
5.72 -1.64 Td
(i;j)Tj
/T1_0 10.91 Tf
13.74 1.64 Td
[(for)-378(1)]TJ
/T1_3 10.91 Tf
26.48 0 Td
(\267)Tj
/T1_4 10.91 Tf
12.32 0 Td
(i)Tj
/T1_3 10.91 Tf
7.6 0 Td
(\267)Tj
/T1_4 10.91 Tf
12.33 0 Td
(n)Tj
/T1_2 7.97 Tf
6.55 -1.64 Td
(c)Tj
/T1_0 10.91 Tf
8.29 1.64 Td
[(and)-377(2)]TJ
/T1_3 10.91 Tf
30.99 0 Td
(\267)Tj
/T1_4 10.91 Tf
12.32 0 Td
(j)Tj
/T1_3 10.91 Tf
8.96 0 Td
(\267)Tj
/T1_4 10.91 Tf
12.33 0 Td
(n)Tj
/T1_2 7.97 Tf
6.54 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
7.51 1.64 Td
[(\257rst)-377(v)26(eri\257es)-377(the)-378(receiv)27(ed)-377(signature)-432(\271)]TJ
/T1_4 10.91 Tf
169.36 0 Td
(\276)Tj
/T1_2 7.97 Tf
6.24 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
3.38 1.64 Td
[(.)-578(If)-378(the)]TJ
-431.99 -21.92 Td
[(v)27(eri\257cation)-276(is)-278(not)-277(correct,)-289(then)]TJ
/T1_1 10.91 Tf
148.1 0 Td
(U)Tj
/T1_2 7.97 Tf
5.73 -1.64 Td
(i;j)Tj
/T1_0 10.91 Tf
12.64 1.64 Td
(rejects)Tj
/T1_1 10.91 Tf
33.71 0 Td
(S)Tj
/T1_2 7.97 Tf
5.73 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
3.38 1.64 Td
[(.)-425(Otherwise,)]TJ
/T1_1 10.91 Tf
61.81 0 Td
(U)Tj
/T1_2 7.97 Tf
5.73 -1.64 Td
(i;j)Tj
/T1_0 10.91 Tf
12.64 1.64 Td
[(uses)-277(its)-277(resp)-28(ectiv)27(e)-277(subgroup)-278(k)27(ey)]TJ
/T1_4 10.91 Tf
153.04 0 Td
(K)Tj
/T1_2 7.97 Tf
9.26 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
6.41 1.64 Td
(to)Tj
-458.18 -21.92 Td
[(decrypt)-346(\271)]TJ
/T1_1 10.91 Tf
39.72 0 Td
(c)Tj
/T1_2 7.97 Tf
5.73 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
7.02 1.63 Td
[(and)-333(obtains)-334(the)-334(iden)27(tit)28(y)]TJ
/T1_1 10.91 Tf
118.53 0 Td
(S)Tj
/T1_2 7.97 Tf
5.73 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
7.02 1.63 Td
[(and)-333(\257nal)-334(group)-334(k)27(ey)]TJ
/T1_4 10.91 Tf
96.09 0 Td
(K)Tj
/T1_0 10.91 Tf
10.04 0 Td
[(.)-446(If)-333(the)-334(iden)26(tit)28(y)]TJ
/T1_1 10.91 Tf
77.89 0 Td
(S)Tj
/T1_2 7.97 Tf
5.73 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
7.02 1.63 Td
[(w)27(as)-333(not)-333(decrypted)]TJ
-380.52 -21.91 Td
[(correctly)83(,)-422(then)]TJ
/T1_1 10.91 Tf
73.92 0 Td
(U)Tj
/T1_2 7.97 Tf
5.73 -1.64 Td
(i;j)Tj
/T1_0 10.91 Tf
14.03 1.64 Td
[(rejects)-417(\271)]TJ
/T1_1 10.91 Tf
35.1 0 Td
(c)Tj
/T1_2 7.97 Tf
5.73 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
3.38 1.64 Td
[(.)-659(Otherwise,)]TJ
/T1_1 10.91 Tf
65.82 0 Td
(U)Tj
/T1_2 7.97 Tf
5.73 -1.64 Td
(i;j)Tj
/T1_0 10.91 Tf
14.03 1.64 Td
[(c)27(hec)28(ks)-404(if)]TJ
/T1_4 10.91 Tf
45.25 0 Td
(\265)Tj
/T1_2 7.97 Tf
5.12 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
7.71 1.64 Td
(=)Tj
/T1_7 10.91 Tf
12.81 0 Td
(H)Tj
/T1_0 10.91 Tf
7.73 0 Td
(\()Tj
/T1_4 10.91 Tf
(K)Tj
/T1_2 7.97 Tf
13.5 -1.64 Td
(i)Tj
/T1_3 10.91 Tf
3.38 1.64 Td
(jj)Tj
/T1_4 10.91 Tf
6.06 0 Td
(K)Tj
/T1_3 10.91 Tf
10.05 0 Td
(jj)Tj
/T1_4 10.91 Tf
6.05 0 Td
(\277)Tj
/T1_2 7.97 Tf
4.77 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
3.38 1.64 Td
[(\).)-659(If)-405(they)-405(are)-405(equal,)]TJ
/T1_1 10.91 Tf
103.25 0 Td
(U)Tj
/T1_2 7.97 Tf
5.73 -1.64 Td
(i;j)Tj
/T1_0 10.91 Tf
-458.26 -20.28 Td
[(accepts)-333(the)-333(\257nal)-333(group)-334(k)27(ey)]TJ
/T1_4 10.91 Tf
131.87 0 Td
(K)Tj
/T1_0 10.91 Tf
13.68 0 Td
[(and)-333(b)-28(oth)]TJ
/T1_4 10.91 Tf
46.96 0 Td
(K)Tj
/T1_2 7.97 Tf
9.26 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
7.02 1.64 Td
(and)Tj
/T1_4 10.91 Tf
21.2 0 Td
(K)Tj
/T1_0 10.91 Tf
13.68 0 Td
[(are)-333(con\257rmed.)]TJ
/T1_8 11.95 Tf
-243.67 -37.82 Td
[(9.2.2)-1125(Join)-375(Proto)-31(col)]TJ
/T1_0 10.91 Tf
0 -28.96 TD
[(Supp)-27(ose)-240(a)-239(set)-240(of)]TJ
/T1_4 10.91 Tf
77.21 0 Td
(m)Tj
/T1_0 10.91 Tf
12.19 0 Td
[(new)-239(users)]TJ
/T1_3 10.91 Tf
47.79 0 Td
(J)Tj
/T1_0 10.91 Tf
12.43 0 Td
(=)Tj
/T1_3 10.91 Tf
11.52 0 Td
(f)Tj
/T1_1 10.91 Tf
(U)Tj
/T1_2 7.97 Tf
11.17 -1.64 Td
(n)Tj
/T1_9 7.97 Tf
(+1)Tj
/T1_4 10.91 Tf
16.46 1.64 Td
(;)Tj
/T1_3 10.91 Tf
4.84 0 Td
[(\242)-166(\242)-167(\242)]TJ
/T1_4 10.91 Tf
16.36 0 Td
(;)Tj
/T1_1 10.91 Tf
4.85 0 Td
(U)Tj
/T1_2 7.97 Tf
5.73 -1.64 Td
(n)Tj
/T1_9 7.97 Tf
5.13 0 Td
(+)Tj
/T1_2 7.97 Tf
6.59 0 Td
(m)Tj
/T1_3 10.91 Tf
7.98 1.64 Td
(g)Tj
/T1_0 10.91 Tf
8.07 0 Td
[(wishes)-239(to)-239(join)-240(subgroup)]TJ
/T1_3 10.91 Tf
112.14 0 Td
(G)Tj
/T1_2 7.97 Tf
6.49 -1.69 Td
(J)Tj
/T1_0 10.91 Tf
8.9 1.69 Td
(=)Tj
/T1_3 10.91 Tf
11.51 0 Td
(f)Tj
/T1_1 10.91 Tf
(U)Tj
/T1_2 7.97 Tf
11.18 -1.69 Td
[(J)24(;)]TJ
/T1_9 7.97 Tf
(1)Tj
/T1_4 10.91 Tf
11.51 1.69 Td
(;)Tj
/T1_3 10.91 Tf
4.85 0 Td
[(\242)-166(\242)-167(\242)]TJ
/T1_4 10.91 Tf
16.36 0 Td
(;)Tj
/T1_1 10.91 Tf
4.85 0 Td
(U)Tj
/T1_2 7.97 Tf
5.72 -1.69 Td
[(J)23(;n)]TJ
/T1_6 5.98 Tf
11.92 -1.34 Td
(J)Tj
/T1_3 10.91 Tf
5.64 3.03 Td
(g)Tj
/T1_0 10.91 Tf
(.)Tj
-459.39 -21.92 Td
[(The)-238(Join)-238(Proto)-28(col)-238(will)-238(b)-28(e)-238(executed)-238(to)-238(establish)-238(a)-238(new)-239(subgroup)-238(k)27(ey)]TJ
/T1_4 10.91 Tf
315.27 0 Td
(K)Tj
/T1_10 7.97 Tf
10.05 3.96 Td
(0)Tj
/T1_2 7.97 Tf
-0.78 -7.19 Td
(J)Tj
/T1_0 10.91 Tf
8.46 3.23 Td
[(for)-238(subgroup)]TJ
/T1_3 10.91 Tf
61.97 0 Td
(G)Tj
/T1_10 7.97 Tf
7.13 3.96 Td
(0)Tj
/T1_2 7.97 Tf
-0.64 -7.19 Td
(J)Tj
/T1_0 10.91 Tf
8.9 3.23 Td
(=)Tj
/T1_3 10.91 Tf
11.51 0 Td
(G)Tj
/T1_2 7.97 Tf
6.49 -1.69 Td
(J)Tj
/T1_11 10.91 Tf
7.69 9.87 Td
(S)Tj
/T1_3 10.91 Tf
10.9 -8.18 Td
(J)Tj
/T1_0 10.91 Tf
12.44 0 Td
(=)Tj
/T1_3 10.91 Tf
-459.39 -21.92 Td
(f)Tj
/T1_1 10.91 Tf
(U)Tj
/T1_2 7.97 Tf
11.18 -1.68 Td
[(J)24(;)]TJ
/T1_9 7.97 Tf
(1)Tj
/T1_4 10.91 Tf
11.51 1.68 Td
(;)Tj
/T1_3 10.91 Tf
4.85 0 Td
[(\242)-166(\242)-167(\242)]TJ
/T1_4 10.91 Tf
16.36 0 Td
(;)Tj
/T1_1 10.91 Tf
4.85 0 Td
(U)Tj
/T1_2 7.97 Tf
5.72 -1.68 Td
[(J)23(;n)]TJ
/T1_6 5.98 Tf
11.92 -1.34 Td
(J)Tj
/T1_9 7.97 Tf
5.14 1.34 Td
(+)Tj
/T1_2 7.97 Tf
(m)Tj
/T1_3 10.91 Tf
14.57 1.68 Td
(g)Tj
/T1_0 10.91 Tf
[(,)-258(where)]TJ
/T1_1 10.91 Tf
41.8 0 Td
(U)Tj
/T1_2 7.97 Tf
5.73 -1.68 Td
[(J)24(;j)]TJ
/T1_0 10.91 Tf
13.77 1.68 Td
[(for)-239(1)]TJ
/T1_3 10.91 Tf
24.15 0 Td
(\267)Tj
/T1_4 10.91 Tf
11.51 0 Td
(j)Tj
/T1_3 10.91 Tf
8.15 0 Td
(\267)Tj
/T1_4 10.91 Tf
11.51 0 Td
(n)Tj
/T1_2 7.97 Tf
6.54 -1.68 Td
(J)Tj
/T1_0 10.91 Tf
8.48 1.68 Td
[(are)-239(the)-239(existing)-239(users)-239(and)]TJ
/T1_1 10.91 Tf
120.83 0 Td
(U)Tj
/T1_2 7.97 Tf
5.72 -1.77 Td
[(J)23(;k)]TJ
/T1_0 10.91 Tf
14.51 1.77 Td
(for)Tj
/T1_4 10.91 Tf
15.67 0 Td
(n)Tj
/T1_2 7.97 Tf
6.54 -1.68 Td
(J)Tj
/T1_0 10.91 Tf
6.24 1.68 Td
[(+)-33(1)]TJ
/T1_3 10.91 Tf
17.34 0 Td
(\267)Tj
/T1_4 10.91 Tf
11.51 0 Td
(k)Tj
/T1_3 10.91 Tf
9.05 0 Td
(\267)Tj
/T1_4 10.91 Tf
11.51 0 Td
(n)Tj
/T1_2 7.97 Tf
6.55 -1.68 Td
(J)Tj
/T1_0 10.91 Tf
6.23 1.68 Td
(+)Tj
/T1_4 10.91 Tf
8.85 0 Td
(m)Tj
/T1_0 10.91 Tf
-458.29 -21.91 Td
[(are)-302(the)-303(new)-302(users,)-309(and)-302(new)-303(\257nal)-302(group)-303(k)27(ey)]TJ
/T1_4 10.91 Tf
205.38 0 Td
(K)Tj
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10.04 3.96 Td
(0)Tj
/T1_0 10.91 Tf
6.09 -3.96 Td
[(for)-302(all)-303(users)-302(in)-303(the)-302(net)26(w)28(ork)-301(to)-303(prev)27(en)28(t)-302(the)-302(new)-303(users)]TJ
-221.51 -21.92 Td
[(from)-371(kno)27(wing)-371(previous)-371(group)-372(comm)27(unications.)-558(The)-371(subgroup)-372(con)27(troller)]TJ
/T1_1 10.91 Tf
350.49 0 Td
(S)Tj
/T1_2 7.97 Tf
5.73 -1.69 Td
(J)Tj
/T1_0 10.91 Tf
9.59 1.69 Td
(=)Tj
/T1_1 10.91 Tf
12.21 0 Td
(U)Tj
/T1_2 7.97 Tf
5.72 -1.69 Td
[(J)23(;)]TJ
/T1_9 7.97 Tf
(1)Tj
/T1_0 10.91 Tf
15.57 1.69 Td
[(will)-371(act)-371(as)-372(the)]TJ
-399.31 -21.91 Td
[(represen)27(tativ)28(e)-450(of)-451(subgroup)]TJ
/T1_3 10.91 Tf
133.72 0 Td
(G)Tj
/T1_10 7.97 Tf
7.13 3.95 Td
(0)Tj
/T1_2 7.97 Tf
-0.64 -7.19 Td
(J)Tj
/T1_0 10.91 Tf
10.78 3.24 Td
[(and)-451(in)27(teract)-450(with)-451(existing)-451(last)-450(user)]TJ
/T1_1 10.91 Tf
178.19 0 Td
(U)Tj
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5.73 -1.69 Td
[(J)24(;n)]TJ
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11.92 -1.34 Td
(J)Tj
/T1_0 10.91 Tf
10.55 3.03 Td
[(and)-451(new)-450(users)]TJ
/T1_1 10.91 Tf
74.89 0 Td
(U)Tj
/T1_2 7.97 Tf
5.72 -1.78 Td
[(J)23(;k)]TJ
/T1_0 10.91 Tf
16.82 1.78 Td
(for)Tj
/T1_4 10.91 Tf
-454.81 -21.92 Td
(n)Tj
/T1_2 7.97 Tf
6.55 -1.69 Td
(J)Tj
/T1_0 10.91 Tf
8.06 1.69 Td
[(+)-201(1)]TJ
/T1_3 10.91 Tf
19.16 0 Td
(\267)Tj
/T1_4 10.91 Tf
11.52 0 Td
(k)Tj
/T1_3 10.91 Tf
9.05 0 Td
(\267)Tj
/T1_4 10.91 Tf
11.51 0 Td
(n)Tj
/T1_2 7.97 Tf
6.55 -1.69 Td
(J)Tj
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8.06 1.69 Td
(+)Tj
/T1_4 10.91 Tf
10.68 0 Td
(m)Tj
/T1_0 10.91 Tf
13.1 0 Td
[(to)-322(establish)-323(the)-323(new)-323(subgroup)-323(k)27(ey)]TJ
/T1_4 10.91 Tf
165.85 0 Td
(K)Tj
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10.04 3.96 Td
(0)Tj
/T1_2 7.97 Tf
-0.78 -7.19 Td
(J)Tj
/T1_0 10.91 Tf
5.87 3.23 Td
[(.)-440(W)82(e)-322(let)]TJ
/T1_1 10.91 Tf
42.15 0 Td
(S)Tj
/T1_2 7.97 Tf
5.72 -1.69 Td
(J)Tj
/T1_0 10.91 Tf
8.9 1.69 Td
(=)Tj
/T1_1 10.91 Tf
11.52 0 Td
(U)Tj
/T1_2 7.97 Tf
5.72 -1.69 Td
[(J)23(;)]TJ
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6.78 0 Td
(1)Tj
/T1_0 10.91 Tf
8.26 1.69 Td
[(b)-27(e)-323(the)-323(left)-323(neigh)27(b)-27(or)]TJ
-374.27 -21.92 Td
[(of)-461(new)-462(user)]TJ
/T1_1 10.91 Tf
62.15 0 Td
(U)Tj
/T1_2 7.97 Tf
5.72 -1.69 Td
[(J)23(;n)]TJ
/T1_6 5.98 Tf
11.93 -1.33 Td
(J)Tj
/T1_9 7.97 Tf
5.13 1.33 Td
(+1)Tj
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16.35 1.69 Td
(and)Tj
/T1_1 10.91 Tf
22.61 0 Td
(U)Tj
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5.72 -1.69 Td
[(J)23(;n)]TJ
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11.92 -1.33 Td
(J)Tj
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10.67 3.02 Td
[(b)-27(e)-462(the)-461(righ)26(t)-460(neigh)27(b)-27(or)-462(of)-461(the)-462(last)-462(new)-461(user)]TJ
/T1_1 10.91 Tf
214.87 0 Td
(U)Tj
/T1_2 7.97 Tf
5.72 -1.69 Td
[(J)24(;n)]TJ
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11.92 -1.33 Td
(J)Tj
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5.14 1.33 Td
(+)Tj
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(m)Tj
/T1_0 10.91 Tf
19.6 1.69 Td
[(for)-461(the)-462(Join)]TJ
-409.45 -21.91 Td
[(Proto)-27(col)-334(\(i.e.)]TJ
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67.13 0 Td
(U)Tj
/T1_2 7.97 Tf
5.73 -1.69 Td
[(J)24(;n)]TJ
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11.92 -1.34 Td
(J)Tj
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5.14 1.34 Td
(+)Tj
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(m)Tj
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(+1)Tj
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28.41 1.69 Td
(=)Tj
/T1_1 10.91 Tf
11.52 0 Td
(U)Tj
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5.72 -1.69 Td
[(J)23(;n)]TJ
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11.92 -1.34 Td
(J)Tj
/T1_0 10.91 Tf
5.64 3.03 Td
(,)Tj
/T1_1 10.91 Tf
6.66 0 Td
(U)Tj
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5.73 -1.69 Td
[(J)24(;n)]TJ
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11.92 -1.34 Td
(J)Tj
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5.13 1.34 Td
(+)Tj
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6.59 0 Td
(m)Tj
/T1_9 7.97 Tf
(+2)Tj
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21.83 1.69 Td
(=)Tj
/T1_1 10.91 Tf
11.51 0 Td
(U)Tj
/T1_2 7.97 Tf
5.73 -1.69 Td
[(J)24(;)]TJ
/T1_9 7.97 Tf
(1)Tj
/T1_0 10.91 Tf
15.15 1.69 Td
(and)Tj
/T1_1 10.91 Tf
21.21 0 Td
(U)Tj
/T1_2 7.97 Tf
5.72 -1.69 Td
[(J)23(;n)]TJ
/T1_6 5.98 Tf
11.92 -1.34 Td
(J)Tj
/T1_9 7.97 Tf
5.14 1.34 Td
(+)Tj
/T1_2 7.97 Tf
(m)Tj
/T1_9 7.97 Tf
(+3)Tj
/T1_0 10.91 Tf
28.42 1.69 Td
(=)Tj
/T1_1 10.91 Tf
11.51 0 Td
(U)Tj
/T1_2 7.97 Tf
5.72 -1.69 Td
[(J)23(;n)]TJ
/T1_6 5.98 Tf
11.92 -1.34 Td
(J)Tj
/T1_9 7.97 Tf
5.14 1.34 Td
(+1)Tj
/T1_0 10.91 Tf
11.32 1.69 Td
(\).)Tj
-344.47 -21.92 Td
[(The)-286(Join)-287(Proto)-28(col)-286(consists)-287(of)-287(3)-286(phases.)-429(During)-287(Phase)-286(1,)-296(subgroup)-287(con)27(troller)]TJ
/T1_1 10.91 Tf
362.08 0 Td
(S)Tj
/T1_2 7.97 Tf
5.72 -1.69 Td
(J)Tj
/T1_0 10.91 Tf
9 1.69 Td
[(of)-286(subgroup)]TJ
/T1_3 10.91 Tf
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(J)Tj
/T1_2 10.91 Tf
9.16 -1.17 Td
[(mo)-27(d)]TJ
/T1_0 10.91 Tf
23.93 0 Td
(p)Tj
/T1_2 10.91 Tf
10.13 0 Td
[(resp)-27(ectiv)27(ely)83(.)]TJ
-409.92 -21.92 Td
(Next,)Tj
/T1_3 10.91 Tf
30.96 0 Td
(U)Tj
/T1_4 7.97 Tf
5.72 -1.78 Td
[(J)23(;k)]TJ
/T1_2 10.91 Tf
16.56 1.78 Td
(stores)Tj
/T1_0 10.91 Tf
32.07 0 Td
(\277)Tj
/T1_1 7.97 Tf
6 3.96 Td
(0)Tj
/T1_4 7.97 Tf
-1.24 -7.19 Td
(J)Tj
/T1_2 10.91 Tf
10.53 3.23 Td
[(and)-426(broadcasts)]TJ
/T1_5 10.91 Tf
77.31 0 Td
(f)Tj
/T1_3 10.91 Tf
(U)Tj
/T1_4 7.97 Tf
11.18 -1.78 Td
[(J)24(;k)]TJ
/T1_5 10.91 Tf
11.9 1.78 Td
(jj)Tj
/T1_0 10.91 Tf
6.06 0 Td
(z)Tj
/T1_1 7.97 Tf
5.55 3.96 Td
(0)Tj
/T1_4 7.97 Tf
-0.48 -7.28 Td
[(J)23(;k)]TJ
/T1_5 10.91 Tf
11.91 3.32 Td
(jj)Tj
/T1_0 10.91 Tf
6.05 0 Td
(\276)Tj
/T1_1 7.97 Tf
6.63 3.96 Td
(0)Tj
/T1_4 7.97 Tf
-0.39 -7.28 Td
[(J)24(;k)]TJ
/T1_5 10.91 Tf
11.9 3.32 Td
(jj)Tj
/T1_3 10.91 Tf
6.06 0 Td
(cert)Tj
/T1_2 10.91 Tf
22.9 0 Td
([)Tj
/T1_3 10.91 Tf
(U)Tj
/T1_4 7.97 Tf
8.76 -1.78 Td
[(J)24(;k)]TJ
/T1_2 10.91 Tf
11.9 1.78 Td
(])Tj
/T1_5 10.91 Tf
(g)Tj
/T1_2 10.91 Tf
[(,)-449(where)]TJ
/T1_0 10.91 Tf
48.97 0 Td
(\276)Tj
/T1_1 7.97 Tf
6.62 3.96 Td
(0)Tj
/T1_4 7.97 Tf
-0.39 -7.28 Td
[(J)24(;k)]TJ
/T1_2 10.91 Tf
16.63 3.32 Td
(=)Tj
/T1_5 10.91 Tf
13.2 0 Td
(S)Tj
/T1_2 10.91 Tf
7.42 0 Td
(\()Tj
/T1_3 10.91 Tf
(U)Tj
/T1_4 7.97 Tf
9.97 -1.78 Td
[(J)24(;k)]TJ
/T1_5 10.91 Tf
11.9 1.78 Td
(jj)Tj
/T1_0 10.91 Tf
6.06 0 Td
(z)Tj
/T1_1 7.97 Tf
5.55 3.96 Td
(0)Tj
/T1_4 7.97 Tf
-0.48 -7.28 Td
[(J)23(;k)]TJ
/T1_5 10.91 Tf
11.91 3.32 Td
(jj)Tj
/T1_0 10.91 Tf
6.05 0 Td
(\277)Tj
/T1_1 7.97 Tf
6.01 3.96 Td
(0)Tj
/T1_4 7.97 Tf
-1.24 -7.19 Td
(J)Tj
/T1_5 10.91 Tf
5.87 3.23 Td
(jj)Tj
/T1_0 10.91 Tf
6.06 0 Td
(v)Tj
/T1_2 10.91 Tf
5.68 0 Td
(\))Tj
-463.63 -21.92 Td
(and)Tj
/T1_3 10.91 Tf
21.21 0 Td
(U)Tj
/T1_4 7.97 Tf
5.72 -1.68 Td
[(J)23(;n)]TJ
/T1_9 5.98 Tf
11.92 -1.34 Td
(J)Tj
/T1_2 10.91 Tf
9.27 3.02 Td
(stores)Tj
/T1_0 10.91 Tf
31.05 0 Td
(\277)Tj
/T1_1 7.97 Tf
6.01 3.96 Td
(0)Tj
/T1_4 7.97 Tf
-1.24 -7.19 Td
(J)Tj
/T1_2 10.91 Tf
9.51 3.23 Td
[(and)-333(broadcasts)]TJ
/T1_5 10.91 Tf
75.28 0 Td
(f)Tj
/T1_3 10.91 Tf
(U)Tj
/T1_4 7.97 Tf
11.18 -1.68 Td
[(J)24(;n)]TJ
/T1_9 5.98 Tf
11.92 -1.34 Td
(J)Tj
/T1_5 10.91 Tf
5.63 3.02 Td
(jj)Tj
/T1_0 10.91 Tf
6.06 0 Td
(z)Tj
/T1_1 7.97 Tf
5.55 3.96 Td
(0)Tj
/T1_4 7.97 Tf
-0.48 -7.19 Td
[(J)23(;n)]TJ
/T1_9 5.98 Tf
11.93 -1.34 Td
(J)Tj
/T1_5 10.91 Tf
5.63 4.57 Td
(jj)Tj
/T1_0 10.91 Tf
6.06 0 Td
(\276)Tj
/T1_1 7.97 Tf
6.62 3.96 Td
(0)Tj
/T1_4 7.97 Tf
-0.39 -7.19 Td
[(J)24(;n)]TJ
/T1_9 5.98 Tf
11.92 -1.34 Td
(J)Tj
/T1_5 10.91 Tf
5.64 4.57 Td
(g)Tj
/T1_2 10.91 Tf
[(,)-333(where)]TJ
/T1_0 10.91 Tf
43.65 0 Td
(\276)Tj
/T1_1 7.97 Tf
6.62 3.96 Td
(0)Tj
/T1_4 7.97 Tf
-0.39 -7.19 Td
[(J)23(;n)]TJ
/T1_9 5.98 Tf
11.92 -1.34 Td
(J)Tj
/T1_2 10.91 Tf
8.67 4.57 Td
(=)Tj
/T1_5 10.91 Tf
11.51 0 Td
(S)Tj
/T1_2 10.91 Tf
7.42 0 Td
(\()Tj
/T1_3 10.91 Tf
(U)Tj
/T1_4 7.97 Tf
9.97 -1.68 Td
[(J)24(;n)]TJ
/T1_9 5.98 Tf
11.92 -1.34 Td
(J)Tj
/T1_5 10.91 Tf
5.63 3.02 Td
(jj)Tj
/T1_0 10.91 Tf
6.06 0 Td
(z)Tj
/T1_1 7.97 Tf
5.55 3.96 Td
(0)Tj
/T1_4 7.97 Tf
-0.48 -7.19 Td
[(J)23(;n)]TJ
/T1_9 5.98 Tf
11.92 -1.34 Td
(J)Tj
/T1_5 10.91 Tf
5.64 4.57 Td
(jj)Tj
/T1_0 10.91 Tf
6.06 0 Td
(\277)Tj
/T1_1 7.97 Tf
6 3.96 Td
(0)Tj
/T1_4 7.97 Tf
-1.24 -7.19 Td
(J)Tj
/T1_5 10.91 Tf
5.88 3.23 Td
(jj)Tj
/T1_0 10.91 Tf
6.05 0 Td
(v)Tj
/T1_2 10.91 Tf
5.68 0 Td
(\).)Tj
-430.04 -21.91 Td
[(Round)-333(3)]TJ
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 0 -309.35 cm
0 0 m
40.75 0 l
S
Q
Q
BT
/T1_2 10.91 Tf
1.0003 0 0 1.0003 117.6528 461.9138 Tm
(:)Tj
/T1_3 10.91 Tf
10.38 0 Td
(S)Tj
/T1_4 7.97 Tf
5.73 -1.69 Td
(J)Tj
/T1_2 10.91 Tf
10.76 1.69 Td
(c)Tj
1.0003 0 0 1.0003 72 769.82 Tm
77.049 -307.82 Td
[(hec)27(ks)-447(the)-448(receiv)26(ed)-447(signatures)]TJ
/T1_0 10.91 Tf
146.431 0 Td
(\276)Tj
/T1_1 7.97 Tf
6.63 3.96 Td
(0)Tj
/T1_4 7.97 Tf
-0.39 -7.28 Td
[(J)24(;k)]TJ
/T1_2 10.91 Tf
16.79 3.32 Td
(for)Tj
/T1_0 10.91 Tf
17.94 0 Td
(n)Tj
/T1_4 7.97 Tf
6.55 -1.69 Td
(J)Tj
/T1_2 10.91 Tf
9.13 1.69 Td
[(+)-298(1)]TJ
/T1_5 10.91 Tf
22.32 0 Td
(\267)Tj
/T1_0 10.91 Tf
13.6 0 Td
(k)Tj
/T1_5 10.91 Tf
11.14 0 Td
(\267)Tj
/T1_0 10.91 Tf
13.6 0 Td
(n)Tj
/T1_4 7.97 Tf
6.55 -1.69 Td
(J)Tj
/T1_2 10.91 Tf
9.13 1.69 Td
(+)Tj
/T1_0 10.91 Tf
11.74 0 Td
(m)Tj
/T1_2 10.91 Tf
14.47 0 Td
(and)Tj
/T1_0 10.91 Tf
22.46 0 Td
(\276)Tj
/T1_1 7.97 Tf
6.62 3.96 Td
(0)Tj
/T1_4 7.97 Tf
-0.39 -7.19 Td
[(J)24(;n)]TJ
/T1_9 5.98 Tf
11.92 -1.34 Td
(J)Tj
/T1_2 10.91 Tf
5.63 4.57 Td
[(.)-789(If)-449(the)]TJ
-428.92 -21.92 Td
[(signature)-488(v)27(eri\257cations)-487(are)-488(correct,)]TJ
/T1_3 10.91 Tf
172.85 0 Td
(S)Tj
/T1_4 7.97 Tf
5.73 -1.69 Td
(J)Tj
/T1_2 10.91 Tf
11.19 1.69 Td
[(c)27(hec)28(ks)-487(the)-488(receiv)27(ed)-487(certi\257cates)]TJ
/T1_3 10.91 Tf
155.68 0 Td
(cert)Tj
/T1_2 10.91 Tf
22.9 0 Td
([)Tj
/T1_3 10.91 Tf
(U)Tj
/T1_4 7.97 Tf
8.75 -1.77 Td
[(J)23(;k)]TJ
/T1_2 10.91 Tf
11.91 1.77 Td
[(].)-908(If)]TJ
/T1_3 10.91 Tf
28.56 0 Td
(S)Tj
/T1_4 7.97 Tf
5.72 -1.69 Td
(J)Tj
/T1_2 10.91 Tf
11.2 1.69 Td
(detects)Tj
-434.49 -21.91 Td
[(in)27(v)56(alid)-381(certi\257cates)-381(and/or)-381(signatures)-382(sen)27(t)-380(b)26(y)-380(certain)-381(malicious)-382(no)-28(des,)-393(then)-381(these)-382(malicious)-381(no)-28(des)]TJ
T*
[(will)-377(b)-28(e)-378(placed)-378(in)27(to)-377(a)-377(list)]TJ
/T1_3 10.91 Tf
121.72 0 Td
(BL)Tj
/T1_11 7.97 Tf
11.46 -1.64 Td
(Z)Tj
/T1_2 10.91 Tf
4.73 1.64 Td
(.)Tj
/T1_3 10.91 Tf
9.33 0 Td
(S)Tj
/T1_4 7.97 Tf
5.72 -1.69 Td
(J)Tj
/T1_2 10.91 Tf
9.99 1.69 Td
[(then)-378(selects)-377(random)]TJ
/T1_0 10.91 Tf
100.37 0 Td
(r)Tj
/T1_1 7.97 Tf
5.22 3.96 Td
(0)Tj
/T1_4 7.97 Tf
-0.3 -7.19 Td
[(J)24(;)]TJ
/T1_7 7.97 Tf
(1)Tj
/T1_5 10.91 Tf
15.35 3.23 Td
(2)Tj
/T1_0 10.91 Tf
11.11 0 Td
(Z)Tj
/T1_1 7.97 Tf
8.23 3.96 Td
(\244)Tj
/T1_4 7.97 Tf
-0.78 -6.66 Td
(q)Tj
/T1_2 10.91 Tf
9.63 2.7 Td
[(and)-377(computes)]TJ
/T1_0 10.91 Tf
70.7 0 Td
(z)Tj
/T1_1 7.97 Tf
5.56 3.96 Td
(0)Tj
/T1_4 7.97 Tf
-0.48 -7.19 Td
[(J)24(;)]TJ
/T1_7 7.97 Tf
(1)Tj
/T1_2 10.91 Tf
15.35 3.23 Td
(=)Tj
/T1_0 10.91 Tf
12.32 0 Td
(g)Tj
/T1_4 7.97 Tf
5.59 5.04 Td
(r)Tj
/T1_10 5.98 Tf
4.06 2.81 Td
(0)Tj
/T1_9 5.98 Tf
-0.24 -5.52 Td
[(J)34(;)]TJ
/T1_12 5.98 Tf
6.13 0 Td
(1)Tj
/T1_2 10.91 Tf
7.68 -2.33 Td
[(mo)-27(d)]TJ
/T1_0 10.91 Tf
23.93 0 Td
(p)Tj
/T1_2 10.91 Tf
-462.38 -21.92 Td
[(and)-333(broadcasts)]TJ
/T1_5 10.91 Tf
75.28 0 Td
(f)Tj
/T1_3 10.91 Tf
(S)Tj
/T1_4 7.97 Tf
11.18 -1.69 Td
(J)Tj
/T1_5 10.91 Tf
5.87 1.69 Td
(jj)Tj
/T1_0 10.91 Tf
6.06 0 Td
(z)Tj
/T1_1 7.97 Tf
5.55 3.96 Td
(0)Tj
/T1_4 7.97 Tf
-0.48 -7.19 Td
[(J)23(;)]TJ
/T1_7 7.97 Tf
(1)Tj
/T1_5 10.91 Tf
11.52 3.23 Td
(jj)Tj
/T1_3 10.91 Tf
6.06 0 Td
(BL)Tj
/T1_11 7.97 Tf
11.45 -1.63 Td
(Z)Tj
/T1_5 10.91 Tf
4.73 1.63 Td
(jj)Tj
/T1_0 10.91 Tf
6.06 0 Td
(\276)Tj
/T1_1 7.97 Tf
6.62 3.96 Td
(0)Tj
/T1_4 7.97 Tf
-0.39 -7.19 Td
[(J)24(;)]TJ
/T1_7 7.97 Tf
(1)Tj
/T1_5 10.91 Tf
11.51 3.23 Td
(jj)Tj
/T1_3 10.91 Tf
6.06 0 Td
(cert)Tj
/T1_2 10.91 Tf
([)Tj
/T1_3 10.91 Tf
(S)Tj
/T1_4 7.97 Tf
31.66 -1.69 Td
(J)Tj
/T1_2 10.91 Tf
5.87 1.69 Td
(])Tj
/T1_5 10.91 Tf
(g)Tj
/T1_2 10.91 Tf
[(,)-333(where)]TJ
/T1_0 10.91 Tf
46.69 0 Td
(\276)Tj
/T1_1 7.97 Tf
6.62 3.96 Td
(0)Tj
/T1_4 7.97 Tf
-0.39 -7.19 Td
[(J)24(;)]TJ
/T1_7 7.97 Tf
(1)Tj
/T1_2 10.91 Tf
14.54 3.23 Td
(=)Tj
/T1_5 10.91 Tf
11.51 0 Td
(S)Tj
/T1_2 10.91 Tf
7.43 0 Td
(\()Tj
/T1_3 10.91 Tf
(S)Tj
/T1_4 7.97 Tf
9.96 -1.69 Td
(J)Tj
/T1_5 10.91 Tf
5.87 1.69 Td
(jj)Tj
/T1_0 10.91 Tf
6.06 0 Td
(\277)Tj
/T1_1 7.97 Tf
6.01 3.96 Td
(0)Tj
/T1_4 7.97 Tf
-1.24 -7.19 Td
(J)Tj
/T1_5 10.91 Tf
5.87 3.23 Td
(jj)Tj
/T1_0 10.91 Tf
6.06 0 Td
(z)Tj
/T1_1 7.97 Tf
5.55 3.96 Td
(0)Tj
/T1_4 7.97 Tf
-0.48 -7.19 Td
[(J)23(;)]TJ
/T1_7 7.97 Tf
(1)Tj
/T1_5 10.91 Tf
11.52 3.23 Td
(jj)Tj
/T1_3 10.91 Tf
6.06 0 Td
(BL)Tj
/T1_11 7.97 Tf
11.45 -1.63 Td
(Z)Tj
/T1_5 10.91 Tf
4.73 1.63 Td
(jj)Tj
/T1_0 10.91 Tf
6.06 0 Td
(v)Tj
/T1_2 10.91 Tf
5.67 0 Td
(\).)Tj
-380.16 -21.91 Td
[(Round)-333(4)]TJ
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 0 -418.93 cm
0 0 m
40.75 0 l
S
Q
Q
BT
/T1_2 10.91 Tf
1.0003 0 0 1.0003 116.3924 352.3031 Tm
(:)Tj
-44.38 -21.92 Td
(\()Tj
/T1_0 10.91 Tf
(i)Tj
/T1_2 10.91 Tf
(\))Tj
1.0003 0 0 1.0003 72 769.82 Tm
17.197 -439.32 Td
[(Eac)27(h)]TJ
/T1_3 10.91 Tf
28.443 0 Td
(U)Tj
/T1_4 7.97 Tf
5.72 -1.78 Td
[(J)24(;k)]TJ
/T1_2 10.91 Tf
16.86 1.78 Td
(for)Tj
/T1_0 10.91 Tf
18.02 0 Td
(n)Tj
/T1_4 7.97 Tf
6.54 -1.69 Td
(J)Tj
/T1_2 10.91 Tf
9.18 1.69 Td
[(+)-303(1)]TJ
/T1_5 10.91 Tf
22.48 0 Td
(\267)Tj
/T1_0 10.91 Tf
13.71 0 Td
(k)Tj
/T1_5 10.91 Tf
11.26 0 Td
(\267)Tj
/T1_0 10.91 Tf
13.71 0 Td
(n)Tj
/T1_4 7.97 Tf
6.55 -1.69 Td
(J)Tj
/T1_2 10.91 Tf
9.18 1.69 Td
(+)Tj
/T1_0 10.91 Tf
11.79 0 Td
(m)Tj
/T1_2 10.91 Tf
14.53 0 Td
[(\257rst)-454(c)27(hec)27(ks)-453(the)-455(receiv)27(ed)-454(signature)]TJ
/T1_0 10.91 Tf
170.78 0 Td
(\276)Tj
/T1_1 7.97 Tf
6.63 3.96 Td
(0)Tj
/T1_4 7.97 Tf
-0.4 -7.19 Td
[(J)23(;)]TJ
/T1_7 7.97 Tf
(1)Tj
/T1_2 10.91 Tf
16.48 3.23 Td
[(and)-454(certi\257cate)]TJ
/T1_3 10.91 Tf
-398.66 -21.92 Td
(cert)Tj
/T1_2 10.91 Tf
22.9 0 Td
([)Tj
/T1_3 10.91 Tf
(S)Tj
/T1_4 7.97 Tf
8.76 -1.69 Td
(J)Tj
/T1_2 10.91 Tf
5.87 1.69 Td
[(].)-573(If)-377(the)-376(v)27(eri\257cations)-376(are)-376(not)-377(correct,)-387(then)]TJ
/T1_3 10.91 Tf
207.97 0 Td
(U)Tj
/T1_4 7.97 Tf
5.73 -1.77 Td
[(J)24(;k)]TJ
/T1_2 10.91 Tf
16.01 1.77 Td
(rejects)Tj
/T1_3 10.91 Tf
34.79 0 Td
(S)Tj
/T1_4 7.97 Tf
5.73 -1.69 Td
(J)Tj
/T1_2 10.91 Tf
5.87 1.69 Td
[(.)-573(Otherwise,)]TJ
/T1_3 10.91 Tf
64.49 0 Td
(U)Tj
/T1_4 7.97 Tf
5.73 -1.77 Td
[(J)24(;k)]TJ
/T1_2 10.91 Tf
16.01 1.77 Td
[(c)27(hec)28(ks)-375(the)-377(list)]TJ
/T1_3 10.91 Tf
-399.86 -21.91 Td
(BL)Tj
/T1_11 7.97 Tf
11.45 -1.64 Td
(Z)Tj
/T1_2 10.91 Tf
7.59 1.64 Td
[(to)-262(iden)27(tify)-261(the)-262(malicious)-262(no)-28(des)-262(to)-262(b)-28(e)-262(blo)-28(c)27(k)27(ed)-261(from)-262(the)-262(GKA.)-262(\(F)82(or)-261(example,)-276(if)]TJ
/T1_3 10.91 Tf
363.23 0 Td
(U)Tj
/T1_4 7.97 Tf
5.73 -1.78 Td
[(J)24(;k)]TJ
/T1_2 10.91 Tf
14.76 1.78 Td
[(disco)28(v)27(ers)-261(that)]TJ
-402.76 -21.92 Td
[(its)-249(neigh)26(b)-26(or)]TJ
/T1_3 10.91 Tf
58.26 0 Td
(U)Tj
/T1_4 7.97 Tf
5.72 -1.78 Td
[(J)24(;k)]TJ
/T1_1 7.97 Tf
11.41 0 Td
(\241)Tj
/T1_7 7.97 Tf
(1)Tj
/T1_2 10.91 Tf
14.04 1.78 Td
[(is)-249(in)-250(the)-250(list)]TJ
/T1_3 10.91 Tf
57.07 0 Td
(BL)Tj
/T1_11 7.97 Tf
11.45 -1.64 Td
(Z)Tj
/T1_2 10.91 Tf
4.73 1.64 Td
[(,)-266(then)]TJ
/T1_3 10.91 Tf
29.87 0 Td
(U)Tj
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(\))Tj
/T1_1 7.97 Tf
4.25 5.9 Td
(r)Tj
/T1_9 5.98 Tf
4.05 2.81 Td
(0)Tj
/T1_2 5.98 Tf
-0.23 -5.51 Td
[(J)35(;n)]TJ
10.73 -2.03 Td
(J)Tj
/T1_10 10.91 Tf
6.13 -1.17 Td
(jj)Tj
/T1_0 10.91 Tf
6.06 0 Td
(SID)Tj
/T1_6 7.97 Tf
17.18 3.96 Td
(0)Tj
/T1_1 7.97 Tf
T*
(J)Tj
/T1_3 10.91 Tf
5.87 3.23 Td
[(\))-302(and)]TJ
/T1_5 10.91 Tf
28.41 0 Td
(X)Tj
/T1_6 7.97 Tf
9.89 3.96 Td
(0)Tj
/T1_1 7.97 Tf
-0.86 -7.19 Td
[(J)23(;n)]TJ
/T1_2 5.98 Tf
11.92 -1.34 Td
(J)Tj
/T1_3 10.91 Tf
8.67 4.57 Td
(=)Tj
/T1_5 10.91 Tf
11.51 0 Td
(L)Tj
/T1_6 7.97 Tf
7.42 3.96 Td
(0)Tj
/T1_1 7.97 Tf
T*
[(J)23(;n)]TJ
/T1_2 5.98 Tf
11.92 -1.34 Td
(J)Tj
/T1_10 10.91 Tf
7.39 4.57 Td
(\251)Tj
/T1_5 10.91 Tf
10.24 0 Td
(R)Tj
/T1_6 7.97 Tf
8.36 3.96 Td
(0)Tj
/T1_1 7.97 Tf
-0.08 -7.19 Td
[(J)24(;n)]TJ
/T1_2 5.98 Tf
11.92 -1.34 Td
(J)Tj
/T1_3 10.91 Tf
5.63 4.57 Td
(.)Tj
-464.84 -21.92 Td
[(Finally)83(,)]TJ
/T1_0 10.91 Tf
41.03 0 Td
(U)Tj
/T1_1 7.97 Tf
5.72 -1.69 Td
[(J)23(;n)]TJ
/T1_2 5.98 Tf
11.93 -1.34 Td
(J)Tj
/T1_3 10.91 Tf
10.7 3.03 Td
(selects)Tj
/T1_5 10.91 Tf
35.49 0 Td
(\267)Tj
/T1_6 7.97 Tf
6.29 3.96 Td
(0)Tj
/T1_1 7.97 Tf
T*
[(J)24(;n)]TJ
/T1_2 5.98 Tf
11.92 -1.34 Td
(J)Tj
/T1_10 10.91 Tf
11.06 4.57 Td
[(2)-497(f)]TJ
/T1_3 10.91 Tf
(0)Tj
/T1_5 10.91 Tf
(;)Tj
/T1_3 10.91 Tf
28.45 0 Td
(1)Tj
/T1_10 10.91 Tf
(g)Tj
/T1_1 7.97 Tf
10.9 3.96 Td
(\270)Tj
/T1_3 10.91 Tf
10.51 -3.96 Td
[(and)-465(broadcasts)]TJ
/T1_10 10.91 Tf
78.16 0 Td
(f)Tj
/T1_0 10.91 Tf
(U)Tj
/T1_1 7.97 Tf
11.18 -1.69 Td
[(J)24(;n)]TJ
/T1_2 5.98 Tf
11.92 -1.34 Td
(J)Tj
/T1_10 10.91 Tf
5.63 3.03 Td
(jj)Tj
/T1_5 10.91 Tf
6.06 0 Td
(\267)Tj
/T1_6 7.97 Tf
6.29 3.96 Td
(0)Tj
/T1_1 7.97 Tf
T*
[(J)24(;n)]TJ
/T1_2 5.98 Tf
11.92 -1.34 Td
(J)Tj
/T1_10 10.91 Tf
5.63 4.57 Td
(jj)Tj
/T1_5 10.91 Tf
6.06 0 Td
(X)Tj
/T1_6 7.97 Tf
9.89 3.96 Td
(0)Tj
/T1_1 7.97 Tf
-0.85 -7.19 Td
[(J)24(;n)]TJ
/T1_2 5.98 Tf
11.92 -1.34 Td
(J)Tj
/T1_10 10.91 Tf
5.63 4.57 Td
(jj)Tj
/T1_3 10.91 Tf
6.64 0 Td
(\271)Tj
/T1_5 10.91 Tf
-0.58 0 Td
(\276)Tj
/T1_6 7.97 Tf
6.62 3.96 Td
(0)Tj
/T1_1 7.97 Tf
-0.39 -7.19 Td
[(J)24(;n)]TJ
/T1_2 5.98 Tf
11.92 -1.34 Td
(J)Tj
/T1_10 10.91 Tf
5.64 4.57 Td
(g)Tj
/T1_3 10.91 Tf
[(,)-498(where)-518(\271)]TJ
/T1_5 10.91 Tf
46.89 0 Td
(\276)Tj
/T1_6 7.97 Tf
6.62 3.96 Td
(0)Tj
/T1_1 7.97 Tf
-0.39 -7.19 Td
[(J)24(;n)]TJ
/T1_2 5.98 Tf
11.92 -1.34 Td
(J)Tj
/T1_3 10.91 Tf
11.06 4.57 Td
(=)Tj
/T1_10 10.91 Tf
-459.39 -21.92 Td
(S)Tj
/T1_3 10.91 Tf
7.42 0 Td
(\()Tj
/T1_0 10.91 Tf
(U)Tj
/T1_1 7.97 Tf
9.97 -1.68 Td
[(J)24(;n)]TJ
/T1_2 5.98 Tf
11.92 -1.34 Td
(J)Tj
/T1_10 10.91 Tf
5.63 3.02 Td
(jj)Tj
/T1_5 10.91 Tf
6.06 0 Td
(\267)Tj
/T1_6 7.97 Tf
6.29 3.96 Td
(0)Tj
/T1_1 7.97 Tf
T*
[(J)24(;n)]TJ
/T1_2 5.98 Tf
11.92 -1.34 Td
(J)Tj
/T1_10 10.91 Tf
5.63 4.57 Td
(jj)Tj
/T1_5 10.91 Tf
6.06 0 Td
(X)Tj
/T1_6 7.97 Tf
9.89 3.96 Td
(0)Tj
/T1_1 7.97 Tf
-0.85 -7.19 Td
[(J)24(;n)]TJ
/T1_2 5.98 Tf
11.92 -1.34 Td
(J)Tj
/T1_10 10.91 Tf
5.63 4.57 Td
(jj)Tj
/T1_5 10.91 Tf
6.06 0 Td
(\277)Tj
/T1_6 7.97 Tf
6 3.96 Td
(0)Tj
/T1_1 7.97 Tf
-1.23 -7.19 Td
(J)Tj
/T1_10 10.91 Tf
5.87 3.23 Td
(jj)Tj
/T1_5 10.91 Tf
6.06 0 Td
(v)Tj
/T1_3 10.91 Tf
5.67 0 Td
(\).)Tj
-125.92 -21.91 Td
[(Round)-333(5)]TJ
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 0 -100.15 cm
0 0 m
40.75 0 l
S
Q
Q
BT
/T1_3 10.91 Tf
1.0003 0 0 1.0003 116.4024 671.1724 Tm
(:)Tj
/T1_0 10.91 Tf
7.89 0 Td
(S)Tj
/T1_1 7.97 Tf
5.72 -1.69 Td
(J)Tj
/T1_3 10.91 Tf
9.51 1.69 Td
(\257rst)Tj
1.0003 0 0 1.0003 72 769.82 Tm
90.039 -98.62 Td
[(c)27(hec)28(ks)-333(the)-334(receiv)27(ed)-333(signatures)-387(\271)]TJ
/T1_5 10.91 Tf
145.971 0 Td
(\276)Tj
/T1_6 7.97 Tf
6.62 3.96 Td
(0)Tj
/T1_1 7.97 Tf
-0.39 -7.28 Td
[(J)23(;k)]TJ
/T1_3 10.91 Tf
15.54 3.32 Td
(for)Tj
/T1_5 10.91 Tf
16.7 0 Td
(n)Tj
/T1_1 7.97 Tf
6.55 -1.69 Td
(J)Tj
/T1_3 10.91 Tf
8.3 1.69 Td
[(+)-222(1)]TJ
/T1_10 10.91 Tf
19.4 0 Td
(\267)Tj
/T1_5 10.91 Tf
11.52 0 Td
(k)Tj
/T1_10 10.91 Tf
9.06 0 Td
(\267)Tj
/T1_5 10.91 Tf
11.52 0 Td
(n)Tj
/T1_1 7.97 Tf
6.55 -1.69 Td
(J)Tj
/T1_3 10.91 Tf
8.29 1.69 Td
(+)Tj
/T1_5 10.91 Tf
10.91 0 Td
(m)Tj
/T1_3 10.91 Tf
13.22 0 Td
[(and)-387(\271)]TJ
/T1_5 10.91 Tf
21.21 0 Td
(\276)Tj
/T1_6 7.97 Tf
6.63 3.96 Td
(0)Tj
/T1_1 7.97 Tf
-0.4 -7.19 Td
[(J)23(;n)]TJ
/T1_2 5.98 Tf
11.93 -1.34 Td
(J)Tj
/T1_3 10.91 Tf
5.63 4.57 Td
[(.)-445(If)-334(there)]TJ
-424.8 -21.92 Td
[(are)-396(in)27(v)56(alid)-396(signatures,)]TJ
/T1_0 10.91 Tf
110.26 0 Td
(S)Tj
/T1_1 7.97 Tf
5.73 -1.69 Td
(J)Tj
/T1_3 10.91 Tf
10.19 1.69 Td
[(will)-396(place)-396(the)-396(iden)27(tities)-395(of)-397(in)27(v)56(alid)-396(users)]TJ
/T1_11 10.91 Tf
193.88 1.97 Td
(e)Tj
/T1_0 10.91 Tf
0.17 -1.97 Td
(U)Tj
/T1_1 7.97 Tf
5.73 -1.77 Td
[(J)24(;k)]TJ
/T1_3 10.91 Tf
16.22 1.77 Td
[(that)-396(generated)-396(the)-396(in)27(v)55(alid)]TJ
-342.18 -21.91 Td
[(signature)-409(to)-410(a)-410(list)]TJ
/T1_0 10.91 Tf
91.34 0 Td
(BL)Tj
/T1_4 7.97 Tf
11.45 -1.64 Td
(X)Tj
/T1_3 10.91 Tf
9.2 1.64 Td
[(and)-409(broadcast)]TJ
/T1_10 10.91 Tf
72.65 0 Td
(f)Tj
/T1_0 10.91 Tf
(S)Tj
/T1_1 7.97 Tf
11.18 -1.69 Td
(J)Tj
/T1_10 10.91 Tf
5.87 1.69 Td
(jj)Tj
/T1_0 10.91 Tf
6.06 0 Td
(BL)Tj
/T1_4 7.97 Tf
11.45 -1.64 Td
(X)Tj
/T1_10 10.91 Tf
4.73 1.64 Td
(jj)Tj
/T1_3 10.91 Tf
6.64 0 Td
(\271)Tj
/T1_5 10.91 Tf
-0.58 0 Td
(\276)Tj
/T1_6 7.97 Tf
6.62 3.95 Td
(0)Tj
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-0.39 -7.19 Td
[(J)24(;)]TJ
/T1_8 7.97 Tf
(1)Tj
/T1_10 10.91 Tf
11.51 3.24 Td
(g)Tj
/T1_3 10.91 Tf
[(,)-428(where)-464(\271)]TJ
/T1_5 10.91 Tf
45.53 0 Td
(\276)Tj
/T1_6 7.97 Tf
6.63 3.95 Td
(0)Tj
/T1_1 7.97 Tf
-0.39 -7.19 Td
[(J)24(;)]TJ
/T1_8 7.97 Tf
(1)Tj
/T1_3 10.91 Tf
15.93 3.24 Td
(=)Tj
/T1_10 10.91 Tf
12.9 0 Td
(S)Tj
/T1_3 10.91 Tf
7.42 0 Td
(\()Tj
/T1_0 10.91 Tf
(S)Tj
/T1_1 7.97 Tf
9.97 -1.69 Td
(J)Tj
/T1_10 10.91 Tf
5.87 1.69 Td
(jj)Tj
/T1_5 10.91 Tf
6.06 0 Td
(\277)Tj
/T1_6 7.97 Tf
6 3.95 Td
(0)Tj
/T1_1 7.97 Tf
-1.23 -7.19 Td
(J)Tj
/T1_10 10.91 Tf
5.87 3.24 Td
(jj)Tj
/T1_0 10.91 Tf
6.06 0 Td
(BL)Tj
/T1_4 7.97 Tf
11.45 -1.64 Td
(X)Tj
/T1_10 10.91 Tf
4.73 1.64 Td
(jj)Tj
/T1_5 10.91 Tf
6.06 0 Td
(v)Tj
/T1_3 10.91 Tf
5.68 0 Td
[(\).)-673(Otherwise,)]TJ
/T1_0 10.91 Tf
-402.27 -21.92 Td
(S)Tj
/T1_1 7.97 Tf
5.73 -1.69 Td
(J)Tj
/T1_3 10.91 Tf
10.79 1.69 Td
(computes)Tj
/T1_5 10.91 Tf
49.83 0 Td
(L)Tj
/T1_6 7.97 Tf
7.42 3.96 Td
(0)Tj
/T1_1 7.97 Tf
T*
[(J)24(;)]TJ
/T1_8 7.97 Tf
(1)Tj
/T1_3 10.91 Tf
16.69 3.23 Td
(=)Tj
/T1_7 10.91 Tf
13.67 0 Td
(H)Tj
/T1_3 10.91 Tf
(\(\()Tj
/T1_5 10.91 Tf
(z)Tj
/T1_6 7.97 Tf
21.76 3.96 Td
(0)Tj
/T1_1 7.97 Tf
-0.48 -7.19 Td
[(J)24(;n)]TJ
/T1_2 5.98 Tf
11.92 -1.34 Td
(J)Tj
/T1_3 10.91 Tf
5.63 4.57 Td
(\))Tj
/T1_1 7.97 Tf
4.24 5.04 Td
(r)Tj
/T1_9 5.98 Tf
4.06 2.81 Td
(0)Tj
/T1_2 5.98 Tf
-0.24 -5.52 Td
[(J)34(;)]TJ
/T1_12 5.98 Tf
6.14 0 Td
(1)Tj
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4.64 -2.33 Td
(jj)Tj
/T1_0 10.91 Tf
6.06 0 Td
(SID)Tj
/T1_6 7.97 Tf
17.18 3.96 Td
(0)Tj
/T1_1 7.97 Tf
T*
(J)Tj
/T1_3 10.91 Tf
5.87 3.23 Td
(\),)Tj
/T1_5 10.91 Tf
12.52 0 Td
(R)Tj
/T1_6 7.97 Tf
8.37 3.96 Td
(0)Tj
/T1_1 7.97 Tf
-0.09 -7.19 Td
[(J)23(;)]TJ
/T1_8 7.97 Tf
(1)Tj
/T1_3 10.91 Tf
16.7 3.23 Td
(=)Tj
/T1_7 10.91 Tf
13.66 0 Td
(H)Tj
/T1_3 10.91 Tf
7.73 0 Td
(\(\()Tj
/T1_5 10.91 Tf
8.48 0 Td
(z)Tj
/T1_6 7.97 Tf
5.55 3.96 Td
(0)Tj
/T1_1 7.97 Tf
-0.48 -7.19 Td
[(J)23(;n)]TJ
/T1_2 5.98 Tf
11.92 -1.34 Td
(J)Tj
/T1_8 7.97 Tf
5.14 1.34 Td
(+1)Tj
/T1_3 10.91 Tf
11.31 3.23 Td
(\))Tj
/T1_1 7.97 Tf
4.25 5.04 Td
(r)Tj
/T1_9 5.98 Tf
4.05 2.81 Td
(0)Tj
/T1_2 5.98 Tf
-0.23 -5.52 Td
[(J)35(;)]TJ
/T1_12 5.98 Tf
6.13 0 Td
(1)Tj
/T1_10 10.91 Tf
4.65 -2.33 Td
(jj)Tj
/T1_0 10.91 Tf
6.06 0 Td
(SID)Tj
/T1_6 7.97 Tf
17.17 3.96 Td
(0)Tj
/T1_1 7.97 Tf
T*
(J)Tj
/T1_3 10.91 Tf
5.87 3.23 Td
(\),)Tj
/T1_5 10.91 Tf
12.52 0 Td
(X)Tj
/T1_6 7.97 Tf
9.89 3.96 Td
(0)Tj
/T1_1 7.97 Tf
-0.85 -7.19 Td
[(J)24(;)]TJ
/T1_8 7.97 Tf
(1)Tj
/T1_3 10.91 Tf
16.7 3.23 Td
(=)Tj
/T1_5 10.91 Tf
13.66 0 Td
(L)Tj
/T1_6 7.97 Tf
7.42 3.96 Td
(0)Tj
/T1_1 7.97 Tf
T*
[(J)23(;)]TJ
/T1_8 7.97 Tf
(1)Tj
/T1_10 10.91 Tf
14.8 3.23 Td
(\251)Tj
/T1_5 10.91 Tf
11.77 0 Td
(R)Tj
/T1_6 7.97 Tf
8.36 3.96 Td
(0)Tj
/T1_1 7.97 Tf
-0.08 -7.19 Td
[(J)24(;)]TJ
/T1_8 7.97 Tf
(1)Tj
/T1_3 10.91 Tf
16.44 3.23 Td
(and)Tj
/T1_11 10.91 Tf
-448.3 -18.43 Td
(c)Tj
/T1_5 10.91 Tf
-2 -3.49 Td
(X)Tj
/T1_6 7.97 Tf
9.89 3.76 Td
(0)Tj
/T1_1 7.97 Tf
-0.85 -7.19 Td
(J)Tj
/T1_3 10.91 Tf
8.9 3.43 Td
(=)Tj
/T1_5 10.91 Tf
11.51 0 Td
(\267)Tj
/T1_6 7.97 Tf
6.28 3.96 Td
(0)Tj
/T1_1 7.97 Tf
T*
[(J)23(;)]TJ
/T1_8 7.97 Tf
(1)Tj
/T1_10 10.91 Tf
13.25 3.23 Td
(\251)Tj
/T1_5 10.91 Tf
10.22 0 Td
(R)Tj
/T1_6 7.97 Tf
8.36 3.96 Td
(0)Tj
/T1_1 7.97 Tf
-0.08 -7.19 Td
[(J)24(;)]TJ
/T1_8 7.97 Tf
(1)Tj
/T1_3 10.91 Tf
11.51 3.23 Td
[(.)-434(Next,)]TJ
/T1_0 10.91 Tf
37.18 0 Td
(S)Tj
/T1_1 7.97 Tf
5.72 -1.69 Td
(J)Tj
/T1_3 10.91 Tf
9.16 1.69 Td
[(c)27(hec)28(ks)-301(the)-302(X)27(OR)-300(equation:)]TJ
/T1_5 10.91 Tf
128.06 0 Td
(X)Tj
/T1_6 7.97 Tf
9.89 3.96 Td
(0)Tj
/T1_1 7.97 Tf
-0.85 -7.19 Td
[(J)24(;)]TJ
/T1_8 7.97 Tf
(1)Tj
/T1_10 10.91 Tf
13.25 3.23 Td
(\251)Tj
/T1_5 10.91 Tf
10.21 0 Td
(X)Tj
/T1_6 7.97 Tf
9.89 3.96 Td
(0)Tj
/T1_1 7.97 Tf
-0.85 -7.19 Td
[(J)24(;n)]TJ
/T1_2 5.98 Tf
11.92 -1.34 Td
(J)Tj
/T1_8 7.97 Tf
5.13 1.34 Td
(+1)Tj
/T1_10 10.91 Tf
13.05 3.23 Td
[(\251)-159(\242)-166(\242)-167(\242)-159(\251)]TJ
/T1_5 10.91 Tf
34.89 0 Td
(X)Tj
/T1_6 7.97 Tf
9.89 3.96 Td
(0)Tj
/T1_1 7.97 Tf
-0.85 -7.19 Td
[(J)24(;n)]TJ
/T1_2 5.98 Tf
11.92 -1.34 Td
(J)Tj
/T1_8 7.97 Tf
5.14 1.34 Td
(+)Tj
/T1_1 7.97 Tf
(m)Tj
/T1_10 10.91 Tf
16.3 3.23 Td
(\251)Tj
/T1_5 10.91 Tf
10.22 0 Td
(X)Tj
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9.89 3.96 Td
(0)Tj
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-0.86 -7.19 Td
[(J)23(;n)]TJ
/T1_2 5.98 Tf
11.92 -1.34 Td
(J)Tj
/T1_3 10.91 Tf
8.67 4.57 Td
[(=)-277(0.)]TJ
-447.88 -21.91 Td
[(If)-225(the)-225(X)27(OR)-224(equation)-225(is)-226(not)-225(correct,)]TJ
/T1_0 10.91 Tf
164.02 0 Td
(S)Tj
/T1_1 7.97 Tf
5.73 -1.69 Td
(J)Tj
/T1_3 10.91 Tf
8.33 1.69 Td
[(will)-224(place)-225(the)-226(in)27(v)56(alid)-224(X)26(OR)-224(equation)-225(to)-225(a)-225(list)]TJ
/T1_0 10.91 Tf
204.99 0 Td
(BL)Tj
/T1_4 7.97 Tf
11.45 -1.64 Td
(X)Tj
/T1_3 10.91 Tf
7.19 1.64 Td
[(and)-224(broadcast)]TJ
/T1_10 10.91 Tf
-401.71 -21.92 Td
(f)Tj
/T1_0 10.91 Tf
(S)Tj
/T1_1 7.97 Tf
11.18 -1.69 Td
(J)Tj
/T1_10 10.91 Tf
5.87 1.69 Td
(jj)Tj
/T1_0 10.91 Tf
6.06 0 Td
(BL)Tj
/T1_4 7.97 Tf
11.45 -1.64 Td
(X)Tj
/T1_10 10.91 Tf
4.73 1.64 Td
(jj)Tj
/T1_3 10.91 Tf
6.64 0 Td
(\271)Tj
/T1_5 10.91 Tf
-0.58 0 Td
(\276)Tj
/T1_6 7.97 Tf
6.62 3.96 Td
(0)Tj
/T1_1 7.97 Tf
-0.39 -7.19 Td
[(J)23(;)]TJ
/T1_8 7.97 Tf
(1)Tj
/T1_10 10.91 Tf
11.52 3.23 Td
(g)Tj
/T1_3 10.91 Tf
[(,)-333(where)-386(\271)]TJ
/T1_5 10.91 Tf
43.65 0 Td
(\276)Tj
/T1_6 7.97 Tf
6.62 3.96 Td
(0)Tj
/T1_1 7.97 Tf
-0.39 -7.19 Td
[(J)24(;)]TJ
/T1_8 7.97 Tf
(1)Tj
/T1_3 10.91 Tf
14.54 3.23 Td
(=)Tj
/T1_10 10.91 Tf
11.51 0 Td
(S)Tj
/T1_3 10.91 Tf
7.43 0 Td
(\()Tj
/T1_0 10.91 Tf
(S)Tj
/T1_1 7.97 Tf
9.96 -1.69 Td
(J)Tj
/T1_10 10.91 Tf
5.87 1.69 Td
(jj)Tj
/T1_5 10.91 Tf
6.06 0 Td
(\277)Tj
/T1_6 7.97 Tf
6.01 3.96 Td
(0)Tj
/T1_1 7.97 Tf
-1.24 -7.19 Td
(J)Tj
/T1_10 10.91 Tf
5.87 3.23 Td
(jj)Tj
/T1_0 10.91 Tf
6.06 0 Td
(BL)Tj
/T1_4 7.97 Tf
11.45 -1.64 Td
(X)Tj
/T1_10 10.91 Tf
4.73 1.64 Td
(jj)Tj
/T1_5 10.91 Tf
6.06 0 Td
(v)Tj
/T1_3 10.91 Tf
5.68 0 Td
[(\).)-444(Otherwise,)-333(if)-333(the)-333(X)27(OR)-332(equation)-333(is)-334(correct,)-333(then)]TJ
/T1_0 10.91 Tf
243.3 0 Td
(S)Tj
/T1_1 7.97 Tf
5.73 -1.69 Td
(J)Tj
/T1_3 10.91 Tf
-462 -20.23 Td
(broadcast)Tj
/T1_10 10.91 Tf
49.77 0 Td
(f)Tj
/T1_0 10.91 Tf
(S)Tj
/T1_1 7.97 Tf
11.18 -1.69 Td
(J)Tj
/T1_10 10.91 Tf
5.87 1.69 Td
(jj)Tj
/T1_11 10.91 Tf
8.06 3.49 Td
(c)Tj
/T1_5 10.91 Tf
-2 -3.49 Td
(X)Tj
/T1_6 7.97 Tf
9.89 3.76 Td
(0)Tj
/T1_1 7.97 Tf
-0.85 -7.19 Td
(J)Tj
/T1_10 10.91 Tf
5.87 3.43 Td
(jj)Tj
/T1_5 10.91 Tf
6.06 0 Td
(X)Tj
/T1_6 7.97 Tf
9.89 3.96 Td
(0)Tj
/T1_1 7.97 Tf
-0.86 -7.19 Td
[(J)23(;)]TJ
/T1_8 7.97 Tf
(1)Tj
/T1_10 10.91 Tf
11.52 3.23 Td
(jj)Tj
/T1_3 10.91 Tf
6.64 0 Td
(\271)Tj
/T1_5 10.91 Tf
-0.58 0 Td
(\276)Tj
/T1_6 7.97 Tf
6.62 3.96 Td
(0)Tj
/T1_1 7.97 Tf
-0.39 -7.19 Td
[(J)24(;)]TJ
/T1_8 7.97 Tf
(1)Tj
/T1_10 10.91 Tf
11.51 3.23 Td
(g)Tj
/T1_3 10.91 Tf
[(,)-333(where)-387(\271)]TJ
/T1_5 10.91 Tf
43.66 0 Td
(\276)Tj
/T1_6 7.97 Tf
6.62 3.96 Td
(0)Tj
/T1_1 7.97 Tf
-0.39 -7.19 Td
[(J)24(;)]TJ
/T1_8 7.97 Tf
(1)Tj
/T1_3 10.91 Tf
14.54 3.23 Td
(=)Tj
/T1_10 10.91 Tf
11.52 0 Td
(S)Tj
/T1_3 10.91 Tf
7.42 0 Td
(\()Tj
/T1_0 10.91 Tf
(S)Tj
/T1_1 7.97 Tf
9.97 -1.69 Td
(J)Tj
/T1_10 10.91 Tf
5.87 1.69 Td
(jj)Tj
/T1_5 10.91 Tf
6.06 0 Td
(\277)Tj
/T1_6 7.97 Tf
6 3.96 Td
(0)Tj
/T1_1 7.97 Tf
-1.24 -7.19 Td
(J)Tj
/T1_10 10.91 Tf
5.87 3.23 Td
(jj)Tj
/T1_11 10.91 Tf
8.06 3.49 Td
(c)Tj
/T1_5 10.91 Tf
-2 -3.49 Td
(X)Tj
/T1_6 7.97 Tf
9.89 3.76 Td
(0)Tj
/T1_1 7.97 Tf
-0.85 -7.19 Td
(J)Tj
/T1_10 10.91 Tf
5.87 3.43 Td
(jj)Tj
/T1_5 10.91 Tf
6.06 0 Td
(X)Tj
/T1_6 7.97 Tf
9.89 3.96 Td
(0)Tj
/T1_1 7.97 Tf
-0.86 -7.19 Td
[(J)23(;)]TJ
/T1_8 7.97 Tf
(1)Tj
/T1_10 10.91 Tf
11.52 3.23 Td
(jj)Tj
/T1_5 10.91 Tf
6.06 0 Td
(v)Tj
/T1_3 10.91 Tf
5.67 0 Td
(\).)Tj
-313.41 -21.91 Td
[(Round)-333(6)]TJ
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 0 -275.48 cm
0 0 m
40.75 0 l
S
Q
Q
BT
/T1_3 10.91 Tf
1.0003 0 0 1.0003 116.3924 495.7933 Tm
(:)Tj
/T1_13 10.91 Tf
-44.38 -21.92 Td
(Case)Tj
1.0003 0 0 1.0003 72 769.82 Tm
30.995 -295.87 Td
[(1)-472(-)]TJ
/T1_0 10.91 Tf
20.745 0 Td
(U)Tj
/T1_1 7.97 Tf
5.72 -1.78 Td
[(J)23(;k)]TJ
/T1_13 10.91 Tf
17.05 1.78 Td
(and)Tj
/T1_0 10.91 Tf
25.18 0 Td
(U)Tj
/T1_1 7.97 Tf
5.73 -1.69 Td
[(J)24(;n)]TJ
/T1_2 5.98 Tf
11.92 -1.34 Td
(J)Tj
/T1_13 10.91 Tf
10.78 3.03 Td
[(receiv)32(es)]TJ
/T1_10 10.91 Tf
47.83 0 Td
(f)Tj
/T1_0 10.91 Tf
(S)Tj
/T1_1 7.97 Tf
11.18 -1.69 Td
(J)Tj
/T1_10 10.91 Tf
5.87 1.69 Td
(jj)Tj
/T1_11 10.91 Tf
8.06 3.49 Td
(c)Tj
/T1_5 10.91 Tf
-2 -3.49 Td
(X)Tj
/T1_6 7.97 Tf
9.89 3.76 Td
(0)Tj
/T1_1 7.97 Tf
-0.86 -7.19 Td
(J)Tj
/T1_10 10.91 Tf
5.87 3.43 Td
(jj)Tj
/T1_5 10.91 Tf
6.06 0 Td
(X)Tj
/T1_6 7.97 Tf
9.89 3.96 Td
(0)Tj
/T1_1 7.97 Tf
-0.85 -7.19 Td
[(J)24(;)]TJ
/T1_8 7.97 Tf
(1)Tj
/T1_10 10.91 Tf
11.51 3.23 Td
(jj)Tj
/T1_3 10.91 Tf
6.65 0 Td
(\271)Tj
/T1_5 10.91 Tf
-0.59 0 Td
(\276)Tj
/T1_6 7.97 Tf
6.63 3.96 Td
(0)Tj
/T1_1 7.97 Tf
-0.4 -7.19 Td
[(J)23(;)]TJ
/T1_8 7.97 Tf
(1)Tj
/T1_10 10.91 Tf
11.52 3.23 Td
(g)Tj
/T1_13 10.91 Tf
10.6 0 Td
(:)Tj
/T1_3 10.91 Tf
10.01 0 Td
(If)Tj
/T1_0 10.91 Tf
11.74 0 Td
(U)Tj
/T1_1 7.97 Tf
5.73 -1.78 Td
[(J)24(;k)]TJ
/T1_3 10.91 Tf
16.37 1.78 Td
(for)Tj
/T1_5 10.91 Tf
17.54 0 Td
(n)Tj
/T1_1 7.97 Tf
6.54 -1.69 Td
(J)Tj
/T1_3 10.91 Tf
8.86 1.69 Td
[(+)-273(1)]TJ
/T1_10 10.91 Tf
21.34 0 Td
(\267)Tj
/T1_5 10.91 Tf
12.91 0 Td
(k)Tj
/T1_10 10.91 Tf
10.45 0 Td
(\267)Tj
/T1_5 10.91 Tf
12.91 0 Td
(n)Tj
/T1_1 7.97 Tf
6.55 -1.69 Td
(J)Tj
/T1_3 10.91 Tf
8.85 1.69 Td
(+)Tj
/T1_5 10.91 Tf
11.47 0 Td
(m)Tj
/T1_3 10.91 Tf
14.05 0 Td
(and)Tj
/T1_0 10.91 Tf
-450.3 -21.92 Td
(U)Tj
/T1_1 7.97 Tf
5.73 -1.68 Td
[(J)24(;n)]TJ
/T1_2 5.98 Tf
11.92 -1.34 Td
(J)Tj
/T1_3 10.91 Tf
8.93 3.02 Td
[(receiv)27(es)]TJ
/T1_10 10.91 Tf
39.74 0 Td
(f)Tj
/T1_0 10.91 Tf
(S)Tj
/T1_1 7.97 Tf
11.18 -1.68 Td
(J)Tj
/T1_10 10.91 Tf
5.87 1.68 Td
(jj)Tj
/T1_11 10.91 Tf
8.06 3.49 Td
(c)Tj
/T1_5 10.91 Tf
-2 -3.49 Td
(X)Tj
/T1_6 7.97 Tf
9.89 3.76 Td
(0)Tj
/T1_1 7.97 Tf
-0.86 -7.19 Td
(J)Tj
/T1_10 10.91 Tf
5.87 3.43 Td
(jj)Tj
/T1_5 10.91 Tf
6.06 0 Td
(X)Tj
/T1_6 7.97 Tf
9.89 3.96 Td
(0)Tj
/T1_1 7.97 Tf
-0.85 -7.19 Td
[(J)24(;)]TJ
/T1_8 7.97 Tf
(1)Tj
/T1_10 10.91 Tf
11.51 3.23 Td
(jj)Tj
/T1_3 10.91 Tf
6.65 0 Td
(\271)Tj
/T1_5 10.91 Tf
-0.59 0 Td
(\276)Tj
/T1_6 7.97 Tf
6.63 3.96 Td
(0)Tj
/T1_1 7.97 Tf
-0.4 -7.19 Td
[(J)23(;)]TJ
/T1_8 7.97 Tf
(1)Tj
/T1_10 10.91 Tf
11.52 3.23 Td
(g)Tj
/T1_3 10.91 Tf
8.75 0 Td
(from)Tj
/T1_0 10.91 Tf
25.44 0 Td
(S)Tj
/T1_1 7.97 Tf
5.73 -1.68 Td
(J)Tj
/T1_3 10.91 Tf
5.87 1.68 Td
[(,)-308(it)-302(means)-302(that)]TJ
/T1_0 10.91 Tf
73.3 0 Td
(S)Tj
/T1_1 7.97 Tf
5.72 -1.68 Td
(J)Tj
/T1_3 10.91 Tf
9.17 1.68 Td
[(has)-302(v)27(eri\257ed)-301(that)-303(all)-302(signatures)-356(\271)]TJ
/T1_5 10.91 Tf
146.39 0 Td
(\276)Tj
/T1_6 7.97 Tf
6.62 3.96 Td
(0)Tj
/T1_1 7.97 Tf
-0.39 -7.19 Td
[(J)23(;i)]TJ
/T1_3 10.91 Tf
13.46 3.23 Td
(for)Tj
/T1_5 10.91 Tf
-454.81 -21.91 Td
(n)Tj
/T1_1 7.97 Tf
6.55 -1.69 Td
(J)Tj
/T1_3 10.91 Tf
7.69 1.69 Td
[(+)-167(1)]TJ
/T1_10 10.91 Tf
18.79 0 Td
(\267)Tj
/T1_5 10.91 Tf
11.52 0 Td
(i)Tj
/T1_10 10.91 Tf
6.78 0 Td
(\267)Tj
/T1_5 10.91 Tf
11.52 0 Td
(n)Tj
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6.54 -1.69 Td
(J)Tj
/T1_3 10.91 Tf
7.7 1.69 Td
(+)Tj
/T1_5 10.91 Tf
10.31 0 Td
(m)Tj
/T1_3 10.91 Tf
12.91 0 Td
[(and)-359(\271)]TJ
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20.91 0 Td
(\276)Tj
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6.62 3.95 Td
(0)Tj
/T1_1 7.97 Tf
-0.39 -7.18 Td
[(J)24(;n)]TJ
/T1_2 5.98 Tf
11.92 -1.34 Td
(J)Tj
/T1_3 10.91 Tf
8.97 4.57 Td
[(are)-305(v)54(alid)-305(and)-306(the)-306(X)27(OR)-305(equation)-306(is)-306(correct)-306(in)-306(Round)-306(5.)-435(In)-306(this)-306(case,)]TJ
/T1_0 10.91 Tf
-148.34 -21.92 Td
(U)Tj
/T1_1 7.97 Tf
5.73 -1.78 Td
[(J)24(;k)]TJ
/T1_3 10.91 Tf
16.15 1.78 Td
(and)Tj
/T1_0 10.91 Tf
21.83 0 Td
(U)Tj
/T1_1 7.97 Tf
5.72 -1.69 Td
[(J)23(;n)]TJ
/T1_2 5.98 Tf
11.92 -1.34 Td
(J)Tj
/T1_3 10.91 Tf
9.89 3.03 Td
[(\257rst)-390(v)27(erify)-389(receiv)27(ed)-389(signature)-444(\271)]TJ
/T1_5 10.91 Tf
144.5 0 Td
(\276)Tj
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6.62 3.96 Td
(0)Tj
/T1_1 7.97 Tf
-0.39 -7.19 Td
[(J)23(;)]TJ
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(1)Tj
/T1_3 10.91 Tf
11.52 3.23 Td
[(.)-614(If)-390(the)-390(v)27(eri\257cation)-390(is)-390(not)-390(correct,)-404(then)]TJ
/T1_0 10.91 Tf
194.93 0 Td
(U)Tj
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5.72 -1.78 Td
[(J)23(;k)]TJ
/T1_3 10.91 Tf
16.16 1.78 Td
(and)Tj
/T1_0 10.91 Tf
-450.3 -21.92 Td
(U)Tj
/T1_1 7.97 Tf
5.73 -1.68 Td
[(J)24(;n)]TJ
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11.92 -1.34 Td
(J)Tj
/T1_3 10.91 Tf
9.27 3.02 Td
(rejects)Tj
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34.32 0 Td
(S)Tj
/T1_1 7.97 Tf
5.73 -1.68 Td
(J)Tj
/T1_3 10.91 Tf
5.87 1.68 Td
[(.)-444(Otherwise,)]TJ
/T1_0 10.91 Tf
62.49 0 Td
(U)Tj
/T1_1 7.97 Tf
5.73 -1.77 Td
[(J)24(;k)]TJ
/T1_3 10.91 Tf
15.54 1.77 Td
(and)Tj
/T1_0 10.91 Tf
21.2 0 Td
(U)Tj
/T1_1 7.97 Tf
5.73 -1.68 Td
[(J)24(;n)]TJ
/T1_2 5.98 Tf
11.92 -1.34 Td
(J)Tj
/T1_3 10.91 Tf
9.27 3.02 Td
(computes)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 166.11 -414.2 cm
0 0 m
8.36 0 l
S
Q
Q
BT
/T1_5 10.91 Tf
1.0003 0 0 1.0003 238.1565 346.5215 Tm
(R)Tj
/T1_6 7.97 Tf
8.36 6.48 Td
(0)Tj
/T1_1 7.97 Tf
0 -9.17 TD
(J)Tj
1.0003 0 0 1.0003 72 769.82 Tm
178.909 -425.87 Td
(;k)Tj
/T1_8 7.97 Tf
6.971 0 Td
(+1)Tj
/T1_3 10.91 Tf
21.27 2.69 Td
(=)Tj
/T1_5 10.91 Tf
18.44 0 Td
(X)Tj
/T1_6 7.97 Tf
9.9 4.5 Td
(0)Tj
/T1_1 7.97 Tf
-0.86 -7.27 Td
[(J)24(;k)]TJ
/T1_8 7.97 Tf
11.4 0 Td
(+1)Tj
/T1_10 10.91 Tf
13.74 2.77 Td
(\251)Tj
/T1_5 10.91 Tf
10.91 0 Td
(R)Tj
/T1_6 7.97 Tf
8.36 4.5 Td
(0)Tj
/T1_1 7.97 Tf
-0.08 -7.27 Td
[(J)24(;k)]TJ
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 166.11 -439.1 cm
0 0 m
8.36 0 l
S
Q
Q
BT
/T1_5 10.91 Tf
1.0003 0 0 1.0003 238.1565 321.6145 Tm
(R)Tj
/T1_6 7.97 Tf
8.36 6.48 Td
(0)Tj
/T1_1 7.97 Tf
0 -9.18 TD
(J)Tj
1.0003 0 0 1.0003 72 769.82 Tm
178.909 -450.78 Td
(;k)Tj
/T1_8 7.97 Tf
6.971 0 Td
(+2)Tj
/T1_3 10.91 Tf
21.27 2.7 Td
(=)Tj
/T1_5 10.91 Tf
18.44 0 Td
(X)Tj
/T1_6 7.97 Tf
9.9 4.5 Td
(0)Tj
/T1_1 7.97 Tf
-0.86 -7.28 Td
[(J)24(;k)]TJ
/T1_8 7.97 Tf
11.4 0 Td
(+2)Tj
/T1_10 10.91 Tf
13.74 2.78 Td
(\251)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 270.68 -439.1 cm
0 0 m
8.36 0 l
S
Q
Q
BT
/T1_5 10.91 Tf
1.0003 0 0 1.0003 342.7558 321.6145 Tm
(R)Tj
/T1_6 7.97 Tf
8.36 6.48 Td
(0)Tj
/T1_1 7.97 Tf
T*
(J)Tj
1.0003 0 0 1.0003 72 769.82 Tm
283.479 -450.78 Td
(;k)Tj
/T1_8 7.97 Tf
6.971 0 Td
(+1)Tj
/T1_3 10.91 Tf
-80.57 -14.24 Td
(.)Tj
0 -3.98 TD
(.)Tj
0 -3.99 TD
(.)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 166.11 -488.91 cm
0 0 m
8.36 0 l
S
Q
Q
BT
/T1_5 10.91 Tf
1.0003 0 0 1.0003 238.1565 271.7906 Tm
(R)Tj
/T1_6 7.97 Tf
8.36 6.48 Td
(0)Tj
/T1_1 7.97 Tf
0 -9.18 TD
(J)Tj
1.0003 0 0 1.0003 72 769.82 Tm
178.909 -500.59 Td
(;k)Tj
/T1_6 7.97 Tf
6.971 0 Td
(\241)Tj
/T1_8 7.97 Tf
(1)Tj
/T1_3 10.91 Tf
21.27 2.7 Td
(=)Tj
/T1_5 10.91 Tf
18.44 0 Td
(X)Tj
/T1_6 7.97 Tf
9.9 4.5 Td
(0)Tj
/T1_1 7.97 Tf
-0.86 -7.28 Td
[(J)24(;k)]TJ
/T1_6 7.97 Tf
11.4 0 Td
(\241)Tj
/T1_8 7.97 Tf
6.59 0 Td
(1)Tj
/T1_10 10.91 Tf
7.15 2.78 Td
(\251)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 270.68 -488.91 cm
0 0 m
8.36 0 l
S
Q
Q
BT
/T1_5 10.91 Tf
1.0003 0 0 1.0003 342.7558 271.7906 Tm
(R)Tj
/T1_6 7.97 Tf
8.36 6.48 Td
(0)Tj
/T1_1 7.97 Tf
T*
(J)Tj
1.0003 0 0 1.0003 72 769.82 Tm
283.479 -500.59 Td
(;k)Tj
/T1_6 7.97 Tf
6.971 0 Td
(\241)Tj
/T1_8 7.97 Tf
(2)Tj
/T1_3 10.91 Tf
-290.45 -36.94 Td
[(and)-364(compares)]TJ
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 69.84 -528.56 cm
0 0 m
8.37 0 l
S
Q
Q
BT
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[(detected)-377(an)-378(in)27(v)55(alid)-376(X)26(OR)-376(equation,)-389(then)-378(list)]TJ
/T1_1 10.91 Tf
216.09 0 Td
(BL)Tj
/T1_5 7.97 Tf
11.45 -1.64 Td
(X)Tj
/T1_6 10.91 Tf
8.85 1.64 Td
[(con)27(tains)-377(the)]TJ
-382.19 -21.92 Td
[(in)28(v)55(alid)-302(X)27(OR)-302(equation)-303(instead)-303(of)-303(in)27(v)56(alid)-302(users')-303(iden)27(tities.)-434(The)-303(detection)-303(proto)-27(col)-303(describ)-28(ed)-303(in)]TJ
0 -21.92 TD
[(Section)-373(9.3)-375(will)-374(b)-28(e)-374(used)-374(to)-375(detect)-374(and)-374(blo)-28(c)27(k)-373(malicious)-375(group)-374(mem)27(b)-27(ers)]TJ
/T1_10 10.91 Tf
342.31 1.97 Td
(e)Tj
/T1_1 10.91 Tf
0.16 -1.97 Td
(U)Tj
/T1_2 7.97 Tf
5.73 -1.77 Td
[(J)24(;k)]TJ
/T1_6 10.91 Tf
15.98 1.77 Td
[(that)-374(sen)27(t)-374(wrong)]TJ
-364.18 -21.91 Td
[(information)-332(to)-334(disrupt)-333(the)-333(GKA.)]TJ
-27.27 -33.87 Td
[(F)83(or)-361(brevit)26(y)84(,)-368(w)26(e)-361(shall)-362(use)-362(the)-362(term)]TJ
/T1_10 10.91 Tf
166.37 1.97 Td
(e)Tj
/T1_1 10.91 Tf
0.16 -1.97 Td
(U)Tj
/T1_2 7.97 Tf
5.73 -1.78 Td
[(J)24(;k)]TJ
/T1_6 10.91 Tf
15.85 1.78 Td
[(to)-362(denote)-362(in)27(v)56(alid)-362(users)-362(and)-362(malicious)-362(group)-362(mem)27(b)-27(ers.)-531(Af-)]TJ
-188.11 -21.92 Td
[(ter)-375(detecting)-376(all)-376(in)27(v)55(alid)-375(users)-375(and)-376(malicious)-376(group)-376(mem)27(b)-27(ers)]TJ
/T1_10 10.91 Tf
292.17 1.97 Td
(e)Tj
/T1_1 10.91 Tf
0.17 -1.97 Td
(U)Tj
/T1_2 7.97 Tf
5.72 -1.77 Td
[(J)23(;k)]TJ
/T1_6 10.91 Tf
11.9 1.77 Td
[(,)-386(the)-376(honest)-376(left)-376(neigh)27(b)-27(or)]TJ
/T1_1 10.91 Tf
126.44 0 Td
(U)Tj
/T1_2 7.97 Tf
5.72 -1.77 Td
[(J)23(;k)]TJ
/T1_8 7.97 Tf
11.41 0 Td
(\241)Tj
/T1_9 7.97 Tf
(1)Tj
/T1_6 10.91 Tf
11.31 1.77 Td
(,)Tj
-464.84 -21.91 Td
[(whic)27(h)-442(has)-442(not)-443(b)-28(een)-443(blo)-28(c)27(k)28(ed,)-470(of)]TJ
/T1_10 10.91 Tf
157.93 1.97 Td
(e)Tj
/T1_1 10.91 Tf
0.16 -1.97 Td
(U)Tj
/T1_2 7.97 Tf
5.73 -1.78 Td
[(J)24(;k)]TJ
/T1_6 10.91 Tf
16.73 1.78 Td
[(will)-442(re-compute)]TJ
/T1_7 10.91 Tf
79.97 0 Td
(L)Tj
/T1_8 7.97 Tf
7.43 3.95 Td
(0)Tj
/T1_2 7.97 Tf
0 -7.27 TD
[(J)24(;k)]TJ
/T1_8 7.97 Tf
11.4 0 Td
(\241)Tj
/T1_9 7.97 Tf
6.59 0 Td
(1)Tj
/T1_6 10.91 Tf
9.75 3.32 Td
(=)Tj
/T1_11 10.91 Tf
13.5 0 Td
(H)Tj
/T1_6 10.91 Tf
7.73 0 Td
(\(\()Tj
/T1_7 10.91 Tf
8.48 0 Td
(z)Tj
/T1_8 7.97 Tf
5.55 3.95 Td
(0)Tj
/T1_2 7.97 Tf
-0.48 -7.27 Td
[(J)24(;k)]TJ
/T1_8 7.97 Tf
11.4 0 Td
(\241)Tj
/T1_9 7.97 Tf
6.59 0 Td
(2)Tj
/T1_6 10.91 Tf
4.73 3.32 Td
(\))Tj
/T1_2 7.97 Tf
4.24 5.1 Td
(r)Tj
/T1_12 5.98 Tf
4.06 2.82 Td
(0)Tj
/T1_3 5.98 Tf
-0.24 -5.59 Td
[(J)34(;k)]TJ
/T1_12 5.98 Tf
10.21 0 Td
(\241)Tj
/T1_13 5.98 Tf
5.75 0 Td
(1)Tj
/T1_4 10.91 Tf
4.65 -2.33 Td
(jj)Tj
/T1_14 10.91 Tf
7.28 3.13 Td
(])Tj
/T1_1 10.91 Tf
-1.22 -3.13 Td
(SID)Tj
/T1_8 7.97 Tf
17.18 3.75 Td
(0)Tj
/T1_2 7.97 Tf
0 -7.19 TD
(J)Tj
/T1_6 10.91 Tf
5.87 3.44 Td
(\),)Tj
/T1_7 10.91 Tf
12.4 0 Td
(R)Tj
/T1_8 7.97 Tf
8.36 3.95 Td
(0)Tj
/T1_2 7.97 Tf
-0.08 -7.27 Td
[(J)24(;k)]TJ
/T1_8 7.97 Tf
11.4 0 Td
(\241)Tj
/T1_9 7.97 Tf
6.59 0 Td
(1)Tj
/T1_6 10.91 Tf
9.75 3.32 Td
(=)Tj
/T1_11 10.91 Tf
-459.39 -21.92 Td
(H)Tj
/T1_6 10.91 Tf
7.73 0 Td
(\(\()Tj
/T1_7 10.91 Tf
8.48 0 Td
(z)Tj
/T1_8 7.97 Tf
5.55 3.96 Td
(0)Tj
/T1_2 7.97 Tf
-0.48 -7.28 Td
[(J)24(;k)]TJ
/T1_9 7.97 Tf
11.4 0 Td
(+1)Tj
/T1_6 10.91 Tf
11.32 3.32 Td
(\))Tj
/T1_2 7.97 Tf
4.24 5.11 Td
(r)Tj
/T1_12 5.98 Tf
4.06 2.81 Td
(0)Tj
/T1_3 5.98 Tf
-0.24 -5.58 Td
[(J)34(;k)]TJ
/T1_12 5.98 Tf
10.21 0 Td
(\241)Tj
/T1_13 5.98 Tf
5.75 0 Td
(1)Tj
/T1_4 10.91 Tf
4.65 -2.34 Td
(jj)Tj
/T1_14 10.91 Tf
7.28 3.13 Td
(])Tj
/T1_1 10.91 Tf
-1.22 -3.13 Td
(SID)Tj
/T1_8 7.97 Tf
17.18 3.76 Td
(0)Tj
/T1_2 7.97 Tf
T*
(J)Tj
/T1_6 10.91 Tf
5.87 3.43 Td
(\),)Tj
/T1_7 10.91 Tf
10.91 0 Td
(X)Tj
/T1_8 7.97 Tf
9.89 3.96 Td
(0)Tj
/T1_2 7.97 Tf
-0.86 -7.28 Td
[(J)23(;k)]TJ
/T1_8 7.97 Tf
11.41 0 Td
(\241)Tj
/T1_9 7.97 Tf
(1)Tj
/T1_6 10.91 Tf
14.35 3.32 Td
(=)Tj
/T1_7 10.91 Tf
11.52 0 Td
(L)Tj
/T1_8 7.97 Tf
7.42 3.96 Td
(0)Tj
/T1_2 7.97 Tf
0 -7.28 TD
[(J)23(;k)]TJ
/T1_8 7.97 Tf
11.41 0 Td
(\241)Tj
/T1_9 7.97 Tf
(1)Tj
/T1_4 10.91 Tf
13.74 3.32 Td
(\251)Tj
/T1_7 10.91 Tf
10.91 0 Td
(R)Tj
/T1_8 7.97 Tf
8.36 3.96 Td
(0)Tj
/T1_2 7.97 Tf
-0.08 -7.28 Td
[(J)24(;k)]TJ
/T1_8 7.97 Tf
11.4 0 Td
(\241)Tj
/T1_9 7.97 Tf
6.59 0 Td
(1)Tj
/T1_6 10.91 Tf
8.37 3.32 Td
[(and)-333(transmit)]TJ
/T1_7 10.91 Tf
65.53 0 Td
(X)Tj
/T1_8 7.97 Tf
9.9 3.96 Td
(0)Tj
/T1_2 7.97 Tf
-0.86 -7.28 Td
[(J)24(;k)]TJ
/T1_8 7.97 Tf
11.4 0 Td
(\241)Tj
/T1_9 7.97 Tf
6.59 0 Td
(1)Tj
/T1_6 10.91 Tf
8.37 3.32 Td
[(with)-333(signature,)-334(where)]TJ
/T1_14 10.91 Tf
108 3.13 Td
(])Tj
/T1_1 10.91 Tf
-1.23 -3.13 Td
(SID)Tj
/T1_8 7.97 Tf
17.18 3.76 Td
(0)Tj
/T1_2 7.97 Tf
0 -7.19 TD
(J)Tj
/T1_6 10.91 Tf
-462 -18.49 Td
[(is)-420(equal)-420(to)]TJ
/T1_1 10.91 Tf
55.92 0 Td
(SID)Tj
/T1_8 7.97 Tf
17.18 3.96 Td
(0)Tj
/T1_2 7.97 Tf
T*
(J)Tj
/T1_6 10.91 Tf
10.46 3.23 Td
[(excluding)-420(the)-420(iden)27(tities)-420(of)-420(the)-420(discarded)-421(users)-420(in)]TJ
/T1_1 10.91 Tf
242.07 0 Td
(BL)Tj
/T1_5 7.97 Tf
11.45 -1.63 Td
(X)Tj
/T1_6 10.91 Tf
4.73 1.63 Td
[(.)-705(The)-421(honest)-420(righ)27(t)-420(neigh-)]TJ
-341.81 -21.91 Td
[(b)-27(or)]TJ
/T1_1 10.91 Tf
20.4 0 Td
(U)Tj
/T1_2 7.97 Tf
5.72 -1.78 Td
[(J)23(;k)]TJ
/T1_9 7.97 Tf
11.41 0 Td
(+1)Tj
/T1_6 10.91 Tf
11.31 1.78 Td
[(,)-410(whic)27(h)-395(has)-395(not)-395(b)-28(een)-395(blo)-28(c)27(k)28(ed,)-410(of)]TJ
/T1_10 10.91 Tf
162.18 1.97 Td
(e)Tj
/T1_1 10.91 Tf
0.17 -1.97 Td
(U)Tj
/T1_2 7.97 Tf
5.72 -1.78 Td
[(J)23(;k)]TJ
/T1_6 10.91 Tf
16.22 1.78 Td
[(will)-394(re-compute)]TJ
/T1_7 10.91 Tf
78.93 0 Td
(L)Tj
/T1_8 7.97 Tf
7.42 3.95 Td
(0)Tj
/T1_2 7.97 Tf
0 -7.27 TD
[(J)23(;k)]TJ
/T1_9 7.97 Tf
11.41 0 Td
(+1)Tj
/T1_6 10.91 Tf
15.46 3.32 Td
(=)Tj
/T1_11 10.91 Tf
12.64 0 Td
(H)Tj
/T1_6 10.91 Tf
7.73 0 Td
(\(\()Tj
/T1_7 10.91 Tf
8.48 0 Td
(z)Tj
/T1_8 7.97 Tf
5.55 3.95 Td
(0)Tj
/T1_2 7.97 Tf
-0.48 -7.27 Td
[(J)24(;k)]TJ
/T1_8 7.97 Tf
11.4 0 Td
(\241)Tj
/T1_9 7.97 Tf
6.59 0 Td
(1)Tj
/T1_6 10.91 Tf
4.73 3.32 Td
(\))Tj
/T1_2 7.97 Tf
4.24 5.1 Td
(r)Tj
/T1_12 5.98 Tf
4.06 2.82 Td
(0)Tj
/T1_3 5.98 Tf
-0.24 -5.59 Td
[(J)34(;k)]TJ
/T1_13 5.98 Tf
10.21 0 Td
(+1)Tj
/T1_4 10.91 Tf
10.23 -2.33 Td
(jj)Tj
/T1_14 10.91 Tf
7.29 3.13 Td
(])Tj
/T1_1 10.91 Tf
-1.23 -3.13 Td
(SID)Tj
/T1_8 7.97 Tf
17.18 3.75 Td
(0)Tj
/T1_2 7.97 Tf
0 -7.19 TD
(J)Tj
/T1_6 10.91 Tf
5.87 3.44 Td
(\),)Tj
/T1_7 10.91 Tf
-460.6 -21.92 Td
(R)Tj
/T1_8 7.97 Tf
8.37 3.96 Td
(0)Tj
/T1_2 7.97 Tf
-0.09 -7.28 Td
[(J)24(;k)]TJ
/T1_9 7.97 Tf
11.41 0 Td
(+1)Tj
/T1_6 10.91 Tf
14.34 3.32 Td
(=)Tj
/T1_11 10.91 Tf
11.51 0 Td
(H)Tj
/T1_6 10.91 Tf
7.73 0 Td
(\(\()Tj
/T1_7 10.91 Tf
8.48 0 Td
(z)Tj
/T1_8 7.97 Tf
5.55 3.96 Td
(0)Tj
/T1_2 7.97 Tf
-0.48 -7.28 Td
[(J)23(;k)]TJ
/T1_9 7.97 Tf
11.41 0 Td
(+2)Tj
/T1_6 10.91 Tf
11.31 3.32 Td
(\))Tj
/T1_2 7.97 Tf
4.24 5.11 Td
(r)Tj
/T1_12 5.98 Tf
4.06 2.81 Td
(0)Tj
/T1_3 5.98 Tf
-0.24 -5.58 Td
[(J)34(;k)]TJ
/T1_13 5.98 Tf
10.21 0 Td
(+1)Tj
/T1_4 10.91 Tf
10.24 -2.34 Td
(jj)Tj
/T1_14 10.91 Tf
7.28 3.13 Td
(])Tj
/T1_1 10.91 Tf
-1.23 -3.13 Td
(SID)Tj
/T1_8 7.97 Tf
17.18 3.76 Td
(0)Tj
/T1_2 7.97 Tf
T*
(J)Tj
/T1_6 10.91 Tf
5.87 3.43 Td
(\),)Tj
/T1_7 10.91 Tf
10.9 0 Td
(X)Tj
/T1_8 7.97 Tf
9.89 3.96 Td
(0)Tj
/T1_2 7.97 Tf
-0.86 -7.28 Td
[(J)23(;k)]TJ
/T1_9 7.97 Tf
11.41 0 Td
(+1)Tj
/T1_6 10.91 Tf
14.34 3.32 Td
(=)Tj
/T1_7 10.91 Tf
11.52 0 Td
(L)Tj
/T1_8 7.97 Tf
7.42 3.96 Td
(0)Tj
/T1_2 7.97 Tf
0 -7.28 TD
[(J)24(;k)]TJ
/T1_9 7.97 Tf
11.4 0 Td
(+1)Tj
/T1_4 10.91 Tf
13.72 3.32 Td
(\251)Tj
/T1_7 10.91 Tf
10.88 0 Td
(R)Tj
/T1_8 7.97 Tf
8.36 3.96 Td
(0)Tj
/T1_2 7.97 Tf
-0.08 -7.28 Td
[(J)24(;k)]TJ
/T1_9 7.97 Tf
11.4 0 Td
(+1)Tj
/T1_6 10.91 Tf
14.94 3.32 Td
[(and)-332(transmit)]TJ
/T1_7 10.91 Tf
65.51 0 Td
(X)Tj
/T1_8 7.97 Tf
9.89 3.96 Td
(0)Tj
/T1_2 7.97 Tf
-0.86 -7.28 Td
[(J)24(;k)]TJ
/T1_9 7.97 Tf
11.4 0 Td
(+1)Tj
/T1_6 10.91 Tf
14.94 3.32 Td
[(with)-332(signature.)-444(It)]TJ
-383.27 -21.92 Td
[(should)-272(b)-28(e)-273(noted)-273(that)-273(if)-273(left)-272(neigh)26(b)-26(or)]TJ
/T1_1 10.91 Tf
172.7 0 Td
(U)Tj
/T1_2 7.97 Tf
5.72 -1.77 Td
[(J)23(;k)]TJ
/T1_8 7.97 Tf
11.41 0 Td
(\241)Tj
/T1_9 7.97 Tf
(1)Tj
/T1_6 10.91 Tf
14.29 1.77 Td
(of)Tj
/T1_10 10.91 Tf
11.59 1.97 Td
(e)Tj
/T1_1 10.91 Tf
0.17 -1.97 Td
(U)Tj
/T1_2 7.97 Tf
5.73 -1.77 Td
[(J)24(;k)]TJ
/T1_6 10.91 Tf
14.87 1.77 Td
[(is)-273(also)-273(an)-273(in)27(v)56(alid)-272(user)-273(or)-273(malicious)-273(group)-273(mem)27(b)-27(er)]TJ
-236.48 -21.91 Td
[(that)-300(has)-301(b)-28(een)-300(blo)-28(c)27(k)28(ed,)-307(then)-300(w)27(e)-300(set)]TJ
/T1_1 10.91 Tf
166.74 0 Td
(U)Tj
/T1_2 7.97 Tf
5.73 -1.78 Td
[(J)24(;k)]TJ
/T1_8 7.97 Tf
11.4 0 Td
(\241)Tj
/T1_9 7.97 Tf
6.59 0 Td
(2)Tj
/T1_6 10.91 Tf
7.76 1.78 Td
(=)Tj
/T1_1 10.91 Tf
11.51 0 Td
(U)Tj
/T1_2 7.97 Tf
5.72 -1.78 Td
[(J)23(;k)]TJ
/T1_8 7.97 Tf
11.41 0 Td
(\241)Tj
/T1_9 7.97 Tf
(1)Tj
/T1_6 10.91 Tf
11.31 1.78 Td
[(.)-433(Similarly)82(,)-306(if)-301(righ)27(t)-300(neigh)27(b)-27(or)]TJ
/T1_1 10.91 Tf
136.16 0 Td
(U)Tj
/T1_2 7.97 Tf
5.72 -1.78 Td
[(J)23(;k)]TJ
/T1_9 7.97 Tf
11.41 0 Td
(+1)Tj
/T1_6 10.91 Tf
14.59 1.78 Td
(of)Tj
/T1_10 10.91 Tf
11.9 1.97 Td
(e)Tj
/T1_1 10.91 Tf
0.17 -1.97 Td
(U)Tj
/T1_2 7.97 Tf
5.72 -1.78 Td
[(J)23(;k)]TJ
/T1_6 10.91 Tf
15.18 1.78 Td
[(is)-300(also)]TJ
-439.02 -21.92 Td
[(an)-318(in)27(v)55(alid)-317(user)-318(or)-319(malicious)-318(group)-319(mem)27(b)-27(er)-318(that)-318(has)-319(b)-28(een)-318(blo)-28(c)27(k)28(ed,)-321(then)-318(w)27(e)-318(set)]TJ
/T1_1 10.91 Tf
374.38 0 Td
(U)Tj
/T1_2 7.97 Tf
5.72 -1.78 Td
[(J)23(;k)]TJ
/T1_9 7.97 Tf
11.41 0 Td
(+2)Tj
/T1_6 10.91 Tf
14.34 1.78 Td
(=)Tj
/T1_1 10.91 Tf
11.51 0 Td
(U)Tj
/T1_2 7.97 Tf
5.73 -1.78 Td
[(J)24(;k)]TJ
/T1_9 7.97 Tf
11.4 0 Td
(+1)Tj
/T1_6 10.91 Tf
11.32 1.78 Td
[(.)-439(All)]TJ
-445.81 -21.92 Td
[(other)-341(users)]TJ
/T1_1 10.91 Tf
56.11 0 Td
(U)Tj
/T1_2 7.97 Tf
5.73 -1.77 Td
[(J)24(;k)]TJ
/T1_6 10.91 Tf
15.63 1.77 Td
[(will)-341(use)-342(the)-342(new)-342(session)-342(iden)27(tit)28(y)]TJ
/T1_14 10.91 Tf
158.65 3.14 Td
(])Tj
/T1_1 10.91 Tf
-1.22 -3.14 Td
(SID)Tj
/T1_8 7.97 Tf
17.17 3.76 Td
(0)Tj
/T1_2 7.97 Tf
0 -7.19 TD
(J)Tj
/T1_6 10.91 Tf
9.6 3.43 Td
[(to)-342(re-compute)]TJ
/T1_7 10.91 Tf
70.5 0 Td
(L)Tj
/T1_8 7.97 Tf
7.43 3.96 Td
(0)Tj
/T1_2 7.97 Tf
0 -7.28 TD
[(J)24(;k)]TJ
/T1_6 10.91 Tf
11.9 3.32 Td
(,)Tj
/T1_7 10.91 Tf
6.78 0 Td
(R)Tj
/T1_8 7.97 Tf
8.37 3.96 Td
(0)Tj
/T1_2 7.97 Tf
-0.09 -7.28 Td
[(J)24(;k)]TJ
/T1_6 10.91 Tf
11.9 3.32 Td
(,)Tj
/T1_7 10.91 Tf
6.78 0 Td
(X)Tj
/T1_8 7.97 Tf
9.9 3.96 Td
(0)Tj
/T1_2 7.97 Tf
-0.86 -7.28 Td
[(J)24(;k)]TJ
/T1_6 10.91 Tf
15.63 3.32 Td
[(as)-342(in)-341(Round)]TJ
-409.91 -21.91 Td
[(4)-423(and)-423(transmit)]TJ
/T1_7 10.91 Tf
77.55 0 Td
(X)Tj
/T1_8 7.97 Tf
9.89 3.96 Td
(0)Tj
/T1_2 7.97 Tf
-0.85 -7.28 Td
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/T1_1 10.91 Tf
6.06 0 Td
(c)Tj
/T1_4 7.97 Tf
5.72 3.96 Td
(0)Tj
/T1_2 7.97 Tf
0 -7.01 TD
(i)Tj
/T1_7 10.91 Tf
3.38 3.05 Td
(jj)Tj
/T1_3 10.91 Tf
6.06 0 Td
(\265)Tj
/T1_4 7.97 Tf
5.43 3.96 Td
(0)Tj
/T1_8 7.97 Tf
-0.31 -6.65 Td
(C)Tj
/T1_7 10.91 Tf
4.73 2.69 Td
(jj)Tj
/T1_3 10.91 Tf
6.06 0 Td
(\276)Tj
/T1_4 7.97 Tf
6.63 3.96 Td
(0)Tj
/T1_8 7.97 Tf
-0.4 -6.65 Td
(C)Tj
/T1_7 10.91 Tf
4.74 2.69 Td
(g)Tj
/T1_0 10.91 Tf
10.68 0 Td
(for)Tj
-454.81 -21.91 Td
(1)Tj
/T1_7 10.91 Tf
8.48 0 Td
(\267)Tj
/T1_3 10.91 Tf
11.51 0 Td
(i)Tj
/T1_7 10.91 Tf
6.79 0 Td
(6)Tj
/T1_0 10.91 Tf
(=)Tj
/T1_3 10.91 Tf
11.51 0 Td
(J)Tj
/T1_7 10.91 Tf
10.13 0 Td
(\267)Tj
/T1_3 10.91 Tf
11.51 0 Td
(n)Tj
/T1_2 7.97 Tf
6.55 -1.64 Td
(c)Tj
/T1_0 10.91 Tf
4.16 1.64 Td
[(,)-333(where)]TJ
/T1_3 10.91 Tf
38.2 0 Td
(\276)Tj
/T1_4 7.97 Tf
6.63 3.95 Td
(0)Tj
/T1_8 7.97 Tf
-0.39 -6.65 Td
(C)Tj
/T1_0 10.91 Tf
7.76 2.7 Td
(=)Tj
/T1_7 10.91 Tf
11.51 0 Td
(S)Tj
/T1_0 10.91 Tf
7.42 0 Td
(\()Tj
/T1_1 10.91 Tf
(C)Tj
/T1_7 10.91 Tf
(jj)Tj
/T1_3 10.91 Tf
16.03 0 Td
(y)Tj
/T1_4 7.97 Tf
5.73 3.95 Td
(0)Tj
/T1_8 7.97 Tf
-0.39 -6.65 Td
(C)Tj
/T1_7 10.91 Tf
4.73 2.7 Td
(jj)Tj
/T1_3 10.91 Tf
6.06 0 Td
(\265)Tj
/T1_4 7.97 Tf
5.43 3.95 Td
(0)Tj
/T1_8 7.97 Tf
-0.31 -6.65 Td
(C)Tj
/T1_0 10.91 Tf
4.73 2.7 Td
(\).)Tj
/T1_12 10.91 Tf
-183.78 -27.9 Td
[(Phase)-383(3:)-511(Distributing)-383(the)-384(Final)-383(Group)-383(Key)]TJ
/T1_0 10.91 Tf
0 -27.89 TD
[(Round)-333(1)]TJ
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 0 -265.52 cm
0 0 m
40.75 0 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 116.3924 505.7561 Tm
(:)Tj
-44.38 -21.92 Td
(\()Tj
/T1_3 10.91 Tf
(i)Tj
/T1_0 10.91 Tf
(\))Tj
/T1_1 10.91 Tf
16.7 0 Td
(S)Tj
/T1_2 7.97 Tf
5.73 -1.68 Td
(J)Tj
/T1_0 10.91 Tf
10.33 1.68 Td
(\257rst)Tj
1.0003 0 0 1.0003 72 769.82 Tm
56.107 -285.91 Td
[(v)27(eri\257es)-409(signature)]TJ
/T1_3 10.91 Tf
85.443 0 Td
(\276)Tj
/T1_4 7.97 Tf
6.62 3.96 Td
(0)Tj
/T1_8 7.97 Tf
-0.39 -6.65 Td
(C)Tj
/T1_0 10.91 Tf
4.73 2.69 Td
[(.)-672(If)-409(the)-410(v)27(eri\257cation)-408(is)-409(not)-410(correct,)-428(then)]TJ
/T1_1 10.91 Tf
197.08 0 Td
(S)Tj
/T1_2 7.97 Tf
5.72 -1.68 Td
(J)Tj
/T1_0 10.91 Tf
10.34 1.68 Td
(rejects)Tj
/T1_1 10.91 Tf
35.15 0 Td
(C)Tj
/T1_0 10.91 Tf
5.72 0 Td
[(.)-672(Otherwise,)]TJ
/T1_1 10.91 Tf
-406.52 -21.91 Td
(S)Tj
/T1_2 7.97 Tf
5.73 -1.69 Td
(J)Tj
/T1_0 10.91 Tf
9.72 1.69 Td
[(computes)-353(new)-354(DH)-354(k)27(ey)]TJ
/T1_3 10.91 Tf
111.68 0 Td
(T)Tj
/T1_4 7.97 Tf
7.89 3.96 Td
(0)Tj
/T1_2 7.97 Tf
-1.52 -7.19 Td
(J)Tj
/T1_0 10.91 Tf
9.27 3.23 Td
[(=)-311(\()]TJ
/T1_3 10.91 Tf
(y)Tj
/T1_4 7.97 Tf
21.86 3.96 Td
(0)Tj
/T1_8 7.97 Tf
-0.39 -6.66 Td
(C)Tj
/T1_0 10.91 Tf
4.73 2.7 Td
(\))Tj
/T1_2 7.97 Tf
4.24 3.96 Td
(K)Tj
/T1_5 5.98 Tf
7.7 2.81 Td
(0)Tj
/T1_6 5.98 Tf
-0.56 -5.52 Td
(J)Tj
/T1_0 10.91 Tf
8.66 -1.25 Td
[(mo)-28(d)]TJ
/T1_3 10.91 Tf
23.94 0 Td
(p)Tj
/T1_0 10.91 Tf
9.34 0 Td
[(shared)-353(with)]TJ
/T1_1 10.91 Tf
59.91 0 Td
(C)Tj
/T1_0 10.91 Tf
[(.)-505(Next,)]TJ
/T1_1 10.91 Tf
44.24 0 Td
(S)Tj
/T1_2 7.97 Tf
5.72 -1.69 Td
(J)Tj
/T1_0 10.91 Tf
9.73 1.69 Td
(uses)Tj
/T1_3 10.91 Tf
23.37 0 Td
(T)Tj
/T1_4 7.97 Tf
7.88 3.96 Td
(0)Tj
/T1_2 7.97 Tf
-1.51 -7.19 Td
(J)Tj
/T1_0 10.91 Tf
9.73 3.23 Td
[(to)-353(decrypt)]TJ
/T1_1 10.91 Tf
53.49 0 Td
(c)Tj
/T1_4 7.97 Tf
5.72 3.96 Td
(0)Tj
/T1_2 7.97 Tf
0 -7.19 TD
(J)Tj
/T1_0 10.91 Tf
9.73 3.23 Td
(and)Tj
-450.3 -21.92 Td
[(obtains)-433(the)-433(new)-434(\257nal)-433(group)-434(k)27(ey)]TJ
/T1_3 10.91 Tf
160.84 0 Td
(K)Tj
/T1_4 7.97 Tf
10.04 3.96 Td
(0)Tj
/T1_0 10.91 Tf
2.8 -3.96 Td
(.)Tj
/T1_1 10.91 Tf
11.15 0 Td
(S)Tj
/T1_2 7.97 Tf
5.73 -1.69 Td
(J)Tj
/T1_0 10.91 Tf
10.59 1.69 Td
[(then)-433(con\257rms)-434(and)-433(accepts)-434(the)-433(new)-433(\257nal)-434(group)-433(k)26(ey)]TJ
/T1_3 10.91 Tf
253.88 0 Td
(K)Tj
/T1_4 7.97 Tf
10.05 3.96 Td
(0)Tj
/T1_0 10.91 Tf
-465.08 -25.87 Td
(if)Tj
/T1_11 10.91 Tf
11.03 0 Td
(H)Tj
/T1_0 10.91 Tf
(\()Tj
/T1_3 10.91 Tf
(K)Tj
/T1_4 7.97 Tf
22.01 3.95 Td
(0)Tj
/T1_7 10.91 Tf
2.79 -3.95 Td
(jj)Tj
/T1_3 10.91 Tf
6.06 0 Td
(y)Tj
/T1_4 7.97 Tf
5.74 3.95 Td
(0)Tj
/T1_8 7.97 Tf
-0.39 -6.65 Td
(C)Tj
/T1_0 10.91 Tf
4.73 2.7 Td
[(\))-435(=)]TJ
/T1_3 10.91 Tf
22.22 0 Td
(\265)Tj
/T1_4 7.97 Tf
5.42 3.95 Td
(0)Tj
/T1_8 7.97 Tf
-0.3 -6.65 Td
(C)Tj
/T1_0 10.91 Tf
4.73 2.7 Td
[(.)-727(Next,)]TJ
/T1_1 10.91 Tf
41.95 0 Td
(S)Tj
/T1_2 7.97 Tf
5.72 -1.69 Td
(J)Tj
/T1_0 10.91 Tf
10.54 1.69 Td
(encrypts)Tj
/T1_3 10.91 Tf
45.05 0 Td
(K)Tj
/T1_4 7.97 Tf
10.04 3.95 Td
(0)Tj
/T1_7 10.91 Tf
2.8 -3.95 Td
(jj)Tj
/T1_1 10.91 Tf
6.05 0 Td
(S)Tj
/T1_2 7.97 Tf
5.73 -1.69 Td
(J)Tj
/T1_0 10.91 Tf
10.54 1.69 Td
[(using)-427(new)-428(subgroup)-428(k)27(ey)]TJ
/T1_3 10.91 Tf
122.12 0 Td
(K)Tj
/T1_4 7.97 Tf
10.04 3.95 Td
(0)Tj
/T1_2 7.97 Tf
-0.78 -7.19 Td
(J)Tj
/T1_0 10.91 Tf
10.54 3.24 Td
(and)Tj
/T1_3 10.91 Tf
22.24 0 Td
(K)Tj
/T1_4 7.97 Tf
10.04 3.95 Td
(0)Tj
/T1_2 7.97 Tf
-0.78 -7.19 Td
(J)Tj
/T1_7 10.91 Tf
5.87 3.24 Td
(jj)Tj
/T1_3 10.91 Tf
6.06 0 Td
(K)Tj
/T1_4 7.97 Tf
10.04 3.95 Td
(0)Tj
/T1_7 10.91 Tf
2.8 -3.95 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(S)Tj
/T1_2 7.97 Tf
5.72 -1.69 Td
(J)Tj
/T1_0 10.91 Tf
10.54 1.69 Td
(using)Tj
-442.97 -21.92 Td
[(previous)-358(subgroup)-359(k)27(ey)]TJ
/T1_3 10.91 Tf
111.28 0 Td
(K)Tj
/T1_2 7.97 Tf
9.26 -1.69 Td
(J)Tj
/T1_0 10.91 Tf
9.78 1.69 Td
[(and)-358(obtains)-371(\271)]TJ
/T1_1 10.91 Tf
59.99 0 Td
(c)Tj
/T1_4 7.97 Tf
5.72 3.96 Td
(0)Tj
/T1_2 7.97 Tf
T*
(J)Tj
/T1_0 10.91 Tf
9.36 3.23 Td
(=)Tj
/T1_7 10.91 Tf
11.97 0 Td
(E)Tj
/T1_2 7.97 Tf
5.76 -2.31 Td
(K)Tj
/T1_5 5.98 Tf
7.7 2.75 Td
(0)Tj
/T1_6 5.98 Tf
-0.56 -5.52 Td
(J)Tj
/T1_0 10.91 Tf
5.63 5.08 Td
(\()Tj
/T1_3 10.91 Tf
(K)Tj
/T1_4 7.97 Tf
14.29 3.96 Td
(0)Tj
/T1_7 10.91 Tf
2.79 -3.96 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(S)Tj
/T1_2 7.97 Tf
5.72 -1.69 Td
(J)Tj
/T1_0 10.91 Tf
5.88 1.69 Td
[(\))-358(and)-371(\271)]TJ
/T1_1 10.91 Tf
29.63 0 Td
(c)Tj
/T1_4 7.97 Tf
5.72 3.96 Td
(00)Tj
/T1_2 7.97 Tf
T*
(J)Tj
/T1_0 10.91 Tf
9.36 3.23 Td
(=)Tj
/T1_7 10.91 Tf
11.97 0 Td
(E)Tj
/T1_2 7.97 Tf
5.76 -1.69 Td
(K)Tj
/T1_6 5.98 Tf
7.14 -1.34 Td
(J)Tj
/T1_0 10.91 Tf
5.63 3.03 Td
(\()Tj
/T1_3 10.91 Tf
(K)Tj
/T1_4 7.97 Tf
14.28 3.96 Td
(0)Tj
/T1_2 7.97 Tf
-0.78 -7.19 Td
(J)Tj
/T1_7 10.91 Tf
5.87 3.23 Td
(jj)Tj
/T1_3 10.91 Tf
6.06 0 Td
(K)Tj
/T1_4 7.97 Tf
10.05 3.96 Td
(0)Tj
/T1_7 10.91 Tf
2.79 -3.96 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(S)Tj
/T1_2 7.97 Tf
5.72 -1.69 Td
(J)Tj
/T1_0 10.91 Tf
5.88 1.69 Td
[(\))-358(resp)-27(ectiv)26(ely)84(.)]TJ
-401.77 -21.92 Td
[(Finally)83(,)]TJ
/T1_1 10.91 Tf
38.5 0 Td
(S)Tj
/T1_2 7.97 Tf
5.73 -1.69 Td
(J)Tj
/T1_0 10.91 Tf
8.59 1.69 Td
[(computes)-250(k)27(ey)-249(con\257rmation)-249(co)-28(de)]TJ
/T1_3 10.91 Tf
153.38 0 Td
(\265)Tj
/T1_4 7.97 Tf
5.42 3.96 Td
(0)Tj
/T1_2 7.97 Tf
-0.3 -7.19 Td
(J)Tj
/T1_0 10.91 Tf
8.9 3.23 Td
(=)Tj
/T1_11 10.91 Tf
11.51 0 Td
(H)Tj
/T1_0 10.91 Tf
(\()Tj
/T1_3 10.91 Tf
(K)Tj
/T1_4 7.97 Tf
22.01 3.96 Td
(0)Tj
/T1_2 7.97 Tf
-0.78 -7.19 Td
(J)Tj
/T1_7 10.91 Tf
5.87 3.23 Td
(jj)Tj
/T1_3 10.91 Tf
6.06 0 Td
(K)Tj
/T1_4 7.97 Tf
10.04 3.96 Td
(0)Tj
/T1_7 10.91 Tf
2.79 -3.96 Td
(jj)Tj
/T1_3 10.91 Tf
6.06 0 Td
(\277)Tj
/T1_4 7.97 Tf
6 3.96 Td
(0)Tj
/T1_2 7.97 Tf
-1.23 -7.19 Td
(J)Tj
/T1_0 10.91 Tf
5.87 3.23 Td
[(\))-249(and)-250(broadcasts)]TJ
/T1_7 10.91 Tf
80.43 0 Td
(f)Tj
/T1_1 10.91 Tf
(S)Tj
/T1_2 7.97 Tf
11.17 -1.69 Td
(J)Tj
/T1_7 10.91 Tf
5.88 1.69 Td
(jj)Tj
/T1_0 10.91 Tf
6.19 0 Td
(\271)Tj
/T1_1 10.91 Tf
-0.14 0 Td
(c)Tj
/T1_4 7.97 Tf
5.73 3.96 Td
(0)Tj
/T1_2 7.97 Tf
T*
(J)Tj
/T1_7 10.91 Tf
5.87 3.23 Td
(jj)Tj
/T1_0 10.91 Tf
6.2 0 Td
(\271)Tj
/T1_1 10.91 Tf
-0.14 0 Td
(c)Tj
/T1_4 7.97 Tf
5.73 3.96 Td
(00)Tj
/T1_2 7.97 Tf
T*
(J)Tj
/T1_7 10.91 Tf
5.87 3.23 Td
(jj)Tj
/T1_3 10.91 Tf
6.06 0 Td
(\265)Tj
/T1_4 7.97 Tf
5.42 3.96 Td
(0)Tj
/T1_2 7.97 Tf
-0.3 -7.19 Td
(J)Tj
/T1_7 10.91 Tf
5.87 3.23 Td
(jj)Tj
/T1_0 10.91 Tf
6.64 0 Td
(\271)Tj
/T1_3 10.91 Tf
-0.58 0 Td
(\276)Tj
/T1_4 7.97 Tf
6.62 3.96 Td
(0)Tj
/T1_2 7.97 Tf
-0.39 -7.19 Td
(J)Tj
/T1_7 10.91 Tf
5.87 3.23 Td
(g)Tj
/T1_0 10.91 Tf
-462.42 -21.91 Td
[(where)-386(\271)]TJ
/T1_3 10.91 Tf
31.54 0 Td
(\276)Tj
/T1_4 7.97 Tf
6.62 3.95 Td
(0)Tj
/T1_2 7.97 Tf
-0.39 -7.19 Td
(J)Tj
/T1_0 10.91 Tf
8.9 3.24 Td
(=)Tj
/T1_7 10.91 Tf
11.51 0 Td
(S)Tj
/T1_0 10.91 Tf
7.42 0 Td
(\()Tj
/T1_1 10.91 Tf
(S)Tj
/T1_2 7.97 Tf
9.97 -1.69 Td
(J)Tj
/T1_7 10.91 Tf
5.87 1.69 Td
(jj)Tj
/T1_3 10.91 Tf
6.06 0 Td
(\277)Tj
/T1_4 7.97 Tf
6 3.95 Td
(0)Tj
/T1_2 7.97 Tf
-1.23 -7.19 Td
(J)Tj
/T1_7 10.91 Tf
5.87 3.24 Td
(jj)Tj
/T1_3 10.91 Tf
6.06 0 Td
(\265)Tj
/T1_4 7.97 Tf
5.42 3.95 Td
(0)Tj
/T1_2 7.97 Tf
-0.3 -7.19 Td
(J)Tj
/T1_7 10.91 Tf
5.87 3.24 Td
(jj)Tj
/T1_3 10.91 Tf
6.06 0 Td
(v)Tj
/T1_0 10.91 Tf
5.67 0 Td
[(\))-333(to)-334(subgroup)-333(mem)27(b)-27(ers)-333(in)]TJ
/T1_7 10.91 Tf
127.42 0 Td
(G)Tj
/T1_4 7.97 Tf
7.14 3.95 Td
(0)Tj
/T1_2 7.97 Tf
-0.65 -7.19 Td
(J)Tj
/T1_0 10.91 Tf
5.87 3.24 Td
(.)Tj
-266.7 -21.92 Td
(\()Tj
/T1_3 10.91 Tf
(ii)Tj
/T1_0 10.91 Tf
[(\))-403(All)-404(other)]TJ
/T1_1 10.91 Tf
68.32 0 Td
(S)Tj
/T1_2 7.97 Tf
5.73 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
7.78 1.64 Td
[(for)-404(1)]TJ
/T1_7 10.91 Tf
27.23 0 Td
(\267)Tj
/T1_3 10.91 Tf
12.79 0 Td
(i)Tj
/T1_7 10.91 Tf
8.07 0 Td
(6)Tj
/T1_0 10.91 Tf
(=)Tj
/T1_3 10.91 Tf
12.8 0 Td
(J)Tj
/T1_7 10.91 Tf
11.4 0 Td
(\267)Tj
/T1_3 10.91 Tf
12.8 0 Td
(n)Tj
/T1_2 7.97 Tf
6.54 -1.64 Td
(c)Tj
/T1_0 10.91 Tf
8.57 1.64 Td
[(\257rst)-404(v)27(eri\257es)-403(signature)]TJ
/T1_3 10.91 Tf
108.62 0 Td
(\276)Tj
/T1_4 7.97 Tf
6.62 3.96 Td
(0)Tj
/T1_8 7.97 Tf
-0.39 -6.66 Td
(C)Tj
/T1_0 10.91 Tf
4.73 2.7 Td
[(.)-655(If)-404(the)-404(v)27(eri\257cation)-403(is)-404(not)-404(correct,)]TJ
/T1_1 10.91 Tf
-301.61 -21.92 Td
(S)Tj
/T1_2 7.97 Tf
5.73 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
7.86 1.63 Td
(rejects)Tj
/T1_1 10.91 Tf
35.18 0 Td
(C)Tj
/T1_0 10.91 Tf
[(.)-678(Otherwise,)]TJ
/T1_1 10.91 Tf
71.85 0 Td
(S)Tj
/T1_2 7.97 Tf
5.73 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
7.87 1.63 Td
[(computes)-411(new)-411(DH)-412(k)27(ey)]TJ
/T1_3 10.91 Tf
114.2 0 Td
(T)Tj
/T1_4 7.97 Tf
7.89 3.96 Td
(0)Tj
/T1_2 7.97 Tf
-1.52 -7.01 Td
(i)Tj
/T1_0 10.91 Tf
8.76 3.05 Td
[(=)-408(\()]TJ
/T1_3 10.91 Tf
(y)Tj
/T1_4 7.97 Tf
22.92 3.96 Td
(0)Tj
/T1_8 7.97 Tf
-0.4 -6.65 Td
(C)Tj
/T1_0 10.91 Tf
4.74 2.69 Td
(\))Tj
/T1_2 7.97 Tf
4.24 3.96 Td
(K)Tj
/T1_6 5.98 Tf
7.14 -1.21 Td
(i)Tj
/T1_0 10.91 Tf
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13.82 1.68 Td
[(uses)-243(previous)-243(subgroup)-243(k)27(ey)]TJ
/T1_5 10.91 Tf
129.67 0 Td
(K)Tj
/T1_2 7.97 Tf
9.26 -1.68 Td
(J)Tj
/T1_0 10.91 Tf
8.53 1.68 Td
[(to)-243(decrypt)-255(\271)]TJ
/T1_1 10.91 Tf
51.08 0 Td
(c)Tj
/T1_4 7.97 Tf
5.72 3.96 Td
(00)Tj
/T1_2 7.97 Tf
T*
(J)Tj
/T1_0 10.91 Tf
8.53 3.23 Td
[(and)-243(obtains)-243(the)-243(iden)26(tit)28(y)]TJ
/T1_1 10.91 Tf
114.58 0 Td
(S)Tj
/T1_2 7.97 Tf
5.73 -1.68 Td
(J)Tj
/T1_0 10.91 Tf
5.87 1.68 Td
(,)Tj
-464.84 -21.91 Td
[(new)-336(subgroup)-336(k)27(ey)]TJ
/T1_5 10.91 Tf
89.55 0 Td
(K)Tj
/T1_4 7.97 Tf
10.04 3.96 Td
(0)Tj
/T1_2 7.97 Tf
-0.78 -7.19 Td
(J)Tj
/T1_0 10.91 Tf
9.54 3.23 Td
[(and)-336(new)-336(\257nal)-336(group)-336(k)27(ey)]TJ
/T1_5 10.91 Tf
118.63 0 Td
(K)Tj
/T1_4 7.97 Tf
10.05 3.96 Td
(0)Tj
/T1_0 10.91 Tf
2.79 -3.96 Td
[(.)-452(If)-336(the)-336(iden)26(tit)28(y)]TJ
/T1_1 10.91 Tf
78.04 0 Td
(S)Tj
/T1_2 7.97 Tf
5.72 -1.69 Td
(J)Tj
/T1_0 10.91 Tf
9.54 1.69 Td
[(w)27(as)-335(not)-336(decrypted)-336(correctly)82(,)]TJ
-333.12 -21.92 Td
(then)Tj
/T1_1 10.91 Tf
25.25 0 Td
(U)Tj
/T1_2 7.97 Tf
5.73 -1.69 Td
[(J)24(;j)]TJ
/T1_0 10.91 Tf
15.21 1.69 Td
[(rejects)-383(\271)]TJ
/T1_1 10.91 Tf
34.73 0 Td
(c)Tj
/T1_4 7.97 Tf
5.73 3.96 Td
(00)Tj
/T1_2 7.97 Tf
T*
(J)Tj
/T1_0 10.91 Tf
5.87 3.23 Td
[(.)-556(Otherwise,)]TJ
/T1_1 10.91 Tf
64.24 0 Td
(U)Tj
/T1_2 7.97 Tf
5.72 -1.69 Td
[(J)23(;j)]TJ
/T1_0 10.91 Tf
15.21 1.69 Td
[(c)27(hec)28(ks)-370(if)]TJ
/T1_5 10.91 Tf
44.51 0 Td
(\265)Tj
/T1_4 7.97 Tf
5.42 3.96 Td
(0)Tj
/T1_2 7.97 Tf
-0.3 -7.19 Td
(J)Tj
/T1_0 10.91 Tf
9.58 3.23 Td
(=)Tj
/T1_6 10.91 Tf
12.2 0 Td
(H)Tj
/T1_0 10.91 Tf
(\()Tj
/T1_5 10.91 Tf
(K)Tj
/T1_4 7.97 Tf
22 3.96 Td
(0)Tj
/T1_2 7.97 Tf
-0.78 -7.19 Td
(J)Tj
/T1_7 10.91 Tf
5.88 3.23 Td
(jj)Tj
/T1_5 10.91 Tf
6.05 0 Td
(K)Tj
/T1_4 7.97 Tf
10.05 3.96 Td
(0)Tj
/T1_7 10.91 Tf
2.79 -3.96 Td
(jj)Tj
/T1_5 10.91 Tf
6.06 0 Td
(\277)Tj
/T1_4 7.97 Tf
6 3.96 Td
(0)Tj
/T1_2 7.97 Tf
-1.23 -7.19 Td
(J)Tj
/T1_0 10.91 Tf
5.87 3.23 Td
[(\).)-557(If)-370(they)-371(are)-371(equal,)]TJ
/T1_1 10.91 Tf
100.55 0 Td
(U)Tj
/T1_2 7.97 Tf
5.72 -1.69 Td
[(J)23(;j)]TJ
/T1_0 10.91 Tf
15.21 1.69 Td
(accepts)Tj
-433.27 -21.91 Td
[(the)-333(new)-333(subgroup)-333(k)26(ey)]TJ
/T1_5 10.91 Tf
108.24 0 Td
(K)Tj
/T1_4 7.97 Tf
10.05 3.95 Td
(0)Tj
/T1_2 7.97 Tf
-0.78 -7.19 Td
(J)Tj
/T1_0 10.91 Tf
9.5 3.24 Td
[(and)-333(new)-333(\257nal)-334(group)-333(k)27(ey)]TJ
/T1_5 10.91 Tf
118.48 0 Td
(K)Tj
/T1_4 7.97 Tf
10.05 3.95 Td
(0)Tj
/T1_0 10.91 Tf
6.43 -3.95 Td
[(and)-333(b)-27(oth)]TJ
/T1_5 10.91 Tf
46.95 0 Td
(K)Tj
/T1_4 7.97 Tf
10.05 3.95 Td
(0)Tj
/T1_2 7.97 Tf
-0.78 -7.19 Td
(J)Tj
/T1_0 10.91 Tf
9.5 3.24 Td
(and)Tj
/T1_5 10.91 Tf
21.21 0 Td
(K)Tj
/T1_4 7.97 Tf
10.04 3.95 Td
(0)Tj
/T1_0 10.91 Tf
6.43 -3.95 Td
[(are)-333(con\257rmed.)]TJ
-365.37 -21.92 Td
(\()Tj
/T1_5 10.91 Tf
(iii)Tj
/T1_0 10.91 Tf
15.51 0 Td
[(\))-314(Eac)27(h)]TJ
/T1_1 10.91 Tf
34.58 0 Td
(U)Tj
/T1_2 7.97 Tf
5.72 -1.64 Td
(i;j)Tj
/T1_0 10.91 Tf
13.05 1.64 Td
[(for)-314(1)]TJ
/T1_7 10.91 Tf
24.96 0 Td
(\267)Tj
/T1_5 10.91 Tf
11.52 0 Td
(i)Tj
/T1_7 10.91 Tf
6.78 0 Td
(6)Tj
/T1_0 10.91 Tf
(=)Tj
/T1_5 10.91 Tf
11.52 0 Td
(J)Tj
/T1_7 10.91 Tf
10.12 0 Td
(\267)Tj
/T1_5 10.91 Tf
11.51 0 Td
(n)Tj
/T1_2 7.97 Tf
6.55 -1.64 Td
(c)Tj
/T1_0 10.91 Tf
7.59 1.64 Td
[(and)-314(2)]TJ
/T1_7 10.91 Tf
29.48 0 Td
(\267)Tj
/T1_5 10.91 Tf
11.52 0 Td
(j)Tj
/T1_7 10.91 Tf
8.14 0 Td
(\267)Tj
/T1_5 10.91 Tf
11.51 0 Td
(n)Tj
/T1_2 7.97 Tf
6.55 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
6.81 1.64 Td
[(\257rst)-314(v)27(eri\257es)-313(the)-314(signature)-368(\271)]TJ
/T1_5 10.91 Tf
124.25 0 Td
(\276)Tj
/T1_4 7.97 Tf
6.63 3.96 Td
(0)Tj
/T1_2 7.97 Tf
-0.39 -7.02 Td
(i)Tj
/T1_0 10.91 Tf
3.38 3.06 Td
[(.)-437(If)-315(the)-314(v)27(eri\257cation)-313(is)]TJ
-367.29 -21.92 Td
[(not)-295(correct,)-304(then)]TJ
/T1_1 10.91 Tf
82.53 0 Td
(U)Tj
/T1_2 7.97 Tf
5.72 -1.63 Td
(i;j)Tj
/T1_0 10.91 Tf
12.84 1.63 Td
(rejects)Tj
/T1_1 10.91 Tf
33.92 0 Td
(S)Tj
/T1_2 7.97 Tf
5.72 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
3.39 1.63 Td
[(.)-431(Otherwise,)]TJ
/T1_1 10.91 Tf
62.03 0 Td
(U)Tj
/T1_2 7.97 Tf
5.72 -1.63 Td
(i;j)Tj
/T1_0 10.91 Tf
12.85 1.63 Td
[(uses)-295(subgroup)-296(k)27(ey)]TJ
/T1_5 10.91 Tf
88.96 0 Td
(K)Tj
/T1_2 7.97 Tf
9.26 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
6.6 1.63 Td
[(to)-296(decrypt)-308(\271)]TJ
/T1_1 10.91 Tf
52.23 0 Td
(c)Tj
/T1_4 7.97 Tf
5.73 3.96 Td
(0)Tj
/T1_2 7.97 Tf
0 -7.01 TD
(i)Tj
/T1_0 10.91 Tf
6.6 3.05 Td
[(and)-296(obtains)-295(the)]TJ
-394.1 -21.91 Td
[(iden)27(tit)28(y)]TJ
/T1_1 10.91 Tf
40.42 0 Td
(S)Tj
/T1_2 7.97 Tf
5.73 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
7.15 1.64 Td
[(and)-345(\257nal)-345(group)-345(k)26(ey)]TJ
/T1_5 10.91 Tf
96.59 0 Td
(K)Tj
/T1_4 7.97 Tf
10.04 3.95 Td
(0)Tj
/T1_0 10.91 Tf
2.8 -3.95 Td
[(.)-480(If)-345(the)-346(iden)27(tit)28(y)]TJ
/T1_1 10.91 Tf
78.64 0 Td
(S)Tj
/T1_2 7.97 Tf
5.73 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
7.15 1.64 Td
[(w)28(as)-345(not)-345(decrypted)-346(correctly)83(,)-348(then)]TJ
/T1_1 10.91 Tf
163.82 0 Td
(U)Tj
/T1_2 7.97 Tf
5.73 -1.64 Td
(i;j)Tj
/T1_0 10.91 Tf
13.38 1.64 Td
(rejects)Tj
-437.04 -21.92 Td
(\271)Tj
/T1_1 10.91 Tf
-0.14 0 Td
(c)Tj
/T1_4 7.97 Tf
5.73 3.96 Td
(0)Tj
/T1_2 7.97 Tf
0 -7.02 TD
(i)Tj
/T1_0 10.91 Tf
3.38 3.06 Td
[(.)-433(Otherwise,)]TJ
/T1_1 10.91 Tf
62.12 0 Td
(U)Tj
/T1_2 7.97 Tf
5.72 -1.64 Td
(i;j)Tj
/T1_0 10.91 Tf
12.92 1.64 Td
[(c)27(hec)28(ks)-302(if)]TJ
/T1_5 10.91 Tf
43.02 0 Td
(\265)Tj
/T1_4 7.97 Tf
5.42 3.96 Td
(0)Tj
/T1_2 7.97 Tf
-0.3 -7.02 Td
(i)Tj
/T1_0 10.91 Tf
6.41 3.06 Td
(=)Tj
/T1_6 10.91 Tf
11.51 0 Td
(H)Tj
/T1_0 10.91 Tf
(\()Tj
/T1_5 10.91 Tf
11.97 0 Td
(K)Tj
/T1_2 7.97 Tf
9.26 -1.64 Td
(i)Tj
/T1_7 10.91 Tf
3.38 1.64 Td
(jj)Tj
/T1_5 10.91 Tf
6.06 0 Td
(K)Tj
/T1_4 7.97 Tf
10.04 3.96 Td
(0)Tj
/T1_7 10.91 Tf
2.79 -3.96 Td
(jj)Tj
/T1_5 10.91 Tf
6.06 0 Td
(\277)Tj
/T1_2 7.97 Tf
4.77 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
3.38 1.64 Td
[(\).)-434(If)-303(they)-302(are)-303(equal,)]TJ
/T1_1 10.91 Tf
96.2 0 Td
(U)Tj
/T1_2 7.97 Tf
5.73 -1.64 Td
(i;j)Tj
/T1_0 10.91 Tf
12.92 1.64 Td
[(accepts)-302(and)-303(con\257rms)-302(the)-303(new)]TJ
-328.49 -21.92 Td
[(\257nal)-333(group)-333(k)27(ey)]TJ
/T1_5 10.91 Tf
74.86 0 Td
(K)Tj
/T1_4 7.97 Tf
10.04 3.96 Td
(0)Tj
/T1_0 10.91 Tf
2.8 -3.96 Td
(.)Tj
/T1_8 11.95 Tf
-87.7 -37.82 Td
[(9.2.3)-1125(Lea)31(v)31(e)-374(Proto)-31(col)]TJ
/T1_0 10.91 Tf
0 -28.96 TD
[(Supp)-27(ose)-408(a)-407(set)-408(of)]TJ
/T1_5 10.91 Tf
84.54 0 Td
(`)Tj
/T1_0 10.91 Tf
8.99 0 Td
(users)Tj
/T1_7 10.91 Tf
28.23 0 Td
(L)Tj
/T1_0 10.91 Tf
11.9 0 Td
(=)Tj
/T1_7 10.91 Tf
12.86 0 Td
(f)Tj
/T1_1 10.91 Tf
(U)Tj
/T1_2 7.97 Tf
11.17 -1.78 Td
(L;l)Tj
/T1_9 5.98 Tf
10.64 -1.1 Td
(1)Tj
/T1_5 10.91 Tf
4.65 2.88 Td
(;)Tj
/T1_7 10.91 Tf
4.85 0 Td
[(\242)-166(\242)-166(\242)]TJ
/T1_5 10.91 Tf
16.35 0 Td
(;)Tj
/T1_1 10.91 Tf
4.85 0 Td
(U)Tj
/T1_2 7.97 Tf
5.73 -1.78 Td
(L;l)Tj
/T1_3 5.98 Tf
10.63 -1.4 Td
(`)Tj
/T1_7 10.91 Tf
4.1 3.18 Td
(g)Tj
/T1_0 10.91 Tf
9.89 0 Td
[(wishes)-407(to)-408(lea)27(v)28(e)-407(subgroup)]TJ
/T1_7 10.91 Tf
124.93 0 Td
(G)Tj
/T1_2 7.97 Tf
6.49 -1.69 Td
(L)Tj
/T1_0 10.91 Tf
10.63 1.69 Td
(=)Tj
/T1_7 10.91 Tf
12.86 0 Td
(f)Tj
/T1_1 10.91 Tf
(U)Tj
/T1_2 7.97 Tf
11.18 -1.69 Td
(L;)Tj
/T1_10 7.97 Tf
(1)Tj
/T1_5 10.91 Tf
12.84 1.69 Td
(;)Tj
/T1_7 10.91 Tf
4.85 0 Td
[(\242)-166(\242)-167(\242)]TJ
/T1_5 10.91 Tf
16.36 0 Td
(;)Tj
/T1_1 10.91 Tf
4.84 0 Td
(U)Tj
/T1_2 7.97 Tf
5.73 -1.69 Td
(L;n)Tj
/T1_3 5.98 Tf
13.24 -1.34 Td
(L)Tj
/T1_7 10.91 Tf
6.06 3.03 Td
(g)Tj
/T1_0 10.91 Tf
(,)Tj
-459.39 -21.92 Td
[(then)-320(the)-321(Lea)27(v)28(e)-320(Proto)-28(col)-321(will)-320(b)-28(e)-321(executed)-320(to)-321(establish)-321(a)-321(new)-320(subgroup)-321(k)27(ey)]TJ
/T1_5 10.91 Tf
354.11 0 Td
(K)Tj
/T1_4 7.97 Tf
10.05 3.96 Td
(0)Tj
/T1_2 7.97 Tf
-0.78 -7.19 Td
(L)Tj
/T1_0 10.91 Tf
9.75 3.23 Td
[(and)-320(new)-321(\257nal)-320(group)]TJ
-373.13 -21.91 Td
[(k)27(ey)]TJ
/T1_5 10.91 Tf
19.73 0 Td
(K)Tj
/T1_4 7.97 Tf
10.04 3.96 Td
(0)Tj
/T1_0 10.91 Tf
6.46 -3.96 Td
[(to)-336(protect)-337(future)-336(group)-337(comm)27(unications)-336(from)-336(the)-337(lea)27(ving)-335(users.)-454(F)82(or)-335(an)26(y)-335(lea)27(ving)-336(user)]TJ
/T1_1 10.91 Tf
408.59 0 Td
(U)Tj
/T1_2 7.97 Tf
5.73 -1.78 Td
(L;l)Tj
/T1_3 5.98 Tf
10.63 -1.21 Td
(i)Tj
/T1_0 10.91 Tf
3.66 2.99 Td
(,)Tj
-464.84 -21.92 Td
[(the)-472(left)-473(neigh)26(b)-26(or)-473(is)-473(denoted)-473(as)]TJ
/T1_1 10.91 Tf
157.43 0 Td
(U)Tj
/T1_2 7.97 Tf
5.73 -1.77 Td
(L;l)Tj
/T1_3 5.98 Tf
10.63 -1.22 Td
(i)Tj
/T1_4 7.97 Tf
3.16 1.22 Td
(\241)Tj
/T1_2 7.97 Tf
6.59 0 Td
(w)Tj
/T1_3 5.98 Tf
6.07 -1.22 Td
(i)Tj
/T1_0 10.91 Tf
8.82 2.99 Td
[(if)-472(the)]TJ
/T1_5 10.91 Tf
31.83 0 Td
(w)Tj
/T1_2 7.97 Tf
7.8 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
8.54 1.63 Td
[(consecutiv)27(e)-472(users)]TJ
/T1_1 10.91 Tf
88.09 0 Td
(U)Tj
/T1_2 7.97 Tf
5.72 -1.77 Td
(L;l)Tj
/T1_3 5.98 Tf
10.64 -1.22 Td
(i)Tj
/T1_5 10.91 Tf
3.66 2.99 Td
(;)Tj
/T1_1 10.91 Tf
4.84 0 Td
(U)Tj
/T1_2 7.97 Tf
5.73 -1.77 Td
(L;l)Tj
/T1_3 5.98 Tf
10.64 -1.22 Td
(i)Tj
/T1_4 7.97 Tf
3.16 1.22 Td
(\241)Tj
/T1_10 7.97 Tf
(1)Tj
/T1_5 10.91 Tf
11.31 1.77 Td
[(;)-166(:)-167(:)-167(:)-166(;)]TJ
/T1_1 10.91 Tf
24.24 0 Td
(U)Tj
/T1_2 7.97 Tf
5.72 -2.22 Td
(L;l)Tj
/T1_3 5.98 Tf
10.64 -1.21 Td
(i)Tj
/T1_4 7.97 Tf
3.16 1.21 Td
(\241)Tj
/T1_10 7.97 Tf
(\()Tj
/T1_2 7.97 Tf
9.88 0 Td
(w)Tj
/T1_3 5.98 Tf
6.07 -1.21 Td
(i)Tj
/T1_4 7.97 Tf
3.16 1.21 Td
(\241)Tj
/T1_10 7.97 Tf
6.59 0 Td
(1\))Tj
/T1_0 10.91 Tf
-459.85 -19.69 Td
[(are)-409(all)-409(lea)26(ving)-408(and)]TJ
/T1_1 10.91 Tf
94.84 0 Td
(U)Tj
/T1_2 7.97 Tf
5.73 -1.78 Td
(L;l)Tj
/T1_3 5.98 Tf
10.63 -1.22 Td
(i)Tj
/T1_4 7.97 Tf
3.16 1.22 Td
(\241)Tj
/T1_2 7.97 Tf
6.59 0 Td
(w)Tj
/T1_3 5.98 Tf
6.07 -1.22 Td
(i)Tj
/T1_0 10.91 Tf
8.13 3 Td
[(is)-409(not)-409(lea)27(ving)-409(the)-409(group.)-673(Similarly)83(,)-428(the)-409(righ)27(t)-409(neigh)27(b)-27(or)-409(is)-410(denoted)-409(as)]TJ
/T1_1 10.91 Tf
-135.15 -21.92 Td
(U)Tj
/T1_2 7.97 Tf
5.73 -2.31 Td
(L;l)Tj
/T1_3 5.98 Tf
10.63 -1.21 Td
(i)Tj
/T1_10 7.97 Tf
3.16 1.21 Td
(+)Tj
/T1_2 7.97 Tf
6.59 0 Td
(w)Tj
/T1_11 5.98 Tf
6.29 2.75 Td
(0)Tj
/T1_3 5.98 Tf
-0.22 -5.4 Td
(i)Tj
/T1_0 10.91 Tf
7.7 4.96 Td
[(if)-369(the)]TJ
/T1_5 10.91 Tf
29.58 0 Td
(w)Tj
/T1_4 7.97 Tf
8.1 3.96 Td
(0)Tj
/T1_2 7.97 Tf
-0.29 -7.02 Td
(i)Tj
/T1_0 10.91 Tf
7.42 3.06 Td
[(consecutiv)28(e)-369(users)]TJ
/T1_1 10.91 Tf
85.83 0 Td
(U)Tj
/T1_2 7.97 Tf
5.73 -1.78 Td
(L;l)Tj
/T1_3 5.98 Tf
10.64 -1.21 Td
(i)Tj
/T1_5 10.91 Tf
3.66 2.99 Td
(;)Tj
/T1_1 10.91 Tf
4.84 0 Td
(U)Tj
/T1_2 7.97 Tf
5.73 -1.78 Td
(L;l)Tj
/T1_3 5.98 Tf
10.63 -1.21 Td
(i)Tj
/T1_10 7.97 Tf
3.16 1.21 Td
(+1)Tj
/T1_5 10.91 Tf
11.32 1.78 Td
[(;)-166(:)-167(:)-167(:)-166(;)]TJ
/T1_1 10.91 Tf
24.24 0 Td
(U)Tj
/T1_2 7.97 Tf
5.72 -2.31 Td
(L;l)Tj
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[(2)-286(N)]TJ
/T1_0 10.91 Tf
20.95 0 Td
(\()Tj
/T1_5 10.91 Tf
(R)Tj
/T1_0 10.91 Tf
[(\),)-339(who)-339(is)-338(a)-339(left)-339(or)-338(righ)27(t)-338(neigh)27(b)-27(or)-339(of)-338(lea)26(ving)-337(users,)-340(ran-)]TJ
-196.79 -21.92 Td
[(domly)-320(selects)]TJ
/T1_1 10.91 Tf
66.8 0 Td
(r)Tj
/T1_2 7.97 Tf
5.22 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.3 -7.28 Td
(L;k)Tj
/T1_5 10.91 Tf
16.26 3.32 Td
(2)Tj
/T1_1 10.91 Tf
10.3 0 Td
(Z)Tj
/T1_2 7.97 Tf
8.22 3.96 Td
(\244)Tj
/T1_3 7.97 Tf
-0.78 -6.65 Td
(q)Tj
/T1_0 10.91 Tf
9.01 2.69 Td
[(and)-321(computes)]TJ
/T1_1 10.91 Tf
69.47 0 Td
(z)Tj
/T1_2 7.97 Tf
5.55 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.48 -7.28 Td
(L;k)Tj
/T1_0 10.91 Tf
16.26 3.32 Td
(=)Tj
/T1_1 10.91 Tf
11.51 0 Td
(g)Tj
/T1_3 7.97 Tf
5.6 5.11 Td
(r)Tj
/T1_9 5.98 Tf
4.05 2.81 Td
(0)Tj
/T1_10 5.98 Tf
-0.23 -5.58 Td
(L;k)Tj
/T1_0 10.91 Tf
15.42 -2.34 Td
[(mo)-27(d)]TJ
/T1_1 10.91 Tf
23.93 0 Td
(p)Tj
/T1_0 10.91 Tf
[(.)-440(Next,)]TJ
/T1_4 10.91 Tf
42.9 0 Td
(V)Tj
/T1_3 7.97 Tf
5.73 -1.77 Td
(L;k)Tj
/T1_0 10.91 Tf
16.73 1.77 Td
(broadcasts)Tj
/T1_5 10.91 Tf
53.94 0 Td
(f)Tj
/T1_4 10.91 Tf
(V)Tj
/T1_3 7.97 Tf
11.17 -1.77 Td
(L;k)Tj
/T1_5 10.91 Tf
13.23 1.77 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(z)Tj
/T1_2 7.97 Tf
5.55 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.48 -7.28 Td
(L;k)Tj
/T1_5 10.91 Tf
13.23 3.32 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(\276)Tj
/T1_2 7.97 Tf
6.62 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.39 -7.28 Td
(L;k)Tj
/T1_5 10.91 Tf
13.23 3.32 Td
(g)Tj
/T1_0 10.91 Tf
(,)Tj
-459.39 -21.91 Td
(where)Tj
/T1_1 10.91 Tf
31.54 0 Td
(\276)Tj
/T1_2 7.97 Tf
6.62 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.39 -7.28 Td
(L;k)Tj
/T1_0 10.91 Tf
16.26 3.32 Td
(=)Tj
/T1_5 10.91 Tf
11.51 0 Td
(S)Tj
/T1_0 10.91 Tf
7.42 0 Td
(\()Tj
/T1_4 10.91 Tf
(V)Tj
/T1_3 7.97 Tf
9.97 -1.78 Td
(L;k)Tj
/T1_5 10.91 Tf
13.22 1.78 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(z)Tj
/T1_2 7.97 Tf
5.55 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.48 -7.28 Td
(L;k)Tj
/T1_5 10.91 Tf
13.23 3.32 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(\277)Tj
/T1_2 7.97 Tf
6 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-1.23 -7.19 Td
(L)Tj
/T1_5 10.91 Tf
6.25 3.23 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(v)Tj
/T1_0 10.91 Tf
5.68 0 Td
[(\))-333(and)-333(stores)]TJ
/T1_1 10.91 Tf
60.14 0 Td
(\277)Tj
/T1_2 7.97 Tf
6 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-1.24 -7.19 Td
(L)Tj
/T1_0 10.91 Tf
6.26 3.23 Td
(.)Tj
-220.49 -21.92 Td
[(Round)-333(3)]TJ
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 0 -265.52 cm
0 0 m
40.75 0 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 116.7325 505.7561 Tm
(:)Tj
/T1_4 10.91 Tf
8.55 0 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.69 Td
(L)Tj
/T1_0 10.91 Tf
10.23 1.69 Td
(c)Tj
1.0003 0 0 1.0003 72 769.82 Tm
73.779 -263.99 Td
[(hec)28(ks)-363(the)-365(receiv)27(ed)-363(signatures)]TJ
/T1_1 10.91 Tf
142.761 0 Td
(\276)Tj
/T1_2 7.97 Tf
6.63 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.4 -7.28 Td
(L;k)Tj
/T1_0 10.91 Tf
17.21 3.32 Td
[(sen)28(t)-364(b)27(y)]TJ
/T1_4 10.91 Tf
38.6 0 Td
(V)Tj
/T1_3 7.97 Tf
5.73 -1.78 Td
(L;k)Tj
/T1_5 10.91 Tf
16.82 1.78 Td
[(2)-329(N)]TJ
/T1_0 10.91 Tf
21.42 0 Td
(\()Tj
/T1_5 10.91 Tf
(R)Tj
/T1_0 10.91 Tf
13.48 0 Td
[(\))-364(in)-364(Round)-365(2.)-537(If)]TJ
/T1_4 10.91 Tf
82.5 0 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.69 Td
(L)Tj
/T1_0 10.91 Tf
10.23 1.69 Td
(detects)Tj
-434.49 -21.92 Td
[(in)27(v)56(alid)-371(signatures)-371(sen)27(t)-371(b)27(y)-371(certain)-371(malicious)-372(no)-28(des,)-381(then)-371(these)-372(malicious)-371(no)-28(des)-372(will)-371(b)-28(e)-371(placed)-372(in)27(to)]TJ
0 -21.91 TD
[(a)-424(list)]TJ
/T1_4 10.91 Tf
29.31 0 Td
(BL)Tj
/T1_11 7.97 Tf
11.45 -1.64 Td
(Z)Tj
/T1_0 10.91 Tf
4.73 1.64 Td
[(.)-717(If)]TJ
/T1_4 10.91 Tf
22.75 0 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.69 Td
(L)Tj
/T1_5 10.91 Tf
10.94 1.69 Td
[(2)-429(N)]TJ
/T1_0 10.91 Tf
22.51 0 Td
(\()Tj
/T1_5 10.91 Tf
(R)Tj
/T1_0 10.91 Tf
13.48 0 Td
[(\),)-446(then)]TJ
/T1_4 10.91 Tf
37.98 0 Td
(S)Tj
/T1_3 7.97 Tf
5.72 -1.69 Td
(L)Tj
/T1_0 10.91 Tf
10.89 1.69 Td
[(selects)-424(random)]TJ
/T1_1 10.91 Tf
76.05 0 Td
(r)Tj
/T1_2 7.97 Tf
5.23 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.31 -7.19 Td
(L;)Tj
/T1_7 7.97 Tf
(1)Tj
/T1_5 10.91 Tf
17.53 3.23 Td
(2)Tj
/T1_1 10.91 Tf
11.95 0 Td
(Z)Tj
/T1_2 7.97 Tf
8.22 3.96 Td
(\244)Tj
/T1_3 7.97 Tf
-0.78 -6.66 Td
(q)Tj
/T1_0 10.91 Tf
10.14 2.7 Td
[(and)-424(computes)]TJ
/T1_1 10.91 Tf
71.72 0 Td
(z)Tj
/T1_2 7.97 Tf
5.56 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.48 -7.19 Td
(L;)Tj
/T1_7 7.97 Tf
(1)Tj
/T1_0 10.91 Tf
17.52 3.23 Td
(=)Tj
/T1_1 10.91 Tf
13.16 0 Td
(g)Tj
/T1_3 7.97 Tf
5.6 5.04 Td
(r)Tj
/T1_9 5.98 Tf
4.05 2.81 Td
(0)Tj
/T1_10 5.98 Tf
-0.23 -5.52 Td
(L;)Tj
/T1_12 5.98 Tf
7.32 0 Td
(1)Tj
/T1_0 10.91 Tf
7.68 -2.33 Td
[(mo)-27(d)]TJ
/T1_1 10.91 Tf
23.93 0 Td
(p)Tj
/T1_0 10.91 Tf
(.)Tj
-459.35 -21.92 Td
[(Otherwise,)-450(if)]TJ
/T1_4 10.91 Tf
66.93 0 Td
(S)Tj
/T1_3 7.97 Tf
5.72 -1.69 Td
(L)Tj
/T1_1 10.91 Tf
12.21 1.69 Td
(=)Tj
/T1_5 10.91 Tf
-1.21 0 Td
[(2)-434(N)]TJ
/T1_0 10.91 Tf
22.56 0 Td
(\()Tj
/T1_5 10.91 Tf
(R)Tj
/T1_0 10.91 Tf
[(\),)-450(then)]TJ
/T1_4 10.91 Tf
51.54 0 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.69 Td
(L)Tj
/T1_0 10.91 Tf
10.91 1.69 Td
(uses)Tj
/T1_1 10.91 Tf
24.17 0 Td
(z)Tj
/T1_2 7.97 Tf
5.56 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.48 -7.19 Td
(L;)Tj
/T1_7 7.97 Tf
8.1 0 Td
(1)Tj
/T1_0 10.91 Tf
9.47 3.23 Td
(=)Tj
/T1_1 10.91 Tf
13.23 0 Td
(z)Tj
/T1_3 7.97 Tf
5.07 -1.69 Td
(L;)Tj
/T1_7 7.97 Tf
(1)Tj
/T1_0 10.91 Tf
17.58 1.69 Td
(=)Tj
/T1_1 10.91 Tf
13.22 0 Td
(g)Tj
/T1_3 7.97 Tf
5.59 3.96 Td
(r)Tj
/T1_10 5.98 Tf
3.82 -1.34 Td
(L;)Tj
/T1_12 5.98 Tf
(1)Tj
/T1_0 10.91 Tf
15 -2.62 Td
[(mo)-28(d)]TJ
/T1_1 10.91 Tf
23.94 0 Td
(p)Tj
/T1_0 10.91 Tf
10.15 0 Td
[(from)-426(the)-428(previous)-427(group)-428(k)27(ey)]TJ
-328.81 -21.91 Td
[(agreemen)27(t.)-443(Finally)82(,)]TJ
/T1_4 10.91 Tf
95.91 0 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.69 Td
(L)Tj
/T1_0 10.91 Tf
9.89 1.69 Td
(broadcasts)Tj
/T1_5 10.91 Tf
54.08 0 Td
(f)Tj
/T1_4 10.91 Tf
(S)Tj
/T1_3 7.97 Tf
11.17 -1.69 Td
(L)Tj
/T1_5 10.91 Tf
6.26 1.69 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(z)Tj
/T1_2 7.97 Tf
5.55 3.95 Td
(0)Tj
/T1_3 7.97 Tf
-0.48 -7.19 Td
(L;)Tj
/T1_7 7.97 Tf
(1)Tj
/T1_5 10.91 Tf
12.84 3.24 Td
(jj)Tj
/T1_4 10.91 Tf
6.06 0 Td
(BL)Tj
/T1_11 7.97 Tf
11.45 -1.64 Td
(Z)Tj
/T1_5 10.91 Tf
4.73 1.64 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(\276)Tj
/T1_2 7.97 Tf
6.62 3.95 Td
(0)Tj
/T1_3 7.97 Tf
-0.39 -7.19 Td
(L;)Tj
/T1_7 7.97 Tf
(1)Tj
/T1_5 10.91 Tf
12.84 3.24 Td
(g)Tj
/T1_0 10.91 Tf
[(,)-332(where)]TJ
/T1_1 10.91 Tf
43.66 0 Td
(\276)Tj
/T1_2 7.97 Tf
6.62 3.95 Td
(0)Tj
/T1_3 7.97 Tf
-0.39 -7.19 Td
(L;)Tj
/T1_7 7.97 Tf
(1)Tj
/T1_0 10.91 Tf
15.87 3.24 Td
(=)Tj
/T1_5 10.91 Tf
11.51 0 Td
(S)Tj
/T1_0 10.91 Tf
7.42 0 Td
(\()Tj
/T1_4 10.91 Tf
(S)Tj
/T1_3 7.97 Tf
9.97 -1.69 Td
(L)Tj
/T1_5 10.91 Tf
6.26 1.69 Td
(jj)Tj
/T1_1 10.91 Tf
6.05 0 Td
(\277)Tj
/T1_2 7.97 Tf
6.01 3.95 Td
(0)Tj
/T1_3 7.97 Tf
-1.24 -7.19 Td
(L)Tj
/T1_5 10.91 Tf
6.26 3.24 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(z)Tj
/T1_2 7.97 Tf
5.55 3.95 Td
(0)Tj
/T1_3 7.97 Tf
-0.48 -7.19 Td
(L;)Tj
/T1_7 7.97 Tf
(1)Tj
/T1_5 10.91 Tf
12.84 3.24 Td
(jj)Tj
/T1_4 10.91 Tf
6.06 0 Td
(BL)Tj
/T1_11 7.97 Tf
11.45 -1.64 Td
(Z)Tj
/T1_5 10.91 Tf
4.73 1.64 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(v)Tj
/T1_0 10.91 Tf
5.68 0 Td
(\).)Tj
-430.33 -21.92 Td
[(Round)-333(4)]TJ
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 0 -375.1 cm
0 0 m
40.75 0 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 116.0123 396.1454 Tm
(:)Tj
1.0003 0 0 1.0003 72 769.82 Tm
51.692 -373.57 Td
[(Eac)27(h)]TJ
/T1_4 10.91 Tf
26.738 0 Td
(V)Tj
/T1_3 7.97 Tf
5.72 -1.69 Td
(L;j)Tj
/T1_0 10.91 Tf
15.75 1.69 Td
[(for)-298(2)]TJ
/T1_5 10.91 Tf
24.8 0 Td
(\267)Tj
/T1_1 10.91 Tf
11.51 0 Td
(j)Tj
/T1_5 10.91 Tf
8.15 0 Td
(\267)Tj
/T1_1 10.91 Tf
11.51 0 Td
(n)Tj
/T1_3 7.97 Tf
6.54 -1.69 Td
(L)Tj
/T1_5 10.91 Tf
7.93 1.69 Td
(\241)Tj
/T1_1 10.91 Tf
10.15 0 Td
(`)Tj
/T1_0 10.91 Tf
7.8 0 Td
[(\257rst)-298(c)27(hec)27(ks)-297(signature)]TJ
/T1_1 10.91 Tf
102.41 0 Td
(\276)Tj
/T1_2 7.97 Tf
6.63 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.39 -7.19 Td
(L;)Tj
/T1_7 7.97 Tf
(1)Tj
/T1_0 10.91 Tf
12.84 3.23 Td
[(.)-432(If)-299(the)-299(v)27(eri\257cation)-297(is)-299(not)-299(correct,)]TJ
-309.78 -21.92 Td
(then)Tj
/T1_4 10.91 Tf
23.95 0 Td
(V)Tj
/T1_3 7.97 Tf
5.73 -1.69 Td
(L;j)Tj
/T1_0 10.91 Tf
15.24 1.69 Td
(rejects)Tj
/T1_4 10.91 Tf
33.44 0 Td
(S)Tj
/T1_3 7.97 Tf
5.72 -1.69 Td
(L)Tj
/T1_0 10.91 Tf
6.26 1.69 Td
[(.)-417(Otherwise,)]TJ
/T1_4 10.91 Tf
61.49 0 Td
(V)Tj
/T1_3 7.97 Tf
5.73 -1.69 Td
(L;j)Tj
/T1_0 10.91 Tf
15.23 1.69 Td
[(c)27(hec)28(ks)-251(the)-252(list)]TJ
/T1_4 10.91 Tf
68.05 0 Td
(BL)Tj
/T1_11 7.97 Tf
11.45 -1.63 Td
(Z)Tj
/T1_0 10.91 Tf
7.48 1.63 Td
[(to)-252(iden)27(tify)-251(the)-252(malicious)-252(no)-28(des)-252(to)-252(b)-28(e)-252(blo)-28(c)27(k)28(ed)]TJ
-259.77 -21.91 Td
[(from)-370(the)-371(GKA)-371(using)-371(the)-371(similar)-371(metho)-28(d)-371(describ)-28(ed)-370(in)-371(the)-371(Initial)-371(Group)-371(Key)-371(Agreemen)27(t)-370(and)-371(Join)]TJ
0 -21.92 TD
[(Proto)-27(col.)-794(Next,)-478(eac)26(h)]TJ
/T1_4 10.91 Tf
109.24 0 Td
(V)Tj
/T1_3 7.97 Tf
5.72 -1.69 Td
(L;j)Tj
/T1_0 10.91 Tf
17.4 1.69 Td
(computes)Tj
/T1_1 10.91 Tf
49.8 0 Td
(L)Tj
/T1_2 7.97 Tf
7.42 3.96 Td
(0)Tj
/T1_3 7.97 Tf
0 -7.19 TD
(L;j)Tj
/T1_0 10.91 Tf
17.63 3.23 Td
(=)Tj
/T1_8 10.91 Tf
13.63 0 Td
(H)Tj
/T1_0 10.91 Tf
(\(\()Tj
/T1_1 10.91 Tf
16.2 0 Td
(z)Tj
/T1_2 7.97 Tf
5.56 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.48 -7.19 Td
(L;j)Tj
/T1_2 7.97 Tf
11.99 0 Td
(\241)Tj
/T1_7 7.97 Tf
(1)Tj
/T1_0 10.91 Tf
11.31 3.23 Td
(\))Tj
/T1_3 7.97 Tf
4.25 5.04 Td
(r)Tj
/T1_9 5.98 Tf
4.05 2.81 Td
(0)Tj
/T1_10 5.98 Tf
-0.23 -5.51 Td
(L;j)Tj
/T1_5 10.91 Tf
11.72 -2.34 Td
(jj)Tj
/T1_4 10.91 Tf
6.06 0 Td
(SID)Tj
/T1_2 7.97 Tf
17.18 3.96 Td
(0)Tj
/T1_3 7.97 Tf
T*
(L)Tj
/T1_0 10.91 Tf
6.25 3.23 Td
(\),)Tj
/T1_1 10.91 Tf
12.49 0 Td
(R)Tj
/T1_2 7.97 Tf
8.37 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.08 -7.19 Td
(L;j)Tj
/T1_0 10.91 Tf
17.63 3.23 Td
(=)Tj
/T1_8 10.91 Tf
13.62 0 Td
(H)Tj
/T1_0 10.91 Tf
7.73 0 Td
(\(\()Tj
/T1_1 10.91 Tf
8.48 0 Td
(z)Tj
/T1_2 7.97 Tf
5.55 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.48 -7.19 Td
(L;j)Tj
/T1_7 7.97 Tf
12 0 Td
(+1)Tj
/T1_0 10.91 Tf
11.31 3.23 Td
(\))Tj
/T1_3 7.97 Tf
4.24 5.04 Td
(r)Tj
/T1_9 5.98 Tf
4.06 2.81 Td
(0)Tj
/T1_10 5.98 Tf
-0.24 -5.51 Td
(L;j)Tj
/T1_5 10.91 Tf
11.73 -2.34 Td
(jj)Tj
/T1_4 10.91 Tf
6.06 0 Td
(SID)Tj
/T1_2 7.97 Tf
17.17 3.96 Td
(0)Tj
/T1_3 7.97 Tf
T*
(L)Tj
/T1_0 10.91 Tf
6.26 3.23 Td
(\),)Tj
-460.6 -21.92 Td
(where)Tj
/T1_1 10.91 Tf
30.94 0 Td
(z)Tj
/T1_2 7.97 Tf
5.55 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.48 -7.28 Td
(L;n)Tj
/T1_10 5.98 Tf
13.25 -1.34 Td
(L)Tj
/T1_2 7.97 Tf
5.55 1.34 Td
(\241)Tj
/T1_3 7.97 Tf
6.59 0 Td
(`)Tj
/T1_7 7.97 Tf
3.45 0 Td
(+1)Tj
/T1_0 10.91 Tf
14.35 3.32 Td
(=)Tj
/T1_1 10.91 Tf
11.51 0 Td
(z)Tj
/T1_2 7.97 Tf
5.55 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.48 -7.19 Td
(L;)Tj
/T1_7 7.97 Tf
(1)Tj
/T1_0 10.91 Tf
15.88 3.23 Td
(and)Tj
/T1_4 10.91 Tf
20.61 0 Td
(SID)Tj
/T1_2 7.97 Tf
17.18 3.96 Td
(0)Tj
/T1_3 7.97 Tf
T*
(L)Tj
/T1_0 10.91 Tf
9.28 3.23 Td
(=)Tj
/T1_8 10.91 Tf
11.51 0 Td
(H)Tj
/T1_0 10.91 Tf
7.73 0 Td
(\()Tj
/T1_1 10.91 Tf
(\277)Tj
/T1_2 7.97 Tf
10.24 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-1.23 -7.19 Td
(L)Tj
/T1_5 10.91 Tf
6.25 3.23 Td
(jj)Tj
/T1_4 10.91 Tf
6.06 0 Td
(V)Tj
/T1_3 7.97 Tf
5.73 -1.69 Td
(L;)Tj
/T1_7 7.97 Tf
(1)Tj
/T1_5 10.91 Tf
12.84 1.69 Td
(jj)Tj
/T1_4 10.91 Tf
6.06 0 Td
(V)Tj
/T1_3 7.97 Tf
5.72 -1.69 Td
(L;)Tj
/T1_7 7.97 Tf
(2)Tj
/T1_5 10.91 Tf
12.84 1.69 Td
[(jj)-166(\242)-167(\242)-167(\242)-166(jj)]TJ
/T1_4 10.91 Tf
28.48 0 Td
(V)Tj
/T1_3 7.97 Tf
5.72 -1.77 Td
(L;n)Tj
/T1_10 5.98 Tf
13.25 -1.34 Td
(L)Tj
/T1_2 7.97 Tf
5.56 1.34 Td
(\241)Tj
/T1_3 7.97 Tf
(`)Tj
/T1_0 10.91 Tf
10.54 1.77 Td
[(\).)-425(If)]TJ
/T1_4 10.91 Tf
22.22 0 Td
(V)Tj
/T1_3 7.97 Tf
5.73 -1.69 Td
(L;j)Tj
/T1_1 10.91 Tf
16.73 1.69 Td
(=)Tj
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-1.21 0 Td
[(2)-277(N)]TJ
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20.85 0 Td
(\()Tj
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(R)Tj
/T1_0 10.91 Tf
[(\),)-289(then)]TJ
/T1_1 10.91 Tf
48.16 0 Td
(r)Tj
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5.22 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.3 -7.19 Td
(L;j)Tj
/T1_0 10.91 Tf
15.52 3.23 Td
(=)Tj
/T1_1 10.91 Tf
11.51 0 Td
(r)Tj
/T1_3 7.97 Tf
4.92 -1.69 Td
(L;j)Tj
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-455.38 -20.22 Td
(and)Tj
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20.21 0 Td
(z)Tj
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5.55 3.95 Td
(0)Tj
/T1_3 7.97 Tf
-0.48 -7.19 Td
(L;j)Tj
/T1_0 10.91 Tf
15.52 3.24 Td
(=)Tj
/T1_1 10.91 Tf
11.51 0 Td
(z)Tj
/T1_3 7.97 Tf
5.07 -1.69 Td
(L;j)Tj
/T1_0 10.91 Tf
12.49 1.69 Td
[(,)-260(where)]TJ
/T1_1 10.91 Tf
36.41 0 Td
(r)Tj
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4.92 -1.69 Td
(L;j)Tj
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15.13 1.69 Td
(and)Tj
/T1_1 10.91 Tf
20.21 0 Td
(z)Tj
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5.07 -1.69 Td
(L;j)Tj
/T1_0 10.91 Tf
15.13 1.69 Td
[(are)-242(from)-242(previous)-242(GKA.)-242(Next,)]TJ
/T1_4 10.91 Tf
144.19 0 Td
(V)Tj
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5.73 -1.69 Td
(L;j)Tj
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15.13 1.69 Td
(generates)Tj
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46.96 0 Td
(X)Tj
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9.89 3.95 Td
(0)Tj
/T1_3 7.97 Tf
-0.86 -7.19 Td
(L;j)Tj
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15.52 3.24 Td
(=)Tj
/T1_1 10.91 Tf
11.51 0 Td
(L)Tj
/T1_2 7.97 Tf
7.43 3.95 Td
(0)Tj
/T1_3 7.97 Tf
T*
(L;j)Tj
/T1_5 10.91 Tf
12.92 3.24 Td
(\251)Tj
/T1_1 10.91 Tf
8.91 0 Td
(R)Tj
/T1_2 7.97 Tf
8.37 3.95 Td
(0)Tj
/T1_3 7.97 Tf
-0.09 -7.19 Td
(L;j)Tj
/T1_0 10.91 Tf
12.49 3.24 Td
(.)Tj
-464.84 -21.92 Td
[(Finally)83(,)]TJ
/T1_4 10.91 Tf
39.75 0 Td
(V)Tj
/T1_3 7.97 Tf
5.73 -1.69 Td
(L;j)Tj
/T1_0 10.91 Tf
16.54 1.69 Td
[(randomly)-371(selects)]TJ
/T1_1 10.91 Tf
83.69 0 Td
(\267)Tj
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6.29 3.96 Td
(0)Tj
/T1_3 7.97 Tf
T*
(L;j)Tj
/T1_5 10.91 Tf
16.21 3.23 Td
[(2)-342(f)]TJ
/T1_0 10.91 Tf
16.45 0 Td
(0)Tj
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(;)Tj
/T1_0 10.91 Tf
10.3 0 Td
(1)Tj
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(g)Tj
/T1_3 7.97 Tf
10.91 3.96 Td
(\270)Tj
/T1_0 10.91 Tf
9.49 -3.96 Td
[(and)-371(broadcasts)]TJ
/T1_5 10.91 Tf
76.12 0 Td
(f)Tj
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(V)Tj
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11.18 -1.69 Td
(L;j)Tj
/T1_5 10.91 Tf
12.49 1.69 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(\267)Tj
/T1_2 7.97 Tf
6.28 3.96 Td
(0)Tj
/T1_3 7.97 Tf
T*
(L;j)Tj
/T1_5 10.91 Tf
12.49 3.23 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(X)Tj
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9.89 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.86 -7.19 Td
(L;j)Tj
/T1_5 10.91 Tf
12.49 3.23 Td
(jj)Tj
/T1_0 10.91 Tf
6.65 0 Td
(\271)Tj
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-0.59 0 Td
(\276)Tj
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6.63 3.96 Td
(0)Tj
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-0.39 -7.19 Td
(L;j)Tj
/T1_5 10.91 Tf
12.49 3.23 Td
(g)Tj
/T1_0 10.91 Tf
[(,)-381(where)-425(\271)]TJ
/T1_1 10.91 Tf
44.59 0 Td
(\276)Tj
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6.62 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.39 -7.19 Td
(L;j)Tj
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16.22 3.23 Td
(=)Tj
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-459.39 -21.92 Td
(S)Tj
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7.42 0 Td
(\()Tj
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(V)Tj
/T1_3 7.97 Tf
9.97 -1.68 Td
(L;j)Tj
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12.49 1.68 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(\267)Tj
/T1_2 7.97 Tf
6.28 3.96 Td
(0)Tj
/T1_3 7.97 Tf
T*
(L;j)Tj
/T1_5 10.91 Tf
12.49 3.23 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(X)Tj
/T1_2 7.97 Tf
9.89 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.85 -7.19 Td
(L;j)Tj
/T1_5 10.91 Tf
12.49 3.23 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(\277)Tj
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6 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-1.24 -7.19 Td
(L)Tj
/T1_5 10.91 Tf
6.26 3.23 Td
(jj)Tj
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6.06 0 Td
(v)Tj
/T1_0 10.91 Tf
5.67 0 Td
(\).)Tj
-111.11 -21.91 Td
[(Round)-333(5)]TJ
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 0 -550.43 cm
0 0 m
40.75 0 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 117.4227 220.7663 Tm
(:)Tj
/T1_4 10.91 Tf
9.94 0 Td
(S)Tj
/T1_3 7.97 Tf
5.72 -1.69 Td
(L)Tj
/T1_0 10.91 Tf
10.93 1.69 Td
(\257rst)Tj
1.0003 0 0 1.0003 72 769.82 Tm
95.544 -548.9 Td
[(c)27(hec)28(ks)-427(the)-428(receiv)27(ed)-427(signatures)-481(\271)]TJ
/T1_1 10.91 Tf
150.066 0 Td
(\276)Tj
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6.63 3.95 Td
(0)Tj
/T1_3 7.97 Tf
-0.39 -7.18 Td
(L;j)Tj
/T1_0 10.91 Tf
17.15 3.23 Td
[(for)-427(2)]TJ
/T1_5 10.91 Tf
27.92 0 Td
(\267)Tj
/T1_1 10.91 Tf
13.23 0 Td
(j)Tj
/T1_5 10.91 Tf
9.86 0 Td
(\267)Tj
/T1_1 10.91 Tf
13.23 0 Td
(n)Tj
/T1_3 7.97 Tf
6.55 -1.69 Td
(L)Tj
/T1_5 10.91 Tf
9.37 1.69 Td
(\241)Tj
/T1_1 10.91 Tf
11.59 0 Td
(`)Tj
/T1_0 10.91 Tf
4.54 0 Td
[(.)-728(If)-427(there)-428(are)-428(in)27(v)55(alid)]TJ
-365.29 -21.92 Td
(signatures,)Tj
/T1_4 10.91 Tf
56.04 0 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.69 Td
(L)Tj
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10.97 1.69 Td
[(will)-433(place)-433(the)-433(iden)27(tities)-432(of)-433(in)27(v)55(alid)-432(users)]TJ
/T1_13 10.91 Tf
196.7 1.97 Td
(e)Tj
/T1_4 10.91 Tf
0.16 -1.97 Td
(V)Tj
/T1_3 7.97 Tf
5.73 -1.69 Td
(L;j)Tj
/T1_0 10.91 Tf
17.21 1.69 Td
[(that)-433(generated)-432(the)-433(in)26(v)56(alid)-432(signature)]TJ
-292.54 -21.92 Td
[(to)-484(a)-485(list)]TJ
/T1_4 10.91 Tf
45.6 0 Td
(BL)Tj
/T1_11 7.97 Tf
11.45 -1.63 Td
(X)Tj
/T1_0 10.91 Tf
10.02 1.63 Td
[(and)-484(broadcast)]TJ
/T1_5 10.91 Tf
74.28 0 Td
(f)Tj
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(S)Tj
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11.18 -1.68 Td
(L)Tj
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6.25 1.68 Td
(jj)Tj
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6.06 0 Td
(BL)Tj
/T1_11 7.97 Tf
11.45 -1.63 Td
(X)Tj
/T1_5 10.91 Tf
4.73 1.63 Td
(jj)Tj
/T1_0 10.91 Tf
6.65 0 Td
(\271)Tj
/T1_1 10.91 Tf
-0.59 0 Td
(\276)Tj
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6.62 3.96 Td
(0)Tj
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-0.39 -7.19 Td
(L;)Tj
/T1_7 7.97 Tf
(1)Tj
/T1_5 10.91 Tf
12.84 3.23 Td
(g)Tj
/T1_0 10.91 Tf
[(,)-521(where)-539(\271)]TJ
/T1_1 10.91 Tf
47.37 0 Td
(\276)Tj
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6.62 3.96 Td
(0)Tj
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-0.39 -7.19 Td
(L;)Tj
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(1)Tj
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18.62 3.23 Td
(=)Tj
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14.26 0 Td
(S)Tj
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7.42 0 Td
(\()Tj
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(S)Tj
/T1_3 7.97 Tf
9.97 -1.68 Td
(L)Tj
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6.25 1.68 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(\277)Tj
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6 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-1.23 -7.19 Td
(L)Tj
/T1_5 10.91 Tf
6.25 3.23 Td
(jj)Tj
/T1_4 10.91 Tf
6.06 0 Td
(BL)Tj
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11.45 -1.63 Td
(X)Tj
/T1_5 10.91 Tf
4.73 1.63 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(v)Tj
/T1_0 10.91 Tf
5.68 0 Td
[(\).)-898(Otherwise,)-522(if)-484(the)]TJ
-367.33 -21.91 Td
[(signature)-439(v)27(eri\257cations)-439(are)-440(correct,)-466(then)]TJ
/T1_4 10.91 Tf
196.61 0 Td
(S)Tj
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5.73 -1.69 Td
(L)Tj
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11.05 1.69 Td
(computes)Tj
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49.69 0 Td
(L)Tj
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7.42 3.96 Td
(0)Tj
/T1_3 7.97 Tf
T*
(L;)Tj
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(1)Tj
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17.81 3.23 Td
(=)Tj
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13.44 0 Td
(H)Tj
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7.73 0 Td
(\(\()Tj
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8.48 0 Td
(z)Tj
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5.55 3.96 Td
(0)Tj
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(L;n)Tj
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13.25 -1.34 Td
(L)Tj
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5.55 1.34 Td
(\241)Tj
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6.59 0 Td
(`)Tj
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3.95 3.32 Td
(\))Tj
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4.25 5.04 Td
(r)Tj
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4.05 2.81 Td
(0)Tj
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-0.23 -5.52 Td
(L;)Tj
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7.32 0 Td
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6.06 0 Td
(SID)Tj
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17.18 3.96 Td
(0)Tj
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T*
(L)Tj
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6.25 3.23 Td
[(\))-439(and)]TJ
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31.4 0 Td
(R)Tj
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8.37 3.96 Td
(0)Tj
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-0.08 -7.19 Td
(L;)Tj
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8.1 0 Td
(1)Tj
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9.7 3.23 Td
(=)Tj
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-459.39 -21.92 Td
(H)Tj
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7.73 0 Td
(\(\()Tj
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8.48 0 Td
(z)Tj
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5.55 3.96 Td
(0)Tj
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-0.48 -7.19 Td
(L;)Tj
/T1_7 7.97 Tf
(2)Tj
/T1_0 10.91 Tf
12.84 3.23 Td
(\))Tj
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4.24 5.04 Td
(r)Tj
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4.06 2.82 Td
(0)Tj
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-0.24 -5.52 Td
(L;)Tj
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(1)Tj
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11.98 -2.34 Td
(jj)Tj
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6.05 0 Td
(SID)Tj
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17.18 3.96 Td
(0)Tj
/T1_3 7.97 Tf
T*
(L)Tj
/T1_0 10.91 Tf
6.26 3.23 Td
[(\))-443(where)]TJ
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41.82 0 Td
(r)Tj
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5.22 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.3 -7.19 Td
(L;)Tj
/T1_7 7.97 Tf
(1)Tj
/T1_0 10.91 Tf
17.87 3.23 Td
(=)Tj
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13.52 0 Td
(r)Tj
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4.92 -1.69 Td
(L;)Tj
/T1_7 7.97 Tf
(1)Tj
/T1_0 10.91 Tf
17.68 1.69 Td
(if)Tj
/T1_4 10.91 Tf
11.2 0 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.69 Td
(L)Tj
/T1_1 10.91 Tf
12.5 1.69 Td
(=)Tj
/T1_5 10.91 Tf
-1.21 0 Td
[(2)-461(N)]TJ
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22.86 0 Td
(\()Tj
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(R)Tj
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13.48 0 Td
(\),)Tj
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12.41 0 Td
(z)Tj
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5.55 3.96 Td
(0)Tj
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-0.48 -7.28 Td
(L;n)Tj
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13.25 -1.34 Td
(L)Tj
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5.55 1.34 Td
(\241)Tj
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6.59 0 Td
(`)Tj
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8.99 3.32 Td
(=)Tj
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13.52 0 Td
(z)Tj
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5.07 -1.78 Td
(L;n)Tj
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13.25 -1.33 Td
(L)Tj
/T1_2 7.97 Tf
5.55 1.33 Td
(\241)Tj
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6.59 0 Td
(`)Tj
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8.79 1.78 Td
(if)Tj
/T1_4 10.91 Tf
11.2 0 Td
(V)Tj
/T1_3 7.97 Tf
5.73 -1.78 Td
(L;n)Tj
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13.24 -1.33 Td
(L)Tj
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5.56 1.33 Td
(\241)Tj
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(`)Tj
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16.79 1.78 Td
(=)Tj
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-1.22 0 Td
[(2)-462(N)]TJ
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22.87 0 Td
(\()Tj
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(R)Tj
/T1_0 10.91 Tf
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(V)Tj
/T1_1 7.97 Tf
5.72 -1.68 Td
(L;j)Tj
/T1_2 10.91 Tf
16.13 1.68 Td
[(from)-333(the)-333(GKA.)]TJ
/T1_4 10.91 Tf
-202.75 -30.88 Td
(\262)Tj
/T1_2 10.91 Tf
10.91 0 Td
[([In)28(v)55(alid)-374(X)27(OR)-375(Equation])-375(If)]TJ
/T1_0 10.91 Tf
129.97 0 Td
(S)Tj
/T1_1 7.97 Tf
5.73 -1.68 Td
(L)Tj
/T1_2 10.91 Tf
10.35 1.68 Td
[(detected)-375(an)-375(in)27(v)55(alid)-374(X)27(OR)-374(equation,)-386(then)-375(list)]TJ
/T1_0 10.91 Tf
215.89 0 Td
(BL)Tj
/T1_5 7.97 Tf
11.46 -1.63 Td
(X)Tj
/T1_2 10.91 Tf
8.82 1.63 Td
[(con)27(tains)-374(the)]TJ
-382.22 -21.91 Td
[(in)28(v)55(alid)-302(X)27(OR)-302(equation)-303(instead)-303(of)-303(in)27(v)56(alid)-302(users')-303(iden)27(tities.)-434(The)-303(detection)-303(proto)-27(col)-303(describ)-28(ed)-303(in)]TJ
0 -21.92 TD
[(Section)-370(9.3)-370(will)-371(b)-28(e)-371(used)-370(to)-371(detect)-371(and)-370(blo)-28(c)27(k)-370(malicious)-371(group)-370(mem)26(b)-26(ers)]TJ
/T1_3 10.91 Tf
341.84 1.97 Td
(e)Tj
/T1_0 10.91 Tf
0.16 -1.97 Td
(V)Tj
/T1_1 7.97 Tf
5.73 -1.69 Td
(L;j)Tj
/T1_2 10.91 Tf
16.53 1.69 Td
[(that)-370(sen)26(t)-369(wrong)]TJ
-364.26 -21.92 Td
[(information)-332(to)-334(disrupt)-333(the)-333(GKA.)]TJ
-27.27 -33.86 Td
[(F)83(or)-358(brevit)26(y)84(,)-365(w)27(e)-358(shall)-359(use)-360(the)-359(term)]TJ
/T1_3 10.91 Tf
166.13 1.97 Td
(e)Tj
/T1_0 10.91 Tf
0.17 -1.97 Td
(V)Tj
/T1_1 7.97 Tf
5.73 -1.69 Td
(L;j)Tj
/T1_2 10.91 Tf
16.4 1.69 Td
[(to)-359(denote)-359(in)27(v)55(alid)-358(users)-359(and)-359(malicious)-359(group)-360(mem)27(b)-27(ers.)-522(Af-)]TJ
-188.43 -21.92 Td
[(ter)-368(detecting)-368(all)-368(in)26(v)56(alid)-367(users)-369(and)-368(malicious)-368(group)-369(mem)27(b)-27(ers)]TJ
/T1_3 10.91 Tf
291.43 1.97 Td
(e)Tj
/T1_0 10.91 Tf
0.16 -1.97 Td
(V)Tj
/T1_1 7.97 Tf
5.73 -1.69 Td
(L;j)Tj
/T1_2 10.91 Tf
12.49 1.69 Td
[(,)-377(the)-368(honest)-368(left)-368(neigh)26(b)-26(or)]TJ
/T1_0 10.91 Tf
126 0 Td
(V)Tj
/T1_1 7.97 Tf
5.72 -1.69 Td
(L;j)Tj
/T1_6 7.97 Tf
12 0 Td
(\241)Tj
/T1_7 7.97 Tf
(1)Tj
/T1_2 10.91 Tf
11.31 1.69 Td
(,)Tj
-464.84 -21.92 Td
[(whic)27(h)-422(has)-424(not)-424(b)-27(een)-424(blo)-28(c)27(k)28(ed,)-445(of)]TJ
/T1_3 10.91 Tf
156.61 1.97 Td
(e)Tj
/T1_0 10.91 Tf
0.17 -1.97 Td
(V)Tj
/T1_1 7.97 Tf
5.72 -1.69 Td
(L;j)Tj
/T1_2 10.91 Tf
17.11 1.69 Td
[(will)-423(re-compute)]TJ
/T1_8 10.91 Tf
79.56 0 Td
(L)Tj
/T1_6 7.97 Tf
7.42 3.96 Td
(0)Tj
/T1_1 7.97 Tf
0 -7.19 TD
(L;j)Tj
/T1_6 7.97 Tf
11.99 0 Td
(\241)Tj
/T1_7 7.97 Tf
6.59 0 Td
(1)Tj
/T1_2 10.91 Tf
9.4 3.23 Td
(=)Tj
/T1_9 10.91 Tf
13.15 0 Td
(H)Tj
/T1_2 10.91 Tf
7.73 0 Td
(\(\()Tj
/T1_8 10.91 Tf
8.48 0 Td
(z)Tj
/T1_6 7.97 Tf
5.55 3.96 Td
(0)Tj
/T1_1 7.97 Tf
-0.48 -7.19 Td
(L;j)Tj
/T1_6 7.97 Tf
11.99 0 Td
(\241)Tj
/T1_7 7.97 Tf
6.59 0 Td
(2)Tj
/T1_2 10.91 Tf
4.73 3.23 Td
(\))Tj
/T1_1 7.97 Tf
4.24 5.04 Td
(r)Tj
/T1_10 5.98 Tf
4.05 2.82 Td
(0)Tj
/T1_11 5.98 Tf
-0.23 -5.52 Td
(L;j)Tj
/T1_10 5.98 Tf
10.73 0 Td
(\241)Tj
/T1_12 5.98 Tf
5.75 0 Td
(1)Tj
/T1_4 10.91 Tf
4.65 -2.34 Td
(jj)Tj
/T1_13 10.91 Tf
7.48 3.14 Td
(])Tj
/T1_0 10.91 Tf
-1.42 -3.14 Td
(SID)Tj
/T1_6 7.97 Tf
17.18 3.76 Td
(0)Tj
/T1_1 7.97 Tf
T*
(L)Tj
/T1_2 10.91 Tf
6.25 3.43 Td
(\),)Tj
/T1_8 10.91 Tf
12.14 0 Td
(R)Tj
/T1_6 7.97 Tf
8.36 3.96 Td
(0)Tj
/T1_1 7.97 Tf
-0.08 -7.19 Td
(L;j)Tj
/T1_6 7.97 Tf
11.99 0 Td
(\241)Tj
/T1_7 7.97 Tf
6.59 0 Td
(1)Tj
/T1_2 10.91 Tf
9.4 3.23 Td
(=)Tj
/T1_9 10.91 Tf
-459.39 -21.91 Td
(H)Tj
/T1_2 10.91 Tf
7.73 0 Td
(\(\()Tj
/T1_8 10.91 Tf
8.48 0 Td
(z)Tj
/T1_6 7.97 Tf
5.55 3.95 Td
(0)Tj
/T1_1 7.97 Tf
-0.48 -7.19 Td
(L;j)Tj
/T1_7 7.97 Tf
11.99 0 Td
(+1)Tj
/T1_2 10.91 Tf
11.32 3.24 Td
(\))Tj
/T1_1 7.97 Tf
4.24 5.04 Td
(r)Tj
/T1_10 5.98 Tf
4.05 2.81 Td
(0)Tj
/T1_11 5.98 Tf
-0.23 -5.52 Td
(L;j)Tj
/T1_10 5.98 Tf
10.73 0 Td
(\241)Tj
/T1_12 5.98 Tf
5.75 0 Td
(1)Tj
/T1_4 10.91 Tf
4.65 -2.33 Td
(jj)Tj
/T1_13 10.91 Tf
7.48 3.13 Td
(])Tj
/T1_0 10.91 Tf
-1.42 -3.13 Td
(SID)Tj
/T1_6 7.97 Tf
17.18 3.75 Td
(0)Tj
/T1_1 7.97 Tf
T*
(L)Tj
/T1_2 10.91 Tf
6.25 3.44 Td
(\),)Tj
/T1_8 10.91 Tf
10.62 0 Td
(X)Tj
/T1_6 7.97 Tf
9.89 3.95 Td
(0)Tj
/T1_1 7.97 Tf
-0.85 -7.19 Td
(L;j)Tj
/T1_6 7.97 Tf
11.99 0 Td
(\241)Tj
/T1_7 7.97 Tf
(1)Tj
/T1_2 10.91 Tf
14.34 3.24 Td
(=)Tj
/T1_8 10.91 Tf
11.52 0 Td
(L)Tj
/T1_6 7.97 Tf
7.42 3.95 Td
(0)Tj
/T1_1 7.97 Tf
T*
(L;j)Tj
/T1_6 7.97 Tf
11.99 0 Td
(\241)Tj
/T1_7 7.97 Tf
(1)Tj
/T1_4 10.91 Tf
13.02 3.24 Td
(\251)Tj
/T1_8 10.91 Tf
10.19 0 Td
(R)Tj
/T1_6 7.97 Tf
8.36 3.95 Td
(0)Tj
/T1_1 7.97 Tf
-0.08 -7.19 Td
(L;j)Tj
/T1_6 7.97 Tf
11.99 0 Td
(\241)Tj
/T1_7 7.97 Tf
(1)Tj
/T1_2 10.91 Tf
14.59 3.24 Td
[(and)-300(transmit)]TJ
/T1_8 10.91 Tf
64.81 0 Td
(X)Tj
/T1_6 7.97 Tf
9.89 3.95 Td
(0)Tj
/T1_1 7.97 Tf
-0.86 -7.19 Td
(L;j)Tj
/T1_6 7.97 Tf
12 0 Td
(\241)Tj
/T1_7 7.97 Tf
(1)Tj
/T1_2 10.91 Tf
14.59 3.24 Td
[(with)-300(signature,)-307(where)]TJ
/T1_13 10.91 Tf
107.16 3.13 Td
(])Tj
/T1_0 10.91 Tf
-1.41 -3.13 Td
(SID)Tj
/T1_6 7.97 Tf
17.18 3.75 Td
(0)Tj
/T1_1 7.97 Tf
T*
(L)Tj
/T1_2 10.91 Tf
-461.62 -18.48 Td
[(is)-418(equal)-418(to)]TJ
/T1_0 10.91 Tf
55.86 0 Td
(SID)Tj
/T1_6 7.97 Tf
17.18 3.96 Td
(0)Tj
/T1_1 7.97 Tf
T*
(L)Tj
/T1_2 10.91 Tf
10.82 3.23 Td
[(excluding)-418(the)-418(iden)27(tities)-418(of)-418(the)-418(discarded)-419(users)-418(in)]TJ
/T1_0 10.91 Tf
241.9 0 Td
(BL)Tj
/T1_5 7.97 Tf
11.45 -1.64 Td
(X)Tj
/T1_2 10.91 Tf
4.73 1.64 Td
[(.)-699(The)-419(honest)-418(righ)27(t)-418(neigh-)]TJ
-341.94 -21.92 Td
[(b)-27(or)]TJ
/T1_0 10.91 Tf
20.18 0 Td
(V)Tj
/T1_1 7.97 Tf
5.72 -1.68 Td
(L;j)Tj
/T1_7 7.97 Tf
11.99 0 Td
(+1)Tj
/T1_2 10.91 Tf
11.32 1.68 Td
[(,)-385(whic)27(h)-374(has)-375(not)-375(b)-28(een)-375(blo)-28(c)27(k)28(ed,)-385(of)]TJ
/T1_3 10.91 Tf
160.53 1.97 Td
(e)Tj
/T1_0 10.91 Tf
0.17 -1.97 Td
(V)Tj
/T1_1 7.97 Tf
5.72 -1.68 Td
(L;j)Tj
/T1_2 10.91 Tf
16.58 1.68 Td
[(will)-375(re-compute)]TJ
/T1_8 10.91 Tf
78.5 0 Td
(L)Tj
/T1_6 7.97 Tf
7.42 3.96 Td
(0)Tj
/T1_1 7.97 Tf
T*
(L;j)Tj
/T1_7 7.97 Tf
11.99 0 Td
(+1)Tj
/T1_2 10.91 Tf
15.1 3.23 Td
(=)Tj
/T1_9 10.91 Tf
12.27 0 Td
(H)Tj
/T1_2 10.91 Tf
7.73 0 Td
(\(\()Tj
/T1_8 10.91 Tf
8.48 0 Td
(z)Tj
/T1_6 7.97 Tf
5.55 3.96 Td
(0)Tj
/T1_1 7.97 Tf
-0.48 -7.19 Td
(L;j)Tj
/T1_6 7.97 Tf
12 0 Td
(\241)Tj
/T1_7 7.97 Tf
(1)Tj
/T1_2 10.91 Tf
11.31 3.23 Td
(\))Tj
/T1_1 7.97 Tf
4.24 5.05 Td
(r)Tj
/T1_10 5.98 Tf
4.06 2.81 Td
(0)Tj
/T1_11 5.98 Tf
-0.24 -5.52 Td
(L;j)Tj
/T1_12 5.98 Tf
10.73 0 Td
(+1)Tj
/T1_4 10.91 Tf
10.24 -2.34 Td
(jj)Tj
/T1_13 10.91 Tf
7.47 3.14 Td
(])Tj
/T1_0 10.91 Tf
-1.41 -3.14 Td
(SID)Tj
/T1_6 7.97 Tf
17.17 3.76 Td
(0)Tj
/T1_1 7.97 Tf
T*
(L)Tj
/T1_2 10.91 Tf
6.26 3.43 Td
(\),)Tj
/T1_8 10.91 Tf
-460.6 -21.91 Td
(R)Tj
/T1_6 7.97 Tf
8.37 3.96 Td
(0)Tj
/T1_1 7.97 Tf
-0.09 -7.19 Td
(L;j)Tj
/T1_7 7.97 Tf
11.99 0 Td
(+1)Tj
/T1_2 10.91 Tf
14.35 3.23 Td
(=)Tj
/T1_9 10.91 Tf
11.51 0 Td
(H)Tj
/T1_2 10.91 Tf
7.73 0 Td
(\(\()Tj
/T1_8 10.91 Tf
8.48 0 Td
(z)Tj
/T1_6 7.97 Tf
5.55 3.96 Td
(0)Tj
/T1_1 7.97 Tf
-0.48 -7.19 Td
(L;j)Tj
/T1_7 7.97 Tf
11.99 0 Td
(+2)Tj
/T1_2 10.91 Tf
11.32 3.23 Td
(\))Tj
/T1_1 7.97 Tf
4.24 5.04 Td
(r)Tj
/T1_10 5.98 Tf
4.05 2.81 Td
(0)Tj
/T1_11 5.98 Tf
-0.23 -5.52 Td
(L;j)Tj
/T1_12 5.98 Tf
10.73 0 Td
(+1)Tj
/T1_4 10.91 Tf
10.23 -2.33 Td
(jj)Tj
/T1_13 10.91 Tf
7.48 3.13 Td
(])Tj
/T1_0 10.91 Tf
-1.42 -3.13 Td
(SID)Tj
/T1_6 7.97 Tf
17.18 3.75 Td
(0)Tj
/T1_1 7.97 Tf
T*
(L)Tj
/T1_2 10.91 Tf
6.26 3.44 Td
(\),)Tj
/T1_8 10.91 Tf
10.54 0 Td
(X)Tj
/T1_6 7.97 Tf
9.89 3.96 Td
(0)Tj
/T1_1 7.97 Tf
-0.85 -7.19 Td
(L;j)Tj
/T1_7 7.97 Tf
11.99 0 Td
(+1)Tj
/T1_2 10.91 Tf
14.34 3.23 Td
(=)Tj
/T1_8 10.91 Tf
11.52 0 Td
(L)Tj
/T1_6 7.97 Tf
7.42 3.96 Td
(0)Tj
/T1_1 7.97 Tf
T*
(L;j)Tj
/T1_7 7.97 Tf
11.99 0 Td
(+1)Tj
/T1_4 10.91 Tf
12.84 3.23 Td
(\251)Tj
/T1_8 10.91 Tf
10.01 0 Td
(R)Tj
/T1_6 7.97 Tf
8.36 3.96 Td
(0)Tj
/T1_1 7.97 Tf
-0.08 -7.19 Td
(L;j)Tj
/T1_7 7.97 Tf
11.99 0 Td
(+1)Tj
/T1_2 10.91 Tf
14.5 3.23 Td
[(and)-292(transmit)]TJ
/T1_8 10.91 Tf
64.63 0 Td
(X)Tj
/T1_6 7.97 Tf
9.89 3.96 Td
(0)Tj
/T1_1 7.97 Tf
-0.86 -7.19 Td
(L;j)Tj
/T1_7 7.97 Tf
12 0 Td
(+1)Tj
/T1_2 10.91 Tf
14.5 3.23 Td
[(with)-291(signature.)-431(It)]TJ
-383.86 -21.92 Td
[(should)-266(b)-28(e)-267(noted)-267(that)-267(if)-267(left)-267(neigh)27(b)-27(or)]TJ
/T1_0 10.91 Tf
172.24 0 Td
(V)Tj
/T1_1 7.97 Tf
5.73 -1.69 Td
(L;j)Tj
/T1_6 7.97 Tf
11.99 0 Td
(\241)Tj
/T1_7 7.97 Tf
(1)Tj
/T1_2 10.91 Tf
14.23 1.69 Td
(of)Tj
/T1_3 10.91 Tf
11.52 1.97 Td
(e)Tj
/T1_0 10.91 Tf
0.17 -1.97 Td
(V)Tj
/T1_1 7.97 Tf
5.73 -1.69 Td
(L;j)Tj
/T1_2 10.91 Tf
15.4 1.69 Td
[(is)-266(also)-267(an)-267(in)27(v)55(alid)-265(user)-267(or)-267(malicious)-267(group)-267(mem)27(b)-27(er)]TJ
-237.01 -21.92 Td
[(that)-286(has)-286(b)-28(een)-286(blo)-28(c)27(k)28(ed,)-295(then)-286(w)27(e)-285(set)]TJ
/T1_0 10.91 Tf
165.67 0 Td
(V)Tj
/T1_1 7.97 Tf
5.73 -1.68 Td
(L;j)Tj
/T1_6 7.97 Tf
11.99 0 Td
(\241)Tj
/T1_7 7.97 Tf
(2)Tj
/T1_2 10.91 Tf
14.34 1.68 Td
(=)Tj
/T1_0 10.91 Tf
11.51 0 Td
(V)Tj
/T1_1 7.97 Tf
5.73 -1.68 Td
(L;j)Tj
/T1_6 7.97 Tf
11.99 0 Td
(\241)Tj
/T1_7 7.97 Tf
6.59 0 Td
(1)Tj
/T1_2 10.91 Tf
4.73 1.68 Td
[(.)-428(Similarly)82(,)-294(if)-287(righ)27(t)-285(neigh)27(b)-27(or)]TJ
/T1_0 10.91 Tf
135.5 0 Td
(V)Tj
/T1_1 7.97 Tf
5.73 -1.68 Td
(L;j)Tj
/T1_7 7.97 Tf
11.99 0 Td
(+1)Tj
/T1_2 10.91 Tf
14.44 1.68 Td
(of)Tj
/T1_3 10.91 Tf
11.74 1.97 Td
(e)Tj
/T1_0 10.91 Tf
0.16 -1.97 Td
(V)Tj
/T1_1 7.97 Tf
5.73 -1.68 Td
(L;j)Tj
/T1_2 10.91 Tf
15.61 1.68 Td
[(is)-286(also)]TJ
-439.18 -21.91 Td
[(an)-310(in)26(v)56(alid)-310(user)-311(or)-310(malicious)-311(group)-311(mem)27(b)-27(er)-311(that)-310(has)-311(b)-28(een)-311(blo)-28(c)27(k)28(ed,)-314(then)-311(w)27(e)-310(set)]TJ
/T1_0 10.91 Tf
373.23 0 Td
(V)Tj
/T1_1 7.97 Tf
5.73 -1.69 Td
(L;j)Tj
/T1_7 7.97 Tf
11.99 0 Td
(+2)Tj
/T1_2 10.91 Tf
14.34 1.69 Td
(=)Tj
/T1_0 10.91 Tf
11.51 0 Td
(V)Tj
/T1_1 7.97 Tf
5.73 -1.69 Td
(L;j)Tj
/T1_7 7.97 Tf
11.99 0 Td
(+1)Tj
/T1_2 10.91 Tf
11.32 1.69 Td
[(.)-436(All)]TJ
-445.84 -21.92 Td
[(other)-327(users)]TJ
/T1_0 10.91 Tf
55.79 0 Td
(V)Tj
/T1_1 7.97 Tf
5.73 -1.69 Td
(L;j)Tj
/T1_2 10.91 Tf
16.06 1.69 Td
[(will)-326(use)-328(the)-327(new)-327(session)-328(iden)27(tit)28(y)]TJ
/T1_13 10.91 Tf
157.88 3.14 Td
(])Tj
/T1_0 10.91 Tf
-1.41 -3.14 Td
(SID)Tj
/T1_6 7.97 Tf
17.17 3.76 Td
(0)Tj
/T1_1 7.97 Tf
T*
(L)Tj
/T1_2 10.91 Tf
9.83 3.43 Td
[(to)-327(re-compute)]TJ
/T1_8 10.91 Tf
70.18 0 Td
(L)Tj
/T1_6 7.97 Tf
7.42 3.96 Td
(0)Tj
/T1_1 7.97 Tf
T*
(L;j)Tj
/T1_2 10.91 Tf
12.49 3.23 Td
(,)Tj
/T1_8 10.91 Tf
6.61 0 Td
(R)Tj
/T1_6 7.97 Tf
8.37 3.96 Td
(0)Tj
/T1_1 7.97 Tf
-0.09 -7.19 Td
(L;j)Tj
/T1_2 10.91 Tf
12.49 3.23 Td
(,)Tj
/T1_8 10.91 Tf
6.62 0 Td
(X)Tj
/T1_6 7.97 Tf
9.89 3.96 Td
(0)Tj
/T1_1 7.97 Tf
-0.86 -7.19 Td
(L;j)Tj
/T1_2 10.91 Tf
16.06 3.23 Td
[(as)-327(in)-327(Round)]TJ
-410.23 -21.91 Td
[(4)-384(and)-384(transmit)]TJ
/T1_8 10.91 Tf
76.28 0 Td
(X)Tj
/T1_6 7.97 Tf
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6.06 0 Td
(c)Tj
/T1_5 7.97 Tf
5.73 3.96 Td
(0)Tj
/T1_3 7.97 Tf
0 -7.01 TD
(i)Tj
/T1_1 10.91 Tf
3.38 3.05 Td
(jj)Tj
/T1_2 10.91 Tf
6.06 0 Td
(\265)Tj
/T1_5 7.97 Tf
5.42 3.96 Td
(0)Tj
/T1_6 7.97 Tf
-0.3 -6.65 Td
(C)Tj
/T1_1 10.91 Tf
4.73 2.69 Td
(jj)Tj
/T1_2 10.91 Tf
6.06 0 Td
(\276)Tj
/T1_5 7.97 Tf
6.62 3.96 Td
(0)Tj
/T1_6 7.97 Tf
-0.39 -6.65 Td
(C)Tj
/T1_1 10.91 Tf
4.73 2.69 Td
(g)Tj
/T1_0 10.91 Tf
10.65 0 Td
(for)Tj
-454.81 -21.91 Td
(1)Tj
/T1_1 10.91 Tf
8.48 0 Td
(\267)Tj
/T1_2 10.91 Tf
11.51 0 Td
(i)Tj
/T1_1 10.91 Tf
6.79 0 Td
(6)Tj
/T1_0 10.91 Tf
(=)Tj
/T1_2 10.91 Tf
11.51 0 Td
(L)Tj
/T1_1 10.91 Tf
10.45 0 Td
(\267)Tj
/T1_2 10.91 Tf
11.52 0 Td
(n)Tj
/T1_3 7.97 Tf
6.54 -1.64 Td
(c)Tj
/T1_0 10.91 Tf
4.17 1.64 Td
[(,)-333(where)]TJ
/T1_2 10.91 Tf
38.2 0 Td
(\276)Tj
/T1_5 7.97 Tf
6.62 3.96 Td
(0)Tj
/T1_6 7.97 Tf
-0.39 -6.66 Td
(C)Tj
/T1_0 10.91 Tf
7.76 2.7 Td
(=)Tj
/T1_1 10.91 Tf
11.51 0 Td
(S)Tj
/T1_0 10.91 Tf
7.43 0 Td
(\()Tj
/T1_4 10.91 Tf
(C)Tj
/T1_1 10.91 Tf
9.96 0 Td
(jj)Tj
/T1_2 10.91 Tf
6.06 0 Td
(y)Tj
/T1_5 7.97 Tf
5.74 3.96 Td
(0)Tj
/T1_6 7.97 Tf
-0.39 -6.66 Td
(C)Tj
/T1_1 10.91 Tf
4.73 2.7 Td
(jj)Tj
/T1_2 10.91 Tf
6.06 0 Td
(\265)Tj
/T1_5 7.97 Tf
5.42 3.96 Td
(0)Tj
/T1_6 7.97 Tf
-0.3 -6.66 Td
(C)Tj
/T1_0 10.91 Tf
4.73 2.7 Td
(\).)Tj
/T1_7 10.91 Tf
-184.11 -27.89 Td
[(Phase)-383(3:)-511(Distributing)-383(the)-384(Final)-383(Group)-383(Key)]TJ
/T1_0 10.91 Tf
0 -27.9 TD
[(Round)-333(1)]TJ
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 0 -90.18 cm
0 0 m
40.75 0 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 116.3924 681.1352 Tm
(:)Tj
-44.38 -21.91 Td
(\()Tj
/T1_2 10.91 Tf
(i)Tj
/T1_0 10.91 Tf
(\))Tj
/T1_4 10.91 Tf
15.89 0 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.69 Td
(L)Tj
/T1_0 10.91 Tf
9.91 1.69 Td
(\257rst)Tj
1.0003 0 0 1.0003 72 769.82 Tm
54.059 -110.57 Td
[(v)27(eri\257es)-334(signature)]TJ
/T1_2 10.91 Tf
83.821 0 Td
(\276)Tj
/T1_5 7.97 Tf
6.63 3.95 Td
(0)Tj
/T1_6 7.97 Tf
-0.39 -6.65 Td
(C)Tj
/T1_0 10.91 Tf
4.73 2.7 Td
[(.)-449(If)-335(the)-335(v)27(eri\257cation)-334(is)-335(not)-335(correct,)-335(then)]TJ
/T1_4 10.91 Tf
188.76 0 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.69 Td
(L)Tj
/T1_0 10.91 Tf
9.91 1.69 Td
(rejects)Tj
/T1_4 10.91 Tf
34.34 0 Td
(C)Tj
/T1_0 10.91 Tf
[(.)-448(Otherwise,)]TJ
/T1_4 10.91 Tf
68.3 0 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.69 Td
(L)Tj
/T1_0 10.91 Tf
-461.62 -20.23 Td
[(computes)-237(new)-237(DH)-237(k)27(ey)]TJ
/T1_2 10.91 Tf
106.59 0 Td
(T)Tj
/T1_5 7.97 Tf
7.89 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-1.52 -7.19 Td
(L)Tj
/T1_0 10.91 Tf
9.29 3.23 Td
[(=)-277(\()]TJ
/T1_2 10.91 Tf
(y)Tj
/T1_5 7.97 Tf
21.49 3.96 Td
(0)Tj
/T1_6 7.97 Tf
-0.39 -6.66 Td
(C)Tj
/T1_0 10.91 Tf
4.73 2.7 Td
(\))Tj
/T1_3 7.97 Tf
4.24 3.96 Td
(K)Tj
/T1_8 5.98 Tf
7.7 2.81 Td
(0)Tj
/T1_9 5.98 Tf
-0.56 -5.52 Td
(L)Tj
/T1_0 10.91 Tf
9.08 -1.25 Td
[(mo)-28(d)]TJ
/T1_2 10.91 Tf
23.94 0 Td
(p)Tj
/T1_0 10.91 Tf
8.07 0 Td
[(shared)-237(with)]TJ
/T1_4 10.91 Tf
57.37 0 Td
(C)Tj
/T1_0 10.91 Tf
[(.)-412(Next,)]TJ
/T1_4 10.91 Tf
42.1 0 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.69 Td
(L)Tj
/T1_0 10.91 Tf
8.84 1.69 Td
(uses)Tj
/T1_2 10.91 Tf
22.1 0 Td
(T)Tj
/T1_5 7.97 Tf
7.89 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-1.52 -7.19 Td
(L)Tj
/T1_0 10.91 Tf
8.84 3.23 Td
[(to)-237(decrypt)]TJ
/T1_4 10.91 Tf
50.95 0 Td
(c)Tj
/T1_5 7.97 Tf
5.73 3.96 Td
(0)Tj
/T1_3 7.97 Tf
0 -7.19 TD
(L)Tj
/T1_0 10.91 Tf
8.84 3.23 Td
[(and)-237(obtain)]TJ
-417.42 -21.92 Td
[(the)-303(new)-304(\257nal)-304(group)-304(k)26(ey)]TJ
/T1_2 10.91 Tf
114.46 0 Td
(K)Tj
/T1_5 7.97 Tf
10.04 3.96 Td
(0)Tj
/T1_0 10.91 Tf
2.8 -3.96 Td
(.)Tj
/T1_4 10.91 Tf
7.77 0 Td
(S)Tj
/T1_3 7.97 Tf
5.72 -1.68 Td
(L)Tj
/T1_0 10.91 Tf
9.57 1.68 Td
[(then)-304(con\257rms)-304(and)-304(accepts)-304(the)-304(\257nal)-304(group)-304(k)27(ey)]TJ
/T1_2 10.91 Tf
219.08 0 Td
(K)Tj
/T1_5 7.97 Tf
10.04 3.96 Td
(0)Tj
/T1_0 10.91 Tf
6.11 -3.96 Td
(if)Tj
/T1_10 10.91 Tf
9.68 0 Td
(H)Tj
/T1_0 10.91 Tf
(\()Tj
/T1_2 10.91 Tf
(K)Tj
/T1_5 7.97 Tf
22.01 3.96 Td
(0)Tj
/T1_1 10.91 Tf
2.79 -3.96 Td
(jj)Tj
/T1_2 10.91 Tf
6.06 0 Td
(y)Tj
/T1_5 7.97 Tf
5.74 3.96 Td
(0)Tj
/T1_6 7.97 Tf
-0.39 -6.65 Td
(C)Tj
/T1_0 10.91 Tf
4.73 2.69 Td
[(\))-277(=)]TJ
/T1_2 10.91 Tf
18.78 0 Td
(\265)Tj
/T1_5 7.97 Tf
5.42 3.96 Td
(0)Tj
/T1_6 7.97 Tf
-0.3 -6.65 Td
(C)Tj
/T1_0 10.91 Tf
4.73 2.69 Td
(.)Tj
-464.84 -21.91 Td
(Next,)Tj
/T1_4 10.91 Tf
31.05 0 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.69 Td
(L)Tj
/T1_0 10.91 Tf
10.97 1.69 Td
(encrypts)Tj
/T1_2 10.91 Tf
45.11 0 Td
(K)Tj
/T1_5 7.97 Tf
10.04 3.95 Td
(0)Tj
/T1_1 10.91 Tf
2.8 -3.95 Td
(jj)Tj
/T1_4 10.91 Tf
6.06 0 Td
(S)Tj
/T1_3 7.97 Tf
5.72 -1.69 Td
(L)Tj
/T1_0 10.91 Tf
10.98 1.69 Td
[(using)-433(new)-433(subgroup)-433(k)27(ey)]TJ
/T1_2 10.91 Tf
122.35 0 Td
(K)Tj
/T1_5 7.97 Tf
10.05 3.95 Td
(0)Tj
/T1_3 7.97 Tf
-0.78 -7.18 Td
(L)Tj
/T1_0 10.91 Tf
10.98 3.23 Td
[(and)-432(obtains)-446(\271)]TJ
/T1_4 10.91 Tf
61.61 0 Td
(c)Tj
/T1_5 7.97 Tf
5.73 3.95 Td
(0)Tj
/T1_3 7.97 Tf
0 -7.18 TD
(L)Tj
/T1_0 10.91 Tf
11.1 3.23 Td
(=)Tj
/T1_1 10.91 Tf
13.32 0 Td
(E)Tj
/T1_3 7.97 Tf
5.76 -2.31 Td
(K)Tj
/T1_8 5.98 Tf
7.7 2.74 Td
(0)Tj
/T1_9 5.98 Tf
-0.56 -5.51 Td
(L)Tj
/T1_0 10.91 Tf
6.05 5.08 Td
(\()Tj
/T1_2 10.91 Tf
(K)Tj
/T1_5 7.97 Tf
14.29 3.95 Td
(0)Tj
/T1_1 10.91 Tf
2.79 -3.95 Td
(jj)Tj
/T1_4 10.91 Tf
6.06 0 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.69 Td
(L)Tj
/T1_0 10.91 Tf
6.25 1.69 Td
[(\).)-743(Finally)82(,)]TJ
/T1_4 10.91 Tf
-416.89 -21.92 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.69 Td
(L)Tj
/T1_0 10.91 Tf
11.04 1.69 Td
[(computes)-439(k)27(ey)-439(con\257rmation)-439(co)-28(de)]TJ
/T1_2 10.91 Tf
161.64 0 Td
(\265)Tj
/T1_5 7.97 Tf
5.43 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.31 -7.19 Td
(L)Tj
/T1_0 10.91 Tf
11.21 3.23 Td
(=)Tj
/T1_10 10.91 Tf
13.44 0 Td
(H)Tj
/T1_0 10.91 Tf
7.73 0 Td
(\()Tj
/T1_2 10.91 Tf
(K)Tj
/T1_5 7.97 Tf
14.28 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.78 -7.19 Td
(L)Tj
/T1_1 10.91 Tf
6.26 3.23 Td
(jj)Tj
/T1_2 10.91 Tf
6.06 0 Td
(K)Tj
/T1_5 7.97 Tf
10.04 3.96 Td
(0)Tj
/T1_1 10.91 Tf
2.79 -3.96 Td
(jj)Tj
/T1_2 10.91 Tf
6.06 0 Td
(\277)Tj
/T1_5 7.97 Tf
6 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-1.23 -7.19 Td
(L)Tj
/T1_0 10.91 Tf
6.25 3.23 Td
[(\))-439(and)-440(broadcasts)]TJ
/T1_1 10.91 Tf
86.63 0 Td
(f)Tj
/T1_4 10.91 Tf
(S)Tj
/T1_3 7.97 Tf
11.18 -1.69 Td
(L)Tj
/T1_1 10.91 Tf
6.25 1.69 Td
(jj)Tj
/T1_0 10.91 Tf
6.2 0 Td
(\271)Tj
/T1_4 10.91 Tf
-0.14 0 Td
(c)Tj
/T1_5 7.97 Tf
5.73 3.96 Td
(0)Tj
/T1_3 7.97 Tf
0 -7.19 TD
(L)Tj
/T1_1 10.91 Tf
6.25 3.23 Td
(jj)Tj
/T1_2 10.91 Tf
6.06 0 Td
(\265)Tj
/T1_5 7.97 Tf
5.43 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.31 -7.19 Td
(L)Tj
/T1_1 10.91 Tf
6.26 3.23 Td
(jj)Tj
/T1_0 10.91 Tf
6.64 0 Td
(\271)Tj
/T1_2 10.91 Tf
-0.58 0 Td
(\276)Tj
/T1_5 7.97 Tf
6.62 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.39 -7.19 Td
(L)Tj
/T1_1 10.91 Tf
6.26 3.23 Td
(g)Tj
/T1_0 10.91 Tf
10.24 0 Td
(where)Tj
-439.38 -21.92 Td
(\271)Tj
/T1_2 10.91 Tf
-0.59 0 Td
(\276)Tj
/T1_5 7.97 Tf
6.62 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.39 -7.19 Td
(L)Tj
/T1_0 10.91 Tf
9.29 3.23 Td
(=)Tj
/T1_1 10.91 Tf
11.51 0 Td
(S)Tj
/T1_0 10.91 Tf
7.42 0 Td
(\()Tj
/T1_4 10.91 Tf
(S)Tj
/T1_3 7.97 Tf
9.97 -1.68 Td
(L)Tj
/T1_1 10.91 Tf
6.25 1.68 Td
(jj)Tj
/T1_2 10.91 Tf
6.06 0 Td
(\277)Tj
/T1_5 7.97 Tf
6 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-1.23 -7.19 Td
(L)Tj
/T1_1 10.91 Tf
6.26 3.23 Td
(jj)Tj
/T1_2 10.91 Tf
6.05 0 Td
(\265)Tj
/T1_5 7.97 Tf
5.43 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.31 -7.19 Td
(L)Tj
/T1_1 10.91 Tf
6.26 3.23 Td
(jj)Tj
/T1_2 10.91 Tf
6.06 0 Td
(v)Tj
/T1_0 10.91 Tf
5.68 0 Td
[(\))-332(to)-334(subgroup)-333(mem)27(b)-27(ers)]TJ
/T1_4 10.91 Tf
114.69 0 Td
(V)Tj
/T1_3 7.97 Tf
5.73 -1.68 Td
(L;j)Tj
/T1_0 10.91 Tf
16.12 1.68 Td
[(for)-333(2)]TJ
/T1_1 10.91 Tf
25.18 0 Td
(\267)Tj
/T1_2 10.91 Tf
11.51 0 Td
(j)Tj
/T1_1 10.91 Tf
8.14 0 Td
(\267)Tj
/T1_2 10.91 Tf
11.52 0 Td
(n)Tj
/T1_3 7.97 Tf
6.54 -1.68 Td
(L)Tj
/T1_1 10.91 Tf
8.68 1.68 Td
(\241)Tj
/T1_2 10.91 Tf
10.91 0 Td
(`)Tj
/T1_0 10.91 Tf
4.54 0 Td
(.)Tj
-320.49 -21.91 Td
(\()Tj
/T1_2 10.91 Tf
(ii)Tj
/T1_0 10.91 Tf
[(\))-402(All)-403(other)]TJ
/T1_4 10.91 Tf
68.29 0 Td
(S)Tj
/T1_3 7.97 Tf
5.72 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
7.77 1.64 Td
[(for)-403(1)]TJ
/T1_1 10.91 Tf
27.2 0 Td
(\267)Tj
/T1_2 10.91 Tf
12.77 0 Td
(i)Tj
/T1_1 10.91 Tf
8.05 0 Td
(6)Tj
/T1_0 10.91 Tf
(=)Tj
/T1_2 10.91 Tf
12.78 0 Td
(L)Tj
/T1_1 10.91 Tf
11.71 0 Td
(\267)Tj
/T1_2 10.91 Tf
12.77 0 Td
(n)Tj
/T1_3 7.97 Tf
6.55 -1.64 Td
(c)Tj
/T1_0 10.91 Tf
8.56 1.64 Td
[(\257rst)-402(v)27(eri\257es)-402(signature)]TJ
/T1_2 10.91 Tf
108.57 0 Td
(\276)Tj
/T1_5 7.97 Tf
6.63 3.96 Td
(0)Tj
/T1_6 7.97 Tf
-0.4 -6.66 Td
(C)Tj
/T1_0 10.91 Tf
4.74 2.7 Td
[(.)-652(If)-403(the)-402(v)26(eri\257cation)-401(is)-403(not)-403(correct,)]TJ
-301.71 -21.92 Td
(then)Tj
/T1_4 10.91 Tf
25.11 0 Td
(S)Tj
/T1_3 7.97 Tf
5.72 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
7.28 1.63 Td
(rejects)Tj
/T1_4 10.91 Tf
34.59 0 Td
(C)Tj
/T1_0 10.91 Tf
[(.)-517(Otherwise,)]TJ
/T1_4 10.91 Tf
69.36 0 Td
(S)Tj
/T1_3 7.97 Tf
5.72 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
7.28 1.63 Td
[(computes)-357(new)-358(DH)-358(k)27(ey)]TJ
/T1_2 10.91 Tf
111.85 0 Td
(T)Tj
/T1_5 7.97 Tf
7.89 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-1.52 -7.01 Td
(i)Tj
/T1_0 10.91 Tf
7.79 3.05 Td
[(=)-317(\()]TJ
/T1_2 10.91 Tf
(y)Tj
/T1_5 7.97 Tf
21.93 3.96 Td
(0)Tj
/T1_6 7.97 Tf
-0.39 -6.65 Td
(C)Tj
/T1_0 10.91 Tf
4.73 2.69 Td
(\))Tj
/T1_3 7.97 Tf
4.24 3.96 Td
(K)Tj
/T1_9 5.98 Tf
7.14 -1.22 Td
(i)Tj
/T1_0 10.91 Tf
6.69 -2.74 Td
[(mo)-27(d)]TJ
/T1_2 10.91 Tf
23.93 0 Td
(p)Tj
/T1_0 10.91 Tf
9.39 0 Td
[(and)-357(uses)]TJ
/T1_2 10.91 Tf
44.88 0 Td
(T)Tj
/T1_5 7.97 Tf
7.89 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-1.52 -7.01 Td
(i)Tj
/T1_0 10.91 Tf
8.21 3.05 Td
[(to)-358(decrypt)]TJ
/T1_4 10.91 Tf
-418.19 -21.92 Td
(c)Tj
/T1_5 7.97 Tf
5.73 3.96 Td
(0)Tj
/T1_3 7.97 Tf
0 -7.01 TD
(i)Tj
/T1_0 10.91 Tf
8.22 3.05 Td
[(and)-443(obtains)-444(the)-444(\257nal)-444(group)-444(k)27(ey)]TJ
/T1_2 10.91 Tf
160.31 0 Td
(K)Tj
/T1_5 7.97 Tf
10.05 3.96 Td
(0)Tj
/T1_0 10.91 Tf
2.79 -3.96 Td
(.)Tj
/T1_4 10.91 Tf
11.5 0 Td
(S)Tj
/T1_3 7.97 Tf
5.72 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
8.22 1.63 Td
[(then)-444(con\257rms)-444(and)-444(accepts)-444(the)-444(\257nal)-444(group)-443(k)26(ey)]TJ
/T1_2 10.91 Tf
231.29 0 Td
(K)Tj
/T1_5 7.97 Tf
10.04 3.96 Td
(0)Tj
/T1_0 10.91 Tf
7.64 -3.96 Td
(if)Tj
/T1_10 10.91 Tf
-461.51 -21.91 Td
(H)Tj
/T1_0 10.91 Tf
7.73 0 Td
(\()Tj
/T1_2 10.91 Tf
(K)Tj
/T1_5 7.97 Tf
14.28 3.96 Td
(0)Tj
/T1_1 10.91 Tf
2.79 -3.96 Td
(jj)Tj
/T1_2 10.91 Tf
6.06 0 Td
(y)Tj
/T1_5 7.97 Tf
5.74 3.96 Td
(0)Tj
/T1_6 7.97 Tf
-0.39 -6.66 Td
(C)Tj
/T1_0 10.91 Tf
4.73 2.7 Td
[(\))-441(=)]TJ
/T1_2 10.91 Tf
22.35 0 Td
(\265)Tj
/T1_5 7.97 Tf
5.42 3.96 Td
(0)Tj
/T1_6 7.97 Tf
-0.3 -6.66 Td
(C)Tj
/T1_0 10.91 Tf
4.73 2.7 Td
[(.)-739(Next,)]TJ
/T1_4 10.91 Tf
42.12 0 Td
(S)Tj
/T1_3 7.97 Tf
5.72 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
8.09 1.64 Td
(encrypts)Tj
/T1_2 10.91 Tf
45.09 0 Td
(K)Tj
/T1_5 7.97 Tf
10.04 3.96 Td
(0)Tj
/T1_1 10.91 Tf
2.8 -3.96 Td
(jj)Tj
/T1_4 10.91 Tf
6.05 0 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
8.09 1.64 Td
[(using)-431(subgroup)-431(k)27(ey)]TJ
/T1_2 10.91 Tf
98.79 0 Td
(K)Tj
/T1_3 7.97 Tf
9.26 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
8.09 1.64 Td
[(and)-431(obtains)-444(\271)]TJ
/T1_4 10.91 Tf
61.58 0 Td
(c)Tj
/T1_5 7.97 Tf
5.72 3.96 Td
(0)Tj
/T1_3 7.97 Tf
0 -7.02 TD
(i)Tj
/T1_0 10.91 Tf
8.2 3.06 Td
(=)Tj
/T1_1 10.91 Tf
13.29 0 Td
(E)Tj
/T1_3 7.97 Tf
5.76 -1.69 Td
(K)Tj
/T1_9 5.98 Tf
7.14 -1.21 Td
(i)Tj
/T1_0 10.91 Tf
3.66 2.9 Td
(\()Tj
/T1_2 10.91 Tf
(K)Tj
/T1_5 7.97 Tf
14.28 3.96 Td
(0)Tj
/T1_1 10.91 Tf
2.8 -3.96 Td
(jj)Tj
/T1_4 10.91 Tf
6.05 0 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
3.38 1.64 Td
(\).)Tj
-460.6 -21.92 Td
[(Finally)83(,)]TJ
/T1_4 10.91 Tf
40.22 0 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
7.81 1.63 Td
[(computes)-405(the)-407(k)27(ey)-405(con\257rmation)-406(co)-28(de)]TJ
/T1_2 10.91 Tf
179.77 0 Td
(\265)Tj
/T1_5 7.97 Tf
5.42 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.3 -7.01 Td
(i)Tj
/T1_0 10.91 Tf
7.73 3.05 Td
(=)Tj
/T1_10 10.91 Tf
12.83 0 Td
(H)Tj
/T1_0 10.91 Tf
7.73 0 Td
(\()Tj
/T1_2 10.91 Tf
(K)Tj
/T1_3 7.97 Tf
13.5 -1.63 Td
(i)Tj
/T1_1 10.91 Tf
3.38 1.63 Td
(jj)Tj
/T1_2 10.91 Tf
6.06 0 Td
(K)Tj
/T1_5 7.97 Tf
10.04 3.96 Td
(0)Tj
/T1_1 10.91 Tf
2.8 -3.96 Td
(jj)Tj
/T1_2 10.91 Tf
6.06 0 Td
(\277)Tj
/T1_3 7.97 Tf
4.76 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
3.38 1.63 Td
[(\))-406(and)-406(broadcasts)]TJ
/T1_1 10.91 Tf
85.54 0 Td
(f)Tj
/T1_4 10.91 Tf
(S)Tj
/T1_3 7.97 Tf
11.18 -1.63 Td
(i)Tj
/T1_1 10.91 Tf
3.38 1.63 Td
(jj)Tj
/T1_0 10.91 Tf
6.2 0 Td
(\271)Tj
/T1_4 10.91 Tf
-0.14 0 Td
(c)Tj
/T1_5 7.97 Tf
5.73 3.96 Td
(0)Tj
/T1_3 7.97 Tf
0 -7.01 TD
(i)Tj
/T1_1 10.91 Tf
3.38 3.05 Td
(jj)Tj
/T1_2 10.91 Tf
6.06 0 Td
(\265)Tj
/T1_5 7.97 Tf
5.42 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.3 -7.01 Td
(i)Tj
/T1_1 10.91 Tf
3.38 3.05 Td
(jj)Tj
/T1_0 10.91 Tf
6.64 0 Td
(\271)Tj
/T1_2 10.91 Tf
-0.58 0 Td
(\276)Tj
/T1_5 7.97 Tf
6.62 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.39 -7.01 Td
(i)Tj
/T1_1 10.91 Tf
3.38 3.05 Td
(g)Tj
/T1_0 10.91 Tf
-462.42 -21.91 Td
[(where)-386(\271)]TJ
/T1_2 10.91 Tf
31.54 0 Td
(\276)Tj
/T1_5 7.97 Tf
6.62 3.95 Td
(0)Tj
/T1_3 7.97 Tf
-0.39 -7.01 Td
(i)Tj
/T1_0 10.91 Tf
6.41 3.06 Td
(=)Tj
/T1_1 10.91 Tf
11.51 0 Td
(S)Tj
/T1_0 10.91 Tf
7.42 0 Td
(\()Tj
/T1_4 10.91 Tf
(S)Tj
/T1_3 7.97 Tf
9.97 -1.64 Td
(i)Tj
/T1_1 10.91 Tf
3.38 1.64 Td
(jj)Tj
/T1_2 10.91 Tf
6.06 0 Td
(\277)Tj
/T1_3 7.97 Tf
4.77 -1.64 Td
(i)Tj
/T1_1 10.91 Tf
3.38 1.64 Td
(jj)Tj
/T1_2 10.91 Tf
6.06 0 Td
(\265)Tj
/T1_5 7.97 Tf
5.42 3.95 Td
(0)Tj
/T1_3 7.97 Tf
-0.3 -7.01 Td
(i)Tj
/T1_1 10.91 Tf
3.38 3.06 Td
(jj)Tj
/T1_2 10.91 Tf
6.05 0 Td
(v)Tj
/T1_0 10.91 Tf
5.68 0 Td
[(\))-333(to)-333(subgroup)-334(mem)27(b)-27(ers)]TJ
/T1_4 10.91 Tf
114.7 0 Td
(U)Tj
/T1_3 7.97 Tf
5.72 -1.64 Td
(i;j)Tj
/T1_0 10.91 Tf
13.25 1.64 Td
[(for)-333(2)]TJ
/T1_1 10.91 Tf
25.18 0 Td
(\267)Tj
/T1_2 10.91 Tf
11.51 0 Td
(j)Tj
/T1_1 10.91 Tf
8.15 0 Td
(\267)Tj
/T1_2 10.91 Tf
11.51 0 Td
(n)Tj
/T1_3 7.97 Tf
6.54 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
3.38 1.64 Td
(.)Tj
-316.9 -21.92 Td
[(Round)-333(2)]TJ
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 0 -375.1 cm
0 0 m
40.75 0 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 116.0123 396.1454 Tm
(:)Tj
1.0003 0 0 1.0003 72 769.82 Tm
51.681 -373.57 Td
[(Eac)27(h)]TJ
/T1_4 10.91 Tf
26.729 0 Td
(V)Tj
/T1_3 7.97 Tf
5.73 -1.69 Td
(L;j)Tj
/T1_0 10.91 Tf
15.74 1.69 Td
(\()Tj
/T1_4 10.91 Tf
(U)Tj
/T1_3 7.97 Tf
9.97 -1.64 Td
(i;j)Tj
/T1_0 10.91 Tf
9.61 1.64 Td
[(\))-298(for)-298(2)]TJ
/T1_1 10.91 Tf
32.29 0 Td
(\267)Tj
/T1_2 10.91 Tf
11.51 0 Td
(j)Tj
/T1_1 10.91 Tf
8.15 0 Td
(\267)Tj
/T1_2 10.91 Tf
11.51 0 Td
(n)Tj
/T1_3 7.97 Tf
6.55 -1.69 Td
(L)Tj
/T1_1 10.91 Tf
7.91 1.69 Td
(\241)Tj
/T1_2 10.91 Tf
10.14 0 Td
(`)Tj
/T1_0 10.91 Tf
7.8 0 Td
(\(1)Tj
/T1_1 10.91 Tf
12.72 0 Td
(\267)Tj
/T1_2 10.91 Tf
11.51 0 Td
(i)Tj
/T1_1 10.91 Tf
6.79 0 Td
(6)Tj
/T1_0 10.91 Tf
(=)Tj
/T1_2 10.91 Tf
11.51 0 Td
(L)Tj
/T1_1 10.91 Tf
10.45 0 Td
(\267)Tj
/T1_2 10.91 Tf
11.51 0 Td
(n)Tj
/T1_3 7.97 Tf
6.55 -1.64 Td
(c)Tj
/T1_0 10.91 Tf
4.16 1.64 Td
[(,)-305(2)]TJ
/T1_1 10.91 Tf
14.85 0 Td
(\267)Tj
/T1_2 10.91 Tf
11.51 0 Td
(j)Tj
/T1_1 10.91 Tf
8.14 0 Td
(\267)Tj
/T1_2 10.91 Tf
11.51 0 Td
(n)Tj
/T1_3 7.97 Tf
6.55 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
3.38 1.64 Td
[(\))-298(v)27(eri\257es)-297(the)-298(signature)-352(\271)]TJ
/T1_2 10.91 Tf
108.92 0 Td
(\276)Tj
/T1_5 7.97 Tf
6.63 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.39 -7.19 Td
(L)Tj
/T1_0 10.91 Tf
-461.62 -18.69 Td
[(\()-53(\271)]TJ
/T1_2 10.91 Tf
4.24 0 Td
(\276)Tj
/T1_5 7.97 Tf
6.62 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.39 -7.01 Td
(i)Tj
/T1_0 10.91 Tf
3.38 3.05 Td
[(\).)-420(If)-262(the)-261(signature)-261(v)26(eri\257cation)-260(of)-315(\271)]TJ
/T1_2 10.91 Tf
153.78 0 Td
(\276)Tj
/T1_5 7.97 Tf
6.62 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.39 -7.19 Td
(L)Tj
/T1_0 10.91 Tf
9.1 3.23 Td
[(\()-54(\271)]TJ
/T1_2 10.91 Tf
4.25 0 Td
(\276)Tj
/T1_5 7.97 Tf
6.62 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.39 -7.01 Td
(i)Tj
/T1_0 10.91 Tf
3.38 3.05 Td
[(\))-261(is)-261(not)-261(correct,)-276(then)]TJ
/T1_4 10.91 Tf
98.75 0 Td
(V)Tj
/T1_3 7.97 Tf
5.72 -1.69 Td
(L;j)Tj
/T1_0 10.91 Tf
15.35 1.69 Td
(\()Tj
/T1_4 10.91 Tf
(U)Tj
/T1_3 7.97 Tf
9.96 -1.63 Td
(i;j)Tj
/T1_0 10.91 Tf
9.62 1.63 Td
[(\))-261(rejects)]TJ
/T1_4 10.91 Tf
40.63 0 Td
(S)Tj
/T1_3 7.97 Tf
5.72 -1.69 Td
(L)Tj
/T1_0 10.91 Tf
9.11 1.69 Td
(\()Tj
/T1_4 10.91 Tf
(S)Tj
/T1_3 7.97 Tf
9.97 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
3.38 1.63 Td
[(\).)-420(Otherwise,)]TJ
/T1_4 10.91 Tf
-405.03 -21.91 Td
(V)Tj
/T1_3 7.97 Tf
5.73 -1.69 Td
(L;j)Tj
/T1_0 10.91 Tf
15.98 1.69 Td
(\()Tj
/T1_4 10.91 Tf
(U)Tj
/T1_3 7.97 Tf
9.96 -1.64 Td
(i;j)Tj
/T1_0 10.91 Tf
9.62 1.64 Td
[(\))-320(uses)-320(subgroup)-320(k)27(ey)]TJ
/T1_2 10.91 Tf
97.49 0 Td
(K)Tj
/T1_5 7.97 Tf
10.04 3.95 Td
(0)Tj
/T1_3 7.97 Tf
-0.78 -7.19 Td
(L)Tj
/T1_0 10.91 Tf
9.75 3.24 Td
(\()Tj
/T1_2 10.91 Tf
(K)Tj
/T1_3 7.97 Tf
13.5 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
3.38 1.64 Td
[(\))-320(to)-320(decrypt)-333(\271)]TJ
/T1_4 10.91 Tf
60.49 0 Td
(c)Tj
/T1_5 7.97 Tf
5.73 3.95 Td
(0)Tj
/T1_3 7.97 Tf
0 -7.19 TD
(L)Tj
/T1_0 10.91 Tf
9.75 3.24 Td
[(\()-12(\271)]TJ
/T1_4 10.91 Tf
4.24 0 Td
(c)Tj
/T1_5 7.97 Tf
5.72 3.95 Td
(0)Tj
/T1_3 7.97 Tf
0 -7.01 TD
(i)Tj
/T1_0 10.91 Tf
3.38 3.06 Td
[(\))-320(and)-320(obtains)-320(the)-320(iden)26(tit)28(y)]TJ
/T1_4 10.91 Tf
125.67 0 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.69 Td
(L)Tj
/T1_0 10.91 Tf
9.75 1.69 Td
(\()Tj
/T1_4 10.91 Tf
(S)Tj
/T1_3 7.97 Tf
9.96 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
3.38 1.64 Td
[(\))-320(and)-320(\257nal)]TJ
-418.47 -21.92 Td
[(group)-365(k)27(ey)]TJ
/T1_2 10.91 Tf
51.32 0 Td
(K)Tj
/T1_5 7.97 Tf
10.04 3.96 Td
(0)Tj
/T1_0 10.91 Tf
2.8 -3.96 Td
[(.)-539(If)-366(the)-365(iden)27(tit)27(y)]TJ
/T1_4 10.91 Tf
79.94 0 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.69 Td
(L)Tj
/T1_0 10.91 Tf
10.24 1.69 Td
(\()Tj
/T1_4 10.91 Tf
(S)Tj
/T1_3 7.97 Tf
9.97 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
3.38 1.64 Td
[(\))-365(w)27(as)-364(not)-365(decrypted)-366(correctly)83(,)-373(then)]TJ
/T1_4 10.91 Tf
173.19 0 Td
(V)Tj
/T1_3 7.97 Tf
5.72 -1.69 Td
(L;j)Tj
/T1_0 10.91 Tf
16.48 1.69 Td
(\()Tj
/T1_4 10.91 Tf
(U)Tj
/T1_3 7.97 Tf
9.97 -1.64 Td
(i;j)Tj
/T1_0 10.91 Tf
9.61 1.64 Td
[(\))-365(rejects)-378(\271)]TJ
/T1_4 10.91 Tf
42.9 0 Td
(c)Tj
/T1_5 7.97 Tf
5.72 3.96 Td
(0)Tj
/T1_3 7.97 Tf
0 -7.19 TD
(L)Tj
/T1_0 10.91 Tf
10.24 3.23 Td
[(\()-12(\271)]TJ
/T1_4 10.91 Tf
4.24 0 Td
(c)Tj
/T1_5 7.97 Tf
5.73 3.96 Td
(0)Tj
/T1_3 7.97 Tf
0 -7.02 TD
(i)Tj
/T1_0 10.91 Tf
3.38 3.06 Td
(\).)Tj
-460.6 -21.92 Td
(Otherwise,)Tj
/T1_4 10.91 Tf
54.29 0 Td
(V)Tj
/T1_3 7.97 Tf
5.72 -1.69 Td
(L;j)Tj
/T1_0 10.91 Tf
15.71 1.69 Td
[(c)27(hec)28(ks)-294(if)]TJ
/T1_2 10.91 Tf
42.85 0 Td
(\265)Tj
/T1_5 7.97 Tf
5.43 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.31 -7.19 Td
(L)Tj
/T1_0 10.91 Tf
9.29 3.23 Td
(=)Tj
/T1_10 10.91 Tf
11.51 0 Td
(H)Tj
/T1_0 10.91 Tf
7.73 0 Td
(\()Tj
/T1_2 10.91 Tf
(K)Tj
/T1_5 7.97 Tf
14.28 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.78 -7.19 Td
(L)Tj
/T1_1 10.91 Tf
6.26 3.23 Td
(jj)Tj
/T1_2 10.91 Tf
6.05 0 Td
(K)Tj
/T1_5 7.97 Tf
10.05 3.96 Td
(0)Tj
/T1_1 10.91 Tf
2.79 -3.96 Td
(jj)Tj
/T1_2 10.91 Tf
6.06 0 Td
(\277)Tj
/T1_5 7.97 Tf
6 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-1.23 -7.19 Td
(L)Tj
/T1_0 10.91 Tf
6.25 3.23 Td
[(\).)-431(If)-296(they)-295(are)-295(equal,)]TJ
/T1_4 10.91 Tf
95.86 0 Td
(V)Tj
/T1_3 7.97 Tf
5.73 -1.69 Td
(L;j)Tj
/T1_0 10.91 Tf
15.7 1.69 Td
[(accepts)-295(the)-295(\257nal)-295(group)-295(k)26(ey)]TJ
/T1_2 10.91 Tf
129.79 0 Td
(K)Tj
/T1_5 7.97 Tf
10.05 3.96 Td
(0)Tj
/T1_0 10.91 Tf
-465.08 -25.87 Td
[(and)-355(b)-28(oth)]TJ
/T1_2 10.91 Tf
47.44 0 Td
(K)Tj
/T1_5 7.97 Tf
10.04 3.95 Td
(0)Tj
/T1_3 7.97 Tf
-0.78 -7.19 Td
(L)Tj
/T1_0 10.91 Tf
10.13 3.24 Td
(and)Tj
/T1_2 10.91 Tf
21.45 0 Td
(K)Tj
/T1_5 7.97 Tf
10.05 3.95 Td
(0)Tj
/T1_0 10.91 Tf
6.67 -3.95 Td
[(are)-355(con\257rmed.)-511(Similarly)83(,)]TJ
/T1_4 10.91 Tf
122.53 0 Td
(U)Tj
/T1_3 7.97 Tf
5.73 -1.64 Td
(i;j)Tj
/T1_0 10.91 Tf
13.49 1.64 Td
[(c)27(hec)28(ks)-355(if)]TJ
/T1_2 10.91 Tf
44.17 0 Td
(\265)Tj
/T1_5 7.97 Tf
5.42 3.95 Td
(0)Tj
/T1_3 7.97 Tf
-0.3 -7.01 Td
(i)Tj
/T1_0 10.91 Tf
6.81 3.06 Td
(=)Tj
/T1_10 10.91 Tf
11.92 0 Td
(H)Tj
/T1_0 10.91 Tf
(\()Tj
/T1_2 10.91 Tf
(K)Tj
/T1_3 7.97 Tf
21.22 -1.64 Td
(i)Tj
/T1_1 10.91 Tf
3.39 1.64 Td
(jj)Tj
/T1_2 10.91 Tf
6.05 0 Td
(K)Tj
/T1_5 7.97 Tf
10.05 3.95 Td
(0)Tj
/T1_1 10.91 Tf
2.79 -3.95 Td
(jj)Tj
/T1_2 10.91 Tf
6.06 0 Td
(\277)Tj
/T1_3 7.97 Tf
4.77 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
3.38 1.64 Td
[(\).)-510(If)-356(they)-355(are)-356(equal,)]TJ
/T1_4 10.91 Tf
-372.48 -21.92 Td
(U)Tj
/T1_3 7.97 Tf
5.73 -1.64 Td
(i;j)Tj
/T1_0 10.91 Tf
13.25 1.64 Td
[(accepts)-332(and)-334(con\257rms)-333(the)-333(new)-334(\257nal)-333(group)-333(k)26(ey)]TJ
/T1_2 10.91 Tf
219.21 0 Td
(K)Tj
/T1_5 7.97 Tf
10.04 3.96 Td
(0)Tj
/T1_0 10.91 Tf
2.8 -3.96 Td
(.)Tj
/T1_11 14.34 Tf
-251.03 -45.44 Td
[(9.3)-1124(Detection)-375(of)-375(Malicious)-375(Group)-375(Mem)30(b)-30(ers)]TJ
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[(c)27(ho)-27(oses)-378(a)-379(random)]TJ
/T1_1 10.91 Tf
89.49 0 Td
(\267)Tj
/T1_4 7.97 Tf
6.29 -1.64 Td
(1)Tj
/T1_8 10.91 Tf
8.58 1.64 Td
[(2)-353(f)]TJ
/T1_0 10.91 Tf
(0)Tj
/T1_1 10.91 Tf
(;)Tj
/T1_0 10.91 Tf
26.88 0 Td
(1)Tj
/T1_8 10.91 Tf
(g)Tj
/T1_2 7.97 Tf
10.91 3.96 Td
(\270)Tj
/T1_0 10.91 Tf
9.57 -3.96 Td
(and)Tj
/T1_1 10.91 Tf
21.7 0 Td
(r)Tj
/T1_4 7.97 Tf
4.92 -1.64 Td
(1)Tj
/T1_8 10.91 Tf
8.59 1.64 Td
(2)Tj
/T1_1 10.91 Tf
11.12 0 Td
(Z)Tj
/T1_3 7.97 Tf
8.23 3.96 Td
(\244)Tj
/T1_2 7.97 Tf
-0.78 -6.66 Td
(p)Tj
/T1_0 10.91 Tf
5.51 2.7 Td
[(,)-390(computes)]TJ
/T1_1 10.91 Tf
56.31 0 Td
(z)Tj
/T1_4 7.97 Tf
5.07 -1.64 Td
(1)Tj
/T1_0 10.91 Tf
8.59 1.64 Td
(=)Tj
/T1_1 10.91 Tf
12.34 0 Td
(g)Tj
/T1_2 7.97 Tf
5.59 3.96 Td
(r)Tj
/T1_9 5.98 Tf
3.82 -1.11 Td
(1)Tj
/T1_0 10.91 Tf
8.78 -2.85 Td
(and)Tj
/T1_1 10.91 Tf
-450.3 -21.92 Td
(\277)Tj
/T1_0 10.91 Tf
10.34 0 Td
(=)Tj
/T1_7 10.91 Tf
12.83 0 Td
(H)Tj
/T1_0 10.91 Tf
(\()Tj
/T1_1 10.91 Tf
11.97 0 Td
(\267)Tj
/T1_4 7.97 Tf
6.28 -1.63 Td
(1)Tj
/T1_8 10.91 Tf
4.73 1.63 Td
(jj)Tj
/T1_0 10.91 Tf
6.06 0 Td
[(0\))-405(and)-406(sends)]TJ
/T1_1 10.91 Tf
66.1 0 Td
(\277)Tj
/T1_8 10.91 Tf
6 0 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(z)Tj
/T1_4 7.97 Tf
5.08 -1.63 Td
(1)Tj
/T1_0 10.91 Tf
4.73 1.63 Td
[(.)-660(Eac)26(h)-404(user)]TJ
/T1_5 10.91 Tf
62.04 0 Td
(U)Tj
/T1_2 7.97 Tf
5.73 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
7.8 1.63 Td
[(for)-405(2)]TJ
/T1_8 10.91 Tf
27.27 0 Td
(\267)Tj
/T1_1 10.91 Tf
12.83 0 Td
(i)Tj
/T1_8 10.91 Tf
8.1 0 Td
(\267)Tj
/T1_1 10.91 Tf
12.82 0 Td
(n)Tj
/T1_0 10.91 Tf
10.97 0 Td
[(c)27(ho)-27(oses)-405(a)-406(random)]TJ
/T1_1 10.91 Tf
90.37 0 Td
(r)Tj
/T1_2 7.97 Tf
4.92 -1.63 Td
(i)Tj
/T1_8 10.91 Tf
7.73 1.63 Td
(2)Tj
/T1_1 10.91 Tf
11.61 0 Td
(Z)Tj
/T1_3 7.97 Tf
8.22 3.96 Td
(\244)Tj
/T1_2 7.97 Tf
-0.78 -6.65 Td
(p)Tj
/T1_0 10.91 Tf
5.51 2.69 Td
[(,)-424(computes)]TJ
/T1_1 10.91 Tf
-415.32 -21.91 Td
(z)Tj
/T1_2 7.97 Tf
5.07 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
6.41 1.64 Td
(=)Tj
/T1_1 10.91 Tf
11.51 0 Td
(g)Tj
/T1_2 7.97 Tf
5.6 3.96 Td
(r)Tj
/T1_10 5.98 Tf
3.82 -1.22 Td
(i)Tj
/T1_0 10.91 Tf
7.29 -2.74 Td
[(and)-333(sends)]TJ
/T1_1 10.91 Tf
50.41 0 Td
(z)Tj
/T1_2 7.97 Tf
5.07 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
3.38 1.64 Td
(.)Tj
/T1_5 10.91 Tf
-98.56 -27.89 Td
[(Round)-524(2')]TJ
/T1_0 10.91 Tf
[(:)-446(Up)-28(on)-335(receipt)-334(of)-335(all)]TJ
/T1_1 10.91 Tf
146.8 0 Td
(z)Tj
/T1_2 7.97 Tf
5.08 -1.64 Td
(j)Tj
/T1_0 10.91 Tf
8.03 1.64 Td
[(for)-334(1)]TJ
/T1_8 10.91 Tf
25.21 0 Td
(\267)Tj
/T1_1 10.91 Tf
11.53 0 Td
(j)Tj
/T1_8 10.91 Tf
8.17 0 Td
(\267)Tj
/T1_1 10.91 Tf
11.54 0 Td
(n)Tj
/T1_0 10.91 Tf
[(,)-334(eac)27(h)]TJ
/T1_5 10.91 Tf
37.78 0 Td
(U)Tj
/T1_2 7.97 Tf
5.73 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
7.03 1.64 Td
[(for)-334(1)]TJ
/T1_8 10.91 Tf
25.21 0 Td
(\267)Tj
/T1_1 10.91 Tf
11.54 0 Td
(i)Tj
/T1_8 10.91 Tf
6.81 0 Td
(\267)Tj
/T1_1 10.91 Tf
11.53 0 Td
(n)Tj
/T1_0 10.91 Tf
10.2 0 Td
(computes)Tj
/T1_1 10.91 Tf
48.55 0 Td
(L)Tj
/T1_2 7.97 Tf
7.42 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
6.43 1.64 Td
(=)Tj
/T1_7 10.91 Tf
11.54 0 Td
(H)Tj
/T1_0 10.91 Tf
(\()Tj
/T1_1 10.91 Tf
(z)Tj
/T1_2 7.97 Tf
17.52 4.97 Td
(r)Tj
/T1_10 5.98 Tf
3.82 -1.22 Td
(i)Tj
/T1_2 7.97 Tf
-4.3 -7.01 Td
(i)Tj
/T1_3 7.97 Tf
2.88 0 Td
(\241)Tj
/T1_4 7.97 Tf
(1)Tj
/T1_8 10.91 Tf
11.31 3.26 Td
(jj)Tj
/T1_5 10.91 Tf
6.06 0 Td
(SID)Tj
/T1_0 10.91 Tf
(\),)Tj
/T1_1 10.91 Tf
-443.42 -21.92 Td
(R)Tj
/T1_2 7.97 Tf
8.28 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
8.72 1.64 Td
(=)Tj
/T1_7 10.91 Tf
13.82 0 Td
(H)Tj
/T1_0 10.91 Tf
(\()Tj
/T1_1 10.91 Tf
(z)Tj
/T1_2 7.97 Tf
17.52 4.97 Td
(r)Tj
/T1_10 5.98 Tf
3.82 -1.21 Td
(i)Tj
/T1_2 7.97 Tf
-4.3 -7.02 Td
(i)Tj
/T1_4 7.97 Tf
2.88 0 Td
(+1)Tj
/T1_8 10.91 Tf
11.31 3.26 Td
(jj)Tj
/T1_5 10.91 Tf
6.06 0 Td
(SID)Tj
/T1_0 10.91 Tf
[(\))-460(and)]TJ
/T1_1 10.91 Tf
49.03 0 Td
(X)Tj
/T1_2 7.97 Tf
9.04 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
8.71 1.64 Td
(=)Tj
/T1_1 10.91 Tf
13.82 0 Td
(L)Tj
/T1_2 7.97 Tf
7.43 -1.64 Td
(i)Tj
/T1_8 10.91 Tf
6.72 1.64 Td
(\251)Tj
/T1_1 10.91 Tf
11.83 0 Td
(R)Tj
/T1_2 7.97 Tf
8.28 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
3.38 1.64 Td
[(,)-492(where)]TJ
/T1_5 10.91 Tf
41.32 0 Td
(SID)Tj
/T1_0 10.91 Tf
22.51 0 Td
(=)Tj
/T1_7 10.91 Tf
13.82 0 Td
(H)Tj
/T1_0 10.91 Tf
7.73 0 Td
(\()Tj
/T1_1 10.91 Tf
(\277)Tj
/T1_8 10.91 Tf
10.24 0 Td
(jj)Tj
/T1_5 10.91 Tf
6.06 0 Td
(U)Tj
/T1_4 7.97 Tf
5.73 -1.64 Td
(1)Tj
/T1_8 10.91 Tf
4.73 1.64 Td
(jj)Tj
/T1_5 10.91 Tf
6.06 0 Td
(U)Tj
/T1_4 7.97 Tf
5.72 -1.64 Td
(2)Tj
/T1_8 10.91 Tf
4.73 1.64 Td
[(jj)-166(\242)-167(\242)-167(\242)-166(jj)]TJ
/T1_5 10.91 Tf
28.48 0 Td
(U)Tj
/T1_2 7.97 Tf
5.72 -1.64 Td
(n)Tj
/T1_0 10.91 Tf
5.64 1.64 Td
[(\).)-825(The)-460(\257rst)-460(user)]TJ
/T1_5 10.91 Tf
88.47 0 Td
(U)Tj
/T1_4 7.97 Tf
5.72 -1.64 Td
(1)Tj
/T1_0 10.91 Tf
9.75 1.64 Td
(in)Tj
-458.78 -21.92 Td
[(additionally)-292(computes)]TJ
/T1_6 10.91 Tf
110.75 2.76 Td
(b)Tj
/T1_1 10.91 Tf
-2.83 -2.76 Td
(X)Tj
/T1_0 10.91 Tf
12.92 0 Td
(=)Tj
/T1_1 10.91 Tf
11.52 0 Td
(\267)Tj
/T1_4 7.97 Tf
6.28 -1.63 Td
(1)Tj
/T1_8 10.91 Tf
6.26 1.63 Td
(\251)Tj
/T1_1 10.91 Tf
10.01 0 Td
(R)Tj
/T1_4 7.97 Tf
8.28 -1.63 Td
(1)Tj
/T1_0 10.91 Tf
4.73 1.63 Td
(.)Tj
/T1_5 10.91 Tf
7.73 0 Td
(U)Tj
/T1_2 7.97 Tf
5.72 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
6.57 1.63 Td
[(for)-292(2)]TJ
/T1_8 10.91 Tf
24.73 0 Td
(\267)Tj
/T1_1 10.91 Tf
11.51 0 Td
(i)Tj
/T1_8 10.91 Tf
6.79 0 Td
(\267)Tj
/T1_1 10.91 Tf
11.51 0 Td
(n)Tj
/T1_0 10.91 Tf
9.73 0 Td
[(then)-292(c)27(ho)-27(oses)-292(a)-292(random)]TJ
/T1_1 10.91 Tf
111.06 0 Td
(\267)Tj
/T1_2 7.97 Tf
6.28 -1.63 Td
(i)Tj
/T1_8 10.91 Tf
6.41 1.63 Td
[(2)-277(f)]TJ
/T1_0 10.91 Tf
(0)Tj
/T1_1 10.91 Tf
(;)Tj
/T1_0 10.91 Tf
26.05 0 Td
(1)Tj
/T1_8 10.91 Tf
(g)Tj
/T1_2 7.97 Tf
10.91 3.96 Td
(\270)Tj
/T1_0 10.91 Tf
8.62 -3.96 Td
[(and)-292(sends)]TJ
-421.54 -21.91 Td
(out)Tj
/T1_1 10.91 Tf
19.39 0 Td
(\267)Tj
/T1_2 7.97 Tf
6.28 -1.64 Td
(i)Tj
/T1_8 10.91 Tf
3.38 1.64 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(X)Tj
/T1_2 7.97 Tf
9.04 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
7.01 1.64 Td
[(and)-333(\257rst)-333(user)]TJ
/T1_5 10.91 Tf
66.83 0 Td
(U)Tj
/T1_4 7.97 Tf
5.73 -1.64 Td
(1)Tj
/T1_0 10.91 Tf
8.36 1.64 Td
[(sends)-333(out)]TJ
/T1_6 10.91 Tf
51.42 2.75 Td
(b)Tj
/T1_1 10.91 Tf
-2.82 -2.75 Td
(X)Tj
/T1_8 10.91 Tf
9.89 0 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(X)Tj
/T1_4 7.97 Tf
9.03 -1.64 Td
(1)Tj
/T1_0 10.91 Tf
4.73 1.64 Td
(.)Tj
/T1_5 10.91 Tf
-210.39 -27.9 Td
[(Computation)-524(of)-525(Key)]TJ
/T1_0 10.91 Tf
103.06 0 Td
(:)Tj
/T1_5 10.91 Tf
7.88 0 Td
(U)Tj
/T1_2 7.97 Tf
5.72 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
7.02 1.63 Td
[(for)-333(1)]TJ
/T1_8 10.91 Tf
25.17 0 Td
(\267)Tj
/T1_1 10.91 Tf
11.52 0 Td
(i)Tj
/T1_8 10.91 Tf
6.78 0 Td
(\267)Tj
/T1_1 10.91 Tf
11.51 0 Td
(n)Tj
/T1_0 10.91 Tf
10.19 0 Td
(computes)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 65.32 -385.89 cm
0 0 m
8.37 0 l
S
Q
Q
BT
/T1_1 10.91 Tf
1.0003 0 0 1.0003 137.3383 374.8394 Tm
(R)Tj
/T1_2 7.97 Tf
8.37 -1.64 Td
(i)Tj
/T1_4 7.97 Tf
2.88 0 Td
(+1)Tj
/T1_0 10.91 Tf
14.35 1.64 Td
(=)Tj
/T1_1 10.91 Tf
11.51 0 Td
(X)Tj
/T1_2 7.97 Tf
9.03 -1.64 Td
(i)Tj
/T1_4 7.97 Tf
2.89 0 Td
(+1)Tj
/T1_8 10.91 Tf
13.73 1.64 Td
(\251)Tj
/T1_1 10.91 Tf
10.91 0 Td
(R)Tj
/T1_2 7.97 Tf
8.28 -1.64 Td
(i)Tj
/T1_1 10.91 Tf
3.38 1.64 Td
(;)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 164 -385.89 cm
0 0 m
8.37 0 l
S
Q
Q
BT
/T1_1 10.91 Tf
1.0003 0 0 1.0003 236.0459 374.8394 Tm
(R)Tj
/T1_2 7.97 Tf
8.37 -1.64 Td
(i)Tj
/T1_4 7.97 Tf
2.88 0 Td
(+2)Tj
/T1_0 10.91 Tf
14.34 1.64 Td
(=)Tj
/T1_1 10.91 Tf
11.51 0 Td
(X)Tj
/T1_2 7.97 Tf
9.04 -1.64 Td
(i)Tj
/T1_4 7.97 Tf
2.88 0 Td
(+2)Tj
/T1_8 10.91 Tf
13.74 1.64 Td
(\251)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 237.67 -385.89 cm
0 0 m
8.36 0 l
S
Q
Q
BT
/T1_1 10.91 Tf
1.0003 0 0 1.0003 309.7365 374.8394 Tm
(R)Tj
/T1_2 7.97 Tf
8.36 -1.64 Td
(i)Tj
/T1_4 7.97 Tf
2.89 0 Td
(+1)Tj
/T1_1 10.91 Tf
11.31 1.64 Td
(;)Tj
/T1_8 10.91 Tf
13.35 0 Td
(\242)Tj
1.0003 0 0 1.0003 72 769.82 Tm
278.424 -394.87 Td
[(\242)-167(\242)]TJ
/T1_1 10.91 Tf
11.516 0 Td
(;)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 303.29 -385.89 cm
0 0 m
8.36 0 l
S
Q
Q
BT
/T1_1 10.91 Tf
1.0003 0 0 1.0003 375.3749 374.8394 Tm
(R)Tj
/T1_2 7.97 Tf
8.36 -1.64 Td
(i)Tj
/T1_3 7.97 Tf
2.88 0 Td
(\241)Tj
/T1_4 7.97 Tf
6.59 0 Td
(1)Tj
/T1_0 10.91 Tf
7.76 1.64 Td
(=)Tj
/T1_1 10.91 Tf
11.51 0 Td
(X)Tj
/T1_2 7.97 Tf
9.04 -1.64 Td
(i)Tj
/T1_3 7.97 Tf
2.88 0 Td
(\241)Tj
/T1_4 7.97 Tf
(1)Tj
/T1_8 10.91 Tf
13.74 1.64 Td
(\251)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 376.95 -385.89 cm
0 0 m
8.37 0 l
S
Q
Q
BT
/T1_1 10.91 Tf
1.0003 0 0 1.0003 449.0555 374.8394 Tm
(R)Tj
/T1_2 7.97 Tf
8.37 -1.64 Td
(i)Tj
/T1_3 7.97 Tf
2.88 0 Td
(\241)Tj
/T1_4 7.97 Tf
6.59 0 Td
(2)Tj
/T1_1 10.91 Tf
4.73 1.64 Td
(:)Tj
/T1_0 10.91 Tf
-399.52 -39.64 Td
(If)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 11.36 -425.53 cm
0 0 m
8.37 0 l
S
Q
Q
BT
/T1_1 10.91 Tf
1.0003 0 0 1.0003 83.3632 335.1883 Tm
(R)Tj
/T1_2 7.97 Tf
8.37 -1.64 Td
(i)Tj
/T1_3 7.97 Tf
2.88 0 Td
(\241)Tj
/T1_4 7.97 Tf
6.59 0 Td
(1)Tj
/T1_0 10.91 Tf
8.52 1.64 Td
(=)Tj
/T1_1 10.91 Tf
12.28 0 Td
(L)Tj
/T1_2 7.97 Tf
7.42 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
3.38 1.64 Td
(,)Tj
1.0003 0 0 1.0003 72 769.82 Tm
68.033 -434.51 Td
(then)Tj
/T1_5 10.91 Tf
25.307 0 Td
(U)Tj
/T1_2 7.97 Tf
5.72 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
7.48 1.64 Td
(uses)Tj
/T1_1 10.91 Tf
23.6 0 Td
(R)Tj
/T1_4 7.97 Tf
8.28 -1.64 Td
(1)Tj
/T1_0 10.91 Tf
8.83 1.64 Td
[(to)-375(obtain)]TJ
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 195.43 -428.29 cm
0 0 m
6.28 0 l
S
Q
Q
BT
/T1_1 10.91 Tf
1.0003 0 0 1.0003 267.4847 335.1883 Tm
(\267)Tj
/T1_4 7.97 Tf
6.28 -1.64 Td
(1)Tj
/T1_0 10.91 Tf
8.82 1.64 Td
(from)Tj
/T1_6 10.91 Tf
29.07 2.75 Td
(b)Tj
/T1_1 10.91 Tf
-2.83 -2.75 Td
(X)Tj
/T1_0 10.91 Tf
9.89 0 Td
(.)Tj
1.0003 0 0 1.0003 72 769.82 Tm
255.923 -434.51 Td
(If)Tj
/T1_7 10.91 Tf
11.357 0 Td
(H)Tj
/T1_0 10.91 Tf
7.73 0 Td
(\()Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 279.25 -428.29 cm
0 0 m
6.28 0 l
S
Q
Q
BT
/T1_1 10.91 Tf
1.0003 0 0 1.0003 351.3282 335.1883 Tm
(\267)Tj
/T1_4 7.97 Tf
6.28 -1.64 Td
(1)Tj
/T1_8 10.91 Tf
4.73 1.64 Td
(jj)Tj
/T1_0 10.91 Tf
6.06 0 Td
(0\))Tj
1.0003 0 0 1.0003 72 769.82 Tm
309.816 -434.51 Td
(=)Tj
/T1_1 10.91 Tf
12.274 0 Td
(\277)Tj
/T1_0 10.91 Tf
10.09 0 Td
[(holds,)-386(then)]TJ
/T1_5 10.91 Tf
57.44 0 Td
(U)Tj
/T1_2 7.97 Tf
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5.07 -1.64 Td
(i;)Tj
/T1_5 7.97 Tf
5.23 0 Td
(1)Tj
/T1_2 10.91 Tf
4.73 1.64 Td
(jj)Tj
/T1_3 10.91 Tf
6.06 0 Td
(BL)Tj
/T1_10 7.97 Tf
11.45 -1.64 Td
(Z)Tj
/T1_2 10.91 Tf
4.74 1.64 Td
(jj)Tj
/T1_1 10.91 Tf
6.05 0 Td
[(0\).)-432(The)-296(v)55(alidit)27(y)-295(of)-296(signature)]TJ
/T1_6 10.91 Tf
137.08 0 Td
(\276)Tj
/T1_4 7.97 Tf
6.23 -1.64 Td
(i;)Tj
/T1_5 7.97 Tf
(1)Tj
/T1_1 10.91 Tf
13.2 1.64 Td
[(is)-295(c)27(hec)27(k)28(ed)-295(b)27(y)]TJ
/T1_3 10.91 Tf
64.88 0 Td
(U)Tj
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5.72 -1.64 Td
(i;j)Tj
/T1_1 10.91 Tf
12.85 1.64 Td
[(for)-295(2)]TJ
/T1_2 10.91 Tf
24.77 0 Td
(\267)Tj
/T1_6 10.91 Tf
11.51 0 Td
(j)Tj
/T1_2 10.91 Tf
8.14 0 Td
(\267)Tj
/T1_6 10.91 Tf
11.51 0 Td
(n)Tj
/T1_4 7.97 Tf
6.55 -1.64 Td
(i)Tj
/T1_1 10.91 Tf
-464.49 -20.28 Td
[(in)-358(Phase)-358(1)-359(Round)-358(4.)-520(If)-358(the)-359(signature)]TJ
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181.93 0 Td
(\276)Tj
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6.23 -1.63 Td
(i;)Tj
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5.23 0 Td
(1)Tj
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8.64 1.63 Td
[(is)-358(not)-359(correct,)-364(then)]TJ
/T1_3 10.91 Tf
95.81 0 Td
(U)Tj
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5.72 -1.63 Td
(i;j)Tj
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13.53 1.63 Td
(rejects)Tj
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34.59 0 Td
(S)Tj
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5.73 -1.63 Td
(i)Tj
/T1_1 10.91 Tf
3.38 1.63 Td
[(.)-519(As)]TJ
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25.09 0 Td
(A)Tj
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12.61 0 Td
[(do)-28(es)-358(not)-358(kno)26(w)]TJ
-398.49 -21.91 Td
[(the)-359(RSA)-359(priv)55(ate)-359(k)27(ey)]TJ
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102.19 0 Td
(d)Tj
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5.68 -1.64 Td
(i)Tj
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7.3 1.64 Td
(of)Tj
/T1_3 10.91 Tf
12.7 0 Td
(S)Tj
/T1_4 7.97 Tf
5.72 -1.64 Td
(i)Tj
/T1_1 10.91 Tf
7.3 1.64 Td
[(and)-359(the)-359(RSA)-359(signature)-360(sc)27(heme)-358(is)-359(assumed)-359(to)-360(b)-27(e)-360(secure,)-365(therefore)]TJ
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318.27 0 Td
(A)Tj
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-459.16 -21.92 Td
[(is)-383(not)-383(able)-383(to)-383(pro)-28(duce)-383(a)-383(v)55(alid)-382(signature)]TJ
/T1_6 10.91 Tf
195.38 0 Td
(\276)Tj
/T1_4 7.97 Tf
6.23 -1.64 Td
(i;)Tj
/T1_5 7.97 Tf
(1)Tj
/T1_1 10.91 Tf
9.97 1.64 Td
[(.)-593(Next)-383(supp)-28(ose)]TJ
/T1_2 10.91 Tf
78.27 0 Td
(A)Tj
/T1_1 10.91 Tf
12.88 0 Td
[(tries)-383(to)-383(imp)-28(ersonate)]TJ
/T1_3 10.91 Tf
100.88 0 Td
(S)Tj
/T1_4 7.97 Tf
5.72 -1.64 Td
(i)Tj
/T1_1 10.91 Tf
7.56 1.64 Td
[(in)-383(Phase)-383(1)]TJ
-416.89 -21.92 Td
[(Round)-339(5,)-342(then)]TJ
/T1_2 10.91 Tf
72.49 0 Td
(A)Tj
/T1_1 10.91 Tf
12.41 0 Td
[(\257rst)-340(generates)]TJ
/T1_6 10.91 Tf
70.61 0 Td
(X)Tj
/T1_4 7.97 Tf
9.04 -1.63 Td
(i;)Tj
/T1_5 7.97 Tf
5.23 0 Td
(1)Tj
/T1_1 10.91 Tf
7.88 1.63 Td
(=)Tj
/T1_6 10.91 Tf
11.64 0 Td
(L)Tj
/T1_4 7.97 Tf
7.42 -1.63 Td
(i;)Tj
/T1_5 7.97 Tf
5.23 0 Td
(1)Tj
/T1_2 10.91 Tf
7.2 1.63 Td
(\251)Tj
/T1_6 10.91 Tf
10.96 0 Td
(R)Tj
/T1_4 7.97 Tf
8.28 -1.63 Td
(i;)Tj
/T1_5 7.97 Tf
5.23 0 Td
(1)Tj
/T1_1 10.91 Tf
8.44 1.63 Td
(and)Tj
/T1_11 10.91 Tf
22.04 2.76 Td
(c)Tj
/T1_6 10.91 Tf
-0.76 -2.76 Td
(X)Tj
/T1_4 7.97 Tf
9.04 -1.63 Td
(i)Tj
/T1_1 10.91 Tf
6.53 1.63 Td
(=)Tj
/T1_6 10.91 Tf
11.63 0 Td
(\267)Tj
/T1_4 7.97 Tf
6.28 -1.63 Td
(i;)Tj
/T1_5 7.97 Tf
(1)Tj
/T1_2 10.91 Tf
12.44 1.63 Td
(\251)Tj
/T1_6 10.91 Tf
10.95 0 Td
(R)Tj
/T1_4 7.97 Tf
8.28 -1.63 Td
(i;)Tj
/T1_5 7.97 Tf
(1)Tj
/T1_1 10.91 Tf
13.68 1.63 Td
(where)Tj
/T1_6 10.91 Tf
31.61 0 Td
(L)Tj
/T1_4 7.97 Tf
7.42 -1.63 Td
(i;)Tj
/T1_5 7.97 Tf
5.23 0 Td
(1)Tj
/T1_1 10.91 Tf
7.88 1.63 Td
(=)Tj
/T1_7 10.91 Tf
11.64 0 Td
(H)Tj
/T1_1 10.91 Tf
(\()Tj
/T1_6 10.91 Tf
(z)Tj
/T1_4 7.97 Tf
17.51 6.14 Td
(r)Tj
/T1_8 5.98 Tf
3.82 -1.22 Td
(i;)Tj
/T1_9 5.98 Tf
4.93 0 Td
(1)Tj
/T1_4 7.97 Tf
-9.23 -8.17 Td
(i;n)Tj
/T1_8 5.98 Tf
10.37 -1.22 Td
(i)Tj
/T1_2 10.91 Tf
3.66 4.47 Td
(jj)Tj
/T1_3 10.91 Tf
6.06 0 Td
(SID)Tj
/T1_4 7.97 Tf
17.18 -1.63 Td
(i)Tj
/T1_1 10.91 Tf
3.38 1.63 Td
(\))Tj
-463.63 -21.91 Td
(and)Tj
/T1_6 10.91 Tf
21.36 0 Td
(R)Tj
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8.28 -1.64 Td
(i;)Tj
/T1_5 7.97 Tf
5.23 0 Td
(1)Tj
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8.01 1.64 Td
(=)Tj
/T1_7 10.91 Tf
11.77 0 Td
(H)Tj
/T1_1 10.91 Tf
(\()Tj
/T1_6 10.91 Tf
(z)Tj
/T1_4 7.97 Tf
17.51 6.13 Td
(r)Tj
/T1_8 5.98 Tf
3.82 -1.21 Td
(i;)Tj
/T1_9 5.98 Tf
4.94 0 Td
(1)Tj
/T1_4 7.97 Tf
-9.24 -8.18 Td
(i;)Tj
/T1_5 7.97 Tf
(2)Tj
/T1_2 10.91 Tf
13.88 3.26 Td
(jj)Tj
/T1_3 10.91 Tf
6.06 0 Td
(SID)Tj
/T1_4 7.97 Tf
17.18 -1.64 Td
(i)Tj
/T1_1 10.91 Tf
3.38 1.64 Td
[(\).)-485(Then,)]TJ
/T1_2 10.91 Tf
44.26 0 Td
(A)Tj
/T1_1 10.91 Tf
12.5 0 Td
[(has)-346(to)-347(compute)-348(the)-347(v)55(alid)-346(signature)-401(\271)]TJ
/T1_6 10.91 Tf
170.4 0 Td
(\276)Tj
/T1_4 7.97 Tf
6.23 -1.64 Td
(i;)Tj
/T1_5 7.97 Tf
5.23 0 Td
(1)Tj
/T1_1 10.91 Tf
8.02 1.64 Td
(=)Tj
/T1_2 10.91 Tf
11.76 0 Td
(S)Tj
/T1_1 10.91 Tf
7.42 0 Td
(\()Tj
/T1_3 10.91 Tf
(S)Tj
/T1_4 7.97 Tf
9.97 -1.64 Td
(i)Tj
/T1_2 10.91 Tf
3.38 1.64 Td
(jj)Tj
/T1_6 10.91 Tf
6.06 0 Td
(\277)Tj
/T1_4 7.97 Tf
4.76 -1.64 Td
(i)Tj
/T1_2 10.91 Tf
3.38 1.64 Td
(jj)Tj
/T1_11 10.91 Tf
6.82 2.75 Td
(c)Tj
/T1_6 10.91 Tf
-0.76 -2.75 Td
(X)Tj
/T1_4 7.97 Tf
9.04 -1.64 Td
(i)Tj
/T1_2 10.91 Tf
3.38 1.64 Td
(jj)Tj
/T1_6 10.91 Tf
6.06 0 Td
(X)Tj
/T1_4 7.97 Tf
9.03 -1.64 Td
(i;)Tj
/T1_5 7.97 Tf
(1)Tj
/T1_2 10.91 Tf
9.97 1.64 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(0\).)Tj
-455.15 -21.92 Td
[(The)-313(v)55(alidit)27(y)-312(of)-313(signature)-367(\271)]TJ
/T1_6 10.91 Tf
120.4 0 Td
(\276)Tj
/T1_4 7.97 Tf
6.23 -1.64 Td
(i;)Tj
/T1_5 7.97 Tf
5.23 0 Td
(1)Tj
/T1_1 10.91 Tf
8.15 1.64 Td
[(is)-313(c)27(hec)27(k)28(ed)-312(b)27(y)]TJ
/T1_3 10.91 Tf
65.45 0 Td
(U)Tj
/T1_4 7.97 Tf
5.73 -1.64 Td
(i;j)Tj
/T1_1 10.91 Tf
13.03 1.64 Td
[(for)-313(2)]TJ
/T1_2 10.91 Tf
24.96 0 Td
(\267)Tj
/T1_6 10.91 Tf
11.51 0 Td
(j)Tj
/T1_2 10.91 Tf
8.15 0 Td
(\267)Tj
/T1_6 10.91 Tf
11.51 0 Td
(n)Tj
/T1_4 7.97 Tf
6.54 -1.64 Td
(i)Tj
/T1_1 10.91 Tf
6.8 1.64 Td
[(in)-313(Phase)-313(1)-314(Round)-313(6.)-438(If)-313(the)-314(signature)]TJ
-293.1 -21.92 Td
(\271)Tj
/T1_6 10.91 Tf
-0.59 0 Td
(\276)Tj
/T1_4 7.97 Tf
6.23 -1.63 Td
(i;)Tj
/T1_5 7.97 Tf
(1)Tj
/T1_1 10.91 Tf
13.9 1.63 Td
[(is)-360(not)-361(correct,)-367(then)]TJ
/T1_3 10.91 Tf
95.91 0 Td
(U)Tj
/T1_4 7.97 Tf
5.72 -1.63 Td
(i;j)Tj
/T1_1 10.91 Tf
13.55 1.63 Td
(rejects)Tj
/T1_3 10.91 Tf
34.62 0 Td
(S)Tj
/T1_4 7.97 Tf
5.73 -1.63 Td
(i)Tj
/T1_1 10.91 Tf
3.38 1.63 Td
[(.)-525(As)]TJ
/T1_2 10.91 Tf
25.18 0 Td
(A)Tj
/T1_1 10.91 Tf
12.64 0 Td
[(do)-27(es)-361(not)-361(kno)27(w)-359(the)-361(RSA)-361(priv)55(ate)-360(k)27(ey)]TJ
/T1_6 10.91 Tf
175.61 0 Td
(d)Tj
/T1_4 7.97 Tf
5.68 -1.63 Td
(i)Tj
/T1_1 10.91 Tf
7.31 1.63 Td
(of)Tj
/T1_3 10.91 Tf
12.72 0 Td
(S)Tj
/T1_4 7.97 Tf
5.73 -1.63 Td
(i)Tj
/T1_1 10.91 Tf
7.31 1.63 Td
[(and)-360(the)]TJ
-431.22 -21.91 Td
[(RSA)-295(signature)-295(sc)27(heme)-294(is)-296(assumed)-295(to)-295(b)-28(e)-295(secure,)-303(therefore)]TJ
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271.45 0 Td
(A)Tj
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11.93 0 Td
[(is)-294(not)-296(able)-295(to)-295(pro)-28(duce)-295(a)-295(v)54(alid)-294(signature)]TJ
-282.79 -21.92 Td
(\271)Tj
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-0.59 0 Td
(\276)Tj
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6.23 -1.64 Td
(i;)Tj
/T1_5 7.97 Tf
(1)Tj
/T1_1 10.91 Tf
9.97 1.64 Td
[(.)-425(Next,)-290(supp)-28(ose)-278(the)-279(adv)27(ersary)]TJ
/T1_2 10.91 Tf
144.4 0 Td
(A)Tj
/T1_1 10.91 Tf
11.75 0 Td
[(tries)-278(to)-279(imp)-27(ersonate)]TJ
/T1_3 10.91 Tf
97.45 0 Td
(S)Tj
/T1_4 7.97 Tf
5.73 -1.64 Td
(i)Tj
/T1_1 10.91 Tf
6.42 1.64 Td
[(in)-278(Phase)-279(2,)-289(then)-279(in)-279(Phase)-278(2)-279(Round)-278(1,)]TJ
/T1_2 10.91 Tf
177.21 0 Td
(A)Tj
/T1_1 10.91 Tf
-459.16 -21.92 Td
(generates)Tj
/T1_6 10.91 Tf
48.06 0 Td
(y)Tj
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5.35 -1.63 Td
(i)Tj
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6.58 1.63 Td
(=)Tj
/T1_6 10.91 Tf
11.68 0 Td
(g)Tj
/T1_4 7.97 Tf
5.59 3.96 Td
(K)Tj
/T1_8 5.98 Tf
7.14 -1.21 Td
(i)Tj
/T1_1 10.91 Tf
6.69 -2.75 Td
[(mo)-27(d)]TJ
/T1_6 10.91 Tf
23.93 0 Td
(p)Tj
/T1_1 10.91 Tf
[(.)-472(Next)]TJ
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40.43 0 Td
(A)Tj
/T1_1 10.91 Tf
12.45 0 Td
[(has)-342(to)-343(generate)-342(the)-343(v)55(alid)-342(signature)]TJ
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169.53 0 Td
(\276)Tj
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6.23 -1.63 Td
(i)Tj
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6.58 1.63 Td
(=)Tj
/T1_2 10.91 Tf
11.69 0 Td
(S)Tj
/T1_1 10.91 Tf
7.42 0 Td
(\()Tj
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(S)Tj
/T1_4 7.97 Tf
9.97 -1.63 Td
(i)Tj
/T1_2 10.91 Tf
3.38 1.63 Td
(jj)Tj
/T1_6 10.91 Tf
6.05 0 Td
(y)Tj
/T1_4 7.97 Tf
5.35 -1.63 Td
(i)Tj
/T1_1 10.91 Tf
3.38 1.63 Td
[(\).)-472(The)-343(v)55(alidit)27(y)]TJ
-397.48 -21.91 Td
(of)Tj
/T1_6 10.91 Tf
12.91 0 Td
(\276)Tj
/T1_4 7.97 Tf
6.24 -1.64 Td
(i)Tj
/T1_1 10.91 Tf
7.5 1.64 Td
[(is)-379(c)27(hec)28(k)28(ed)-378(b)27(y)]TJ
/T1_3 10.91 Tf
67.59 0 Td
(C)Tj
/T1_1 10.91 Tf
9.85 0 Td
[(in)-378(Phase)-379(2)-378(Round)-379(2.)-580(If)-379(signature)]TJ
/T1_6 10.91 Tf
164.85 0 Td
(\276)Tj
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6.23 -1.64 Td
(i)Tj
/T1_1 10.91 Tf
7.51 1.64 Td
[(is)-378(not)-379(correct,)-390(then)]TJ
/T1_3 10.91 Tf
96.74 0 Td
(C)Tj
/T1_1 10.91 Tf
9.85 0 Td
(rejects)Tj
/T1_3 10.91 Tf
34.82 0 Td
(S)Tj
/T1_4 7.97 Tf
5.73 -1.64 Td
(i)Tj
/T1_1 10.91 Tf
3.38 1.64 Td
[(.)-579(As)]TJ
/T1_2 10.91 Tf
25.96 0 Td
(A)Tj
/T1_1 10.91 Tf
-459.16 -21.92 Td
[(do)-27(es)-289(not)-289(kno)26(w)-288(the)-289(RSA)-289(priv)55(ate)-289(k)27(ey)]TJ
/T1_6 10.91 Tf
170.15 0 Td
(d)Tj
/T1_4 7.97 Tf
5.68 -1.63 Td
(i)Tj
/T1_1 10.91 Tf
6.53 1.63 Td
(of)Tj
/T1_3 10.91 Tf
11.94 0 Td
(S)Tj
/T1_4 7.97 Tf
5.72 -1.63 Td
(i)Tj
/T1_1 10.91 Tf
6.54 1.63 Td
[(and)-288(the)-290(RSA)-289(signature)-289(sc)27(heme)-288(is)-289(assumed)-289(to)-289(b)-28(e)-289(secure,)]TJ
-206.56 -21.92 Td
(therefore)Tj
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45.75 0 Td
(A)Tj
/T1_1 10.91 Tf
12.28 0 Td
[(is)-327(not)-328(able)-328(to)-328(pro)-28(duce)-328(a)-327(v)54(alid)-327(signature)]TJ
/T1_6 10.91 Tf
190.56 0 Td
(\276)Tj
/T1_4 7.97 Tf
6.23 -1.63 Td
(i)Tj
/T1_1 10.91 Tf
3.38 1.63 Td
[(.)-442(Therefore,)]TJ
/T1_2 10.91 Tf
60.28 0 Td
(A)Tj
/T1_1 10.91 Tf
12.29 0 Td
[(is)-327(not)-328(able)-328(to)-328(imp)-27(ersonate)]TJ
/T1_3 10.91 Tf
128 0 Td
(S)Tj
/T1_4 7.97 Tf
5.72 -1.63 Td
(i)Tj
/T1_1 10.91 Tf
-464.49 -20.28 Td
[(to)-333(establish)-333(the)-333(subgroup)-334(k)27(ey)]TJ
/T1_6 10.91 Tf
144.11 0 Td
(K)Tj
/T1_4 7.97 Tf
9.26 -1.64 Td
(i)Tj
/T1_1 10.91 Tf
7.02 1.64 Td
[(and)-333(\257nal)-333(group)-334(k)27(ey)]TJ
/T1_6 10.91 Tf
96.06 0 Td
(K)Tj
/T1_1 10.91 Tf
10.05 0 Td
(.)Tj
-249.57 -21.92 Td
[(Next,)-449(w)27(e)-425(consider)]TJ
/T1_2 10.91 Tf
91.53 0 Td
(A)Tj
/T1_1 10.91 Tf
13.36 0 Td
[(tries)-425(to)-426(imp)-28(ersonate)-426(user)]TJ
/T1_3 10.91 Tf
126.4 0 Td
(U)Tj
/T1_4 7.97 Tf
5.72 -1.63 Td
(i;j)Tj
/T1_1 10.91 Tf
9.62 1.63 Td
[(.)-722(Then)-426(in)-425(Phase)-426(1)-426(Round)-426(2,)]TJ
/T1_2 10.91 Tf
146.64 0 Td
(A)Tj
/T1_1 10.91 Tf
13.35 0 Td
(generates)Tj
/T1_6 10.91 Tf
-423.55 -21.91 Td
(z)Tj
/T1_4 7.97 Tf
5.07 -1.64 Td
(i;j)Tj
/T1_1 10.91 Tf
15.3 1.64 Td
(=)Tj
/T1_6 10.91 Tf
14.16 0 Td
(g)Tj
/T1_4 7.97 Tf
5.6 3.95 Td
(r)Tj
/T1_8 5.98 Tf
3.82 -1.21 Td
(i;j)Tj
/T1_1 10.91 Tf
12.36 -2.74 Td
[(mo)-27(d)]TJ
/T1_6 10.91 Tf
23.93 0 Td
(p)Tj
/T1_1 10.91 Tf
[(.)-881(Next,)]TJ
/T1_2 10.91 Tf
49.81 0 Td
(A)Tj
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T*
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[(\257rst)-292(use)-292(the)-293(public)-292(k)26(ey)-291(in)-293(the)-292(certi\257cate)-293(to)-292(v)27(erify)-292(the)-292(signature.)-431(If)-292(signature)-293(is)-292(not)-293(v)55(alid,)-300(then)-292(there)]TJ
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[(insider)-397(attac)27(ks)-397(to)-397(disrupt)-398(and)-397(halt)-398(the)-397(Initial)-398(GKA)-397(Proto)-28(col)-398(b)27(y)-396(sending)-398(wrong)-397(information)-398(that)]TJ
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17.81 0 Td
(n)Tj
/T1_2 7.97 Tf
6.55 -1.69 Td
(J)Tj
/T1_0 10.91 Tf
9.04 1.69 Td
[(+)-290(1)]TJ
/T1_5 10.91 Tf
21.99 0 Td
(\267)Tj
/T1_3 10.91 Tf
13.38 0 Td
(k)Tj
/T1_5 10.91 Tf
10.91 0 Td
(\267)Tj
/T1_3 10.91 Tf
13.38 0 Td
(n)Tj
/T1_2 7.97 Tf
6.54 -1.69 Td
(J)Tj
/T1_0 10.91 Tf
9.04 1.69 Td
(+)Tj
/T1_3 10.91 Tf
11.65 0 Td
(m)Tj
/T1_0 10.91 Tf
14.33 0 Td
[(tries)-436(to)-435(obtain)-436(the)-436(previous)]TJ
-333.25 -21.91 Td
[(subgroup)-492(k)27(ey)]TJ
/T1_3 10.91 Tf
70.51 0 Td
(K)Tj
/T1_2 7.97 Tf
9.27 -1.69 Td
(J)Tj
/T1_0 10.91 Tf
11.79 1.69 Td
(=)Tj
/T1_9 10.91 Tf
14.41 0 Td
(H)Tj
/T1_0 10.91 Tf
(\()Tj
/T1_3 10.91 Tf
(\267)Tj
/T1_2 7.97 Tf
18.25 -1.69 Td
[(J)24(;)]TJ
/T1_10 7.97 Tf
(1)Tj
/T1_5 10.91 Tf
11.51 1.69 Td
(jj)Tj
/T1_3 10.91 Tf
6.06 0 Td
(\267)Tj
/T1_2 7.97 Tf
6.28 -1.69 Td
[(J)23(;)]TJ
/T1_10 7.97 Tf
(2)Tj
/T1_5 10.91 Tf
11.52 1.69 Td
[(jj)-492(\242)-166(\242)-167(\242)-167(jj)]TJ
/T1_3 10.91 Tf
32.03 0 Td
(\267)Tj
/T1_2 7.97 Tf
6.28 -1.69 Td
[(J)23(;n)]TJ
/T1_11 5.98 Tf
11.92 -1.34 Td
(J)Tj
/T1_5 10.91 Tf
5.64 3.03 Td
(jj)Tj
/T1_0 10.91 Tf
6.06 0 Td
[(0\))-492(from)-492(the)-493(Join)-492(Proto)-28(col,)-532(then)]TJ
/T1_1 10.91 Tf
164.5 0 Td
(U)Tj
/T1_2 7.97 Tf
5.73 -1.78 Td
[(J)24(;k)]TJ
/T1_0 10.91 Tf
17.27 1.78 Td
[(\257rst)-492(obtains)]TJ
/T1_3 10.91 Tf
-409.03 -21.92 Td
(K)Tj
/T1_6 7.97 Tf
10.04 3.96 Td
(0)Tj
/T1_2 7.97 Tf
-0.78 -7.19 Td
(J)Tj
/T1_0 10.91 Tf
9.82 3.23 Td
(=)Tj
/T1_9 10.91 Tf
12.44 0 Td
(H)Tj
/T1_0 10.91 Tf
(\()Tj
/T1_3 10.91 Tf
(\267)Tj
/T1_6 7.97 Tf
18.25 3.96 Td
(0)Tj
/T1_2 7.97 Tf
0 -7.19 TD
[(J)24(;)]TJ
/T1_10 7.97 Tf
(1)Tj
/T1_5 10.91 Tf
11.51 3.23 Td
(jj)Tj
/T1_3 10.91 Tf
6.06 0 Td
(\267)Tj
/T1_6 7.97 Tf
6.29 3.96 Td
(0)Tj
/T1_2 7.97 Tf
T*
[(J)24(;n)]TJ
/T1_11 5.98 Tf
11.92 -1.34 Td
(J)Tj
/T1_10 7.97 Tf
5.13 1.34 Td
(+1)Tj
/T1_5 10.91 Tf
11.32 3.23 Td
[(jj)-166(\242)-167(\242)-166(\242)-167(jj)]TJ
/T1_3 10.91 Tf
28.47 0 Td
(\267)Tj
/T1_6 7.97 Tf
6.29 3.96 Td
(0)Tj
/T1_2 7.97 Tf
T*
[(J)24(;n)]TJ
/T1_11 5.98 Tf
11.92 -1.34 Td
(J)Tj
/T1_10 7.97 Tf
5.14 1.34 Td
(+)Tj
/T1_2 7.97 Tf
(m)Tj
/T1_5 10.91 Tf
14.57 3.23 Td
(jj)Tj
/T1_3 10.91 Tf
6.06 0 Td
(v)Tj
/T1_0 10.91 Tf
5.67 0 Td
[(\))-384(from)-384(the)-384(Join)-384(Proto)-28(col.)-596(As)]TJ
/T1_3 10.91 Tf
145.11 0 Td
(\267)Tj
/T1_6 7.97 Tf
6.29 3.96 Td
(0)Tj
/T1_2 7.97 Tf
T*
[(J)24(;)]TJ
/T1_10 7.97 Tf
(1)Tj
/T1_0 10.91 Tf
15.7 3.23 Td
(and)Tj
/T1_3 10.91 Tf
21.76 0 Td
(\267)Tj
/T1_2 7.97 Tf
6.28 -1.69 Td
[(J)23(;)]TJ
/T1_10 7.97 Tf
(1)Tj
/T1_0 10.91 Tf
15.71 1.69 Td
[(are)-383(random)-384(and)]TJ
-390.97 -21.92 Td
[(indep)-27(enden)27(t)-384(to)-384(eac)27(h)-383(other,)-397(therefore)]TJ
/T1_3 10.91 Tf
179.93 0 Td
(K)Tj
/T1_6 7.97 Tf
10.04 3.96 Td
(0)Tj
/T1_2 7.97 Tf
-0.78 -7.19 Td
(J)Tj
/T1_0 10.91 Tf
10.06 3.23 Td
(and)Tj
/T1_3 10.91 Tf
21.76 0 Td
(K)Tj
/T1_2 7.97 Tf
9.27 -1.69 Td
(J)Tj
/T1_0 10.91 Tf
10.06 1.69 Td
[(are)-384(indep)-27(enden)26(t)-383(to)-384(eac)27(h)-384(other)-384(as)-384(the)-384(output)-385(of)]TJ
-240.34 -21.91 Td
[(the)-423(hash)-423(function)]TJ
/T1_9 10.91 Tf
89.96 0 Td
(H)Tj
/T1_0 10.91 Tf
12.34 0 Td
[(is)-423(indep)-28(enden)27(t.)-714(Since)]TJ
/T1_1 10.91 Tf
110.4 0 Td
(U)Tj
/T1_2 7.97 Tf
5.73 -1.78 Td
[(J)24(;k)]TJ
/T1_0 10.91 Tf
16.52 1.78 Td
[(kno)28(ws)]TJ
/T1_3 10.91 Tf
33.76 0 Td
(\267)Tj
/T1_6 7.97 Tf
6.28 3.95 Td
(0)Tj
/T1_2 7.97 Tf
T*
[(J)23(;)]TJ
/T1_10 7.97 Tf
(1)Tj
/T1_0 10.91 Tf
11.52 3.24 Td
(,)Tj
/T1_3 10.91 Tf
7.89 0 Td
(\267)Tj
/T1_6 7.97 Tf
6.28 3.95 Td
(0)Tj
/T1_2 7.97 Tf
0 -7.27 TD
[(J)23(;k)]TJ
/T1_0 10.91 Tf
16.53 3.32 Td
(for)Tj
/T1_3 10.91 Tf
17.67 0 Td
(n)Tj
/T1_2 7.97 Tf
6.55 -1.69 Td
(J)Tj
/T1_0 10.91 Tf
8.95 1.69 Td
[(+)-281(1)]TJ
/T1_5 10.91 Tf
21.68 0 Td
(\267)Tj
/T1_3 10.91 Tf
13.15 0 Td
(k)Tj
/T1_5 10.91 Tf
10.69 0 Td
(\267)Tj
/T1_3 10.91 Tf
13.15 0 Td
(n)Tj
/T1_2 7.97 Tf
6.54 -1.69 Td
(J)Tj
/T1_0 10.91 Tf
8.95 1.69 Td
(+)Tj
/T1_3 10.91 Tf
11.57 0 Td
(m)Tj
/T1_0 10.91 Tf
14.19 0 Td
(and)Tj
-450.3 -21.92 Td
(also)Tj
/T1_3 10.91 Tf
22.5 0 Td
(\267)Tj
/T1_2 7.97 Tf
6.28 -1.69 Td
[(J)24(;j)]TJ
/T1_0 10.91 Tf
15.42 1.69 Td
[(for)-390(2)]TJ
/T1_5 10.91 Tf
26.84 0 Td
(\267)Tj
/T1_3 10.91 Tf
12.55 0 Td
(j)Tj
/T1_5 10.91 Tf
9.18 0 Td
(\267)Tj
/T1_3 10.91 Tf
12.55 0 Td
(n)Tj
/T1_2 7.97 Tf
6.55 -1.69 Td
(J)Tj
/T1_0 10.91 Tf
10.13 1.69 Td
[(from)-390(the)-390(previous)-390(GKA,)-391(w)27(e)-389(consider)-391(whether)]TJ
/T1_1 10.91 Tf
224.61 0 Td
(U)Tj
/T1_2 7.97 Tf
5.73 -1.78 Td
[(J)24(;k)]TJ
/T1_0 10.91 Tf
16.16 1.78 Td
[(can)-390(obtain)]TJ
/T1_3 10.91 Tf
55.17 0 Td
(\267)Tj
/T1_2 7.97 Tf
6.28 -1.69 Td
[(J)23(;)]TJ
/T1_10 7.97 Tf
(1)Tj
/T1_0 10.91 Tf
15.78 1.69 Td
(from)Tj
-445.73 -21.92 Td
[(the)-403(information)-404(he)-404(kno)26(ws)-403(in)-404(the)-404(Join)-404(Proto)-27(col)-404(and)-404(compute)-404(the)-404(previous)-404(subgroup)-404(k)26(ey)]TJ
/T1_3 10.91 Tf
430.07 0 Td
(K)Tj
/T1_2 7.97 Tf
9.26 -1.68 Td
(J)Tj
/T1_0 10.91 Tf
5.87 1.68 Td
[(.)-656(As)]TJ
/T1_3 10.91 Tf
-445.2 -21.91 Td
(\277)Tj
/T1_6 7.97 Tf
6 3.95 Td
(0)Tj
/T1_2 7.97 Tf
-1.23 -7.19 Td
(J)Tj
/T1_0 10.91 Tf
9.85 3.24 Td
(and)Tj
/T1_3 10.91 Tf
21.54 0 Td
(\277)Tj
/T1_2 7.97 Tf
4.77 -1.69 Td
(J)Tj
/T1_0 10.91 Tf
9.85 1.69 Td
[(are)-364(random)-365(and)-365(indep)-28(enden)27(t)-363(to)-365(eac)27(h)-364(other,)-373(therefore,)]TJ
/T1_1 10.91 Tf
262.38 0 Td
(SID)Tj
/T1_6 7.97 Tf
17.18 3.95 Td
(0)Tj
/T1_2 7.97 Tf
0 -7.19 TD
(J)Tj
/T1_0 10.91 Tf
9.47 3.24 Td
(=)Tj
/T1_9 10.91 Tf
12.08 0 Td
(H)Tj
/T1_0 10.91 Tf
7.73 0 Td
(\()Tj
/T1_3 10.91 Tf
(\277)Tj
/T1_6 7.97 Tf
10.24 3.95 Td
(0)Tj
/T1_2 7.97 Tf
-1.23 -7.19 Td
(J)Tj
/T1_5 10.91 Tf
5.87 3.24 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(U)Tj
/T1_2 7.97 Tf
5.72 -1.69 Td
[(J)23(;)]TJ
/T1_10 7.97 Tf
(1)Tj
/T1_5 10.91 Tf
11.52 1.69 Td
[(jj)-166(\242)-167(\242)-166(\242)-167(jj)]TJ
/T1_1 10.91 Tf
28.48 0 Td
(U)Tj
/T1_2 7.97 Tf
5.72 -1.69 Td
[(J)23(;n)]TJ
/T1_11 5.98 Tf
11.92 -1.34 Td
(J)Tj
/T1_10 7.97 Tf
5.14 1.34 Td
(+)Tj
/T1_2 7.97 Tf
(m)Tj
/T1_0 10.91 Tf
14.57 1.69 Td
(\))Tj
-463.63 -21.92 Td
(and)Tj
/T1_1 10.91 Tf
22.04 0 Td
(SID)Tj
/T1_2 7.97 Tf
17.18 -1.69 Td
(J)Tj
/T1_0 10.91 Tf
10.3 1.69 Td
(=)Tj
/T1_9 10.91 Tf
12.91 0 Td
(H)Tj
/T1_0 10.91 Tf
(\()Tj
/T1_3 10.91 Tf
11.97 0 Td
(\277)Tj
/T1_2 7.97 Tf
4.76 -1.69 Td
(J)Tj
/T1_5 10.91 Tf
5.87 1.69 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(U)Tj
/T1_2 7.97 Tf
5.73 -1.69 Td
[(J)24(;)]TJ
/T1_10 7.97 Tf
(1)Tj
/T1_5 10.91 Tf
11.51 1.69 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(U)Tj
/T1_2 7.97 Tf
5.73 -1.69 Td
[(J)24(;)]TJ
/T1_10 7.97 Tf
(2)Tj
/T1_5 10.91 Tf
11.51 1.69 Td
[(jj)-166(\242)-167(\242)-167(\242)-166(jj)]TJ
/T1_1 10.91 Tf
28.48 0 Td
(U)Tj
/T1_2 7.97 Tf
5.73 -1.69 Td
[(J)24(;n)]TJ
/T1_11 5.98 Tf
11.92 -1.34 Td
(J)Tj
/T1_0 10.91 Tf
5.63 3.03 Td
[(\))-410(are)-410(indep)-28(enden)27(t)-409(to)-410(eac)26(h)-409(other)-410(as)-410(the)-410(output)-411(of)-410(the)-410(hash)]TJ
-183.39 -21.92 Td
(function)Tj
/T1_9 10.91 Tf
41.92 0 Td
(H)Tj
/T1_0 10.91 Tf
10.57 0 Td
[(is)-259(indep)-28(enden)27(t.)-420(F)83(urthermore,)-274(as)]TJ
/T1_3 10.91 Tf
154.19 0 Td
(r)Tj
/T1_6 7.97 Tf
5.22 3.96 Td
(0)Tj
/T1_2 7.97 Tf
-0.3 -7.19 Td
[(J)24(;)]TJ
/T1_10 7.97 Tf
(1)Tj
/T1_0 10.91 Tf
14.35 3.23 Td
(and)Tj
/T1_3 10.91 Tf
20.41 0 Td
(r)Tj
/T1_2 7.97 Tf
4.92 -1.68 Td
[(J)23(;)]TJ
/T1_10 7.97 Tf
(1)Tj
/T1_0 10.91 Tf
14.36 1.68 Td
[(are)-260(random)-260(and)-261(indep)-27(enden)26(t)-259(to)-260(eac)26(h)-259(other,)]TJ
-265.64 -21.91 Td
(therefore)Tj
/T1_3 10.91 Tf
45.18 0 Td
(g)Tj
/T1_2 7.97 Tf
5.6 5.9 Td
(r)Tj
/T1_12 5.98 Tf
4.05 2.81 Td
(0)Tj
/T1_11 5.98 Tf
-0.23 -5.51 Td
[(J)35(;)]TJ
/T1_13 5.98 Tf
6.13 0 Td
(1)Tj
/T1_2 7.97 Tf
4.15 2.7 Td
(r)Tj
/T1_12 5.98 Tf
4.06 2.81 Td
(0)Tj
/T1_11 5.98 Tf
-0.24 -5.51 Td
[(J)34(;n)]TJ
10.73 -2.03 Td
(J)Tj
/T1_13 5.98 Tf
5.14 2.03 Td
(+1)Tj
/T1_0 10.91 Tf
13.25 -3.2 Td
(and)Tj
/T1_3 10.91 Tf
20.59 0 Td
(g)Tj
/T1_2 7.97 Tf
5.59 3.96 Td
(r)Tj
/T1_11 5.98 Tf
3.82 -1.34 Td
[(J)35(;)]TJ
/T1_13 5.98 Tf
6.13 0 Td
(1)Tj
/T1_2 7.97 Tf
4.15 1.34 Td
(r)Tj
/T1_11 5.98 Tf
3.82 -1.34 Td
[(J)34(;)]TJ
/T1_13 5.98 Tf
6.13 0 Td
(2)Tj
/T1_0 10.91 Tf
7.67 -2.62 Td
[(are)-276(indep)-27(enden)26(t)-275(to)-276(eac)26(h)-275(other.)-425(Hence,)]TJ
/T1_3 10.91 Tf
182.88 0 Td
(R)Tj
/T1_6 7.97 Tf
8.36 3.96 Td
(0)Tj
/T1_2 7.97 Tf
-0.08 -7.19 Td
[(J)24(;)]TJ
/T1_10 7.97 Tf
(1)Tj
/T1_0 10.91 Tf
14.54 3.23 Td
(=)Tj
/T1_9 10.91 Tf
11.52 0 Td
(H)Tj
/T1_0 10.91 Tf
(\()Tj
/T1_3 10.91 Tf
(g)Tj
/T1_2 7.97 Tf
17.56 5.9 Td
(r)Tj
/T1_12 5.98 Tf
4.05 2.81 Td
(0)Tj
/T1_11 5.98 Tf
-0.23 -5.51 Td
[(J)35(;)]TJ
/T1_13 5.98 Tf
6.13 0 Td
(1)Tj
/T1_2 7.97 Tf
4.15 2.7 Td
(r)Tj
/T1_12 5.98 Tf
4.05 2.81 Td
(0)Tj
/T1_11 5.98 Tf
-0.23 -5.51 Td
[(J)35(;n)]TJ
10.73 -2.03 Td
(J)Tj
/T1_13 5.98 Tf
5.14 2.03 Td
(+1)Tj
/T1_5 10.91 Tf
10.23 -3.2 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(SID)Tj
/T1_6 7.97 Tf
17.18 3.96 Td
(0)Tj
/T1_2 7.97 Tf
T*
(J)Tj
/T1_0 10.91 Tf
5.87 3.23 Td
(\))Tj
-463.63 -21.92 Td
(and)Tj
/T1_3 10.91 Tf
21.65 0 Td
(R)Tj
/T1_2 7.97 Tf
8.28 -1.69 Td
[(J)24(;)]TJ
/T1_10 7.97 Tf
(1)Tj
/T1_0 10.91 Tf
15.27 1.69 Td
(=)Tj
/T1_9 10.91 Tf
12.25 0 Td
(H)Tj
/T1_0 10.91 Tf
(\()Tj
/T1_3 10.91 Tf
11.97 0 Td
(g)Tj
/T1_2 7.97 Tf
5.59 3.96 Td
(r)Tj
/T1_11 5.98 Tf
3.82 -1.34 Td
[(J)35(;)]TJ
/T1_13 5.98 Tf
6.13 0 Td
(1)Tj
/T1_2 7.97 Tf
4.15 1.34 Td
(r)Tj
/T1_11 5.98 Tf
3.82 -1.34 Td
[(J)34(;)]TJ
/T1_13 5.98 Tf
6.13 0 Td
(2)Tj
/T1_5 10.91 Tf
4.65 -2.62 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(SID)Tj
/T1_2 7.97 Tf
17.18 -1.69 Td
(J)Tj
/T1_0 10.91 Tf
5.87 1.69 Td
[(\))-373(are)-374(indep)-27(enden)26(t)-372(to)-374(eac)27(h)-373(other)-374(as)-373(the)-374(output)-374(of)-373(the)-374(hash)-374(function)]TJ
/T1_9 10.91 Tf
327.33 0 Td
(H)Tj
/T1_0 10.91 Tf
-460.15 -21.92 Td
[(is)-432(indep)-28(enden)27(t.)-743(Hence,)]TJ
/T1_14 10.91 Tf
120.16 3.49 Td
(c)Tj
/T1_3 10.91 Tf
-2 -3.49 Td
(X)Tj
/T1_6 7.97 Tf
9.89 3.76 Td
(0)Tj
/T1_2 7.97 Tf
-0.86 -7.19 Td
(J)Tj
/T1_0 10.91 Tf
10.71 3.43 Td
(=)Tj
/T1_3 10.91 Tf
13.33 0 Td
(\267)Tj
/T1_6 7.97 Tf
6.28 3.96 Td
(0)Tj
/T1_2 7.97 Tf
T*
[(J)24(;)]TJ
/T1_10 7.97 Tf
(1)Tj
/T1_5 10.91 Tf
14.66 3.23 Td
(\251)Tj
/T1_3 10.91 Tf
11.63 0 Td
(R)Tj
/T1_6 7.97 Tf
8.37 3.96 Td
(0)Tj
/T1_2 7.97 Tf
-0.09 -7.19 Td
[(J)23(;)]TJ
/T1_10 7.97 Tf
(1)Tj
/T1_0 10.91 Tf
16.24 3.23 Td
(and)Tj
/T1_14 10.91 Tf
24.29 2.76 Td
(c)Tj
/T1_3 10.91 Tf
-2 -2.76 Td
(X)Tj
/T1_2 7.97 Tf
9.04 -1.68 Td
(J)Tj
/T1_0 10.91 Tf
10.71 1.68 Td
(=)Tj
/T1_3 10.91 Tf
13.32 0 Td
(\267)Tj
/T1_2 7.97 Tf
6.29 -1.68 Td
[(J)24(;)]TJ
/T1_10 7.97 Tf
(1)Tj
/T1_5 10.91 Tf
14.66 1.68 Td
(\251)Tj
/T1_3 10.91 Tf
11.63 0 Td
(R)Tj
/T1_2 7.97 Tf
8.28 -1.68 Td
[(J)24(;)]TJ
/T1_10 7.97 Tf
(1)Tj
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4.16 1.63 Td
[(,)-426(and)]TJ
/T1_3 10.91 Tf
29.7 0 Td
(g)Tj
/T1_2 7.97 Tf
5.59 3.96 Td
(r)Tj
/T1_12 5.98 Tf
4.06 2.81 Td
(0)Tj
/T1_10 5.98 Tf
-0.24 -5.08 Td
(C)Tj
/T1_2 7.97 Tf
3.67 2.27 Td
(K)Tj
/T1_12 5.98 Tf
7.71 2.81 Td
(0)Tj
/T1_4 5.98 Tf
-0.57 -5.52 Td
(J)Tj
/T1_0 10.91 Tf
10.08 -1.25 Td
(and)Tj
/T1_3 10.91 Tf
22.02 0 Td
(g)Tj
/T1_2 7.97 Tf
5.59 3.96 Td
(r)Tj
/T1_10 5.98 Tf
3.83 -1 Td
(C)Tj
/T1_2 7.97 Tf
3.67 1 Td
(K)Tj
/T1_4 5.98 Tf
7.14 -1.34 Td
(J)Tj
/T1_0 10.91 Tf
10.08 -2.62 Td
[(are)-407(indep)-28(enden)27(t)-407(to)-407(eac)26(h)-406(other)-408(resp)-28(ectiv)27(ely)83(.)-666(Hence,)]TJ
/T1_3 10.91 Tf
252.13 0 Td
(K)Tj
/T1_11 7.97 Tf
10.04 3.96 Td
(0)Tj
/T1_0 10.91 Tf
7.24 -3.96 Td
(and)Tj
/T1_3 10.91 Tf
22.02 0 Td
(K)Tj
/T1_0 10.91 Tf
14.49 0 Td
(are)Tj
-453.3 -21.91 Td
[(indep)-27(enden)27(t)-430(to)-431(eac)27(h)-430(other.)-736(F)82(urthermore,)-454(if)]TJ
/T1_1 10.91 Tf
217.45 0 Td
(U)Tj
/T1_2 7.97 Tf
5.73 -1.78 Td
[(J)24(;k)]TJ
/T1_0 10.91 Tf
16.6 1.78 Td
[(can)-430(obtain)]TJ
/T1_3 10.91 Tf
56.04 0 Td
(g)Tj
/T1_2 7.97 Tf
5.6 3.95 Td
(r)Tj
/T1_10 5.98 Tf
3.82 -0.99 Td
(C)Tj
/T1_2 7.97 Tf
3.67 0.99 Td
(r)Tj
/T1_10 5.98 Tf
3.82 -0.99 Td
(C)Tj
/T1_0 10.91 Tf
8.87 -2.96 Td
(from)Tj
/T1_3 10.91 Tf
26.84 0 Td
(y)Tj
/T1_10 7.97 Tf
5.35 -1.64 Td
(C)Tj
/T1_0 10.91 Tf
9.53 1.64 Td
(=)Tj
/T1_3 10.91 Tf
13.28 0 Td
(g)Tj
/T1_2 7.97 Tf
5.59 3.95 Td
(r)Tj
/T1_10 5.98 Tf
3.82 -0.99 Td
(C)Tj
/T1_0 10.91 Tf
8.87 -2.96 Td
(and)Tj
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22.26 0 Td
(g)Tj
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5.6 3.95 Td
(r)Tj
/T1_10 5.98 Tf
3.82 -0.99 Td
(C)Tj
/T1_2 7.97 Tf
3.67 0.99 Td
(K)Tj
/T1_4 5.98 Tf
7.14 -1.21 Td
(i)Tj
/T1_0 10.91 Tf
8.36 -2.74 Td
(from)Tj
/T1_3 10.91 Tf
-445.73 -21.92 Td
(y)Tj
/T1_10 7.97 Tf
5.35 -1.64 Td
(C)Tj
/T1_0 10.91 Tf
9.1 1.64 Td
(=)Tj
/T1_3 10.91 Tf
12.85 0 Td
(g)Tj
/T1_2 7.97 Tf
5.6 3.96 Td
(r)Tj
/T1_10 5.98 Tf
3.82 -1 Td
(C)Tj
/T1_0 10.91 Tf
8.61 -2.96 Td
(and)Tj
/T1_3 10.91 Tf
22.01 0 Td
(y)Tj
/T1_2 7.97 Tf
5.35 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
7.75 1.64 Td
(=)Tj
/T1_3 10.91 Tf
12.85 0 Td
(g)Tj
/T1_2 7.97 Tf
5.59 3.96 Td
(K)Tj
/T1_4 5.98 Tf
7.14 -1.22 Td
(i)Tj
/T1_0 10.91 Tf
8.1 -2.74 Td
[(for)-407(1)]TJ
/T1_8 10.91 Tf
27.32 0 Td
(\267)Tj
/T1_3 10.91 Tf
12.86 0 Td
(i)Tj
/T1_8 10.91 Tf
8.12 0 Td
(\267)Tj
/T1_3 10.91 Tf
12.86 0 Td
(n)Tj
/T1_2 7.97 Tf
6.54 -1.64 Td
(c)Tj
/T1_0 10.91 Tf
8.61 1.64 Td
[(resp)-27(ectiv)27(ely)83(,)-425(then)]TJ
/T1_1 10.91 Tf
88.24 0 Td
(U)Tj
/T1_2 7.97 Tf
5.73 -1.78 Td
[(J)24(;k)]TJ
/T1_0 10.91 Tf
16.34 1.78 Td
[(can)-407(obtain)-407(the)-407(previous)-407(group)-407(k)27(ey)]TJ
/T1_3 10.91 Tf
-300.74 -21.92 Td
(K)Tj
/T1_0 10.91 Tf
13.07 0 Td
(=)Tj
/T1_3 10.91 Tf
11.51 0 Td
(g)Tj
/T1_2 7.97 Tf
5.6 3.96 Td
(r)Tj
/T1_10 5.98 Tf
3.82 -1 Td
(C)Tj
/T1_2 7.97 Tf
3.67 1 Td
(r)Tj
/T1_10 5.98 Tf
3.82 -1 Td
(C)Tj
/T1_6 7.97 Tf
3.67 1 Td
(+)Tj
/T1_2 7.97 Tf
6.59 0 Td
(r)Tj
/T1_10 5.98 Tf
3.82 -1 Td
(C)Tj
/T1_2 7.97 Tf
3.67 1 Td
(K)Tj
/T1_5 5.98 Tf
7.14 -1.11 Td
(1)Tj
/T1_6 7.97 Tf
4.15 1.11 Td
(+)Tj
/T1_2 7.97 Tf
(r)Tj
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10.41 -1 Td
(C)Tj
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3.67 1 Td
(K)Tj
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7.14 -1.11 Td
(2)Tj
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4.15 1.11 Td
(+)Tj
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(\242\242\242)Tj
/T1_6 7.97 Tf
13.64 0 Td
(+)Tj
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(r)Tj
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10.4 -1 Td
(C)Tj
/T1_2 7.97 Tf
3.67 1 Td
(K)Tj
/T1_4 5.98 Tf
7.14 -1.34 Td
(J)Tj
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5.14 1.34 Td
(+)Tj
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6.59 0 Td
(\242\242\242)Tj
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(+)Tj
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(r)Tj
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17.46 -1 Td
(C)Tj
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3.67 1 Td
(K)Tj
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7.14 -1 Td
(n)Tj
4.6 -0.99 Td
(c)Tj
/T1_0 10.91 Tf
4.83 -1.97 Td
[(.)-440(But)-323(this)-322(is)-322(not)-323(p)-27(ossible)-323(for)]TJ
/T1_1 10.91 Tf
138.11 0 Td
(U)Tj
/T1_2 7.97 Tf
5.73 -1.77 Td
[(J)24(;k)]TJ
/T1_0 10.91 Tf
15.41 1.77 Td
[(to)-322(obtain)]TJ
/T1_3 10.91 Tf
47.02 0 Td
(g)Tj
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5.6 3.96 Td
(r)Tj
/T1_10 5.98 Tf
3.82 -1 Td
(C)Tj
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3.67 1 Td
(r)Tj
/T1_10 5.98 Tf
3.82 -1 Td
(C)Tj
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7.69 -2.96 Td
(from)Tj
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25.66 0 Td
(y)Tj
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5.34 -1.63 Td
(C)Tj
/T1_0 10.91 Tf
8.25 1.63 Td
(and)Tj
/T1_3 10.91 Tf
-450.3 -21.91 Td
(g)Tj
/T1_2 7.97 Tf
5.59 3.95 Td
(r)Tj
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3.82 -0.99 Td
(C)Tj
/T1_2 7.97 Tf
3.68 0.99 Td
(K)Tj
/T1_4 5.98 Tf
7.14 -1.21 Td
(i)Tj
/T1_0 10.91 Tf
6.98 -2.74 Td
(from)Tj
/T1_3 10.91 Tf
25.47 0 Td
(y)Tj
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5.35 -1.64 Td
(C)Tj
/T1_0 10.91 Tf
8.06 1.64 Td
(and)Tj
/T1_3 10.91 Tf
20.89 0 Td
(y)Tj
/T1_2 7.97 Tf
5.35 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
6.7 1.64 Td
[(resp)-28(ectiv)27(ely)-304(as)-305(this)-305(is)-305(the)]TJ
/T1_7 10.91 Tf
122.33 0 Td
(CDH)Tj
/T1_0 10.91 Tf
25.9 0 Td
[(problem)-304(and)-305(is)-305(assumed)-305(to)-305(b)-28(e)-305(di\261cult.)-435(Hence,)]TJ
-247.26 -21.92 Td
[(the)-333(Join)-333(Proto)-28(col)-333(ac)27(hiev)27(es)-332(bac)27(kw)28(ard)-333(secrecy)83(.)]TJ
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
6.1 w
q 1 0 0 1 464.82 -295.87 cm
0 0 m
0 6.1 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 88.9347 451.941 Tm
(The)Tj
1.0003 0 0 1.0003 72 769.82 Tm
39.186 -317.79 Td
[(Join)-318(proto)-28(col)-318(also)-318(has)-318(to)-318(ensure)-318(that)-318(the)-318(adv)27(ersary)-317(who)-318(ea)26(v)28(esdrops)-317(on)-318(the)-318(comm)27(unication)]TJ
-39.186 -21.91 Td
[(cannot)-333(obtain)-333(new)-333(subgroup)-334(k)27(ey)]TJ
/T1_3 10.91 Tf
159.14 0 Td
(K)Tj
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10.04 3.95 Td
(0)Tj
/T1_2 7.97 Tf
-0.78 -7.18 Td
(J)Tj
/T1_0 10.91 Tf
9.51 3.23 Td
[(and)-333(new)-333(\257nal)-333(group)-334(k)27(ey)]TJ
/T1_3 10.91 Tf
118.48 0 Td
(K)Tj
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10.04 3.95 Td
(0)Tj
/T1_0 10.91 Tf
2.8 -3.95 Td
(.)Tj
/T1_13 10.91 Tf
-309.23 -29.92 Td
[(Theorem)-383(33)]TJ
/T1_14 10.91 Tf
71.25 0 Td
[(A)25(n)-354(adversary)]TJ
/T1_8 10.91 Tf
67.42 0 Td
(A)Tj
/T1_14 10.91 Tf
12.58 0 Td
[(is)-355(not)-355(able)-355(to)-356(obtain)-355(the)-355(new)-356(sub)51(gr)51(oup)-355(key)]TJ
/T1_3 10.91 Tf
203.63 0 Td
(K)Tj
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10.04 3.96 Td
(0)Tj
/T1_2 7.97 Tf
-0.78 -7.19 Td
(J)Tj
/T1_14 10.91 Tf
9.75 3.23 Td
[(and)-355(new)-355(\257nal)-355(gr)50(oup)]TJ
-373.89 -21.92 Td
(key)Tj
/T1_3 10.91 Tf
19.69 0 Td
(K)Tj
/T1_11 7.97 Tf
10.05 3.96 Td
(0)Tj
/T1_14 10.91 Tf
7.16 -3.96 Td
[(in)-399(the)-401(Join)-400(Pr)50(oto)51(c)51(ol)-399(pr)50(ovide)51(d)-399(the)-400(VK-GKA)-400(pr)50(oto)51(c)51(ol,)-410(VST)76(AR)-399(pr)50(oto)51(c)51(ol,)-410(the)-400(RSA)-400(signatur)50(e)]TJ
-36.9 -21.91 Td
[(scheme)-357(and)-358(the)-358(symmetric)-358(key)-357(encryption)-358(scheme)]TJ
/T1_7 10.91 Tf
241.64 0 Td
(SKE)Tj
/T1_14 10.91 Tf
24.05 0 Td
[(ar)51(e)-357(se)50(cur)51(e.)]TJ
-243.88 -29.92 Td
[(Pr)50(o)52(of:)]TJ
/T1_0 10.91 Tf
39.19 0 Td
[(In)-348(this)-347(pro)-28(of,)-352(w)27(e)-347(consider)-348(t)27(w)28(o)-347(cases,)-351(that)-348(is)-348(\(a\))-348(the)-348(adv)27(ersary)]TJ
/T1_8 10.91 Tf
298.44 0 Td
(A)Tj
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12.5 0 Td
[(tries)-348(to)-348(imp)-27(ersonate)]TJ
-371.94 -21.92 Td
[(subgroup)-405(con)27(troller)]TJ
/T1_1 10.91 Tf
97.75 0 Td
(S)Tj
/T1_2 7.97 Tf
5.73 -1.69 Td
(J)Tj
/T1_0 10.91 Tf
5.87 1.69 Td
[(,)-423(subgroup)-405(con)27(troller)]TJ
/T1_1 10.91 Tf
105.4 0 Td
(S)Tj
/T1_2 7.97 Tf
5.73 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
7.79 1.64 Td
[(for)-405(1)]TJ
/T1_8 10.91 Tf
27.27 0 Td
(\267)Tj
/T1_3 10.91 Tf
12.82 0 Td
(i)Tj
/T1_8 10.91 Tf
8.09 0 Td
(6)Tj
/T1_0 10.91 Tf
(=)Tj
/T1_3 10.91 Tf
12.82 0 Td
(J)Tj
/T1_8 10.91 Tf
11.43 0 Td
(\267)Tj
/T1_3 10.91 Tf
12.82 0 Td
(n)Tj
/T1_2 7.97 Tf
6.55 -1.64 Td
(c)Tj
/T1_0 10.91 Tf
4.16 1.64 Td
[(,)-423(new)-405(users)]TJ
/T1_1 10.91 Tf
59.05 0 Td
(U)Tj
/T1_2 7.97 Tf
5.73 -1.78 Td
[(J)24(;k)]TJ
/T1_0 10.91 Tf
16.32 1.78 Td
(for)Tj
/T1_3 10.91 Tf
17.48 0 Td
(n)Tj
/T1_2 7.97 Tf
6.54 -1.69 Td
(J)Tj
/T1_0 10.91 Tf
8.82 1.69 Td
[(+)-270(1)]TJ
/T1_8 10.91 Tf
21.22 0 Td
(\267)Tj
/T1_3 10.91 Tf
-459.39 -21.92 Td
(k)Tj
/T1_8 10.91 Tf
9.6 0 Td
(\267)Tj
/T1_3 10.91 Tf
12.07 0 Td
(n)Tj
/T1_2 7.97 Tf
6.55 -1.68 Td
(J)Tj
/T1_0 10.91 Tf
8.51 1.68 Td
(+)Tj
/T1_3 10.91 Tf
11.13 0 Td
(m)Tj
/T1_0 10.91 Tf
9.57 0 Td
[(,)-371(user)]TJ
/T1_1 10.91 Tf
30.53 0 Td
(U)Tj
/T1_2 7.97 Tf
5.73 -1.68 Td
[(J)24(;n)]TJ
/T1_4 5.98 Tf
11.92 -1.34 Td
(J)Tj
/T1_0 10.91 Tf
9.6 3.02 Td
[(or)-363(main)-364(con)27(troller)]TJ
/T1_1 10.91 Tf
90.46 0 Td
(C)Tj
/T1_0 10.91 Tf
9.69 0 Td
[(to)-363(establish)-364(the)-364(new)-363(subgroup)-364(k)27(ey)]TJ
/T1_3 10.91 Tf
168.52 0 Td
(K)Tj
/T1_11 7.97 Tf
10.04 3.96 Td
(0)Tj
/T1_2 7.97 Tf
-0.78 -7.19 Td
(J)Tj
/T1_0 10.91 Tf
9.84 3.23 Td
[(and)-363(new)-364(\257nal)]TJ
-402.98 -21.91 Td
[(group)-468(k)27(ey)]TJ
/T1_3 10.91 Tf
53.58 0 Td
(K)Tj
/T1_11 7.97 Tf
10.04 3.95 Td
(0)Tj
/T1_0 10.91 Tf
7.9 -3.95 Td
[(\(w)27(e)-468(do)-469(not)-468(consider)]TJ
/T1_8 10.91 Tf
103.25 0 Td
(A)Tj
/T1_0 10.91 Tf
13.82 0 Td
[(tries)-468(to)-469(imp)-28(ersonate)-468(users)]TJ
/T1_1 10.91 Tf
132.57 0 Td
(U)Tj
/T1_2 7.97 Tf
5.72 -1.64 Td
(i;j)Tj
/T1_0 10.91 Tf
14.73 1.64 Td
[(for)-468(1)]TJ
/T1_8 10.91 Tf
29.11 0 Td
(\267)Tj
/T1_3 10.91 Tf
13.98 0 Td
(i)Tj
/T1_8 10.91 Tf
9.24 0 Td
(6)Tj
/T1_0 10.91 Tf
(=)Tj
/T1_3 10.91 Tf
13.98 0 Td
(J)Tj
/T1_8 10.91 Tf
12.58 0 Td
(\267)Tj
/T1_3 10.91 Tf
13.98 0 Td
(n)Tj
/T1_2 7.97 Tf
6.54 -1.64 Td
(c)Tj
/T1_0 10.91 Tf
9.28 1.64 Td
(and)Tj
-450.3 -21.92 Td
(2)Tj
/T1_8 10.91 Tf
8.88 0 Td
(\267)Tj
/T1_3 10.91 Tf
11.92 0 Td
(j)Tj
/T1_8 10.91 Tf
8.55 0 Td
(\267)Tj
/T1_3 10.91 Tf
11.91 0 Td
(n)Tj
/T1_2 7.97 Tf
6.55 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
7.25 1.64 Td
(and)Tj
/T1_1 10.91 Tf
21.45 0 Td
(U)Tj
/T1_2 7.97 Tf
5.73 -1.69 Td
[(J)24(;j)]TJ
/T1_0 10.91 Tf
15.04 1.69 Td
[(for)-355(2)]TJ
/T1_8 10.91 Tf
25.82 0 Td
(\267)Tj
/T1_3 10.91 Tf
11.91 0 Td
(j)Tj
/T1_8 10.91 Tf
8.55 0 Td
(\267)Tj
/T1_3 10.91 Tf
11.91 0 Td
(n)Tj
/T1_2 7.97 Tf
6.55 -1.69 Td
(J)Tj
/T1_8 10.91 Tf
8.45 1.69 Td
(\241)Tj
/T1_0 10.91 Tf
11.07 0 Td
[(1)-355(as)]TJ
/T1_1 10.91 Tf
22.96 0 Td
(U)Tj
/T1_2 7.97 Tf
5.73 -1.64 Td
(i;j)Tj
/T1_0 10.91 Tf
13.49 1.64 Td
(and)Tj
/T1_1 10.91 Tf
21.45 0 Td
(U)Tj
/T1_2 7.97 Tf
5.72 -1.69 Td
[(J)23(;j)]TJ
/T1_0 10.91 Tf
15.04 1.69 Td
[(do)-28(es)-355(not)-356(send)-355(an)27(y)-355(information)-355(in)-356(the)-355(Join)]TJ
-265.93 -21.92 Td
[(Proto)-27(col\))-365(and)-364(\(b\))-364(the)-365(adv)27(ersary)]TJ
/T1_8 10.91 Tf
157.71 0 Td
(A)Tj
/T1_0 10.91 Tf
12.68 0 Td
[(tries)-364(to)-365(obtain)-364(the)-364(new)-365(subgroup)-364(k)27(ey)]TJ
/T1_3 10.91 Tf
182.2 0 Td
(K)Tj
/T1_11 7.97 Tf
10.04 3.96 Td
(0)Tj
/T1_2 7.97 Tf
-0.78 -7.19 Td
(J)Tj
/T1_0 10.91 Tf
9.85 3.23 Td
[(and)-364(new)-364(\257nal)-365(group)]TJ
-371.7 -21.91 Td
[(k)27(ey)]TJ
/T1_3 10.91 Tf
20.44 0 Td
(K)Tj
/T1_11 7.97 Tf
10.04 3.96 Td
(0)Tj
/T1_0 10.91 Tf
7.17 -3.96 Td
[(from)-401(the)-402(public)-401(information)-402(in)-401(the)-402(Join)-402(Proto)-27(col.)-649(F)82(or)-401(case)-401(\(a\),)-419(w)27(e)-401(\257rst)-401(consider)]TJ
/T1_8 10.91 Tf
396.44 0 Td
(A)Tj
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13.09 0 Td
(tries)Tj
-447.18 -21.92 Td
[(to)-400(imp)-28(ersonate)-400(subgroup)-401(con)27(troller)]TJ
/T1_1 10.91 Tf
174.04 0 Td
(S)Tj
/T1_2 7.97 Tf
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-459.09 -21.92 Td
(S)Tj
/T1_1 7.97 Tf
5.73 -1.69 Td
(J)Tj
/T1_2 10.91 Tf
10.13 1.69 Td
[(and)-391(the)-391(RSA)-391(signature)-391(sc)27(heme)-391(is)-391(assumed)-391(to)-391(b)-28(e)-391(secure,)-405(therefore)]TJ
/T1_3 10.91 Tf
322.19 0 Td
(A)Tj
/T1_2 10.91 Tf
12.97 0 Td
[(is)-391(not)-391(able)-391(to)-391(pro)-28(duce)-391(a)]TJ
-351.02 -21.91 Td
[(v)55(alid)-428(signature)-483(\271)]TJ
/T1_0 10.91 Tf
75.8 0 Td
(\276)Tj
/T1_6 7.97 Tf
6.62 3.95 Td
(0)Tj
/T1_1 7.97 Tf
-0.39 -7.19 Td
[(J)24(;)]TJ
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(1)Tj
/T1_2 10.91 Tf
11.51 3.24 Td
[(.)-732(Next,)-453(supp)-28(ose)-429(the)-429(adv)27(ersary)]TJ
/T1_3 10.91 Tf
154.45 0 Td
(A)Tj
/T1_2 10.91 Tf
13.39 0 Td
[(tries)-428(to)-429(imp)-28(ersonate)]TJ
/T1_4 10.91 Tf
102.38 0 Td
(S)Tj
/T1_1 7.97 Tf
5.72 -1.69 Td
(J)Tj
/T1_2 10.91 Tf
10.55 1.69 Td
[(in)-429(Phase)-429(2.)-732(Then)]TJ
-380.03 -21.92 Td
[(in)-413(Phase)-413(2)-413(Round)-413(1,)]TJ
/T1_3 10.91 Tf
105.5 0 Td
(A)Tj
/T1_2 10.91 Tf
13.22 0 Td
(generates)Tj
/T1_0 10.91 Tf
48.82 0 Td
(y)Tj
/T1_6 7.97 Tf
5.74 3.96 Td
(0)Tj
/T1_1 7.97 Tf
-0.39 -7.19 Td
(J)Tj
/T1_2 10.91 Tf
10.35 3.23 Td
(=)Tj
/T1_0 10.91 Tf
12.96 0 Td
(g)Tj
/T1_1 7.97 Tf
5.59 3.96 Td
(K)Tj
/T1_10 5.98 Tf
7.7 2.81 Td
(0)Tj
/T1_5 5.98 Tf
-0.56 -5.52 Td
(J)Tj
/T1_2 10.91 Tf
8.66 -1.25 Td
[(mo)-28(d)]TJ
/T1_0 10.91 Tf
23.94 0 Td
(p)Tj
/T1_2 10.91 Tf
5.48 0 Td
[(.)-683(Next)]TJ
/T1_3 10.91 Tf
38.02 0 Td
(A)Tj
/T1_2 10.91 Tf
13.21 0 Td
[(has)-412(to)-413(generate)-413(the)-413(v)54(alid)-412(signature)]TJ
/T1_0 10.91 Tf
-298.24 -21.92 Td
(\276)Tj
/T1_6 7.97 Tf
6.62 3.96 Td
(0)Tj
/T1_1 7.97 Tf
-0.39 -7.19 Td
(J)Tj
/T1_2 10.91 Tf
10.26 3.23 Td
(=)Tj
/T1_3 10.91 Tf
12.86 0 Td
(S)Tj
/T1_2 10.91 Tf
7.42 0 Td
(\()Tj
/T1_4 10.91 Tf
4.25 0 Td
(S)Tj
/T1_1 7.97 Tf
5.72 -1.69 Td
(J)Tj
/T1_3 10.91 Tf
5.87 1.69 Td
(jj)Tj
/T1_0 10.91 Tf
6.06 0 Td
(y)Tj
/T1_6 7.97 Tf
5.74 3.96 Td
(0)Tj
/T1_1 7.97 Tf
-0.39 -7.19 Td
(J)Tj
/T1_2 10.91 Tf
5.87 3.23 Td
[(\).)-667(The)-408(v)54(alidit)28(y)-407(of)]TJ
/T1_0 10.91 Tf
90.91 0 Td
(\276)Tj
/T1_6 7.97 Tf
6.62 3.96 Td
(0)Tj
/T1_1 7.97 Tf
-0.39 -7.19 Td
(J)Tj
/T1_2 10.91 Tf
10.32 3.23 Td
[(is)-407(c)26(hec)28(k)28(ed)-407(b)27(y)]TJ
/T1_4 10.91 Tf
68.54 0 Td
(C)Tj
/T1_2 10.91 Tf
10.18 0 Td
[(in)-407(Phase)-408(2)-408(Round)-407(2.)-668(If)-408(signature)]TJ
/T1_0 10.91 Tf
167.72 0 Td
(\276)Tj
/T1_6 7.97 Tf
6.62 3.96 Td
(0)Tj
/T1_1 7.97 Tf
-0.39 -7.19 Td
(J)Tj
/T1_2 10.91 Tf
10.32 3.23 Td
[(is)-407(not)]TJ
-440.34 -21.91 Td
[(correct,)-513(then)]TJ
/T1_4 10.91 Tf
67.82 0 Td
(C)Tj
/T1_2 10.91 Tf
10.93 0 Td
(rejects)Tj
/T1_4 10.91 Tf
35.89 0 Td
(S)Tj
/T1_1 7.97 Tf
5.73 -1.69 Td
(J)Tj
/T1_2 10.91 Tf
5.87 1.69 Td
[(.)-875(As)]TJ
/T1_3 10.91 Tf
30.27 0 Td
(A)Tj
/T1_2 10.91 Tf
13.91 0 Td
[(do)-27(es)-478(not)-477(kno)27(w)-476(the)-478(RSA)-477(priv)55(ate)-476(k)27(ey)]TJ
/T1_0 10.91 Tf
184.51 0 Td
(d)Tj
/T1_1 7.97 Tf
5.68 -1.69 Td
(J)Tj
/T1_2 10.91 Tf
11.08 1.69 Td
(of)Tj
/T1_4 10.91 Tf
13.99 0 Td
(S)Tj
/T1_1 7.97 Tf
5.72 -1.69 Td
(J)Tj
/T1_2 10.91 Tf
11.08 1.69 Td
[(and)-476(the)-478(RSA)]TJ
-402.48 -21.92 Td
[(signature)-334(sc)27(heme)-333(is)-334(assumed)-334(to)-334(b)-28(e)-334(secure,)-335(therefore)]TJ
/T1_3 10.91 Tf
249.28 0 Td
(A)Tj
/T1_2 10.91 Tf
12.35 0 Td
[(is)-334(not)-334(able)-334(to)-334(pro)-28(duce)-334(a)-334(v)54(alid)-333(signature)]TJ
/T1_0 10.91 Tf
191.11 0 Td
(\276)Tj
/T1_6 7.97 Tf
6.62 3.96 Td
(0)Tj
/T1_1 7.97 Tf
-0.39 -7.19 Td
(J)Tj
/T1_2 10.91 Tf
5.87 3.23 Td
(.)Tj
-464.84 -21.92 Td
[(Next,)-383(w)27(e)-372(consider)]TJ
/T1_3 10.91 Tf
89.67 0 Td
(A)Tj
/T1_2 10.91 Tf
12.78 0 Td
[(tries)-373(to)-373(imp)-28(ersonate)]TJ
/T1_4 10.91 Tf
100.55 0 Td
(S)Tj
/T1_1 7.97 Tf
5.73 -1.68 Td
(J)Tj
/T1_2 10.91 Tf
9.94 1.68 Td
[(in)-373(Phase)-373(3.)-565(Then)-373(in)-373(Phase)-374(3)-373(Round)-373(1,)]TJ
/T1_3 10.91 Tf
192.1 0 Td
(A)Tj
/T1_2 10.91 Tf
12.78 0 Td
(generates)Tj
-423.41 -21.91 Td
(\271)Tj
/T1_4 10.91 Tf
-0.14 0 Td
(c)Tj
/T1_6 7.97 Tf
5.73 3.95 Td
(0)Tj
/T1_1 7.97 Tf
0 -7.18 TD
(J)Tj
/T1_2 10.91 Tf
9.18 3.23 Td
(=)Tj
/T1_3 10.91 Tf
11.8 0 Td
(E)Tj
/T1_1 7.97 Tf
5.76 -2.31 Td
(K)Tj
/T1_10 5.98 Tf
7.7 2.74 Td
(0)Tj
/T1_5 5.98 Tf
-0.56 -5.51 Td
(J)Tj
/T1_2 10.91 Tf
5.63 5.08 Td
(\()Tj
/T1_0 10.91 Tf
(K)Tj
/T1_6 7.97 Tf
14.29 3.95 Td
(0)Tj
/T1_3 10.91 Tf
2.79 -3.95 Td
(jj)Tj
/T1_4 10.91 Tf
6.06 0 Td
(S)Tj
/T1_1 7.97 Tf
5.72 -1.69 Td
(J)Tj
/T1_2 10.91 Tf
5.88 1.69 Td
[(\))-348(and)-362(\271)]TJ
/T1_4 10.91 Tf
29.42 0 Td
(c)Tj
/T1_6 7.97 Tf
5.73 3.95 Td
(00)Tj
/T1_1 7.97 Tf
T*
(J)Tj
/T1_2 10.91 Tf
9.19 3.23 Td
(=)Tj
/T1_3 10.91 Tf
11.79 0 Td
(E)Tj
/T1_1 7.97 Tf
5.76 -1.69 Td
(K)Tj
/T1_5 5.98 Tf
7.14 -1.34 Td
(J)Tj
/T1_2 10.91 Tf
5.63 3.03 Td
(\()Tj
/T1_0 10.91 Tf
4.25 0 Td
(K)Tj
/T1_6 7.97 Tf
10.04 3.95 Td
(0)Tj
/T1_1 7.97 Tf
-0.78 -7.18 Td
(J)Tj
/T1_3 10.91 Tf
5.87 3.23 Td
(jj)Tj
/T1_0 10.91 Tf
6.06 0 Td
(K)Tj
/T1_6 7.97 Tf
10.04 3.95 Td
(0)Tj
/T1_3 10.91 Tf
2.8 -3.95 Td
(jj)Tj
/T1_4 10.91 Tf
6.05 0 Td
(S)Tj
/T1_1 7.97 Tf
5.73 -1.69 Td
(J)Tj
/T1_2 10.91 Tf
5.87 1.69 Td
[(\))-349(and)]TJ
/T1_0 10.91 Tf
29.43 0 Td
(\265)Tj
/T1_6 7.97 Tf
5.42 3.95 Td
(0)Tj
/T1_1 7.97 Tf
-0.3 -7.18 Td
(J)Tj
/T1_2 10.91 Tf
9.19 3.23 Td
(=)Tj
/T1_9 10.91 Tf
11.79 0 Td
(H)Tj
/T1_2 10.91 Tf
7.73 0 Td
(\()Tj
/T1_0 10.91 Tf
(K)Tj
/T1_6 7.97 Tf
14.28 3.95 Td
(0)Tj
/T1_1 7.97 Tf
-0.78 -7.18 Td
(J)Tj
/T1_3 10.91 Tf
5.87 3.23 Td
(jj)Tj
/T1_0 10.91 Tf
6.06 0 Td
(K)Tj
/T1_6 7.97 Tf
10.05 3.95 Td
(0)Tj
/T1_3 10.91 Tf
2.79 -3.95 Td
(jj)Tj
/T1_0 10.91 Tf
6.06 0 Td
(\277)Tj
/T1_6 7.97 Tf
6 3.95 Td
(0)Tj
/T1_1 7.97 Tf
-1.23 -7.18 Td
(J)Tj
/T1_2 10.91 Tf
5.87 3.23 Td
[(\).)-491(Next,)]TJ
/T1_3 10.91 Tf
42.54 0 Td
(A)Tj
/T1_2 10.91 Tf
12.51 0 Td
[(needs)-349(to)-349(compute)]TJ
-383.85 -21.92 Td
[(v)55(alid)-326(signature)-381(\271)]TJ
/T1_0 10.91 Tf
73.58 0 Td
(\276)Tj
/T1_6 7.97 Tf
6.62 3.96 Td
(0)Tj
/T1_1 7.97 Tf
-0.39 -7.19 Td
(J)Tj
/T1_2 10.91 Tf
8.9 3.23 Td
(=)Tj
/T1_3 10.91 Tf
11.51 0 Td
(S)Tj
/T1_2 10.91 Tf
7.42 0 Td
(\()Tj
/T1_4 10.91 Tf
4.25 0 Td
(S)Tj
/T1_1 7.97 Tf
5.72 -1.69 Td
(J)Tj
/T1_3 10.91 Tf
5.87 1.69 Td
(jj)Tj
/T1_0 10.91 Tf
6.06 0 Td
(\277)Tj
/T1_6 7.97 Tf
6 3.96 Td
(0)Tj
/T1_1 7.97 Tf
-1.23 -7.19 Td
(J)Tj
/T1_3 10.91 Tf
5.87 3.23 Td
(jj)Tj
/T1_0 10.91 Tf
6.06 0 Td
(\265)Tj
/T1_6 7.97 Tf
5.42 3.96 Td
(0)Tj
/T1_1 7.97 Tf
-0.3 -7.19 Td
(J)Tj
/T1_3 10.91 Tf
5.87 3.23 Td
(jj)Tj
/T1_0 10.91 Tf
6.06 0 Td
(v)Tj
/T1_2 10.91 Tf
5.68 0 Td
[(\).)-442(The)-327(v)55(alidit)27(y)-326(of)-381(\271)]TJ
/T1_0 10.91 Tf
85.82 0 Td
(\276)Tj
/T1_6 7.97 Tf
6.62 3.96 Td
(0)Tj
/T1_1 7.97 Tf
-0.39 -7.19 Td
(J)Tj
/T1_2 10.91 Tf
9.44 3.23 Td
[(is)-327(c)27(hec)27(k)28(ed)-326(b)27(y)]TJ
/T1_4 10.91 Tf
65.91 0 Td
(U)Tj
/T1_1 7.97 Tf
5.73 -1.69 Td
[(J)24(;j)]TJ
/T1_2 10.91 Tf
14.73 1.69 Td
[(for)-327(2)]TJ
/T1_3 10.91 Tf
25.11 0 Td
(\267)Tj
/T1_0 10.91 Tf
11.52 0 Td
(j)Tj
/T1_3 10.91 Tf
8.14 0 Td
(\267)Tj
/T1_0 10.91 Tf
11.51 0 Td
(n)Tj
/T1_1 7.97 Tf
6.55 -1.69 Td
(J)Tj
/T1_2 10.91 Tf
9.44 1.69 Td
(and)Tj
/T1_4 10.91 Tf
21.14 0 Td
(U)Tj
/T1_1 7.97 Tf
5.73 -1.78 Td
[(J)24(;k)]TJ
/T1_2 10.91 Tf
-455.97 -20.14 Td
(for)Tj
/T1_0 10.91 Tf
16.57 0 Td
(n)Tj
/T1_1 7.97 Tf
6.54 -1.68 Td
(J)Tj
/T1_2 10.91 Tf
8.05 1.68 Td
[(+)-199(1)]TJ
/T1_3 10.91 Tf
19.14 0 Td
(\267)Tj
/T1_0 10.91 Tf
11.51 0 Td
(k)Tj
/T1_3 10.91 Tf
9.05 0 Td
(\267)Tj
/T1_0 10.91 Tf
11.51 0 Td
(n)Tj
/T1_1 7.97 Tf
6.55 -1.68 Td
(J)Tj
/T1_2 10.91 Tf
8.04 1.68 Td
(+)Tj
/T1_0 10.91 Tf
10.66 0 Td
(m)Tj
/T1_2 10.91 Tf
13.08 0 Td
[(in)-322(Phase)-322(3)-322(Round)-321(2.)-441(If)-322(the)-322(signature)-375(\271)]TJ
/T1_0 10.91 Tf
178.28 0 Td
(\276)Tj
/T1_6 7.97 Tf
6.62 3.96 Td
(0)Tj
/T1_1 7.97 Tf
-0.39 -7.19 Td
(J)Tj
/T1_2 10.91 Tf
9.38 3.23 Td
[(is)-322(not)-322(correct,)-324(then)]TJ
/T1_4 10.91 Tf
94.17 0 Td
(U)Tj
/T1_1 7.97 Tf
5.73 -1.68 Td
[(J)24(;j)]TJ
/T1_2 10.91 Tf
14.67 1.68 Td
(and)Tj
/T1_4 10.91 Tf
21.08 0 Td
(U)Tj
/T1_1 7.97 Tf
5.73 -1.77 Td
[(J)24(;k)]TJ
/T1_2 10.91 Tf
-455.97 -20.14 Td
(rejects)Tj
/T1_4 10.91 Tf
34.86 0 Td
(S)Tj
/T1_1 7.97 Tf
5.73 -1.69 Td
(J)Tj
/T1_2 10.91 Tf
5.87 1.69 Td
[(.)-593(As)]TJ
/T1_3 10.91 Tf
26.16 0 Td
(A)Tj
/T1_2 10.91 Tf
12.88 0 Td
[(do)-27(es)-383(not)-383(kno)27(w)-382(the)-383(RSA)-383(priv)54(ate)-382(k)27(ey)]TJ
/T1_0 10.91 Tf
177.31 0 Td
(d)Tj
/T1_1 7.97 Tf
5.68 -1.69 Td
(J)Tj
/T1_2 10.91 Tf
10.05 1.69 Td
(of)Tj
/T1_4 10.91 Tf
12.96 0 Td
(S)Tj
/T1_1 7.97 Tf
5.72 -1.69 Td
(J)Tj
/T1_2 10.91 Tf
10.05 1.69 Td
[(and)-383(the)-382(RSA)-383(signature)-383(sc)27(heme)-382(is)]TJ
-307.27 -21.92 Td
[(assumed)-330(to)-330(b)-28(e)-330(secure,)-331(therefore)]TJ
/T1_3 10.91 Tf
153.4 0 Td
(A)Tj
/T1_2 10.91 Tf
12.31 0 Td
[(is)-329(not)-330(able)-331(to)-330(pro)-28(duce)-330(a)-330(v)55(alid)-329(signature)-384(\271)]TJ
/T1_0 10.91 Tf
190.76 0 Td
(\276)Tj
/T1_6 7.97 Tf
6.62 3.96 Td
(0)Tj
/T1_1 7.97 Tf
-0.39 -7.19 Td
(J)Tj
/T1_2 10.91 Tf
5.87 3.23 Td
[(.)-443(Therefore,)]TJ
/T1_3 10.91 Tf
60.31 0 Td
(A)Tj
/T1_2 10.91 Tf
12.31 0 Td
[(is)-329(not)]TJ
-441.19 -21.92 Td
[(able)-333(to)-333(imp)-28(ersonate)]TJ
/T1_4 10.91 Tf
97.94 0 Td
(S)Tj
/T1_1 7.97 Tf
5.73 -1.68 Td
(J)Tj
/T1_2 10.91 Tf
9.5 1.68 Td
[(to)-333(establish)-334(the)-333(subgroup)-333(k)27(ey)]TJ
/T1_0 10.91 Tf
144.12 0 Td
(K)Tj
/T1_6 7.97 Tf
10.04 3.96 Td
(0)Tj
/T1_1 7.97 Tf
-0.78 -7.19 Td
(J)Tj
/T1_2 10.91 Tf
9.51 3.23 Td
[(and)-332(\257nal)-334(group)-333(k)27(ey)]TJ
/T1_0 10.91 Tf
96.06 0 Td
(K)Tj
/T1_6 7.97 Tf
10.04 3.96 Td
(0)Tj
/T1_2 10.91 Tf
2.8 -3.96 Td
(.)Tj
-368.03 -21.91 Td
[(Next,)-388(w)27(e)-376(consider)]TJ
/T1_3 10.91 Tf
89.8 0 Td
(A)Tj
/T1_2 10.91 Tf
12.82 0 Td
[(wishes)-376(to)-377(imp)-28(ersonate)-377(subgroup)-377(con)27(troller)]TJ
/T1_4 10.91 Tf
207.53 0 Td
(S)Tj
/T1_1 7.97 Tf
5.73 -1.64 Td
(i)Tj
/T1_2 10.91 Tf
7.49 1.64 Td
[(for)-376(1)]TJ
/T1_3 10.91 Tf
26.44 0 Td
(\267)Tj
/T1_0 10.91 Tf
12.31 0 Td
(i)Tj
/T1_3 10.91 Tf
7.58 0 Td
(6)Tj
/T1_2 10.91 Tf
(=)Tj
/T1_0 10.91 Tf
12.3 0 Td
(J)Tj
/T1_3 10.91 Tf
10.92 0 Td
(\267)Tj
/T1_0 10.91 Tf
12.31 0 Td
(n)Tj
/T1_1 7.97 Tf
6.54 -1.64 Td
(c)Tj
/T1_2 10.91 Tf
4.17 1.64 Td
[(.)-575(As)]TJ
/T1_4 10.91 Tf
25.89 0 Td
(S)Tj
/T1_1 7.97 Tf
5.73 -1.64 Td
(i)Tj
/T1_2 10.91 Tf
-464.49 -20.28 Td
[(for)-403(1)]TJ
/T1_3 10.91 Tf
27.2 0 Td
(\267)Tj
/T1_0 10.91 Tf
12.78 0 Td
(i)Tj
/T1_3 10.91 Tf
8.05 0 Td
(6)Tj
/T1_2 10.91 Tf
(=)Tj
/T1_0 10.91 Tf
12.78 0 Td
(J)Tj
/T1_3 10.91 Tf
11.4 0 Td
(\267)Tj
/T1_0 10.91 Tf
12.78 0 Td
(n)Tj
/T1_1 7.97 Tf
6.54 -1.63 Td
(c)Tj
/T1_2 10.91 Tf
8.56 1.63 Td
[(do)-27(es)-404(not)-403(send)-403(an)27(y)-402(information)-403(in)-403(Phase)-403(1)-403(and)-403(2,)-421(hence)-403(w)27(e)-402(only)-403(consider)]TJ
/T1_3 10.91 Tf
359.07 0 Td
(A)Tj
/T1_2 10.91 Tf
-459.16 -21.91 Td
[(tries)-377(to)-378(imp)-28(ersonate)]TJ
/T1_4 10.91 Tf
100.71 0 Td
(S)Tj
/T1_1 7.97 Tf
5.72 -1.64 Td
(i)Tj
/T1_2 10.91 Tf
7.5 1.64 Td
[(in)-378(Phase)-378(3.)-578(Then)-378(in)-378(Phase)-378(3)-378(Round)-378(1,)]TJ
/T1_3 10.91 Tf
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/T1_0 10.91 Tf
12.53 0 Td
(generates)Tj
/T1_4 10.91 Tf
48.13 0 Td
(\267)Tj
/T1_6 7.97 Tf
6.29 3.96 Td
(0)Tj
/T1_3 7.97 Tf
0 -7.28 TD
[(J)24(;k)]TJ
/T1_1 10.91 Tf
15.23 3.32 Td
[(2)-305(f)]TJ
/T1_0 10.91 Tf
16.05 0 Td
(0)Tj
/T1_4 10.91 Tf
(;)Tj
/T1_0 10.91 Tf
10.3 0 Td
(1)Tj
/T1_1 10.91 Tf
(g)Tj
/T1_3 7.97 Tf
10.91 3.96 Td
(\270)Tj
/T1_0 10.91 Tf
9.25 -3.96 Td
(\()Tj
/T1_4 10.91 Tf
(\267)Tj
/T1_6 7.97 Tf
10.53 3.96 Td
(0)Tj
/T1_3 7.97 Tf
0 -7.19 TD
[(J)24(;n)]TJ
/T1_5 5.98 Tf
11.92 -1.34 Td
(J)Tj
/T1_1 10.91 Tf
8.96 4.57 Td
[(2)-305(f)]TJ
/T1_0 10.91 Tf
(0)Tj
/T1_4 10.91 Tf
(;)Tj
/T1_0 10.91 Tf
26.36 0 Td
(1)Tj
/T1_1 10.91 Tf
(g)Tj
/T1_3 7.97 Tf
10.9 3.96 Td
(\270)Tj
/T1_0 10.91 Tf
5.44 -3.96 Td
[(\))-350(and)]TJ
/T1_4 10.91 Tf
29.45 0 Td
(X)Tj
/T1_6 7.97 Tf
9.89 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.86 -7.28 Td
[(J)23(;k)]TJ
/T1_0 10.91 Tf
15.23 3.32 Td
(=)Tj
/T1_4 10.91 Tf
11.82 0 Td
(L)Tj
/T1_6 7.97 Tf
7.42 3.96 Td
(0)Tj
/T1_3 7.97 Tf
0 -7.28 TD
[(J)24(;k)]TJ
/T1_1 10.91 Tf
14.45 3.32 Td
(\251)Tj
/T1_4 10.91 Tf
11.02 0 Td
(R)Tj
/T1_6 7.97 Tf
8.37 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.09 -7.28 Td
[(J)23(;k)]TJ
/T1_0 10.91 Tf
15.72 3.32 Td
(\()Tj
/T1_4 10.91 Tf
(X)Tj
/T1_6 7.97 Tf
14.13 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.85 -7.19 Td
[(J)24(;n)]TJ
/T1_5 5.98 Tf
11.92 -1.34 Td
(J)Tj
/T1_0 10.91 Tf
8.96 4.57 Td
(=)Tj
/T1_4 10.91 Tf
11.82 0 Td
(L)Tj
/T1_6 7.97 Tf
7.42 3.96 Td
(0)Tj
/T1_3 7.97 Tf
0 -7.19 TD
[(J)24(;n)]TJ
/T1_5 5.98 Tf
11.92 -1.34 Td
(J)Tj
/T1_1 10.91 Tf
8.18 4.57 Td
(\251)Tj
/T1_4 10.91 Tf
11.02 0 Td
(R)Tj
/T1_6 7.97 Tf
8.37 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.08 -7.19 Td
[(J)24(;n)]TJ
/T1_5 5.98 Tf
11.92 -1.34 Td
(J)Tj
/T1_0 10.91 Tf
5.63 4.57 Td
(\),)Tj
-460.6 -21.92 Td
(where)Tj
/T1_4 10.91 Tf
31.92 0 Td
(L)Tj
/T1_6 7.97 Tf
7.42 3.96 Td
(0)Tj
/T1_3 7.97 Tf
0 -7.28 TD
[(J)24(;k)]TJ
/T1_0 10.91 Tf
15.56 3.32 Td
(=)Tj
/T1_8 10.91 Tf
12.15 0 Td
(H)Tj
/T1_0 10.91 Tf
7.73 0 Td
(\(\()Tj
/T1_4 10.91 Tf
8.48 0 Td
(z)Tj
/T1_6 7.97 Tf
5.55 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.48 -7.28 Td
[(J)24(;k)]TJ
/T1_6 7.97 Tf
11.4 0 Td
(\241)Tj
/T1_9 7.97 Tf
6.59 0 Td
(1)Tj
/T1_0 10.91 Tf
4.73 3.32 Td
(\))Tj
/T1_3 7.97 Tf
4.24 5.11 Td
(r)Tj
/T1_7 5.98 Tf
4.06 2.81 Td
(0)Tj
/T1_5 5.98 Tf
-0.24 -5.58 Td
[(J)34(;k)]TJ
/T1_1 10.91 Tf
11.2 -2.34 Td
(jj)Tj
/T1_2 10.91 Tf
6.06 0 Td
(SID)Tj
/T1_6 7.97 Tf
17.18 3.96 Td
(0)Tj
/T1_3 7.97 Tf
0 -7.19 TD
(J)Tj
/T1_0 10.91 Tf
5.87 3.23 Td
[(\))-368(\()]TJ
/T1_4 10.91 Tf
(L)Tj
/T1_6 7.97 Tf
19.92 3.96 Td
(0)Tj
/T1_3 7.97 Tf
T*
[(J)24(;n)]TJ
/T1_5 5.98 Tf
11.92 -1.34 Td
(J)Tj
/T1_0 10.91 Tf
9.3 4.57 Td
(=)Tj
/T1_8 10.91 Tf
12.14 0 Td
(H)Tj
/T1_0 10.91 Tf
7.73 0 Td
(\(\()Tj
/T1_4 10.91 Tf
8.48 0 Td
(z)Tj
/T1_6 7.97 Tf
5.55 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.48 -7.19 Td
[(J)23(;n)]TJ
/T1_5 5.98 Tf
11.92 -1.34 Td
(J)Tj
/T1_9 7.97 Tf
5.14 1.34 Td
(+)Tj
/T1_3 7.97 Tf
6.59 0 Td
(m)Tj
/T1_0 10.91 Tf
7.98 3.23 Td
(\))Tj
/T1_3 7.97 Tf
4.24 5.91 Td
(r)Tj
/T1_7 5.98 Tf
4.06 2.81 Td
(0)Tj
/T1_5 5.98 Tf
-0.24 -5.52 Td
[(J)34(;n)]TJ
10.74 -2.02 Td
(J)Tj
/T1_1 10.91 Tf
6.13 -1.18 Td
(jj)Tj
/T1_2 10.91 Tf
6.06 0 Td
(SID)Tj
/T1_6 7.97 Tf
17.17 3.96 Td
(0)Tj
/T1_3 7.97 Tf
T*
(J)Tj
/T1_0 10.91 Tf
5.87 3.23 Td
(\)\),)Tj
/T1_4 10.91 Tf
15.63 0 Td
(R)Tj
/T1_6 7.97 Tf
8.36 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.08 -7.28 Td
[(J)24(;k)]TJ
/T1_0 10.91 Tf
15.56 3.32 Td
(=)Tj
/T1_8 10.91 Tf
12.15 0 Td
(H)Tj
/T1_0 10.91 Tf
(\(\()Tj
/T1_4 10.91 Tf
(z)Tj
/T1_6 7.97 Tf
21.76 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.48 -7.28 Td
[(J)24(;k)]TJ
/T1_9 7.97 Tf
11.4 0 Td
(+1)Tj
/T1_0 10.91 Tf
11.32 3.32 Td
(\))Tj
/T1_3 7.97 Tf
4.24 5.11 Td
(r)Tj
/T1_7 5.98 Tf
4.06 2.81 Td
(0)Tj
/T1_5 5.98 Tf
-0.24 -5.58 Td
[(J)34(;k)]TJ
/T1_1 10.91 Tf
11.2 -2.34 Td
(jj)Tj
/T1_2 10.91 Tf
6.06 0 Td
(SID)Tj
/T1_6 7.97 Tf
17.18 3.96 Td
(0)Tj
/T1_3 7.97 Tf
T*
(J)Tj
/T1_0 10.91 Tf
5.87 3.23 Td
(\))Tj
-463.63 -21.91 Td
(\()Tj
/T1_4 10.91 Tf
(R)Tj
/T1_6 7.97 Tf
12.61 3.95 Td
(0)Tj
/T1_3 7.97 Tf
-0.09 -7.19 Td
[(J)23(;n)]TJ
/T1_5 5.98 Tf
11.92 -1.33 Td
(J)Tj
/T1_0 10.91 Tf
8.67 4.57 Td
(=)Tj
/T1_8 10.91 Tf
11.51 0 Td
(H)Tj
/T1_0 10.91 Tf
(\(\()Tj
/T1_4 10.91 Tf
(z)Tj
/T1_6 7.97 Tf
21.76 3.95 Td
(0)Tj
/T1_3 7.97 Tf
-0.48 -7.19 Td
[(J)24(;)]TJ
/T1_9 7.97 Tf
(1)Tj
/T1_0 10.91 Tf
11.51 3.24 Td
(\))Tj
/T1_3 7.97 Tf
4.24 5.9 Td
(r)Tj
/T1_7 5.98 Tf
4.06 2.81 Td
(0)Tj
/T1_5 5.98 Tf
-0.24 -5.51 Td
[(J)34(;n)]TJ
10.74 -2.03 Td
(J)Tj
/T1_1 10.91 Tf
6.13 -1.17 Td
(jj)Tj
/T1_2 10.91 Tf
6.06 0 Td
(SID)Tj
/T1_6 7.97 Tf
17.17 3.95 Td
(0)Tj
/T1_3 7.97 Tf
T*
(J)Tj
/T1_0 10.91 Tf
5.88 3.24 Td
[(\)\))-305(and)]TJ
/T1_2 10.91 Tf
32.73 0 Td
(SID)Tj
/T1_6 7.97 Tf
17.17 3.95 Td
(0)Tj
/T1_3 7.97 Tf
T*
(J)Tj
/T1_0 10.91 Tf
8.9 3.24 Td
(=)Tj
/T1_8 10.91 Tf
11.52 0 Td
(H)Tj
/T1_0 10.91 Tf
(\()Tj
/T1_4 10.91 Tf
(\277)Tj
/T1_6 7.97 Tf
17.96 3.95 Td
(0)Tj
/T1_3 7.97 Tf
-1.23 -7.19 Td
(J)Tj
/T1_1 10.91 Tf
5.87 3.24 Td
(jj)Tj
/T1_2 10.91 Tf
6.06 0 Td
(U)Tj
/T1_3 7.97 Tf
5.73 -1.69 Td
[(J)24(;)]TJ
/T1_9 7.97 Tf
(1)Tj
/T1_1 10.91 Tf
11.51 1.69 Td
[(jj)-166(\242)-167(\242)-167(\242)-166(jj)]TJ
/T1_2 10.91 Tf
28.48 0 Td
(U)Tj
/T1_3 7.97 Tf
5.72 -1.69 Td
[(J)23(;n)]TJ
/T1_5 5.98 Tf
11.92 -1.34 Td
(J)Tj
/T1_9 7.97 Tf
5.14 1.34 Td
(+)Tj
/T1_3 7.97 Tf
(m)Tj
/T1_1 10.91 Tf
14.57 1.69 Td
(jj)Tj
/T1_2 10.91 Tf
6.06 0 Td
(U)Tj
/T1_3 7.97 Tf
5.73 -1.69 Td
[(J)24(;n)]TJ
/T1_5 5.98 Tf
11.92 -1.34 Td
(J)Tj
/T1_0 10.91 Tf
5.63 3.03 Td
[(\).)-435(Then)]TJ
/T1_1 10.91 Tf
40.2 0 Td
(A)Tj
/T1_0 10.91 Tf
12.05 0 Td
[(has)-306(to)-306(compute)]TJ
-395.09 -21.92 Td
[(the)-482(v)55(alid)-482(signature)-536(\271)]TJ
/T1_4 10.91 Tf
97.37 0 Td
(\276)Tj
/T1_6 7.97 Tf
6.62 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.39 -7.28 Td
[(J)24(;k)]TJ
/T1_0 10.91 Tf
17.64 3.32 Td
(=)Tj
/T1_1 10.91 Tf
14.23 0 Td
(S)Tj
/T1_0 10.91 Tf
7.42 0 Td
(\()Tj
/T1_2 10.91 Tf
(U)Tj
/T1_3 7.97 Tf
9.96 -1.78 Td
[(J)23(;k)]TJ
/T1_1 10.91 Tf
11.91 1.78 Td
(jj)Tj
/T1_4 10.91 Tf
6.06 0 Td
(\267)Tj
/T1_6 7.97 Tf
6.28 3.96 Td
(0)Tj
/T1_3 7.97 Tf
0 -7.28 TD
[(J)24(;k)]TJ
/T1_1 10.91 Tf
11.9 3.32 Td
(jj)Tj
/T1_4 10.91 Tf
6.06 0 Td
(X)Tj
/T1_6 7.97 Tf
9.89 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.85 -7.28 Td
[(J)24(;k)]TJ
/T1_1 10.91 Tf
11.9 3.32 Td
(jj)Tj
/T1_4 10.91 Tf
6.06 0 Td
(\277)Tj
/T1_6 7.97 Tf
6 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-1.24 -7.19 Td
(J)Tj
/T1_1 10.91 Tf
5.88 3.23 Td
(jj)Tj
/T1_4 10.91 Tf
6.05 0 Td
(v)Tj
/T1_0 10.91 Tf
5.68 0 Td
[(\))-482(\()-54(\271)]TJ
/T1_4 10.91 Tf
13.75 0 Td
(\276)Tj
/T1_6 7.97 Tf
6.62 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.39 -7.19 Td
[(J)24(;n)]TJ
/T1_5 5.98 Tf
11.92 -1.34 Td
(J)Tj
/T1_0 10.91 Tf
11.37 4.57 Td
(=)Tj
/T1_1 10.91 Tf
14.23 0 Td
(S)Tj
/T1_0 10.91 Tf
7.42 0 Td
(\()Tj
/T1_2 10.91 Tf
(U)Tj
/T1_3 7.97 Tf
9.96 -1.69 Td
[(J)23(;n)]TJ
/T1_5 5.98 Tf
11.92 -1.34 Td
(J)Tj
/T1_1 10.91 Tf
5.64 3.03 Td
(jj)Tj
/T1_4 10.91 Tf
6.06 0 Td
(\267)Tj
/T1_6 7.97 Tf
6.28 3.96 Td
(0)Tj
/T1_3 7.97 Tf
0 -7.19 TD
[(J)23(;n)]TJ
/T1_5 5.98 Tf
11.92 -1.34 Td
(J)Tj
/T1_1 10.91 Tf
5.64 4.57 Td
(jj)Tj
/T1_4 10.91 Tf
6.06 0 Td
(X)Tj
/T1_6 7.97 Tf
9.89 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.86 -7.19 Td
[(J)24(;n)]TJ
/T1_5 5.98 Tf
11.92 -1.34 Td
(J)Tj
/T1_1 10.91 Tf
5.64 4.57 Td
(jj)Tj
/T1_4 10.91 Tf
6.05 0 Td
(\277)Tj
/T1_6 7.97 Tf
6.01 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-1.24 -7.19 Td
(J)Tj
/T1_1 10.91 Tf
5.87 3.23 Td
(jj)Tj
/T1_4 10.91 Tf
6.06 0 Td
(v)Tj
/T1_0 10.91 Tf
5.68 0 Td
[(\)\).)-891(The)]TJ
-427.85 -21.92 Td
[(v)55(alidit)28(y)-393(of)-447(\271)]TJ
/T1_4 10.91 Tf
52.81 0 Td
(\276)Tj
/T1_6 7.97 Tf
6.63 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.4 -7.28 Td
[(J)23(;k)]TJ
/T1_0 10.91 Tf
16.2 3.32 Td
[(\()-53(\271)]TJ
/T1_4 10.91 Tf
4.24 0 Td
(\276)Tj
/T1_6 7.97 Tf
6.62 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.39 -7.19 Td
[(J)23(;n)]TJ
/T1_5 5.98 Tf
11.92 -1.34 Td
(J)Tj
/T1_0 10.91 Tf
5.64 4.57 Td
[(\))-393(is)-393(c)27(hec)27(k)28(ed)-392(b)27(y)]TJ
/T1_2 10.91 Tf
76.6 0 Td
(S)Tj
/T1_3 7.97 Tf
5.72 -1.69 Td
(J)Tj
/T1_0 10.91 Tf
10.17 1.69 Td
[(in)-393(Phase)-393(1)-394(Round)-393(5.)-625(If)-393(the)-394(signature)-447(\271)]TJ
/T1_4 10.91 Tf
185.75 0 Td
(\276)Tj
/T1_6 7.97 Tf
6.62 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.39 -7.28 Td
[(J)24(;k)]TJ
/T1_0 10.91 Tf
16.19 3.32 Td
[(\()-54(\271)]TJ
/T1_4 10.91 Tf
4.25 0 Td
(\276)Tj
/T1_6 7.97 Tf
6.62 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.39 -7.19 Td
[(J)24(;n)]TJ
/T1_5 5.98 Tf
11.92 -1.34 Td
(J)Tj
/T1_0 10.91 Tf
5.63 4.57 Td
[(\))-393(is)-394(not)]TJ
-431.96 -21.91 Td
[(correct,)-358(then)]TJ
/T1_2 10.91 Tf
64.79 0 Td
(S)Tj
/T1_3 7.97 Tf
5.72 -1.69 Td
(J)Tj
/T1_0 10.91 Tf
9.73 1.69 Td
(rejects)Tj
/T1_2 10.91 Tf
34.55 0 Td
(U)Tj
/T1_3 7.97 Tf
5.73 -1.78 Td
[(J)24(;k)]TJ
/T1_0 10.91 Tf
15.76 1.78 Td
(\()Tj
/T1_2 10.91 Tf
(U)Tj
/T1_3 7.97 Tf
9.96 -1.69 Td
[(J)23(;n)]TJ
/T1_5 5.98 Tf
11.93 -1.34 Td
(J)Tj
/T1_0 10.91 Tf
5.63 3.03 Td
[(\).)-505(As)]TJ
/T1_1 10.91 Tf
29.13 0 Td
(A)Tj
/T1_0 10.91 Tf
12.57 0 Td
[(do)-27(es)-354(not)-354(kno)27(w)-353(the)-353(RSA)-354(priv)54(ate)-352(k)26(ey)]TJ
/T1_4 10.91 Tf
175.09 0 Td
(d)Tj
/T1_3 7.97 Tf
5.67 -1.78 Td
[(J)23(;k)]TJ
/T1_0 10.91 Tf
15.77 1.78 Td
(\()Tj
/T1_4 10.91 Tf
(d)Tj
/T1_3 7.97 Tf
9.91 -1.69 Td
[(J)23(;n)]TJ
/T1_5 5.98 Tf
11.92 -1.34 Td
(J)Tj
/T1_0 10.91 Tf
5.64 3.03 Td
[(\))-353(of)]TJ
/T1_2 10.91 Tf
20.74 0 Td
(U)Tj
/T1_3 7.97 Tf
5.73 -1.78 Td
[(J)24(;k)]TJ
/T1_0 10.91 Tf
-455.97 -20.14 Td
(\()Tj
/T1_2 10.91 Tf
(U)Tj
/T1_3 7.97 Tf
9.97 -1.69 Td
[(J)24(;n)]TJ
/T1_5 5.98 Tf
11.92 -1.34 Td
(J)Tj
/T1_0 10.91 Tf
5.63 3.03 Td
[(\))-335(and)-336(the)-335(RSA)-336(signature)-336(sc)27(heme)-334(is)-336(assumed)-336(to)-335(b)-28(e)-336(secure,)-336(therefore)]TJ
/T1_1 10.91 Tf
323.28 0 Td
(A)Tj
/T1_0 10.91 Tf
12.36 0 Td
[(is)-336(not)-335(able)-336(to)-335(pro)-28(duce)]TJ
-363.16 -21.92 Td
[(a)-333(v)55(alid)-333(signature)-387(\271)]TJ
/T1_4 10.91 Tf
82.8 0 Td
(\276)Tj
/T1_6 7.97 Tf
6.62 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.39 -7.28 Td
[(J)24(;k)]TJ
/T1_0 10.91 Tf
15.53 3.32 Td
[(\()-54(\271)]TJ
/T1_4 10.91 Tf
4.25 0 Td
(\276)Tj
/T1_6 7.97 Tf
6.62 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.39 -7.19 Td
[(J)24(;n)]TJ
/T1_5 5.98 Tf
11.92 -1.34 Td
(J)Tj
/T1_0 10.91 Tf
5.63 4.57 Td
[(\).)-444(Therefore,)]TJ
/T1_1 10.91 Tf
64.59 0 Td
(A)Tj
/T1_0 10.91 Tf
12.34 0 Td
[(is)-333(not)-334(able)-333(to)-333(imp)-28(ersonate)]TJ
/T1_2 10.91 Tf
128.3 0 Td
(U)Tj
/T1_3 7.97 Tf
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6.91 -3.96 Td
[(from)-377(Phase)]TJ
-413.52 -21.92 Td
[(2)-335(of)-335(the)-336(Join)-335(Proto)-28(col.)-451(But)-336(Phase)-335(2)-336(of)-335(the)-336(Join)-335(Proto)-28(col)-335(\(without)-336(the)-335(signature)-336(information)-335(sen)26(t\))]TJ
0 -21.91 TD
[(is)-412(just)-412(the)-413(VST)83(AR)-412(proto)-28(col)-412(\(describ)-28(ed)-412(in)-413(Section)-412(9.4.1\))-413(where)-412(subgroup)-412(con)26(troller)]TJ
/T1_5 10.91 Tf
406.88 0 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.69 Td
(J)Tj
/T1_0 10.91 Tf
10.36 1.69 Td
(computes)Tj
-422.97 -21.92 Td
[(and)-364(sends)]TJ
/T1_1 10.91 Tf
51.09 0 Td
(y)Tj
/T1_2 7.97 Tf
5.73 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.39 -7.19 Td
(J)Tj
/T1_0 10.91 Tf
9.47 3.23 Td
(=)Tj
/T1_1 10.91 Tf
12.07 0 Td
(g)Tj
/T1_3 7.97 Tf
5.59 3.96 Td
(K)Tj
/T1_6 5.98 Tf
7.7 2.81 Td
(0)Tj
/T1_7 5.98 Tf
-0.56 -5.52 Td
(J)Tj
/T1_0 10.91 Tf
9.61 -1.25 Td
[(in)-364(Phase)-364(2)-364(Round)-365(1)-364(while)]TJ
/T1_5 10.91 Tf
128.41 0 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
7.35 1.63 Td
[(for)-364(1)]TJ
/T1_4 10.91 Tf
26.08 0 Td
(\267)Tj
/T1_1 10.91 Tf
12.07 0 Td
(i)Tj
/T1_4 10.91 Tf
7.35 0 Td
(6)Tj
/T1_0 10.91 Tf
(=)Tj
/T1_1 10.91 Tf
12.07 0 Td
(J)Tj
/T1_4 10.91 Tf
10.69 0 Td
(\267)Tj
/T1_1 10.91 Tf
12.08 0 Td
(n)Tj
/T1_3 7.97 Tf
6.54 -1.63 Td
(c)Tj
/T1_0 10.91 Tf
8.14 1.63 Td
(uses)Tj
/T1_1 10.91 Tf
23.48 0 Td
(y)Tj
/T1_3 7.97 Tf
5.35 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
6.97 1.63 Td
(=)Tj
/T1_1 10.91 Tf
12.08 0 Td
(g)Tj
/T1_3 7.97 Tf
5.59 3.96 Td
(K)Tj
/T1_7 5.98 Tf
7.14 -1.22 Td
(i)Tj
/T1_0 10.91 Tf
7.63 -2.74 Td
(that)Tj
/T1_5 10.91 Tf
23.97 0 Td
(C)Tj
/T1_0 10.91 Tf
9.7 0 Td
[(kno)28(ws)]TJ
-438.73 -21.91 Td
[(from)-402(previous)-403(GKA,)-402(and)-403(Phase)-402(2)-403(Round)-402(2)-403(and)-403(Phase)-402(3)-403(Round)-402(1)-403(are)-402(the)-403(same)-402(as)-403(Round)-403(2)-402(and)]TJ
0 -21.92 TD
[(Computation)-278(of)-278(Key)-278(of)-279(VST)83(AR)-278(proto)-27(col)-279(resp)-27(ectiv)26(ely)84(.)-425(By)-279(Theorem)-278(28,)-289(it)-279(is)-278(sho)27(wn)-278(that)-278(the)-278(VST)82(AR)]TJ
T*
[(proto)-27(col)-331(is)-330(secure.)-444(Hence)-330(the)-330(adv)26(ersary)]TJ
/T1_4 10.91 Tf
191.29 0 Td
(A)Tj
/T1_0 10.91 Tf
12.31 0 Td
[(is)-330(not)-331(able)-330(to)-331(obtain)-330(the)-330(\257nal)-331(group)-330(k)27(ey)]TJ
/T1_1 10.91 Tf
194 0 Td
(K)Tj
/T1_2 7.97 Tf
10.04 3.96 Td
(0)Tj
/T1_0 10.91 Tf
6.4 -3.96 Td
[(from)-330(Phase)]TJ
-414.04 -21.91 Td
[(2)-382(of)-383(the)-383(Join)-383(Proto)-27(col.)-593(Next,)-395(w)27(e)-382(consider)-383(the)-383(adv)27(ersary)]TJ
/T1_4 10.91 Tf
275.56 0 Td
(A)Tj
/T1_0 10.91 Tf
12.88 0 Td
[(tries)-382(to)-383(obtain)-383(the)-383(new)-383(subgroup)-382(k)26(ey)]TJ
/T1_1 10.91 Tf
-288.44 -21.92 Td
(K)Tj
/T1_2 7.97 Tf
10.04 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.78 -7.19 Td
(J)Tj
/T1_0 10.91 Tf
10.04 3.23 Td
[(and)-381(new)-382(\257nal)-382(group)-382(k)26(ey)]TJ
/T1_1 10.91 Tf
121.14 0 Td
(K)Tj
/T1_2 7.97 Tf
10.04 3.96 Td
(0)Tj
/T1_0 10.91 Tf
6.96 -3.96 Td
[(from)-381(the)-382(public)-382(exc)26(hange)-381(information,)-394(that)-382(is,)-407(\271)]TJ
/T1_5 10.91 Tf
227.68 0 Td
(c)Tj
/T1_2 7.97 Tf
5.72 3.96 Td
(0)Tj
/T1_3 7.97 Tf
0 -7.19 TD
(J)Tj
/T1_0 10.91 Tf
5.87 3.23 Td
[(,)-406(\271)]TJ
/T1_5 10.91 Tf
7.33 0 Td
(c)Tj
/T1_2 7.97 Tf
5.73 3.96 Td
(00)Tj
/T1_3 7.97 Tf
T*
(J)Tj
/T1_0 10.91 Tf
10.03 3.23 Td
[(and)-394(\271)]TJ
/T1_5 10.91 Tf
21.74 0 Td
(c)Tj
/T1_2 7.97 Tf
5.73 3.96 Td
(0)Tj
/T1_3 7.97 Tf
0 -7.02 TD
(i)Tj
/T1_0 10.91 Tf
7.54 3.06 Td
(for)Tj
-454.81 -21.92 Td
(1)Tj
/T1_4 10.91 Tf
8.95 0 Td
(\267)Tj
/T1_1 10.91 Tf
11.98 0 Td
(i)Tj
/T1_4 10.91 Tf
7.25 0 Td
(6)Tj
/T1_0 10.91 Tf
(=)Tj
/T1_1 10.91 Tf
11.98 0 Td
(J)Tj
/T1_4 10.91 Tf
10.59 0 Td
(\267)Tj
/T1_1 10.91 Tf
11.98 0 Td
(n)Tj
/T1_3 7.97 Tf
6.54 -1.63 Td
(c)Tj
/T1_0 10.91 Tf
4.17 1.63 Td
[(,)-365(in)-359(Phase)-358(3)-359(of)-359(the)-359(Join)-359(Proto)-28(col.)-521(The)-359(new)-359(subgroup)-359(k)26(ey)]TJ
/T1_1 10.91 Tf
279.39 0 Td
(K)Tj
/T1_2 7.97 Tf
10.04 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.78 -7.19 Td
(J)Tj
/T1_0 10.91 Tf
9.79 3.23 Td
[(and)-358(new)-359(\257nal)-359(group)]TJ
-371.88 -21.91 Td
[(k)27(ey)]TJ
/T1_1 10.91 Tf
20.4 0 Td
(K)Tj
/T1_2 7.97 Tf
10.04 3.95 Td
(0)Tj
/T1_0 10.91 Tf
7.14 -3.95 Td
[(are)-398(the)-398(plain)27(text)-398(of)-410(\271)]TJ
/T1_5 10.91 Tf
98.29 0 Td
(c)Tj
/T1_2 7.97 Tf
5.73 3.95 Td
(00)Tj
/T1_3 7.97 Tf
0 -7.19 TD
(J)Tj
/T1_0 10.91 Tf
10.08 3.24 Td
(=)Tj
/T1_4 10.91 Tf
12.69 0 Td
(E)Tj
/T1_3 7.97 Tf
5.76 -1.69 Td
(K)Tj
/T1_7 5.98 Tf
7.14 -1.34 Td
(J)Tj
/T1_0 10.91 Tf
5.63 3.03 Td
(\()Tj
/T1_1 10.91 Tf
(K)Tj
/T1_2 7.97 Tf
14.28 3.95 Td
(0)Tj
/T1_3 7.97 Tf
-0.78 -7.19 Td
(J)Tj
/T1_4 10.91 Tf
5.88 3.24 Td
(jj)Tj
/T1_1 10.91 Tf
6.05 0 Td
(K)Tj
/T1_2 7.97 Tf
10.05 3.95 Td
(0)Tj
/T1_4 10.91 Tf
2.79 -3.95 Td
(jj)Tj
/T1_5 10.91 Tf
6.06 0 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.69 Td
(J)Tj
/T1_0 10.91 Tf
5.87 1.69 Td
[(\))-397(and)-399(the)-398(new)-398(group)-399(k)27(ey)]TJ
/T1_1 10.91 Tf
125.15 0 Td
(K)Tj
/T1_2 7.97 Tf
10.05 3.95 Td
(0)Tj
/T1_0 10.91 Tf
7.13 -3.95 Td
[(is)-398(the)-398(plain)26(text)-397(of)]TJ
-381.02 -21.92 Td
(\271)Tj
/T1_5 10.91 Tf
-0.14 0 Td
(c)Tj
/T1_2 7.97 Tf
5.73 3.96 Td
(0)Tj
/T1_3 7.97 Tf
T*
(J)Tj
/T1_0 10.91 Tf
8.9 3.23 Td
(=)Tj
/T1_4 10.91 Tf
11.51 0 Td
(E)Tj
/T1_3 7.97 Tf
5.75 -2.31 Td
(K)Tj
/T1_6 5.98 Tf
7.71 2.75 Td
(0)Tj
/T1_7 5.98 Tf
-0.57 -5.52 Td
(J)Tj
/T1_0 10.91 Tf
5.64 5.08 Td
(\()Tj
/T1_1 10.91 Tf
(K)Tj
/T1_2 7.97 Tf
14.28 3.96 Td
(0)Tj
/T1_4 10.91 Tf
2.8 -3.96 Td
(jj)Tj
/T1_5 10.91 Tf
6.05 0 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.69 Td
(J)Tj
/T1_0 10.91 Tf
5.87 1.69 Td
[(\))-317(and)-330(\271)]TJ
/T1_5 10.91 Tf
28.73 0 Td
(c)Tj
/T1_2 7.97 Tf
5.73 3.96 Td
(0)Tj
/T1_3 7.97 Tf
0 -7.01 TD
(i)Tj
/T1_0 10.91 Tf
6.41 3.05 Td
(=)Tj
/T1_4 10.91 Tf
11.51 0 Td
(E)Tj
/T1_3 7.97 Tf
5.76 -1.69 Td
(K)Tj
/T1_7 5.98 Tf
7.14 -1.21 Td
(i)Tj
/T1_0 10.91 Tf
3.65 2.9 Td
(\()Tj
/T1_1 10.91 Tf
4.25 0 Td
(K)Tj
/T1_2 7.97 Tf
10.04 3.96 Td
(0)Tj
/T1_4 10.91 Tf
2.79 -3.96 Td
(jj)Tj
/T1_5 10.91 Tf
6.06 0 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
3.38 1.64 Td
[(\))-317(for)-317(1)]TJ
/T1_4 10.91 Tf
32.7 0 Td
(\267)Tj
/T1_1 10.91 Tf
11.51 0 Td
(i)Tj
/T1_4 10.91 Tf
6.79 0 Td
(6)Tj
/T1_0 10.91 Tf
(=)Tj
/T1_1 10.91 Tf
11.51 0 Td
(J)Tj
/T1_4 10.91 Tf
10.13 0 Td
(\267)Tj
/T1_1 10.91 Tf
11.51 0 Td
(n)Tj
/T1_3 7.97 Tf
6.54 -1.64 Td
(c)Tj
/T1_0 10.91 Tf
4.17 1.64 Td
[(.)-438(As)]TJ
/T1_4 10.91 Tf
23.76 0 Td
(A)Tj
/T1_0 10.91 Tf
12.17 0 Td
[(do)-27(es)-317(not)-317(kno)26(w)-316(the)-317(new)-317(subgroup)]TJ
-311.37 -21.92 Td
[(k)27(ey)]TJ
/T1_1 10.91 Tf
19.73 0 Td
(K)Tj
/T1_2 7.97 Tf
10.05 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.78 -7.19 Td
(J)Tj
/T1_0 10.91 Tf
5.87 3.23 Td
[(,)-337(existing)-337(subgroup)-338(k)27(eys)]TJ
/T1_1 10.91 Tf
118.54 0 Td
(K)Tj
/T1_3 7.97 Tf
9.26 -1.68 Td
(J)Tj
/T1_0 10.91 Tf
9.55 1.68 Td
(and)Tj
/T1_1 10.91 Tf
21.24 0 Td
(K)Tj
/T1_3 7.97 Tf
9.27 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
7.05 1.63 Td
[(for)-337(1)]TJ
/T1_4 10.91 Tf
25.29 0 Td
(\267)Tj
/T1_1 10.91 Tf
11.58 0 Td
(i)Tj
/T1_4 10.91 Tf
6.86 0 Td
(6)Tj
/T1_0 10.91 Tf
(=)Tj
/T1_1 10.91 Tf
11.58 0 Td
(J)Tj
/T1_4 10.91 Tf
10.19 0 Td
(\267)Tj
/T1_1 10.91 Tf
11.59 0 Td
(n)Tj
/T1_3 7.97 Tf
6.54 -1.63 Td
(c)Tj
/T1_0 10.91 Tf
4.17 1.63 Td
[(,)-337(and)-338(the)-337(symmetric)-337(k)27(ey)-336(encryption)]TJ
-297.58 -21.91 Td
[(sc)27(heme)]TJ
/T1_8 10.91 Tf
37.65 0 Td
(SKE)Tj
/T1_0 10.91 Tf
24.1 0 Td
[(is)-362(assumed)-363(to)-363(b)-28(e)-363(secure,)-370(therefore)]TJ
/T1_4 10.91 Tf
166.54 0 Td
(A)Tj
/T1_0 10.91 Tf
12.67 0 Td
[(is)-362(not)-363(able)-363(to)-363(obtain)-363(the)-362(new)-363(subgroup)-363(k)27(ey)]TJ
/T1_1 10.91 Tf
211.78 0 Td
(K)Tj
/T1_2 7.97 Tf
10.04 3.95 Td
(0)Tj
/T1_3 7.97 Tf
-0.78 -7.18 Td
(J)Tj
/T1_0 10.91 Tf
-462 -18.69 Td
[(and)-333(new)-334(\257nal)-334(group)-333(k)27(ey)]TJ
/T1_1 10.91 Tf
118.5 0 Td
(K)Tj
/T1_2 7.97 Tf
10.04 3.96 Td
(0)Tj
/T1_0 10.91 Tf
6.44 -3.96 Td
[(from)-345(\271)]TJ
/T1_5 10.91 Tf
25.78 0 Td
(c)Tj
/T1_2 7.97 Tf
5.73 3.96 Td
(00)Tj
/T1_3 7.97 Tf
0 -7.19 TD
(J)Tj
/T1_0 10.91 Tf
9.51 3.23 Td
[(and)-333(the)-334(new)-333(group)-334(k)27(ey)]TJ
/T1_1 10.91 Tf
113.05 0 Td
(K)Tj
/T1_2 7.97 Tf
10.04 3.96 Td
(0)Tj
/T1_0 10.91 Tf
6.43 -3.96 Td
[(from)-346(\271)]TJ
/T1_5 10.91 Tf
25.79 0 Td
(c)Tj
/T1_2 7.97 Tf
5.72 3.96 Td
(0)Tj
/T1_3 7.97 Tf
T*
(J)Tj
/T1_0 10.91 Tf
9.51 3.23 Td
[(and)-346(\271)]TJ
/T1_5 10.91 Tf
21.21 0 Td
(c)Tj
/T1_2 7.97 Tf
5.73 3.96 Td
(0)Tj
/T1_3 7.97 Tf
0 -7.01 TD
(i)Tj
/T1_0 10.91 Tf
7.02 3.05 Td
[(for)-333(1)]TJ
/T1_4 10.91 Tf
25.18 0 Td
(\267)Tj
/T1_1 10.91 Tf
11.52 0 Td
(i)Tj
/T1_4 10.91 Tf
6.79 0 Td
(6)Tj
/T1_0 10.91 Tf
(=)Tj
/T1_1 10.91 Tf
11.52 0 Td
(J)Tj
/T1_4 10.91 Tf
10.13 0 Td
(\267)Tj
/T1_1 10.91 Tf
11.52 0 Td
(n)Tj
/T1_3 7.97 Tf
6.55 -1.64 Td
(c)Tj
/T1_0 10.91 Tf
-463.71 -20.28 Td
[(resp)-27(ectiv)27(ely)83(.)-441(Hence,)]TJ
/T1_4 10.91 Tf
98.13 0 Td
(A)Tj
/T1_0 10.91 Tf
12.25 0 Td
[(is)-324(not)-324(able)-324(to)-325(obtain)-324(the)-324(new)-324(subgroup)-325(k)27(ey)]TJ
/T1_1 10.91 Tf
207.99 0 Td
(K)Tj
/T1_2 7.97 Tf
10.05 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.78 -7.19 Td
(J)Tj
/T1_0 10.91 Tf
9.4 3.23 Td
[(and)-324(new)-324(\257nal)-325(group)-324(k)27(ey)]TJ
/T1_1 10.91 Tf
117.99 0 Td
(K)Tj
/T1_2 7.97 Tf
10.05 3.96 Td
(0)Tj
/T1_0 10.91 Tf
-465.08 -25.87 Td
[(in)-333(the)-333(Join)-333(Proto)-28(col.)]TJ
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
6.1 w
q 1 0 0 1 464.82 -405.45 cm
0 0 m
0 6.1 l
S
Q
Q
BT
/T1_9 10.91 Tf
1.0003 0 0 1.0003 72 334.3281 Tm
(Theorem)Tj
1.0003 0 0 1.0003 72 769.82 Tm
53.274 -435.37 Td
(34)Tj
/T1_10 10.91 Tf
17.976 0 Td
[(Assume)-484(that)-485(the)-485(c)50(omputation)-483(of)-485(RSA)-484(signatur)50(e)-484(veri\257c)50(ation)-483(is)-485(e\261cient,)-516(then)-485(the)]TJ
-71.25 -21.92 Td
[(pr)51(op)51(ose)51(d)-357(Join)-358(pr)50(oto)52(c)51(ol)-357(is)-358(r)50(esistant)-357(to)-357(DoS)-358(attack)-358(and)-358(insider)-357(attack.)]TJ
21.81 -29.92 Td
[(Pr)50(o)52(of:)]TJ
/T1_0 10.91 Tf
37.74 0 Td
[(Supp)-27(ose)-253(an)-253(adv)27(ersary)-251(launc)26(hes)-251(a)-253(DoS)-252(attac)26(k)-251(on)-253(the)-253(prop)-27(osed)-253(Join)-253(proto)-27(col)-253(whic)27(h)-252(stops)]TJ
-59.55 -21.91 Td
[(the)-271(GKA)-271(from)-271(pro)-28(ducing)-272(the)-271(new)-271(\257nal)-271(group)-272(k)27(ey)83(.)-422(In)-272(Phase)-271(1)-271(of)-272(the)-271(Join)-271(Proto)-28(col,)-284(w)27(e)-270(only)-272(consider)]TJ
0 -21.92 TD
[(the)-383(DoS)-384(attac)26(k)28(er)-383(launc)27(h)-383(DoS)-384(attac)27(k)-383(on)-384(subgroup)-384(con)27(troller)]TJ
/T1_5 10.91 Tf
292.35 0 Td
(S)Tj
/T1_3 7.97 Tf
5.72 -1.69 Td
(J)Tj
/T1_0 10.91 Tf
10.06 1.69 Td
[(as)-383(the)-384(other)-384(subgroup)-384(con)26(trollers)]TJ
/T1_5 10.91 Tf
-308.13 -21.92 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
7.91 1.63 Td
[(for)-415(1)]TJ
/T1_4 10.91 Tf
27.56 0 Td
(\267)Tj
/T1_1 10.91 Tf
13.01 0 Td
(i)Tj
/T1_4 10.91 Tf
8.28 0 Td
(6)Tj
/T1_0 10.91 Tf
(=)Tj
/T1_1 10.91 Tf
13.01 0 Td
(J)Tj
/T1_4 10.91 Tf
11.62 0 Td
(\267)Tj
/T1_1 10.91 Tf
13.01 0 Td
(n)Tj
/T1_3 7.97 Tf
6.54 -1.63 Td
(c)Tj
/T1_0 10.91 Tf
8.7 1.63 Td
[(do)-415(not)-415(send)-416(an)27(y)-415(information)-415(in)-416(Phase)-415(1.)-692(Then)-415(in)-416(Phase)-415(1)-416(Round)-415(2,)]TJ
/T1_5 10.91 Tf
340.9 0 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.68 Td
(J)Tj
/T1_0 10.91 Tf
-462 -20.23 Td
[(is)-389(able)-390(to)-390(detect)-389(the)-390(in)27(v)55(alid)-388(signatures)-390(or)-390(certi\257cates)-389(b)26(y)-388(v)27(erifying)-389(the)-390(signatures)-389(and)-390(certi\257cates.)]TJ
T*
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(K)Tj
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10.04 3.95 Td
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(L)Tj
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10.01 3.24 Td
(=)Tj
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12.23 0 Td
(H)Tj
/T1_3 10.91 Tf
7.73 0 Td
(\()Tj
/T1_8 10.91 Tf
(\267)Tj
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10.52 3.95 Td
(0)Tj
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(L;)Tj
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(1)Tj
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12.84 3.24 Td
(jj)Tj
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6.06 0 Td
(\267)Tj
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6.28 3.95 Td
(0)Tj
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T*
(L;)Tj
/T1_10 7.97 Tf
(2)Tj
/T1_7 10.91 Tf
12.84 3.24 Td
[(jj)-166(\242)-167(\242)-167(\242)-166(jj)]TJ
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28.48 0 Td
(\267)Tj
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6.28 3.95 Td
(0)Tj
/T1_5 7.97 Tf
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(L;n)Tj
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13.25 -1.34 Td
(L)Tj
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5.56 1.34 Td
(\241)Tj
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(`)Tj
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10.54 3.32 Td
(jj)Tj
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6.06 0 Td
(v)Tj
/T1_3 10.91 Tf
5.67 0 Td
[(\).)-563(Then)-373(lea)27(ving)-372(user)]TJ
/T1_4 10.91 Tf
103.27 0 Td
(U)Tj
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5.72 -1.78 Td
(L;l)Tj
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10.64 -1.41 Td
(k)Tj
/T1_3 10.91 Tf
9.14 3.19 Td
[(kno)28(ws)]TJ
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33.21 0 Td
(\267)Tj
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6.28 -1.69 Td
(L;j)Tj
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16.56 1.69 Td
[(for)-372(1)]TJ
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26.33 0 Td
(\267)Tj
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12.23 0 Td
(j)Tj
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(\267)Tj
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(n)Tj
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6.54 -1.69 Td
(L)Tj
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6.26 1.69 Td
[(,)-382(previous)]TJ
-420.89 -21.92 Td
[(subgroup)-242(k)27(ey)]TJ
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65.06 0 Td
(K)Tj
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(L)Tj
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(=)Tj
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(H)Tj
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(\267)Tj
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(L;)Tj
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(2)Tj
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12.84 1.69 Td
[(jj)-166(\242)-167(\242)-166(\242)-167(jj)]TJ
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28.47 0 Td
(\267)Tj
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6.29 -1.69 Td
(L;n)Tj
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13.24 -1.34 Td
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(jj)Tj
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(R)Tj
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(L;j)Tj
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15.52 1.69 Td
(=)Tj
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(H)Tj
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(\()Tj
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(z)Tj
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17.51 6.26 Td
(r)Tj
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3.82 -1.34 Td
(L;j)Tj
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-4.3 -8.35 Td
(L;j)Tj
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12 0 Td
(+1)Tj
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(jj)Tj
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6.06 0 Td
(SID)Tj
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17.18 -1.69 Td
(L)Tj
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6.25 1.69 Td
[(\))-242(and)]TJ
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27.11 0 Td
(L)Tj
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7.42 -1.69 Td
(L;j)Tj
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15.52 1.69 Td
(=)Tj
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11.51 0 Td
(H)Tj
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7.73 0 Td
(\()Tj
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(z)Tj
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9.79 6.26 Td
(r)Tj
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3.82 -1.34 Td
(L;j)Tj
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-4.3 -8.35 Td
(L;j)Tj
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11.99 0 Td
(\241)Tj
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(1)Tj
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(jj)Tj
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(SID)Tj
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17.17 -1.69 Td
(L)Tj
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6.26 1.69 Td
(\))Tj
-463.63 -21.92 Td
[(for)-299(1)]TJ
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24.81 0 Td
(\267)Tj
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(j)Tj
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(\267)Tj
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(n)Tj
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6.54 -1.68 Td
(L)Tj
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6.26 1.68 Td
[(,)-306(where)]TJ
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37.54 0 Td
(SID)Tj
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17.18 -1.68 Td
(L)Tj
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9.28 1.68 Td
(=)Tj
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(H)Tj
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7.73 0 Td
(\()Tj
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(\277)Tj
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9.01 -1.68 Td
(L)Tj
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6.25 1.68 Td
(jj)Tj
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(U)Tj
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5.73 -1.68 Td
(L;)Tj
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(1)Tj
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12.84 1.68 Td
(jj)Tj
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(U)Tj
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5.72 -1.68 Td
(L;)Tj
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(2)Tj
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12.84 1.68 Td
[(jj)-166(\242)-167(\242)-167(\242)-166(jj)]TJ
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28.48 0 Td
(U)Tj
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5.72 -1.68 Td
(L;n)Tj
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13.25 -1.34 Td
(L)Tj
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6.05 3.02 Td
(\).)Tj
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(U)Tj
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5.72 -1.77 Td
(L;l)Tj
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10.64 -1.41 Td
(k)Tj
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8.34 3.18 Td
[(also)-299(kno)27(ws)]TJ
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53.92 0 Td
(\267)Tj
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6.28 3.96 Td
(0)Tj
/T1_5 7.97 Tf
0 -7.19 TD
(L;j)Tj
/T1_3 10.91 Tf
15.76 3.23 Td
[(for)-299(2)]TJ
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24.81 0 Td
(\267)Tj
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11.51 0 Td
(j)Tj
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8.14 0 Td
(\267)Tj
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11.51 0 Td
(n)Tj
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6.55 -1.68 Td
(L)Tj
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7.94 1.68 Td
(\241)Tj
/T1_8 10.91 Tf
10.18 0 Td
(`)Tj
/T1_3 10.91 Tf
-463.33 -21.91 Td
[(from)-280(the)-280(Lea)27(v)28(e)-279(Proto)-28(col.)-427(But)-280(the)-280(new)-280(subgroup)-280(k)27(ey)-279(is)]TJ
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259.11 0 Td
(K)Tj
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10.05 3.95 Td
(0)Tj
/T1_5 7.97 Tf
-0.78 -7.18 Td
(L)Tj
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9.28 3.23 Td
(=)Tj
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11.51 0 Td
(H)Tj
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7.73 0 Td
(\()Tj
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(\267)Tj
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10.52 3.95 Td
(0)Tj
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0 -7.18 TD
(L;)Tj
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(1)Tj
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12.84 3.23 Td
(jj)Tj
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6.06 0 Td
(\267)Tj
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6.29 3.95 Td
(0)Tj
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T*
(L;)Tj
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(2)Tj
/T1_7 10.91 Tf
12.84 3.23 Td
[(jj)-166(\242)-167(\242)-166(\242)-167(jj)]TJ
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28.47 0 Td
(\267)Tj
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6.29 3.95 Td
(0)Tj
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(L;n)Tj
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13.24 -1.34 Td
(L)Tj
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5.56 1.34 Td
(\241)Tj
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(`)Tj
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10.54 3.32 Td
(jj)Tj
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6.06 0 Td
(v)Tj
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5.68 0 Td
[(\).)-426(As)]TJ
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27.46 0 Td
(\267)Tj
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6.28 3.95 Td
(0)Tj
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(1)Tj
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-455.03 -18.69 Td
[(is)-329(random)-329(and)-330(indep)-28(enden)27(t)-328(of)]TJ
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146.2 0 Td
(\267)Tj
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(L;)Tj
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(1)Tj
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16.43 1.69 Td
[(from)-329(the)-329(previous)-330(GKA,)-329(hence)]TJ
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149.95 0 Td
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9.26 -1.69 Td
(L)Tj
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9.85 1.69 Td
[(are)-329(indep)-28(enden)27(t)-329(to)]TJ
-378.25 -21.92 Td
[(eac)27(h)-403(other)-404(as)-404(the)-404(output)-404(of)-404(the)-404(hash)-404(function)]TJ
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(H)Tj
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12.13 0 Td
[(is)-404(indep)-27(enden)26(t.)-655(As)-404(eac)27(h)-403(remaining)-404(user)]TJ
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197.87 0 Td
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(L;k)Tj
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17.54 1.77 Td
(2)Tj
-460.6 -21.91 Td
(N)Tj
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10.56 0 Td
(\()Tj
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(R)Tj
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13.48 0 Td
[(\),)-312(who)-308(is)-308(a)-308(left)-308(or)-308(righ)27(t)-307(neigh)27(b)-27(or)-307(of)-308(lea)27(ving)-307(users,)-313(selects)-308(new)-308(random)]TJ
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330.22 0 Td
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(0)Tj
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-0.3 -7.28 Td
(L;k)Tj
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16.25 3.32 Td
(2)Tj
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10.3 0 Td
(Z)Tj
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8.23 3.96 Td
(\244)Tj
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-0.78 -6.66 Td
(q)Tj
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8.87 2.7 Td
[(and)-307(computes)]TJ
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(0)Tj
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(=)Tj
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5.59 5.11 Td
(r)Tj
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(L;k)Tj
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[(in)-394(Phase)-394(1)-395(Round)-394(2)-394(of)-394(the)-395(Lea)27(v)28(e)-393(Proto)-28(col,)-410(therefore,)]TJ
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(L;k)Tj
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(and)Tj
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(L;k)Tj
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17.52 1.78 Td
[(are)-394(random)-394(and)]TJ
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[(indep)-27(enden)27(t)-394(to)-394(eac)26(h)-393(other.)-628(Hence,)]TJ
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(L;k)Tj
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11.9 1.4 Td
(r)Tj
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3.82 -1.4 Td
(L;k)Tj
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11.4 0 Td
(+1)Tj
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[(,)-410(and)]TJ
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29.37 0 Td
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5.6 5.11 Td
(r)Tj
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(0)Tj
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(L;k)Tj
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11.9 2.77 Td
(r)Tj
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4.05 2.81 Td
(0)Tj
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-0.23 -5.58 Td
(L;k)Tj
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11.4 0 Td
(\241)Tj
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8.95 -2.34 Td
(and)Tj
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-450.3 -21.91 Td
(g)Tj
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5.59 3.96 Td
(r)Tj
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(L;k)Tj
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11.9 1.41 Td
(r)Tj
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3.82 -1.41 Td
(L;k)Tj
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11.4 0 Td
(\241)Tj
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(1)Tj
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(\(where)Tj
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37.53 0 Td
(r)Tj
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5.22 3.96 Td
(0)Tj
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-0.3 -7.28 Td
(L;k)Tj
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12.73 0 Td
(+1)Tj
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17.27 3.32 Td
(=)Tj
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14.44 0 Td
(r)Tj
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4.92 -1.78 Td
(L;k)Tj
/T1_10 7.97 Tf
12.73 0 Td
(+1)Tj
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16.71 1.78 Td
(if)Tj
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11.75 0 Td
(V)Tj
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5.73 -1.78 Td
(L;k)Tj
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(+1)Tj
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18.48 1.78 Td
(=)Tj
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-1.21 0 Td
[(2)-546(N)]TJ
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23.78 0 Td
(\()Tj
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(R)Tj
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[(\))-494(and)]TJ
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46.08 0 Td
(r)Tj
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5.23 3.96 Td
(0)Tj
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-0.31 -7.28 Td
(L;k)Tj
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12.73 0 Td
(\241)Tj
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6.59 0 Td
(1)Tj
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10.68 3.32 Td
(=)Tj
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14.44 0 Td
(r)Tj
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4.92 -1.78 Td
(L;k)Tj
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12.73 0 Td
(\241)Tj
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6.59 0 Td
(1)Tj
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10.12 1.78 Td
(if)Tj
/T1_4 10.91 Tf
11.75 0 Td
(V)Tj
/T1_5 7.97 Tf
5.73 -1.78 Td
(L;k)Tj
/T1_9 7.97 Tf
12.73 0 Td
(\241)Tj
/T1_10 7.97 Tf
(1)Tj
/T1_8 10.91 Tf
18.48 1.78 Td
(=)Tj
/T1_7 10.91 Tf
-1.21 0 Td
[(2)-546(N)]TJ
/T1_3 10.91 Tf
23.78 0 Td
(\()Tj
/T1_7 10.91 Tf
4.25 0 Td
(R)Tj
/T1_3 10.91 Tf
9.24 0 Td
(\)\))Tj
-459.39 -21.92 Td
[(are)-394(indep)-28(enden)27(t)-394(to)-395(eac)27(h)-394(other.)-629(F)82(urthermore,)-409(as)]TJ
/T1_8 10.91 Tf
236.51 0 Td
(\277)Tj
/T1_9 7.97 Tf
6 3.96 Td
(0)Tj
/T1_5 7.97 Tf
-1.23 -7.19 Td
(L)Tj
/T1_3 10.91 Tf
10.56 3.23 Td
(and)Tj
/T1_8 10.91 Tf
21.88 0 Td
(\277)Tj
/T1_5 7.97 Tf
4.77 -1.69 Td
(L)Tj
/T1_3 10.91 Tf
10.56 1.69 Td
[(are)-394(random)-395(and)-395(indep)-28(enden)27(t)-394(to)-395(eac)27(h)]TJ
-289.05 -21.91 Td
[(other,)-497(hence)]TJ
/T1_4 10.91 Tf
65.05 0 Td
(SID)Tj
/T1_9 7.97 Tf
17.18 3.95 Td
(0)Tj
/T1_5 7.97 Tf
-0.01 -7.19 Td
(L)Tj
/T1_3 10.91 Tf
11.67 3.24 Td
(=)Tj
/T1_2 10.91 Tf
13.9 0 Td
(H)Tj
/T1_3 10.91 Tf
(\()Tj
/T1_8 10.91 Tf
(\277)Tj
/T1_9 7.97 Tf
17.97 3.95 Td
(0)Tj
/T1_5 7.97 Tf
-1.24 -7.19 Td
(L)Tj
/T1_7 10.91 Tf
6.26 3.24 Td
(jj)Tj
/T1_4 10.91 Tf
6.06 0 Td
(V)Tj
/T1_5 7.97 Tf
5.72 -1.69 Td
(L;)Tj
/T1_10 7.97 Tf
(1)Tj
/T1_7 10.91 Tf
12.84 1.69 Td
(jj)Tj
/T1_4 10.91 Tf
6.06 0 Td
(V)Tj
/T1_5 7.97 Tf
5.73 -1.69 Td
(L;)Tj
/T1_10 7.97 Tf
(2)Tj
/T1_7 10.91 Tf
12.84 1.69 Td
[(jj)-166(\242)-166(\242)-167(\242)-167(jj)]TJ
/T1_4 10.91 Tf
28.47 0 Td
(V)Tj
/T1_5 7.97 Tf
5.73 -1.78 Td
(L;n)Tj
/T1_6 5.98 Tf
13.24 -1.34 Td
(L)Tj
/T1_9 7.97 Tf
5.56 1.34 Td
(\241)Tj
/T1_5 7.97 Tf
(`)Tj
/T1_3 10.91 Tf
10.54 1.78 Td
[(\))-464(and)]TJ
/T1_4 10.91 Tf
31.94 0 Td
(SID)Tj
/T1_5 7.97 Tf
17.18 -1.69 Td
(L)Tj
/T1_3 10.91 Tf
11.67 1.69 Td
(=)Tj
/T1_2 10.91 Tf
13.89 0 Td
(H)Tj
/T1_3 10.91 Tf
7.73 0 Td
(\()Tj
/T1_8 10.91 Tf
(\277)Tj
/T1_5 7.97 Tf
9.01 -1.69 Td
(L)Tj
/T1_7 10.91 Tf
6.25 1.69 Td
(jj)Tj
/T1_4 10.91 Tf
6.06 0 Td
(U)Tj
/T1_5 7.97 Tf
5.73 -1.69 Td
(L;)Tj
/T1_10 7.97 Tf
(1)Tj
/T1_7 10.91 Tf
12.84 1.69 Td
(jj)Tj
/T1_4 10.91 Tf
6.06 0 Td
(U)Tj
/T1_5 7.97 Tf
5.72 -1.69 Td
(L;)Tj
/T1_10 7.97 Tf
(2)Tj
/T1_7 10.91 Tf
12.84 1.69 Td
[(jj)-166(\242)-167(\242)-167(\242)-166(jj)]TJ
/T1_4 10.91 Tf
28.48 0 Td
(U)Tj
/T1_5 7.97 Tf
5.72 -1.69 Td
(L;n)Tj
/T1_6 5.98 Tf
13.25 -1.34 Td
(L)Tj
/T1_3 10.91 Tf
6.05 3.03 Td
[(\))-464(are)]TJ
-443.99 -21.92 Td
[(indep)-27(enden)27(t)-328(to)-328(eac)27(h)-328(other)-328(as)-328(the)-328(output)-329(of)-328(the)-328(hash)-329(function)]TJ
/T1_2 10.91 Tf
294.92 0 Td
(H)Tj
/T1_3 10.91 Tf
11.31 0 Td
[(is)-327(indep)-28(enden)27(t.)-442(Therefore,)]TJ
/T1_8 10.91 Tf
129.36 0 Td
(R)Tj
/T1_9 7.97 Tf
8.36 3.96 Td
(0)Tj
/T1_5 7.97 Tf
-0.08 -7.19 Td
(L;j)Tj
/T1_3 10.91 Tf
15.52 3.23 Td
(=)Tj
/T1_2 10.91 Tf
-459.39 -21.92 Td
(H)Tj
/T1_3 10.91 Tf
7.73 0 Td
(\()Tj
/T1_8 10.91 Tf
(g)Tj
/T1_5 7.97 Tf
9.83 5.04 Td
(r)Tj
/T1_11 5.98 Tf
4.06 2.82 Td
(0)Tj
/T1_6 5.98 Tf
-0.24 -5.52 Td
(L;j)Tj
/T1_5 7.97 Tf
11.23 2.7 Td
(r)Tj
/T1_11 5.98 Tf
4.05 2.82 Td
(0)Tj
/T1_6 5.98 Tf
-0.23 -5.52 Td
(L;j)Tj
/T1_12 5.98 Tf
10.73 0 Td
(+1)Tj
/T1_7 10.91 Tf
10.23 -2.34 Td
(jj)Tj
/T1_4 10.91 Tf
6.06 0 Td
(SID)Tj
/T1_9 7.97 Tf
17.18 3.96 Td
(0)Tj
/T1_5 7.97 Tf
0 -7.19 TD
(L)Tj
/T1_3 10.91 Tf
6.26 3.23 Td
[(\))-430(and)]TJ
/T1_8 10.91 Tf
31.21 0 Td
(R)Tj
/T1_5 7.97 Tf
8.29 -1.69 Td
(L;j)Tj
/T1_3 10.91 Tf
17.3 1.69 Td
(=)Tj
/T1_2 10.91 Tf
13.29 0 Td
(H)Tj
/T1_3 10.91 Tf
(\()Tj
/T1_8 10.91 Tf
(g)Tj
/T1_5 7.97 Tf
17.56 3.96 Td
(r)Tj
/T1_6 5.98 Tf
3.82 -1.34 Td
(L;j)Tj
/T1_5 7.97 Tf
11.23 1.34 Td
(r)Tj
/T1_6 5.98 Tf
3.82 -1.34 Td
(L;j)Tj
/T1_12 5.98 Tf
10.73 0 Td
(+1)Tj
/T1_7 10.91 Tf
10.23 -2.62 Td
(jj)Tj
/T1_4 10.91 Tf
6.06 0 Td
(SID)Tj
/T1_5 7.97 Tf
17.18 -1.69 Td
(L)Tj
/T1_3 10.91 Tf
6.25 1.69 Td
[(\),)-456(and)]TJ
/T1_8 10.91 Tf
34.52 0 Td
(L)Tj
/T1_9 7.97 Tf
7.42 3.96 Td
(0)Tj
/T1_5 7.97 Tf
T*
(L;j)Tj
/T1_3 10.91 Tf
17.3 3.23 Td
(=)Tj
/T1_2 10.91 Tf
13.29 0 Td
(H)Tj
/T1_3 10.91 Tf
7.73 0 Td
(\()Tj
/T1_8 10.91 Tf
(g)Tj
/T1_5 7.97 Tf
9.83 5.04 Td
(r)Tj
/T1_11 5.98 Tf
4.06 2.82 Td
(0)Tj
/T1_6 5.98 Tf
-0.24 -5.52 Td
(L;j)Tj
/T1_5 7.97 Tf
11.23 2.7 Td
(r)Tj
/T1_11 5.98 Tf
4.06 2.82 Td
(0)Tj
/T1_6 5.98 Tf
-0.24 -5.52 Td
(L;j)Tj
/T1_11 5.98 Tf
10.73 0 Td
(\241)Tj
/T1_12 5.98 Tf
(1)Tj
/T1_7 10.91 Tf
10.4 -2.34 Td
(jj)Tj
/T1_4 10.91 Tf
6.06 0 Td
(SID)Tj
/T1_9 7.97 Tf
17.18 3.96 Td
(0)Tj
/T1_5 7.97 Tf
T*
(L)Tj
/T1_3 10.91 Tf
6.26 3.23 Td
[(\))-430(and)]TJ
/T1_8 10.91 Tf
31.22 0 Td
(L)Tj
/T1_5 7.97 Tf
7.42 -1.69 Td
(L;j)Tj
/T1_3 10.91 Tf
17.3 1.69 Td
(=)Tj
/T1_2 10.91 Tf
-459.39 -21.91 Td
(H)Tj
/T1_3 10.91 Tf
7.73 0 Td
(\()Tj
/T1_8 10.91 Tf
(g)Tj
/T1_5 7.97 Tf
9.83 3.95 Td
(r)Tj
/T1_6 5.98 Tf
3.82 -1.34 Td
(L;j)Tj
/T1_5 7.97 Tf
11.23 1.34 Td
(r)Tj
/T1_6 5.98 Tf
3.82 -1.34 Td
(L;j)Tj
/T1_11 5.98 Tf
10.73 0 Td
(\241)Tj
/T1_12 5.98 Tf
5.75 0 Td
(1)Tj
/T1_7 10.91 Tf
4.65 -2.61 Td
(jj)Tj
/T1_4 10.91 Tf
6.06 0 Td
(SID)Tj
/T1_5 7.97 Tf
17.18 -1.69 Td
(L)Tj
/T1_3 10.91 Tf
6.25 1.69 Td
[(\))-356(\(where)]TJ
/T1_8 10.91 Tf
44.17 0 Td
(r)Tj
/T1_9 7.97 Tf
5.22 3.95 Td
(0)Tj
/T1_5 7.97 Tf
-0.3 -7.19 Td
(L;j)Tj
/T1_3 10.91 Tf
15.94 3.24 Td
(=)Tj
/T1_8 10.91 Tf
11.94 0 Td
(r)Tj
/T1_5 7.97 Tf
4.92 -1.69 Td
(L;j)Tj
/T1_3 10.91 Tf
16.38 1.69 Td
(if)Tj
/T1_4 10.91 Tf
10.25 0 Td
(V)Tj
/T1_5 7.97 Tf
5.73 -1.69 Td
(L;j)Tj
/T1_8 10.91 Tf
17.15 1.69 Td
(=)Tj
/T1_7 10.91 Tf
-1.21 0 Td
[(2)-316(N)]TJ
/T1_3 10.91 Tf
21.28 0 Td
(\()Tj
/T1_7 10.91 Tf
(R)Tj
/T1_3 10.91 Tf
[(\)\))-356(are)-357(indep)-27(enden)26(t)-355(to)-357(eac)27(h)-356(other)-357(resp)-27(ectiv)26(ely)]TJ
-238.52 -21.92 Td
[(as)-320(the)-321(output)-320(of)-321(the)-321(hash)-320(function)]TJ
/T1_2 10.91 Tf
166.38 0 Td
(H)Tj
/T1_3 10.91 Tf
11.22 0 Td
[(is)-320(indep)-28(enden)27(t.)-439(Hence)-321(lea)27(ving)-319(user)]TJ
/T1_4 10.91 Tf
168.89 0 Td
(U)Tj
/T1_5 7.97 Tf
5.73 -1.78 Td
(L;l)Tj
/T1_6 5.98 Tf
10.64 -1.4 Td
(k)Tj
/T1_3 10.91 Tf
8.56 3.18 Td
[(is)-320(not)-321(able)-321(to)-320(obtain)]TJ
/T1_8 10.91 Tf
-371.42 -21.92 Td
(R)Tj
/T1_9 7.97 Tf
8.37 3.96 Td
(0)Tj
/T1_5 7.97 Tf
-0.09 -7.19 Td
(L;j)Tj
/T1_3 10.91 Tf
17 3.23 Td
(and)Tj
/T1_8 10.91 Tf
22.09 0 Td
(L)Tj
/T1_9 7.97 Tf
7.42 3.96 Td
(0)Tj
/T1_5 7.97 Tf
T*
(L;j)Tj
/T1_3 10.91 Tf
17 3.23 Td
[(for)-413(1)]TJ
/T1_7 10.91 Tf
27.52 0 Td
(\267)Tj
/T1_8 10.91 Tf
12.97 0 Td
(j)Tj
/T1_7 10.91 Tf
9.61 0 Td
(\267)Tj
/T1_8 10.91 Tf
12.97 0 Td
(n)Tj
/T1_5 7.97 Tf
6.55 -1.69 Td
(L)Tj
/T1_7 10.91 Tf
9.26 1.69 Td
(\241)Tj
/T1_8 10.91 Tf
11.49 0 Td
(`)Tj
/T1_3 10.91 Tf
9.06 0 Td
(and)Tj
/T1_8 10.91 Tf
22.08 0 Td
(\267)Tj
/T1_9 7.97 Tf
6.29 3.96 Td
(0)Tj
/T1_5 7.97 Tf
T*
(L;)Tj
/T1_10 7.97 Tf
8.1 0 Td
(1)Tj
/T1_3 10.91 Tf
9.25 3.23 Td
(from)Tj
/T1_8 10.91 Tf
26.66 0 Td
(R)Tj
/T1_5 7.97 Tf
8.28 -1.69 Td
(L;j)Tj
/T1_3 10.91 Tf
17 1.69 Td
(and)Tj
/T1_8 10.91 Tf
22.08 0 Td
(L)Tj
/T1_5 7.97 Tf
7.43 -1.69 Td
(L;j)Tj
/T1_3 10.91 Tf
17 1.69 Td
[(for)-413(1)]TJ
/T1_7 10.91 Tf
27.51 0 Td
(\267)Tj
/T1_8 10.91 Tf
12.98 0 Td
(j)Tj
/T1_7 10.91 Tf
9.6 0 Td
(\267)Tj
/T1_8 10.91 Tf
12.98 0 Td
(n)Tj
/T1_5 7.97 Tf
6.54 -1.69 Td
(L)Tj
/T1_3 10.91 Tf
10.77 1.69 Td
[(that)-413(he)-414(kno)27(ws.)]TJ
-395.77 -21.91 Td
[(On)-462(the)-463(other)-463(hand,)-495(if)-463(the)-462(lea)26(ving)-461(user)]TJ
/T1_4 10.91 Tf
196.26 0 Td
(U)Tj
/T1_5 7.97 Tf
5.73 -1.78 Td
(L;l)Tj
/T1_6 5.98 Tf
10.63 -1.41 Td
(k)Tj
/T1_3 10.91 Tf
10.12 3.19 Td
[(is)-462(able)-463(to)-463(obtain)]TJ
/T1_8 10.91 Tf
86.9 0 Td
(g)Tj
/T1_5 7.97 Tf
5.59 5.04 Td
(r)Tj
/T1_11 5.98 Tf
4.06 2.81 Td
(0)Tj
/T1_6 5.98 Tf
-0.24 -5.52 Td
(L;j)Tj
/T1_5 7.97 Tf
11.23 2.71 Td
(r)Tj
/T1_11 5.98 Tf
4.05 2.81 Td
(0)Tj
/T1_6 5.98 Tf
-0.23 -5.52 Td
(L;j)Tj
/T1_12 5.98 Tf
10.73 0 Td
(+1)Tj
/T1_3 10.91 Tf
15.28 -2.33 Td
(from)Tj
/T1_8 10.91 Tf
27.19 0 Td
(z)Tj
/T1_9 7.97 Tf
5.56 3.95 Td
(0)Tj
/T1_5 7.97 Tf
-0.48 -7.19 Td
(L;j)Tj
/T1_3 10.91 Tf
17.87 3.24 Td
(=)Tj
/T1_8 10.91 Tf
13.86 0 Td
(g)Tj
/T1_5 7.97 Tf
5.6 5.04 Td
(r)Tj
/T1_11 5.98 Tf
4.05 2.81 Td
(0)Tj
/T1_6 5.98 Tf
-0.23 -5.52 Td
(L;j)Tj
/T1_3 10.91 Tf
16.77 -2.33 Td
(and)Tj
/T1_8 10.91 Tf
-450.3 -21.92 Td
(z)Tj
/T1_9 7.97 Tf
5.55 3.96 Td
(0)Tj
/T1_5 7.97 Tf
-0.48 -7.19 Td
(L;j)Tj
/T1_10 7.97 Tf
11.99 0 Td
(+1)Tj
/T1_3 10.91 Tf
14.88 3.23 Td
(=)Tj
/T1_8 10.91 Tf
12.04 0 Td
(g)Tj
/T1_5 7.97 Tf
5.59 5.04 Td
(r)Tj
/T1_11 5.98 Tf
4.05 2.81 Td
(0)Tj
/T1_6 5.98 Tf
-0.23 -5.51 Td
(L;j)Tj
/T1_12 5.98 Tf
10.73 0 Td
(+1)Tj
/T1_3 10.91 Tf
14.19 -2.34 Td
[(for)-362(1)]TJ
/T1_7 10.91 Tf
26.02 0 Td
(\267)Tj
/T1_8 10.91 Tf
12.04 0 Td
(j)Tj
/T1_7 10.91 Tf
8.67 0 Td
(\267)Tj
/T1_8 10.91 Tf
12.04 0 Td
(n)Tj
/T1_5 7.97 Tf
6.54 -1.69 Td
(L)Tj
/T1_7 10.91 Tf
8.89 1.69 Td
(\241)Tj
/T1_8 10.91 Tf
11.12 0 Td
(`)Tj
/T1_3 10.91 Tf
8.5 0 Td
(\(where)Tj
/T1_8 10.91 Tf
36.09 0 Td
(r)Tj
/T1_9 7.97 Tf
5.22 3.96 Td
(0)Tj
/T1_5 7.97 Tf
-0.3 -7.19 Td
(L;j)Tj
/T1_3 10.91 Tf
16.05 3.23 Td
(=)Tj
/T1_8 10.91 Tf
12.04 0 Td
(r)Tj
/T1_5 7.97 Tf
4.92 -1.69 Td
(L;j)Tj
/T1_3 10.91 Tf
16.44 1.69 Td
(and)Tj
/T1_8 10.91 Tf
21.52 0 Td
(z)Tj
/T1_9 7.97 Tf
5.55 3.96 Td
(0)Tj
/T1_5 7.97 Tf
-0.48 -7.19 Td
(L;j)Tj
/T1_3 10.91 Tf
16.05 3.23 Td
(=)Tj
/T1_8 10.91 Tf
12.04 0 Td
(z)Tj
/T1_5 7.97 Tf
5.07 -1.69 Td
(L;j)Tj
/T1_3 10.91 Tf
16.44 1.69 Td
(if)Tj
/T1_4 10.91 Tf
10.32 0 Td
(V)Tj
/T1_5 7.97 Tf
5.72 -1.69 Td
(L;j)Tj
/T1_8 10.91 Tf
17.26 1.69 Td
(=)Tj
/T1_7 10.91 Tf
-1.21 0 Td
[(2)-326(N)]TJ
/T1_3 10.91 Tf
21.38 0 Td
(\()Tj
/T1_7 10.91 Tf
4.25 0 Td
(R)Tj
/T1_3 10.91 Tf
9.24 0 Td
[(\)\),)-369(then)]TJ
/T1_4 10.91 Tf
40.7 0 Td
(U)Tj
/T1_5 7.97 Tf
5.72 -1.78 Td
(L;l)Tj
/T1_6 5.98 Tf
10.64 -1.4 Td
(k)Tj
/T1_3 10.91 Tf
-462.8 -18.74 Td
[(can)-421(obtain)]TJ
/T1_8 10.91 Tf
55.86 0 Td
(R)Tj
/T1_9 7.97 Tf
8.36 3.96 Td
(0)Tj
/T1_5 7.97 Tf
-0.08 -7.19 Td
(L;j)Tj
/T1_3 10.91 Tf
17.12 3.23 Td
(=)Tj
/T1_2 10.91 Tf
13.13 0 Td
(H)Tj
/T1_3 10.91 Tf
(\()Tj
/T1_8 10.91 Tf
(g)Tj
/T1_5 7.97 Tf
17.55 5.05 Td
(r)Tj
/T1_11 5.98 Tf
4.06 2.81 Td
(0)Tj
/T1_6 5.98 Tf
-0.23 -5.52 Td
(L;j)Tj
/T1_5 7.97 Tf
11.22 2.71 Td
(r)Tj
/T1_11 5.98 Tf
4.06 2.81 Td
(0)Tj
/T1_6 5.98 Tf
-0.24 -5.52 Td
(L;j)Tj
/T1_12 5.98 Tf
10.73 0 Td
(+1)Tj
/T1_7 10.91 Tf
10.24 -2.34 Td
(jj)Tj
/T1_4 10.91 Tf
6.06 0 Td
(SID)Tj
/T1_9 7.97 Tf
17.18 3.96 Td
(0)Tj
/T1_5 7.97 Tf
T*
(L)Tj
/T1_3 10.91 Tf
6.25 3.23 Td
[(\))-421(for)-422(1)]TJ
/T1_7 10.91 Tf
36.59 0 Td
(\267)Tj
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4.17 1.63 Td
[(,)-343(and)]TJ
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[(are)-341(inde-)]TJ
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[(indep)-27(enden)27(t)-359(to)-360(eac)27(h)-359(other.)-524(Then)-359(lea)27(ving)-359(user)]TJ
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223.56 0 Td
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(L;l)Tj
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(k)Tj
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9 3.18 Td
[(only)-359(has)-360(the)-359(public)-360(information)-360(from)-359(Phase)-360(2)]TJ
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[(of)-305(the)-305(Lea)27(v)28(e)-304(Proto)-28(col.)-435(But)-305(Phase)-305(2)-305(of)-305(the)-305(Lea)27(v)28(e)-304(Proto)-28(col)-305(\(without)-305(the)-305(signature)-305(information)-305(sen)26(t\))]TJ
0 -21.91 TD
[(is)-409(just)-410(the)-410(VST)83(AR)-409(proto)-28(col)-410(\(describ)-27(ed)-410(in)-410(Section)-409(9.4.1\))-410(where)-410(subgroup)-410(con)27(troller)]TJ
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(L)Tj
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10.72 1.69 Td
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[(and)-361(sends)]TJ
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51.02 0 Td
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[(in)-361(Phase)-361(2)-361(Round)-361(1)-361(while)]TJ
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128.21 0 Td
(S)Tj
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5.73 -1.64 Td
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7.31 1.64 Td
[(for)-361(1)]TJ
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(C)Tj
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[(from)-402(previous)-403(GKA,)-402(and)-403(Phase)-402(2)-403(Round)-402(2)-403(and)-403(Phase)-402(3)-403(Round)-402(1)-403(are)-402(the)-403(same)-402(as)-403(Round)-403(2)-402(and)]TJ
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[(proto)-27(col)-370(is)-369(secure.)-553(Hence)-369(the)-370(lea)27(ving)-368(user)]TJ
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205.58 0 Td
(U)Tj
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(L;l)Tj
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9.1 3.18 Td
[(is)-369(not)-369(able)-370(to)-369(obtain)-369(the)-370(\257nal)-369(group)-370(k)27(ey)]TJ
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(from)Tj
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[(Phase)-398(2)-398(of)-398(the)-398(Lea)26(v)28(e)-397(Proto)-28(col.)-639(Next,)-414(w)27(e)-398(consider)-398(the)-398(lea)27(ving)-397(user)]TJ
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10.64 -1.41 Td
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9.41 3.18 Td
[(tries)-398(to)-398(obtain)-398(the)-398(\257nal)]TJ
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[(group)-414(k)26(ey)]TJ
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52.4 0 Td
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7.32 -3.96 Td
[(from)-415(the)-414(public)-415(do)27(wn\260o)27(w)-413(information,)-436(that)-415(is,)-447(\271)]TJ
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[(and)-427(\271)]TJ
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22.1 0 Td
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(0)Tj
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7.91 3.06 Td
[(for)-414(1)]TJ
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27.54 0 Td
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[(,)-434(in)]TJ
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[(Phase)-378(3)-379(of)-379(the)-379(Lea)27(v)28(e)-378(Proto)-28(col.)-580(The)-379(new)-379(group)-379(k)27(ey)]TJ
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10.04 3.96 Td
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[(is)-379(the)-379(plain)27(text)-378(of)-391(\271)]TJ
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[(\))-378(for)-377(1)]TJ
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6.55 -1.63 Td
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4.17 1.63 Td
[(.)-576(As)-378(the)-378(lea)27(ving)-376(user)]TJ
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9.19 3.18 Td
[(do)-27(es)-378(not)-377(kno)27(w)-377(new)-378(subgroup)-377(k)27(ey)]TJ
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[(and)-350(existing)-351(subgroup)-351(k)27(eys)]TJ
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133.67 0 Td
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9.26 -1.64 Td
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7.21 1.64 Td
[(for)-351(1)]TJ
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[(,)-355(and)-351(the)-351(symmetric)-351(k)27(ey)-350(encryption)-351(sc)27(heme)]TJ
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[(is)-325(assumed)-325(to)-325(b)-27(e)-325(secure,)-327(therefore)-325(it)-325(is)-325(also)-325(not)-325(p)-28(ossible)-325(for)]TJ
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[(to)-325(obtain)]TJ
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[(for)-333(1)]TJ
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25.17 0 Td
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[(.)-444(Hence,)-333(the)-334(Lea)27(v)28(e)-332(Proto)-28(col)-333(pro)26(vides)-332(bac)27(kw)28(ard)-333(secrecy)83(.)]TJ
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[(\(not)-503(a)-503(le)50(aving)-502(user)]TJ
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[(sub)51(gr)51(oup)-334(key)]TJ
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[(and)-335(new)-335(\257nal)-335(gr)51(oup)-335(key)]TJ
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115.96 0 Td
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[(in)-334(the)-335(L)50(e)51(ave)-334(Pr)50(oto)51(c)51(ol)-334(pr)50(ovide)51(d)-334(the)-335(VK-GKA)-335(pr)50(oto)51(c)52(ol,)]TJ
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[(the)-312(VST)76(AR)-312(pr)50(oto)51(c)51(ol,)-320(the)-313(RSA)-312(signatur)50(e)-312(scheme)-312(and)-313(the)-312(symmetric)-313(key)-312(encryption)-313(scheme)]TJ
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429.68 0 Td
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[(tries)-348(to)-348(imp)-27(ersonate)]TJ
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[(subgroup)-276(con)27(troller)]TJ
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94.95 0 Td
(S)Tj
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5.72 -1.69 Td
(L)Tj
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9.29 1.69 Td
(=)Tj
/T1_3 10.91 Tf
11.51 0 Td
(V)Tj
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5.72 -1.69 Td
(L;)Tj
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(1)Tj
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12.84 1.69 Td
[(,)-288(subgroup)-276(con)27(troller)]TJ
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101.12 0 Td
(S)Tj
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5.72 -1.64 Td
(i)Tj
/T1_1 10.91 Tf
6.4 1.64 Td
[(for)-276(1)]TJ
/T1_2 10.91 Tf
24.56 0 Td
(\267)Tj
/T1_6 10.91 Tf
11.51 0 Td
(i)Tj
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6.78 0 Td
(6)Tj
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(=)Tj
/T1_6 10.91 Tf
11.52 0 Td
(L)Tj
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10.45 0 Td
(\267)Tj
/T1_6 10.91 Tf
11.51 0 Td
(n)Tj
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6.55 -1.64 Td
(c)Tj
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4.16 1.64 Td
[(,)-287(remaining)-277(users)]TJ
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83.27 0 Td
(V)Tj
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5.73 -1.69 Td
(L;j)Tj
/T1_2 10.91 Tf
15.52 1.69 Td
[(2)-277(G)]TJ
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17.43 3.96 Td
(0)Tj
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-0.64 -7.19 Td
(L)Tj
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-461.62 -18.69 Td
[(for)-322(2)]TJ
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25.05 0 Td
(\267)Tj
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11.51 0 Td
(j)Tj
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8.15 0 Td
(\267)Tj
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11.51 0 Td
(n)Tj
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(L)Tj
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8.43 1.69 Td
(\241)Tj
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10.66 0 Td
(`)Tj
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8.06 0 Td
[(or)-322(main)-322(con)27(troller)]TJ
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89.09 0 Td
(C)Tj
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9.24 0 Td
[(to)-322(establish)-322(the)-322(new)-322(subgroup)-322(k)26(ey)]TJ
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165.8 0 Td
(K)Tj
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(0)Tj
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(L)Tj
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9.77 3.23 Td
[(and)-322(new)-322(\257nal)-322(group)]TJ
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[(k)27(ey)]TJ
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20.14 0 Td
(K)Tj
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10.05 3.96 Td
(0)Tj
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6.88 -3.96 Td
[(\(w)27(e)-373(do)-375(not)-375(consider)]TJ
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99.14 0 Td
(A)Tj
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12.8 0 Td
[(tries)-374(to)-375(imp)-28(ersonate)-374(users)]TJ
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128.47 0 Td
(U)Tj
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(i;j)Tj
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13.7 1.63 Td
[(for)-375(1)]TJ
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26.38 0 Td
(\267)Tj
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12.27 0 Td
(i)Tj
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(6)Tj
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(=)Tj
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12.26 0 Td
(L)Tj
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11.21 0 Td
(\267)Tj
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(n)Tj
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6.55 -1.63 Td
(c)Tj
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8.25 1.63 Td
[(and)-374(2)]TJ
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30.9 0 Td
(\267)Tj
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12.26 0 Td
(j)Tj
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8.9 0 Td
(\267)Tj
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(n)Tj
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(i)Tj
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(as)Tj
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(U)Tj
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(i;j)Tj
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14.11 1.64 Td
[(do)-27(es)-412(not)-412(send)-412(an)27(y)-411(information)-412(in)-412(the)-412(Lea)27(v)28(e)-411(Proto)-28(col\))-412(and)-412(\(b\))]TJ
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308.01 0 Td
(A)Tj
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13.2 0 Td
[(tries)-412(to)-411(obtain)-412(the)-412(new)]TJ
-355.29 -21.92 Td
[(subgroup)-333(k)27(ey)]TJ
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67.04 0 Td
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(0)Tj
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(L)Tj
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9.9 3.23 Td
[(and)-332(new)-334(\257nal)-333(group)-333(k)26(ey)]TJ
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118.48 0 Td
(K)Tj
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10.04 3.96 Td
(0)Tj
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6.43 -3.96 Td
[(from)-333(the)-333(public)-334(information)-333(in)-333(the)-334(Lea)27(v)28(e)-332(Proto)-28(col.)]TJ
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[(F)83(or)-384(case)-385(\(a\),)-398(w)27(e)-384(\257rst)-385(consider)]TJ
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147.84 0 Td
(A)Tj
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12.91 0 Td
[(tries)-384(to)-385(imp)-28(ersonate)-385(subgroup)-384(con)26(troller)]TJ
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198.24 0 Td
(S)Tj
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5.72 -1.69 Td
(L)Tj
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6.26 1.69 Td
[(.)-599(Then)-384(in)-385(Phase)]TJ
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[(1)-458(Round)-459(1,)]TJ
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60.94 0 Td
(A)Tj
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13.71 0 Td
(generates)Tj
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49.32 0 Td
(\277)Tj
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(0)Tj
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(L)Tj
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11.56 3.23 Td
(=)Tj
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13.79 0 Td
(H)Tj
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(\()Tj
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(\267)Tj
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18.25 3.96 Td
(0)Tj
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0 -7.19 TD
(L;)Tj
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(1)Tj
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12.84 3.23 Td
(jj)Tj
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6.06 0 Td
(v)Tj
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5.67 0 Td
[(\).)-820(Next)-458(in)-459(Phase)-459(1)-458(Round)-459(3,)]TJ
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152.35 0 Td
(A)Tj
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13.71 0 Td
[(\257rst)-458(generates)]TJ
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73.2 0 Td
(z)Tj
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(0)Tj
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-0.48 -7.19 Td
(L;)Tj
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(1)Tj
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18.15 3.23 Td
(=)Tj
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-459.39 -21.92 Td
(g)Tj
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5.59 5.04 Td
(r)Tj
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4.06 2.82 Td
(0)Tj
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-0.24 -5.52 Td
(L;)Tj
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(1)Tj
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15.01 -2.34 Td
[(mo)-27(d)]TJ
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23.93 0 Td
(p)Tj
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[(,)-533(then)]TJ
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40.92 0 Td
(A)Tj
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14.09 0 Td
[(needs)-493(to)-493(compute)-493(the)-494(v)55(alid)-493(signature)]TJ
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190.27 0 Td
(\276)Tj
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6.62 3.96 Td
(0)Tj
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(L;)Tj
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(1)Tj
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(=)Tj
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14.42 0 Td
(S)Tj
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7.42 0 Td
(\()Tj
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(S)Tj
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(L)Tj
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6.25 1.69 Td
(jj)Tj
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6.06 0 Td
(\277)Tj
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6 3.96 Td
(0)Tj
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-1.23 -7.19 Td
(L)Tj
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6.26 3.23 Td
(jj)Tj
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6.05 0 Td
(z)Tj
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5.56 3.96 Td
(0)Tj
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-0.48 -7.19 Td
(L;)Tj
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(1)Tj
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12.84 3.23 Td
(jj)Tj
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6.06 0 Td
(BL)Tj
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11.45 -1.63 Td
(Z)Tj
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4.73 1.63 Td
(jj)Tj
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6.06 0 Td
(v)Tj
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5.67 0 Td
[(\).)-924(The)]TJ
-431.73 -21.91 Td
[(v)55(alidit)28(y)-472(of)-472(signature)]TJ
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103.41 0 Td
(\276)Tj
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6.62 3.95 Td
(0)Tj
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(L;)Tj
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(1)Tj
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18 3.24 Td
[(is)-472(c)27(hec)28(k)28(ed)-472(b)27(y)]TJ
/T1_3 10.91 Tf
70.66 0 Td
(V)Tj
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5.72 -1.69 Td
(L;j)Tj
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17.65 1.69 Td
[(for)-472(2)]TJ
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29.22 0 Td
(\267)Tj
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14.05 0 Td
(j)Tj
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(\267)Tj
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14.05 0 Td
(n)Tj
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(L)Tj
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9.69 1.69 Td
(\241)Tj
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11.92 0 Td
(`)Tj
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9.7 0 Td
[(in)-472(Phase)-473(1)-472(Round)-473(4.)-862(If)-473(the)]TJ
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(signature)Tj
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(L;)Tj
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8.1 0 Td
(1)Tj
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9.02 3.23 Td
[(is)-393(not)-393(correct,)-408(then)]TJ
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97.42 0 Td
(V)Tj
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(L;j)Tj
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(rejects)Tj
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34.98 0 Td
(S)Tj
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5.73 -1.69 Td
(L)Tj
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6.25 1.69 Td
[(.)-624(As)]TJ
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26.61 0 Td
(A)Tj
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12.99 0 Td
[(do)-27(es)-394(not)-393(kno)27(w)-392(the)-393(RSA)-394(priv)55(ate)-392(k)27(ey)]TJ
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178.1 0 Td
(d)Tj
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(L)Tj
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-461.62 -20.23 Td
(of)Tj
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(S)Tj
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(L)Tj
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10.32 1.69 Td
[(and)-372(the)-372(RSA)-373(signature)-372(sc)26(heme)-371(is)-373(assumed)-372(to)-372(b)-28(e)-373(secure,)-382(therefore)]TJ
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319.9 0 Td
(A)Tj
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12.77 0 Td
[(is)-372(not)-372(able)-373(to)-372(pro)-28(duce)]TJ
-361.56 -21.91 Td
[(a)-361(v)54(alid)-360(signature)]TJ
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83.72 0 Td
(\276)Tj
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6.62 3.95 Td
(0)Tj
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-0.39 -7.19 Td
(L;)Tj
/T1_5 7.97 Tf
(1)Tj
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12.84 3.24 Td
[(.)-529(Next)-362(supp)-27(ose)]TJ
/T1_2 10.91 Tf
77.1 0 Td
(A)Tj
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12.65 0 Td
[(tries)-361(to)-362(imp)-28(ersonate)]TJ
/T1_3 10.91 Tf
100.17 0 Td
(S)Tj
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5.73 -1.69 Td
(L)Tj
/T1_1 10.91 Tf
10.2 1.69 Td
[(in)-361(Phase)-361(1)-362(Round)-361(5,)-369(then)]TJ
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127.71 0 Td
(A)Tj
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12.65 0 Td
(\257rst)Tj
-449 -21.92 Td
(generates)Tj
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47.2 0 Td
(X)Tj
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9.89 3.96 Td
(0)Tj
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-0.85 -7.19 Td
(L;)Tj
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(1)Tj
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15.87 3.23 Td
(=)Tj
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11.51 0 Td
(L)Tj
/T1_7 7.97 Tf
7.42 3.96 Td
(0)Tj
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T*
(L;)Tj
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(1)Tj
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13.76 3.23 Td
(\251)Tj
/T1_6 10.91 Tf
9.4 0 Td
(R)Tj
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8.36 3.96 Td
(0)Tj
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-0.08 -7.19 Td
(L;)Tj
/T1_5 7.97 Tf
(1)Tj
/T1_1 10.91 Tf
15.72 3.23 Td
(and)Tj
/T1_13 10.91 Tf
22.65 3.49 Td
(c)Tj
/T1_6 10.91 Tf
-2.2 -3.49 Td
(X)Tj
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9.89 3.76 Td
(0)Tj
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-0.85 -7.19 Td
(L)Tj
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9.28 3.43 Td
(=)Tj
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11.51 0 Td
(\267)Tj
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6.29 3.96 Td
(0)Tj
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T*
(L;)Tj
/T1_5 7.97 Tf
(1)Tj
/T1_2 10.91 Tf
13.76 3.23 Td
(\251)Tj
/T1_6 10.91 Tf
9.39 0 Td
(R)Tj
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8.37 3.96 Td
(0)Tj
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-0.09 -7.19 Td
(L;)Tj
/T1_5 7.97 Tf
(1)Tj
/T1_1 10.91 Tf
15.73 3.23 Td
(where)Tj
/T1_6 10.91 Tf
30.78 0 Td
(L)Tj
/T1_7 7.97 Tf
7.42 3.96 Td
(0)Tj
/T1_4 7.97 Tf
T*
(L;)Tj
/T1_5 7.97 Tf
(1)Tj
/T1_1 10.91 Tf
15.87 3.23 Td
(=)Tj
/T1_8 10.91 Tf
11.51 0 Td
(H)Tj
/T1_1 10.91 Tf
7.73 0 Td
(\(\()Tj
/T1_6 10.91 Tf
8.48 0 Td
(z)Tj
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5.55 3.96 Td
(0)Tj
/T1_4 7.97 Tf
-0.48 -7.28 Td
(L;n)Tj
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13.25 -1.34 Td
(L)Tj
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5.55 1.34 Td
(\241)Tj
/T1_4 7.97 Tf
6.59 0 Td
(`)Tj
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3.96 3.32 Td
(\))Tj
/T1_4 7.97 Tf
4.24 5.04 Td
(r)Tj
/T1_9 5.98 Tf
4.05 2.81 Td
(0)Tj
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-0.23 -5.51 Td
(L;)Tj
/T1_11 5.98 Tf
7.32 0 Td
(1)Tj
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4.65 -2.34 Td
(jj)Tj
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6.06 0 Td
(SID)Tj
/T1_7 7.97 Tf
17.18 3.96 Td
(0)Tj
/T1_4 7.97 Tf
T*
(L)Tj
/T1_1 10.91 Tf
6.25 3.23 Td
[(\))-264(and)]TJ
/T1_6 10.91 Tf
27.58 0 Td
(R)Tj
/T1_7 7.97 Tf
8.36 3.96 Td
(0)Tj
/T1_4 7.97 Tf
-0.08 -7.19 Td
(L;)Tj
/T1_5 7.97 Tf
(1)Tj
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15.87 3.23 Td
(=)Tj
/T1_8 10.91 Tf
-459.39 -21.92 Td
(H)Tj
/T1_1 10.91 Tf
7.73 0 Td
(\(\()Tj
/T1_6 10.91 Tf
8.48 0 Td
(z)Tj
/T1_7 7.97 Tf
5.55 3.96 Td
(0)Tj
/T1_4 7.97 Tf
-0.48 -7.19 Td
(L;)Tj
/T1_5 7.97 Tf
(2)Tj
/T1_1 10.91 Tf
12.84 3.23 Td
(\))Tj
/T1_4 7.97 Tf
4.24 5.05 Td
(r)Tj
/T1_9 5.98 Tf
4.06 2.81 Td
(0)Tj
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-0.24 -5.52 Td
(L;)Tj
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(1)Tj
/T1_2 10.91 Tf
11.98 -2.34 Td
(jj)Tj
/T1_3 10.91 Tf
6.05 0 Td
(SID)Tj
/T1_7 7.97 Tf
17.18 3.96 Td
(0)Tj
/T1_4 7.97 Tf
T*
(L)Tj
/T1_1 10.91 Tf
6.26 3.23 Td
[(\).)-417(Then,)]TJ
/T1_2 10.91 Tf
42.62 0 Td
(A)Tj
/T1_1 10.91 Tf
11.45 0 Td
[(has)-252(to)-252(compute)-252(the)-252(v)54(alid)-251(signature)-305(\271)]TJ
/T1_6 10.91 Tf
164.18 0 Td
(\276)Tj
/T1_7 7.97 Tf
6.63 3.96 Td
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[(wishes)-375(to)-376(imp)-28(ersonate)-376(subgroup)-376(con)27(troller)]TJ
/T1_2 10.91 Tf
207.47 0 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
7.48 1.63 Td
[(for)-375(1)]TJ
/T1_1 10.91 Tf
26.41 0 Td
(\267)Tj
/T1_4 10.91 Tf
12.28 0 Td
(i)Tj
/T1_1 10.91 Tf
7.56 0 Td
(6)Tj
/T1_0 10.91 Tf
(=)Tj
/T1_4 10.91 Tf
12.28 0 Td
(L)Tj
/T1_1 10.91 Tf
11.22 0 Td
(\267)Tj
/T1_4 10.91 Tf
12.29 0 Td
(n)Tj
/T1_3 7.97 Tf
6.54 -1.63 Td
(c)Tj
/T1_0 10.91 Tf
4.17 1.63 Td
[(.)-571(As)]TJ
/T1_2 10.91 Tf
25.84 0 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
-464.49 -20.28 Td
[(for)-401(1)]TJ
/T1_1 10.91 Tf
27.17 0 Td
(\267)Tj
/T1_4 10.91 Tf
12.76 0 Td
(i)Tj
/T1_1 10.91 Tf
8.03 0 Td
(6)Tj
/T1_0 10.91 Tf
(=)Tj
/T1_4 10.91 Tf
12.76 0 Td
(L)Tj
/T1_1 10.91 Tf
11.7 0 Td
(\267)Tj
/T1_4 10.91 Tf
12.75 0 Td
(n)Tj
/T1_3 7.97 Tf
6.55 -1.64 Td
(c)Tj
/T1_0 10.91 Tf
8.55 1.64 Td
[(do)-27(es)-402(not)-402(send)-402(an)27(y)-401(information)-402(in)-402(Phase)-402(1)-402(and)-402(2,)-419(hence)-401(w)26(e)-401(only)-401(consider)]TJ
/T1_1 10.91 Tf
358.89 0 Td
(A)Tj
/T1_0 10.91 Tf
-459.16 -21.92 Td
[(tries)-377(to)-378(imp)-28(ersonate)]TJ
/T1_2 10.91 Tf
100.71 0 Td
(S)Tj
/T1_3 7.97 Tf
5.72 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
7.5 1.63 Td
[(in)-378(Phase)-378(3.)-578(Then)-378(in)-378(Phase)-378(3)-378(Round)-378(1,)]TJ
/T1_1 10.91 Tf
192.67 0 Td
(A)Tj
/T1_0 10.91 Tf
12.83 0 Td
[(generates)-390(\271)]TJ
/T1_2 10.91 Tf
48.44 0 Td
(c)Tj
/T1_5 7.97 Tf
5.73 3.96 Td
(0)Tj
/T1_3 7.97 Tf
0 -7.01 TD
(i)Tj
/T1_0 10.91 Tf
7.22 3.05 Td
(=)Tj
/T1_1 10.91 Tf
12.32 0 Td
(E)Tj
/T1_3 7.97 Tf
5.76 -1.69 Td
(K)Tj
/T1_6 5.98 Tf
7.13 -1.21 Td
(i)Tj
/T1_0 10.91 Tf
3.66 2.9 Td
(\()Tj
/T1_4 10.91 Tf
(K)Tj
/T1_5 7.97 Tf
14.29 3.96 Td
(0)Tj
/T1_1 10.91 Tf
2.79 -3.96 Td
(jj)Tj
/T1_2 10.91 Tf
6.06 0 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
3.38 1.63 Td
[(\))-377(and)]TJ
/T1_4 10.91 Tf
-441.94 -21.92 Td
(\265)Tj
/T1_5 7.97 Tf
5.42 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.3 -7.01 Td
(i)Tj
/T1_0 10.91 Tf
6.72 3.05 Td
(=)Tj
/T1_7 10.91 Tf
11.83 0 Td
(H)Tj
/T1_0 10.91 Tf
(\()Tj
/T1_4 10.91 Tf
11.97 0 Td
(K)Tj
/T1_3 7.97 Tf
9.26 -1.63 Td
(i)Tj
/T1_1 10.91 Tf
3.38 1.63 Td
(jj)Tj
/T1_4 10.91 Tf
6.06 0 Td
(K)Tj
/T1_5 7.97 Tf
10.04 3.96 Td
(0)Tj
/T1_1 10.91 Tf
2.79 -3.96 Td
(jj)Tj
/T1_4 10.91 Tf
6.06 0 Td
(\277)Tj
/T1_3 7.97 Tf
4.77 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
3.38 1.63 Td
[(\).)-496(Next,)]TJ
/T1_1 10.91 Tf
42.61 0 Td
(A)Tj
/T1_0 10.91 Tf
12.53 0 Td
[(needs)-350(to)-351(compute)-350(v)54(alid)-349(signature)-404(\271)]TJ
/T1_4 10.91 Tf
161.96 0 Td
(\276)Tj
/T1_5 7.97 Tf
6.62 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.39 -7.01 Td
(i)Tj
/T1_0 10.91 Tf
6.72 3.05 Td
(=)Tj
/T1_1 10.91 Tf
11.83 0 Td
(S)Tj
/T1_0 10.91 Tf
7.42 0 Td
(\()Tj
/T1_2 10.91 Tf
(S)Tj
/T1_3 7.97 Tf
9.97 -1.63 Td
(i)Tj
/T1_1 10.91 Tf
3.38 1.63 Td
(jj)Tj
/T1_4 10.91 Tf
6.05 0 Td
(\277)Tj
/T1_3 7.97 Tf
4.77 -1.63 Td
(i)Tj
/T1_1 10.91 Tf
3.38 1.63 Td
(jj)Tj
/T1_4 10.91 Tf
6.06 0 Td
(\265)Tj
/T1_5 7.97 Tf
5.42 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.3 -7.01 Td
(i)Tj
/T1_1 10.91 Tf
3.38 3.05 Td
(jj)Tj
/T1_4 10.91 Tf
6.06 0 Td
(v)Tj
/T1_0 10.91 Tf
5.68 0 Td
[(\).)-496(The)-350(v)54(alidit)28(y)-349(of)]TJ
-383.94 -21.91 Td
(\271)Tj
/T1_4 10.91 Tf
-0.59 0 Td
(\276)Tj
/T1_5 7.97 Tf
6.62 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.39 -7.02 Td
(i)Tj
/T1_0 10.91 Tf
7.6 3.06 Td
[(is)-386(c)27(hec)28(k)28(ed)-386(b)27(y)]TJ
/T1_2 10.91 Tf
67.84 0 Td
(U)Tj
/T1_3 7.97 Tf
5.73 -1.64 Td
(i;j)Tj
/T1_0 10.91 Tf
13.83 1.64 Td
[(for)-386(2)]TJ
/T1_1 10.91 Tf
26.72 0 Td
(\267)Tj
/T1_4 10.91 Tf
12.48 0 Td
(j)Tj
/T1_1 10.91 Tf
9.11 0 Td
(\267)Tj
/T1_4 10.91 Tf
12.48 0 Td
(n)Tj
/T1_3 7.97 Tf
6.54 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
7.6 1.64 Td
[(in)-386(Phase)-386(3)-387(Round)-387(2.)-604(If)-386(the)-387(signature)-440(\271)]TJ
/T1_4 10.91 Tf
184.99 0 Td
(\276)Tj
/T1_5 7.97 Tf
6.63 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.4 -7.02 Td
(i)Tj
/T1_0 10.91 Tf
7.6 3.06 Td
[(is)-386(not)-387(correct,)-399(then)]TJ
/T1_2 10.91 Tf
-374.98 -21.92 Td
(U)Tj
/T1_3 7.97 Tf
5.73 -1.63 Td
(i;j)Tj
/T1_0 10.91 Tf
13.24 1.63 Td
(rejects)Tj
/T1_2 10.91 Tf
34.31 0 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
3.38 1.63 Td
[(.)-444(As)]TJ
/T1_1 10.91 Tf
23.98 0 Td
(A)Tj
/T1_0 10.91 Tf
12.34 0 Td
[(do)-27(es)-333(not)-332(kno)26(w)-331(the)-333(RSA)-333(priv)55(ate)-332(k)27(ey)]TJ
/T1_4 10.91 Tf
173.47 0 Td
(d)Tj
/T1_3 7.97 Tf
5.68 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
7.01 1.63 Td
(of)Tj
/T1_2 10.91 Tf
12.41 0 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
7 1.63 Td
[(and)-332(the)-333(RSA)-333(signature)-332(sc)26(heme)-331(is)]TJ
-310.01 -21.91 Td
[(assumed)-341(to)-342(b)-28(e)-342(secure,)-344(therefore)]TJ
/T1_1 10.91 Tf
154.05 0 Td
(A)Tj
/T1_0 10.91 Tf
12.44 0 Td
[(is)-341(not)-342(able)-342(to)-342(pro)-27(duce)-342(a)-342(v)54(alid)-340(signature)-396(\271)]TJ
/T1_4 10.91 Tf
191.78 0 Td
(\276)Tj
/T1_5 7.97 Tf
6.62 3.95 Td
(0)Tj
/T1_3 7.97 Tf
-0.39 -7.01 Td
(i)Tj
/T1_0 10.91 Tf
3.38 3.06 Td
[(.)-470(Therefore,)]TJ
/T1_1 10.91 Tf
60.74 0 Td
(A)Tj
/T1_0 10.91 Tf
12.44 0 Td
[(is)-341(not)]TJ
-441.06 -21.92 Td
[(able)-333(to)-333(imp)-28(ersonate)]TJ
/T1_2 10.91 Tf
97.94 0 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
3.38 1.64 Td
(.)Tj
-90.12 -21.92 Td
[(Next,)-454(consider)-430(if)]TJ
/T1_1 10.91 Tf
85.62 0 Td
(A)Tj
/T1_0 10.91 Tf
13.39 0 Td
[(tries)-430(to)-430(imp)-28(ersonate)-430(remaining)-430(users)]TJ
/T1_2 10.91 Tf
182.86 0 Td
(V)Tj
/T1_3 7.97 Tf
5.73 -1.69 Td
(L;j)Tj
/T1_0 10.91 Tf
17.18 1.69 Td
[(for)-429(2)]TJ
/T1_1 10.91 Tf
27.98 0 Td
(\267)Tj
/T1_4 10.91 Tf
13.27 0 Td
(j)Tj
/T1_1 10.91 Tf
9.9 0 Td
(\267)Tj
/T1_4 10.91 Tf
13.27 0 Td
(n)Tj
/T1_3 7.97 Tf
6.55 -1.69 Td
(L)Tj
/T1_1 10.91 Tf
9.38 1.69 Td
(\241)Tj
/T1_4 10.91 Tf
11.61 0 Td
(`)Tj
/T1_0 10.91 Tf
4.54 0 Td
[(.)-734(Then)-430(in)]TJ
-418.21 -21.91 Td
[(Phase)-409(1)-410(Round)-410(2,)]TJ
/T1_1 10.91 Tf
91.77 0 Td
(A)Tj
/T1_0 10.91 Tf
13.18 0 Td
[(can)-409(only)-410(try)-410(to)-410(imp)-28(ersonate)-410(remaining)-409(user)]TJ
/T1_2 10.91 Tf
216.63 0 Td
(V)Tj
/T1_3 7.97 Tf
5.73 -1.78 Td
(L;k)Tj
/T1_1 10.91 Tf
17.65 1.78 Td
[(2)-405(N)]TJ
/T1_0 10.91 Tf
22.25 0 Td
(\()Tj
/T1_1 10.91 Tf
(R)Tj
/T1_0 10.91 Tf
13.48 0 Td
[(\),)-429(who)-410(is)-409(a)-410(left)-410(or)]TJ
-380.69 -21.92 Td
[(righ)27(t)-398(neigh)27(b)-27(or)-399(of)-400(lea)27(ving)-398(users,)-416(as)-399(only)]TJ
/T1_2 10.91 Tf
193.62 0 Td
(V)Tj
/T1_3 7.97 Tf
5.72 -1.78 Td
(L;k)Tj
/T1_1 10.91 Tf
17.46 1.78 Td
[(2)-387(N)]TJ
/T1_0 10.91 Tf
22.06 0 Td
(\()Tj
/T1_1 10.91 Tf
(R)Tj
/T1_0 10.91 Tf
13.48 0 Td
[(\))-399(sends)-399(information)-399(in)-400(Phase)-399(1)-399(Round)-400(2.)-642(In)]TJ
-252.34 -21.92 Td
[(this)-377(case,)]TJ
/T1_1 10.91 Tf
48.47 0 Td
(A)Tj
/T1_0 10.91 Tf
12.83 0 Td
(generates)Tj
/T1_4 10.91 Tf
48.45 0 Td
(z)Tj
/T1_5 7.97 Tf
5.55 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.48 -7.28 Td
(L;k)Tj
/T1_0 10.91 Tf
17.06 3.32 Td
(=)Tj
/T1_4 10.91 Tf
12.32 0 Td
(g)Tj
/T1_3 7.97 Tf
5.6 5.11 Td
(r)Tj
/T1_8 5.98 Tf
4.05 2.81 Td
(0)Tj
/T1_6 5.98 Tf
-0.23 -5.58 Td
(L;k)Tj
/T1_0 10.91 Tf
15.42 -2.34 Td
[(mo)-28(d)]TJ
/T1_4 10.91 Tf
23.94 0 Td
(p)Tj
/T1_0 10.91 Tf
9.6 0 Td
[(in)-378(Phase)-378(1)-377(Round)-378(2)-378(\257rst.)-578(Next,)]TJ
/T1_1 10.91 Tf
158.85 0 Td
(A)Tj
/T1_0 10.91 Tf
12.83 0 Td
[(has)-377(to)-378(compute)-378(the)]TJ
-374.26 -21.91 Td
[(v)55(alid)-334(signature)]TJ
/T1_4 10.91 Tf
73.74 0 Td
(\276)Tj
/T1_5 7.97 Tf
6.62 3.95 Td
(0)Tj
/T1_3 7.97 Tf
-0.39 -7.27 Td
(L;k)Tj
/T1_0 10.91 Tf
16.29 3.32 Td
(=)Tj
/T1_1 10.91 Tf
11.54 0 Td
(S)Tj
/T1_0 10.91 Tf
7.42 0 Td
(\()Tj
/T1_2 10.91 Tf
(V)Tj
/T1_3 7.97 Tf
9.97 -1.78 Td
(L;k)Tj
/T1_1 10.91 Tf
13.23 1.78 Td
(jj)Tj
/T1_4 10.91 Tf
6.05 0 Td
(z)Tj
/T1_5 7.97 Tf
5.56 3.95 Td
(0)Tj
/T1_3 7.97 Tf
-0.48 -7.27 Td
(L;k)Tj
/T1_1 10.91 Tf
13.22 3.32 Td
(jj)Tj
/T1_4 10.91 Tf
6.06 0 Td
(\277)Tj
/T1_5 7.97 Tf
6 3.95 Td
(0)Tj
/T1_3 7.97 Tf
-1.23 -7.19 Td
(L)Tj
/T1_1 10.91 Tf
6.26 3.24 Td
(jj)Tj
/T1_4 10.91 Tf
6.05 0 Td
(v)Tj
/T1_0 10.91 Tf
5.68 0 Td
[(\).)-449(The)-335(v)55(alidit)28(y)-334(of)]TJ
/T1_4 10.91 Tf
86.14 0 Td
(\276)Tj
/T1_5 7.97 Tf
6.62 3.95 Td
(0)Tj
/T1_3 7.97 Tf
-0.39 -7.27 Td
(L;k)Tj
/T1_0 10.91 Tf
16.88 3.32 Td
[(is)-335(c)27(hec)28(k)28(ed)-334(b)27(y)]TJ
/T1_2 10.91 Tf
66.16 0 Td
(S)Tj
/T1_3 7.97 Tf
5.72 -1.69 Td
(L)Tj
/T1_0 10.91 Tf
9.91 1.69 Td
[(in)-334(Phase)-335(1)-335(Round)]TJ
-382.63 -21.92 Td
[(3.)-443(If)-330(the)-330(signature)]TJ
/T1_4 10.91 Tf
90.25 0 Td
(\276)Tj
/T1_5 7.97 Tf
6.62 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.39 -7.28 Td
(L;k)Tj
/T1_0 10.91 Tf
16.83 3.32 Td
[(is)-329(not)-331(correct,)-330(then)]TJ
/T1_2 10.91 Tf
94.5 0 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.69 Td
(L)Tj
/T1_0 10.91 Tf
9.85 1.69 Td
(rejects)Tj
/T1_2 10.91 Tf
34.29 0 Td
(V)Tj
/T1_3 7.97 Tf
5.73 -1.78 Td
(L;k)Tj
/T1_1 10.91 Tf
16.26 1.78 Td
[(2)-277(N)]TJ
/T1_0 10.91 Tf
20.85 0 Td
(\()Tj
/T1_1 10.91 Tf
(R)Tj
/T1_0 10.91 Tf
13.48 0 Td
[(\).)-443(As)]TJ
/T1_1 10.91 Tf
28.19 0 Td
(A)Tj
/T1_0 10.91 Tf
12.31 0 Td
[(do)-27(es)-330(not)-330(kno)26(w)-329(the)-330(RSA)]TJ
-354.5 -21.92 Td
[(priv)55(ate)-337(k)27(ey)]TJ
/T1_4 10.91 Tf
56.47 0 Td
(d)Tj
/T1_3 7.97 Tf
5.68 -1.77 Td
(L;k)Tj
/T1_0 10.91 Tf
16.91 1.77 Td
(of)Tj
/T1_2 10.91 Tf
12.47 0 Td
(V)Tj
/T1_3 7.97 Tf
5.72 -1.77 Td
(L;k)Tj
/T1_1 10.91 Tf
16.34 1.77 Td
[(2)-284(N)]TJ
/T1_0 10.91 Tf
20.93 0 Td
(\()Tj
/T1_1 10.91 Tf
(R)Tj
/T1_0 10.91 Tf
[(\))-337(and)-337(the)-338(RSA)-338(signature)-337(sc)26(heme)-336(is)-338(assumed)-337(to)-338(b)-28(e)-338(secure,)-338(therefore)]TJ
/T1_1 10.91 Tf
-134.52 -21.91 Td
(A)Tj
/T1_0 10.91 Tf
12.93 0 Td
[(is)-387(not)-387(able)-388(to)-387(pro)-28(duce)-387(a)-387(v)54(alid)-386(signature)]TJ
/T1_4 10.91 Tf
195.75 0 Td
(\276)Tj
/T1_5 7.97 Tf
6.62 3.95 Td
(0)Tj
/T1_3 7.97 Tf
-0.39 -7.27 Td
(L;k)Tj
/T1_0 10.91 Tf
13.23 3.32 Td
[(.)-606(Next)-387(supp)-28(ose)]TJ
/T1_1 10.91 Tf
78.5 0 Td
(A)Tj
/T1_0 10.91 Tf
12.93 0 Td
[(tries)-387(to)-387(imp)-28(ersonate)-387(remaining)]TJ
-319.57 -21.92 Td
(user)Tj
/T1_2 10.91 Tf
24 0 Td
(V)Tj
/T1_3 7.97 Tf
5.72 -1.69 Td
(L;j)Tj
/T1_0 10.91 Tf
17.01 1.69 Td
[(for)-414(2)]TJ
/T1_1 10.91 Tf
27.54 0 Td
(\267)Tj
/T1_4 10.91 Tf
12.98 0 Td
(j)Tj
/T1_1 10.91 Tf
9.62 0 Td
(\267)Tj
/T1_4 10.91 Tf
12.98 0 Td
(n)Tj
/T1_3 7.97 Tf
6.55 -1.69 Td
(L)Tj
/T1_1 10.91 Tf
9.27 1.69 Td
(\241)Tj
/T1_4 10.91 Tf
11.49 0 Td
(`)Tj
/T1_0 10.91 Tf
9.07 0 Td
[(in)-414(Phase)-414(1)-414(Round)-415(4,)-435(then)]TJ
/T1_1 10.91 Tf
131.31 0 Td
(A)Tj
/T1_0 10.91 Tf
13.22 0 Td
(generates)Tj
/T1_4 10.91 Tf
48.84 0 Td
(\267)Tj
/T1_5 7.97 Tf
6.29 3.96 Td
(0)Tj
/T1_3 7.97 Tf
0 -7.19 TD
(L;j)Tj
/T1_1 10.91 Tf
16.99 3.23 Td
[(2)-412(f)]TJ
/T1_0 10.91 Tf
(0)Tj
/T1_4 10.91 Tf
(;)Tj
/T1_0 10.91 Tf
27.53 0 Td
(1)Tj
/T1_1 10.91 Tf
(g)Tj
/T1_3 7.97 Tf
10.9 3.96 Td
(\270)Tj
/T1_0 10.91 Tf
9.96 -3.96 Td
(and)Tj
/T1_4 10.91 Tf
22.09 0 Td
(X)Tj
/T1_5 7.97 Tf
9.89 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.85 -7.19 Td
(L;j)Tj
/T1_0 10.91 Tf
16.99 3.23 Td
(=)Tj
/T1_4 10.91 Tf
-459.39 -21.92 Td
(L)Tj
/T1_5 7.97 Tf
7.42 3.96 Td
(0)Tj
/T1_3 7.97 Tf
T*
(L;j)Tj
/T1_1 10.91 Tf
15.56 3.23 Td
(\251)Tj
/T1_4 10.91 Tf
11.56 0 Td
(R)Tj
/T1_5 7.97 Tf
8.36 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.08 -7.19 Td
(L;j)Tj
/T1_0 10.91 Tf
12.49 3.23 Td
[(,)-444(where)]TJ
/T1_4 10.91 Tf
40.39 0 Td
(L)Tj
/T1_5 7.97 Tf
7.42 3.96 Td
(0)Tj
/T1_3 7.97 Tf
T*
(L;j)Tj
/T1_0 10.91 Tf
17.14 3.23 Td
(=)Tj
/T1_7 10.91 Tf
13.13 0 Td
(H)Tj
/T1_0 10.91 Tf
7.73 0 Td
(\(\()Tj
/T1_4 10.91 Tf
8.48 0 Td
(z)Tj
/T1_5 7.97 Tf
5.55 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.48 -7.19 Td
(L;j)Tj
/T1_5 7.97 Tf
11.99 0 Td
(\241)Tj
/T1_9 7.97 Tf
6.59 0 Td
(1)Tj
/T1_0 10.91 Tf
4.73 3.23 Td
(\))Tj
/T1_3 7.97 Tf
4.24 5.05 Td
(r)Tj
/T1_8 5.98 Tf
4.05 2.81 Td
(0)Tj
/T1_6 5.98 Tf
-0.23 -5.52 Td
(L;j)Tj
/T1_1 10.91 Tf
11.73 -2.34 Td
(jj)Tj
/T1_2 10.91 Tf
6.05 0 Td
(SID)Tj
/T1_5 7.97 Tf
17.18 3.96 Td
(0)Tj
/T1_3 7.97 Tf
T*
(L)Tj
/T1_0 10.91 Tf
6.26 3.23 Td
(\),)Tj
/T1_4 10.91 Tf
12.12 0 Td
(R)Tj
/T1_5 7.97 Tf
8.36 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.08 -7.19 Td
(L;j)Tj
/T1_0 10.91 Tf
17.14 3.23 Td
(=)Tj
/T1_7 10.91 Tf
13.13 0 Td
(H)Tj
/T1_0 10.91 Tf
(\(\()Tj
/T1_4 10.91 Tf
(z)Tj
/T1_5 7.97 Tf
21.76 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.48 -7.19 Td
(L;j)Tj
/T1_9 7.97 Tf
11.99 0 Td
(+1)Tj
/T1_0 10.91 Tf
11.32 3.23 Td
(\))Tj
/T1_3 7.97 Tf
4.24 5.05 Td
(r)Tj
/T1_8 5.98 Tf
4.05 2.81 Td
(0)Tj
/T1_6 5.98 Tf
-0.23 -5.52 Td
(L;j)Tj
/T1_1 10.91 Tf
11.72 -2.34 Td
(jj)Tj
/T1_2 10.91 Tf
6.06 0 Td
(SID)Tj
/T1_5 7.97 Tf
17.18 3.96 Td
(0)Tj
/T1_3 7.97 Tf
T*
(L)Tj
/T1_0 10.91 Tf
6.26 3.23 Td
(\),)Tj
/T1_4 10.91 Tf
12.12 0 Td
(z)Tj
/T1_5 7.97 Tf
5.55 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.48 -7.28 Td
(L;n)Tj
/T1_6 5.98 Tf
13.24 -1.34 Td
(L)Tj
/T1_5 7.97 Tf
5.56 1.34 Td
(\241)Tj
/T1_3 7.97 Tf
(`)Tj
/T1_9 7.97 Tf
(+1)Tj
/T1_0 10.91 Tf
26.01 3.32 Td
(=)Tj
/T1_4 10.91 Tf
13.13 0 Td
(z)Tj
/T1_5 7.97 Tf
5.55 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.48 -7.19 Td
(L;)Tj
/T1_9 7.97 Tf
(1)Tj
/T1_0 10.91 Tf
12.84 3.23 Td
(,)Tj
/T1_2 10.91 Tf
-464.84 -21.91 Td
(SID)Tj
/T1_5 7.97 Tf
17.18 3.96 Td
(0)Tj
/T1_3 7.97 Tf
T*
(L)Tj
/T1_0 10.91 Tf
9.5 3.23 Td
(=)Tj
/T1_7 10.91 Tf
11.73 0 Td
(H)Tj
/T1_0 10.91 Tf
7.73 0 Td
(\()Tj
/T1_4 10.91 Tf
(\277)Tj
/T1_5 7.97 Tf
10.24 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-1.24 -7.19 Td
(L)Tj
/T1_1 10.91 Tf
6.26 3.23 Td
(jj)Tj
/T1_2 10.91 Tf
6.06 0 Td
(V)Tj
/T1_3 7.97 Tf
5.72 -1.69 Td
(L;)Tj
/T1_9 7.97 Tf
(1)Tj
/T1_1 10.91 Tf
12.85 1.69 Td
(jj)Tj
/T1_2 10.91 Tf
6.05 0 Td
(V)Tj
/T1_3 7.97 Tf
5.73 -1.69 Td
(L;)Tj
/T1_9 7.97 Tf
(2)Tj
/T1_1 10.91 Tf
12.84 1.69 Td
[(jj)-166(\242)-167(\242)-166(\242)-167(jj)]TJ
/T1_2 10.91 Tf
28.48 0 Td
(V)Tj
/T1_3 7.97 Tf
5.72 -1.78 Td
(L;n)Tj
/T1_6 5.98 Tf
13.25 -1.34 Td
(L)Tj
/T1_5 7.97 Tf
5.55 1.34 Td
(\241)Tj
/T1_3 7.97 Tf
6.59 0 Td
(`)Tj
/T1_0 10.91 Tf
3.95 1.78 Td
[(\))-345(and)]TJ
/T1_4 10.91 Tf
29.35 0 Td
(r)Tj
/T1_5 7.97 Tf
5.22 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.3 -7.19 Td
(L;j)Tj
/T1_0 10.91 Tf
15.74 3.23 Td
(=)Tj
/T1_4 10.91 Tf
11.73 0 Td
(r)Tj
/T1_3 7.97 Tf
4.92 -1.69 Td
(L;j)Tj
/T1_0 10.91 Tf
16.26 1.69 Td
(and)Tj
/T1_4 10.91 Tf
21.33 0 Td
(z)Tj
/T1_5 7.97 Tf
5.55 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.47 -7.19 Td
(L;j)Tj
/T1_0 10.91 Tf
15.73 3.23 Td
(=)Tj
/T1_4 10.91 Tf
11.73 0 Td
(z)Tj
/T1_3 7.97 Tf
5.08 -1.69 Td
(L;j)Tj
/T1_0 10.91 Tf
16.25 1.69 Td
(if)Tj
/T1_2 10.91 Tf
10.13 0 Td
(V)Tj
/T1_3 7.97 Tf
5.73 -1.69 Td
(L;j)Tj
/T1_4 10.91 Tf
16.95 1.69 Td
(=)Tj
/T1_1 10.91 Tf
-1.22 0 Td
[(2)-298(N)]TJ
/T1_0 10.91 Tf
21.08 0 Td
(\()Tj
/T1_1 10.91 Tf
(R)Tj
/T1_0 10.91 Tf
13.48 0 Td
[(\).)-480(Then)]TJ
/T1_1 10.91 Tf
41.12 0 Td
(A)Tj
/T1_0 10.91 Tf
12.48 0 Td
(has)Tj
-452.06 -21.92 Td
[(to)-346(compute)-347(the)-347(v)54(alid)-346(signature)-401(\271)]TJ
/T1_4 10.91 Tf
150.79 0 Td
(\276)Tj
/T1_5 7.97 Tf
6.63 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.39 -7.19 Td
(L;j)Tj
/T1_0 10.91 Tf
15.76 3.23 Td
(=)Tj
/T1_1 10.91 Tf
11.76 0 Td
(S)Tj
/T1_0 10.91 Tf
7.43 0 Td
(\()Tj
/T1_2 10.91 Tf
(V)Tj
/T1_3 7.97 Tf
9.96 -1.69 Td
(L;j)Tj
/T1_1 10.91 Tf
12.49 1.69 Td
(jj)Tj
/T1_4 10.91 Tf
6.06 0 Td
(\267)Tj
/T1_5 7.97 Tf
6.29 3.96 Td
(0)Tj
/T1_3 7.97 Tf
T*
(L;j)Tj
/T1_1 10.91 Tf
12.49 3.23 Td
(jj)Tj
/T1_4 10.91 Tf
6.05 0 Td
(X)Tj
/T1_5 7.97 Tf
9.9 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.86 -7.19 Td
(L;j)Tj
/T1_1 10.91 Tf
12.49 3.23 Td
(jj)Tj
/T1_4 10.91 Tf
6.06 0 Td
(\277)Tj
/T1_5 7.97 Tf
6 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-1.23 -7.19 Td
(L)Tj
/T1_1 10.91 Tf
6.25 3.23 Td
(jj)Tj
/T1_4 10.91 Tf
6.06 0 Td
(v)Tj
/T1_0 10.91 Tf
5.68 0 Td
[(\).)-485(The)-347(v)55(alidit)28(y)-346(of)-401(\271)]TJ
/T1_4 10.91 Tf
86.93 0 Td
(\276)Tj
/T1_5 7.97 Tf
6.62 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.39 -7.19 Td
(L;j)Tj
/T1_0 10.91 Tf
16.28 3.23 Td
[(is)-346(c)27(hec)28(k)27(ed)-346(b)27(y)]TJ
/T1_2 10.91 Tf
-405.11 -21.92 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.68 Td
(L)Tj
/T1_0 10.91 Tf
10.35 1.68 Td
[(in)-375(Phase)-376(1)-376(Round)-375(5.)-572(If)-376(the)-376(signature)-429(\271)]TJ
/T1_4 10.91 Tf
183.82 0 Td
(\276)Tj
/T1_5 7.97 Tf
6.62 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.39 -7.19 Td
(L;j)Tj
/T1_0 10.91 Tf
16.59 3.23 Td
[(is)-375(not)-376(correct,)-386(then)]TJ
/T1_2 10.91 Tf
96.6 0 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.68 Td
(L)Tj
/T1_0 10.91 Tf
10.35 1.68 Td
(rejects)Tj
/T1_2 10.91 Tf
34.79 0 Td
(V)Tj
/T1_3 7.97 Tf
5.73 -1.68 Td
(L;j)Tj
/T1_0 10.91 Tf
12.49 1.68 Td
[(.)-571(As)]TJ
/T1_1 10.91 Tf
25.84 0 Td
(A)Tj
/T1_0 10.91 Tf
12.81 0 Td
[(do)-27(es)-376(not)]TJ
-427.06 -21.91 Td
[(kno)27(w)-370(the)-371(RSA)-371(priv)55(ate)-370(k)27(ey)]TJ
/T1_4 10.91 Tf
131.59 0 Td
(d)Tj
/T1_3 7.97 Tf
5.68 -1.69 Td
(L;j)Tj
/T1_0 10.91 Tf
16.54 1.69 Td
[(of)-370(remaining)-371(user)]TJ
/T1_2 10.91 Tf
87.69 0 Td
(V)Tj
/T1_3 7.97 Tf
5.73 -1.69 Td
(L;j)Tj
/T1_0 10.91 Tf
16.53 1.69 Td
[(and)-371(the)-371(RSA)-371(signature)-371(sc)27(heme)-370(is)-371(assumed)]TJ
-263.76 -21.92 Td
[(to)-334(b)-27(e)-335(secure,)-334(therefore)]TJ
/T1_1 10.91 Tf
109.85 0 Td
(A)Tj
/T1_0 10.91 Tf
12.36 0 Td
[(is)-333(not)-334(able)-335(to)-334(pro)-27(duce)-335(a)-334(v)55(alid)-333(signature)-388(\271)]TJ
/T1_4 10.91 Tf
191.1 0 Td
(\276)Tj
/T1_5 7.97 Tf
6.63 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.39 -7.19 Td
(L;j)Tj
/T1_0 10.91 Tf
12.49 3.23 Td
[(.)-446(Therefore,)]TJ
/T1_1 10.91 Tf
60.38 0 Td
(A)Tj
/T1_0 10.91 Tf
12.35 0 Td
[(is)-334(not)-334(able)-334(to)]TJ
-404.77 -21.91 Td
[(imp)-27(ersonate)-334(remaining)-333(users)]TJ
/T1_2 10.91 Tf
139.93 0 Td
(V)Tj
/T1_3 7.97 Tf
5.73 -1.69 Td
(L;j)Tj
/T1_0 10.91 Tf
16.12 1.69 Td
[(for)-333(2)]TJ
/T1_1 10.91 Tf
25.18 0 Td
(\267)Tj
/T1_4 10.91 Tf
11.51 0 Td
(j)Tj
/T1_1 10.91 Tf
8.14 0 Td
(\267)Tj
/T1_4 10.91 Tf
11.52 0 Td
(n)Tj
/T1_3 7.97 Tf
6.54 -1.69 Td
(L)Tj
/T1_1 10.91 Tf
8.68 1.69 Td
(\241)Tj
/T1_4 10.91 Tf
10.91 0 Td
(`)Tj
/T1_0 10.91 Tf
4.54 0 Td
(.)Tj
-231.87 -21.92 Td
[(Next,)-467(w)26(e)-439(consider)]TJ
/T1_1 10.91 Tf
92.06 0 Td
(A)Tj
/T1_0 10.91 Tf
13.52 0 Td
[(tries)-440(to)-441(imp)-28(ersonate)]TJ
/T1_2 10.91 Tf
102.76 0 Td
(C)Tj
/T1_0 10.91 Tf
5.72 0 Td
[(.)-767(Then)-441(in)-440(Phase)-441(2)-441(Round)-441(2,)]TJ
/T1_1 10.91 Tf
148.14 0 Td
(A)Tj
/T1_0 10.91 Tf
13.52 0 Td
(generates)Tj
/T1_4 10.91 Tf
49.13 0 Td
(T)Tj
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7.88 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-1.51 -7.19 Td
(L)Tj
/T1_0 10.91 Tf
11.24 3.23 Td
(=)Tj
-459.39 -21.92 Td
(\()Tj
/T1_4 10.91 Tf
(y)Tj
/T1_5 7.97 Tf
9.98 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.39 -7.19 Td
(L)Tj
/T1_0 10.91 Tf
6.25 3.23 Td
(\))Tj
/T1_3 7.97 Tf
4.25 3.96 Td
(r)Tj
/T1_8 5.98 Tf
4.05 2.81 Td
(0)Tj
/T1_10 5.98 Tf
-0.23 -5.08 Td
(C)Tj
/T1_0 10.91 Tf
7.2 -1.69 Td
[(mo)-27(d)]TJ
/T1_4 10.91 Tf
23.93 0 Td
(p)Tj
/T1_0 10.91 Tf
9.17 0 Td
(and)Tj
/T1_4 10.91 Tf
21.25 0 Td
(T)Tj
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7.89 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-1.51 -7.01 Td
(i)Tj
/T1_0 10.91 Tf
7.42 3.05 Td
(=)Tj
/T1_4 10.91 Tf
11.59 0 Td
(y)Tj
/T1_3 7.97 Tf
5.74 6.03 Td
(r)Tj
/T1_8 5.98 Tf
4.06 2.82 Td
(0)Tj
/T1_10 5.98 Tf
-0.24 -5.09 Td
(C)Tj
/T1_3 7.97 Tf
-4.21 -7.01 Td
(i)Tj
/T1_0 10.91 Tf
11.41 3.25 Td
[(mo)-27(d)]TJ
/T1_4 10.91 Tf
23.93 0 Td
(p)Tj
/T1_0 10.91 Tf
9.17 0 Td
[(for)-338(1)]TJ
/T1_1 10.91 Tf
25.31 0 Td
(\267)Tj
/T1_4 10.91 Tf
11.59 0 Td
(i)Tj
/T1_1 10.91 Tf
6.87 0 Td
(6)Tj
/T1_0 10.91 Tf
(=)Tj
/T1_4 10.91 Tf
11.59 0 Td
(L)Tj
/T1_1 10.91 Tf
10.54 0 Td
(\267)Tj
/T1_4 10.91 Tf
11.59 0 Td
(n)Tj
/T1_3 7.97 Tf
6.55 -1.63 Td
(c)Tj
/T1_0 10.91 Tf
4.16 1.63 Td
[(,)-339(\257nal)-337(group)-338(k)27(ey)]TJ
/T1_4 10.91 Tf
81.73 0 Td
(K)Tj
/T1_5 7.97 Tf
10.05 3.96 Td
(0)Tj
/T1_0 10.91 Tf
5.9 -3.96 Td
[(=)-285(\()]TJ
/T1_4 10.91 Tf
(y)Tj
/T1_5 7.97 Tf
21.57 3.96 Td
(0)Tj
/T1_10 7.97 Tf
-0.39 -6.65 Td
(C)Tj
/T1_1 10.91 Tf
7.19 2.69 Td
(\242)Tj
/T1_4 10.91 Tf
5.49 0 Td
(y)Tj
/T1_5 7.97 Tf
5.73 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.39 -7.19 Td
(L)Tj
/T1_1 10.91 Tf
8.71 3.23 Td
(\242)Tj
/T1_11 10.91 Tf
5.49 8.18 Td
(Q)Tj
/T1_3 7.97 Tf
10.3 -3.15 Td
(n)Tj
/T1_6 5.98 Tf
5.14 -1 Td
(c)Tj
/T1_3 7.97 Tf
-5.14 -7.28 Td
(i)Tj
/T1_9 7.97 Tf
2.88 0 Td
(=1)Tj
/T1_3 7.97 Tf
(;i)Tj
/T1_5 7.97 Tf
16.05 0 Td
(6)Tj
/T1_9 7.97 Tf
(=)Tj
/T1_3 7.97 Tf
6.59 0 Td
(L)Tj
/T1_4 10.91 Tf
8.07 3.25 Td
(y)Tj
/T1_3 7.97 Tf
5.35 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
3.38 1.63 Td
(\))Tj
/T1_3 7.97 Tf
4.24 3.96 Td
(r)Tj
/T1_8 5.98 Tf
4.06 2.81 Td
(0)Tj
/T1_10 5.98 Tf
-0.24 -5.08 Td
(C)Tj
/T1_0 10.91 Tf
4.17 -1.69 Td
(,)Tj
/T1_4 10.91 Tf
-464.84 -21.91 Td
(\265)Tj
/T1_5 7.97 Tf
5.42 3.95 Td
(0)Tj
/T1_10 7.97 Tf
-0.3 -6.65 Td
(C)Tj
/T1_0 10.91 Tf
8.26 2.7 Td
(=)Tj
/T1_7 10.91 Tf
12.02 0 Td
(H)Tj
/T1_0 10.91 Tf
7.73 0 Td
(\()Tj
/T1_4 10.91 Tf
(K)Tj
/T1_5 7.97 Tf
14.28 3.95 Td
(0)Tj
/T1_1 10.91 Tf
2.79 -3.95 Td
(jj)Tj
/T1_4 10.91 Tf
6.06 0 Td
(y)Tj
/T1_5 7.97 Tf
5.74 3.95 Td
(0)Tj
/T1_10 7.97 Tf
-0.39 -6.65 Td
(C)Tj
/T1_0 10.91 Tf
4.73 2.7 Td
(\),)Tj
/T1_2 10.91 Tf
11.28 0 Td
(c)Tj
/T1_5 7.97 Tf
5.73 3.95 Td
(0)Tj
/T1_3 7.97 Tf
T*
(L)Tj
/T1_0 10.91 Tf
9.79 3.24 Td
(=)Tj
/T1_1 10.91 Tf
12.01 0 Td
(E)Tj
/T1_3 7.97 Tf
5.76 -2.31 Td
(T)Tj
/T1_8 5.98 Tf
6.11 2.74 Td
(0)Tj
/T1_6 5.98 Tf
-1.18 -5.52 Td
(L)Tj
/T1_0 10.91 Tf
6.05 5.09 Td
(\()Tj
/T1_4 10.91 Tf
(K)Tj
/T1_5 7.97 Tf
14.29 3.95 Td
(0)Tj
/T1_0 10.91 Tf
2.79 -3.95 Td
[(\))-361(and)]TJ
/T1_2 10.91 Tf
29.69 0 Td
(c)Tj
/T1_5 7.97 Tf
5.72 3.95 Td
(0)Tj
/T1_3 7.97 Tf
0 -7.01 TD
(i)Tj
/T1_0 10.91 Tf
6.92 3.06 Td
(=)Tj
/T1_1 10.91 Tf
12.01 0 Td
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0.4 w
q 1 0 0 1 182.77 -48.01 cm
0 0 m
0 13.54 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 273.7865 725.8577 Tm
(Exp.)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 242.96 -48.01 cm
0 0 m
0 13.54 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 320.9997 725.8577 Tm
(Sign)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 275.51 -48.01 cm
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0 13.54 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 368.0029 725.8577 Tm
(Sign)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 336.92 -48.01 cm
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0 13.54 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 418.7271 725.8577 Tm
(Cert)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 377.58 -48.01 cm
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0 13.54 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 455.6674 725.8577 Tm
(Msgs)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 413.59 -48.01 cm
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0 13.54 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 504.391 725.8577 Tm
(Msgs)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 475 -48.01 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 476.99 -48.01 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 0 -61.56 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 1.99 -61.56 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 182.77 -61.56 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 242.96 -61.56 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 321.5699 712.3139 Tm
(Gen)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 275.51 -61.56 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 366.9226 712.3139 Tm
(V)Tj
1.0003 0 0 1.0003 72 769.82 Tm
302.117 -57.49 Td
(erif)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 336.92 -61.56 cm
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S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 417.9768 712.3139 Tm
(V)Tj
1.0003 0 0 1.0003 72 769.82 Tm
353.157 -57.49 Td
(erif)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 377.58 -61.56 cm
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0 13.55 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 457.2378 712.3139 Tm
(Sen)Tj
1.0003 0 0 1.0003 72 769.82 Tm
401.811 -57.49 Td
(t)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 413.59 -61.56 cm
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0 13.55 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 495.4285 712.3139 Tm
(Receiv)Tj
1.0003 0 0 1.0003 72 769.82 Tm
454.382 -57.49 Td
(ed)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 475 -61.56 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 476.99 -61.56 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 0 -61.76 cm
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476.99 0 l
S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 0 -63.75 cm
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476.99 0 l
S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 0 -77.49 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 1.99 -77.49 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 22.5 -77.49 cm
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0 13.54 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 100.488 696.3694 Tm
(Kim's)Tj
1.0003 0 0 1.0003 72 769.82 Tm
60.054 -73.43 Td
([KLL04])Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 105.1 -77.49 cm
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0 13.54 l
S
Q
Q
BT
/T1_1 10.91 Tf
1.0003 0 0 1.0003 211.419 696.3694 Tm
(U)Tj
/T1_2 7.97 Tf
5.73 -1.63 Td
(i)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 182.77 -77.49 cm
0 0 m
0 13.54 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 282.1988 696.3694 Tm
(3)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 242.96 -77.49 cm
0 0 m
0 13.54 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 328.5818 696.3694 Tm
(2)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 275.51 -77.49 cm
0 0 m
0 13.54 l
S
Q
Q
BT
/T1_3 10.91 Tf
1.0003 0 0 1.0003 365.6322 696.3694 Tm
(n)Tj
/T1_0 10.91 Tf
8.97 0 Td
(+)Tj
1.0003 0 0 1.0003 72 769.82 Tm
313.43 -73.43 Td
(1)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 336.92 -77.49 cm
0 0 m
0 13.54 l
S
Q
Q
BT
/T1_3 10.91 Tf
1.0003 0 0 1.0003 416.6865 696.3694 Tm
(n)Tj
/T1_4 10.91 Tf
8.97 0 Td
(\241)Tj
/T1_0 10.91 Tf
10.9 0 Td
(1)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 377.58 -77.49 cm
0 0 m
0 13.54 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 464.97 696.3694 Tm
(2)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 413.59 -77.49 cm
0 0 m
0 13.54 l
S
Q
Q
BT
/T1_3 10.91 Tf
1.0003 0 0 1.0003 503.7509 696.3694 Tm
(n)Tj
/T1_0 10.91 Tf
8.97 0 Td
(+)Tj
1.0003 0 0 1.0003 72 769.82 Tm
451.51 -73.43 Td
(1)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 475 -77.49 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 476.99 -77.49 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 22.5 -77.69 cm
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454.49 0 l
S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 0 -91.04 cm
0 0 m
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 1.99 -91.04 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 82.2829 682.8256 Tm
(I)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 22.5 -91.04 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 114.2318 682.8256 Tm
(NLKKW)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 105.1 -91.04 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_1 10.91 Tf
1.0003 0 0 1.0003 213.1095 682.8256 Tm
(C)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 182.77 -91.04 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_3 10.91 Tf
1.0003 0 0 1.0003 272.2561 682.8256 Tm
(n)Tj
/T1_0 10.91 Tf
8.97 0 Td
(+)Tj
1.0003 0 0 1.0003 72 769.82 Tm
220.08 -86.97 Td
(1)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 242.96 -91.04 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 328.5818 682.8256 Tm
(1)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 275.51 -91.04 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_3 10.91 Tf
1.0003 0 0 1.0003 365.6322 682.8256 Tm
(n)Tj
/T1_4 10.91 Tf
8.97 0 Td
(\241)Tj
/T1_0 10.91 Tf
10.91 0 Td
(1)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 336.92 -91.04 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_3 10.91 Tf
1.0003 0 0 1.0003 416.6865 682.8256 Tm
(n)Tj
/T1_4 10.91 Tf
8.97 0 Td
(\241)Tj
/T1_0 10.91 Tf
10.9 0 Td
(1)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 377.58 -91.04 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 464.97 682.8256 Tm
(1)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 413.59 -91.04 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_3 10.91 Tf
1.0003 0 0 1.0003 503.7509 682.8256 Tm
(n)Tj
/T1_4 10.91 Tf
8.97 0 Td
(\241)Tj
/T1_0 10.91 Tf
10.9 0 Td
(1)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 475 -91.04 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 476.99 -91.04 cm
0 0 m
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 105.1 -91.24 cm
0 0 m
371.89 0 l
S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 0 -104.58 cm
0 0 m
0 13.54 l
S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 1.99 -104.58 cm
0 0 m
0 13.54 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 79.9722 669.2719 Tm
(G)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 22.5 -104.58 cm
0 0 m
0 13.54 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 112.0512 669.2719 Tm
([NLK)Tj
/T1_5 7.97 Tf
26.51 3.96 Td
(+)Tj
/T1_0 10.91 Tf
7.08 -3.96 Td
(04])Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 105.1 -104.58 cm
0 0 m
0 13.54 l
S
Q
Q
BT
/T1_1 10.91 Tf
1.0003 0 0 1.0003 201.2862 669.2719 Tm
(U)Tj
/T1_2 7.97 Tf
5.73 -1.64 Td
(i)Tj
/T1_4 10.91 Tf
6.41 1.64 Td
(6)Tj
/T1_0 10.91 Tf
(=)Tj
/T1_1 10.91 Tf
11.51 0 Td
(C)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 182.77 -104.58 cm
0 0 m
0 13.54 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 282.1988 669.2719 Tm
(2)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 242.96 -104.58 cm
0 0 m
0 13.54 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 328.5818 669.2719 Tm
(1)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 275.51 -104.58 cm
0 0 m
0 13.54 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 375.575 669.2719 Tm
(1)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 336.92 -104.58 cm
0 0 m
0 13.54 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 426.6193 669.2719 Tm
(1)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 377.58 -104.58 cm
0 0 m
0 13.54 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 464.97 669.2719 Tm
(1)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 413.59 -104.58 cm
0 0 m
0 13.54 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 513.6936 669.2719 Tm
(1)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 475 -104.58 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 476.99 -104.58 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 22.5 -104.78 cm
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454.49 0 l
S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 0 -118.13 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 1.99 -118.13 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 80.0122 655.7281 Tm
(K)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 22.5 -118.13 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 113.7317 655.7281 Tm
(Prop)Tj
1.0003 0 0 1.0003 72 769.82 Tm
65.231 -114.06 Td
(osed)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 105.1 -118.13 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_1 10.91 Tf
1.0003 0 0 1.0003 213.1095 655.7281 Tm
(C)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 182.77 -118.13 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_3 10.91 Tf
1.0003 0 0 1.0003 270.1755 655.7281 Tm
(n)Tj
/T1_2 7.97 Tf
6.55 -1.64 Td
(c)Tj
/T1_0 10.91 Tf
6.58 1.64 Td
(+)Tj
1.0003 0 0 1.0003 72 769.82 Tm
222.16 -114.06 Td
(2)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 242.96 -118.13 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 328.5818 655.7281 Tm
(1)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 275.51 -118.13 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_3 10.91 Tf
1.0003 0 0 1.0003 372.9442 655.7281 Tm
(n)Tj
/T1_2 7.97 Tf
6.55 -1.64 Td
(c)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 336.92 -118.13 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_3 10.91 Tf
1.0003 0 0 1.0003 423.9985 655.7281 Tm
(n)Tj
/T1_2 7.97 Tf
6.54 -1.64 Td
(c)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 377.58 -118.13 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 464.97 655.7281 Tm
(1)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 413.59 -118.13 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_3 10.91 Tf
1.0003 0 0 1.0003 511.0629 655.7281 Tm
(n)Tj
/T1_2 7.97 Tf
6.54 -1.64 Td
(c)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 475 -118.13 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 476.99 -118.13 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 105.1 -118.33 cm
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371.89 0 l
S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 0 -131.67 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 1.99 -131.67 cm
0 0 m
0 13.54 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 80.1623 642.1743 Tm
(A)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 22.5 -131.67 cm
0 0 m
0 13.54 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 125.515 642.1743 Tm
(IKA)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 105.1 -131.67 cm
0 0 m
0 13.54 l
S
Q
Q
BT
/T1_1 10.91 Tf
1.0003 0 0 1.0003 211.419 642.1743 Tm
(S)Tj
/T1_2 7.97 Tf
5.73 -1.64 Td
(i)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 182.77 -131.67 cm
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0 13.54 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 282.1988 642.1743 Tm
(5)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 242.96 -131.67 cm
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0 13.54 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 328.5818 642.1743 Tm
(4)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 275.51 -131.67 cm
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0 13.54 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 361.211 642.1743 Tm
(2)Tj
/T1_3 10.91 Tf
(n)Tj
/T1_2 7.97 Tf
12 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
5.81 1.64 Td
(+)Tj
1.0003 0 0 1.0003 72 769.82 Tm
317.85 -127.61 Td
(1)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 336.92 -131.67 cm
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0 13.54 l
S
Q
Q
BT
/T1_3 10.91 Tf
1.0003 0 0 1.0003 414.996 642.1743 Tm
(n)Tj
/T1_2 7.97 Tf
6.54 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
5.81 1.64 Td
(+)Tj
1.0003 0 0 1.0003 72 769.82 Tm
366.149 -127.61 Td
(1)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 377.58 -131.67 cm
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0 13.54 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 464.97 642.1743 Tm
(5)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 413.59 -131.67 cm
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0 13.54 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 499.3296 642.1743 Tm
(2)Tj
/T1_3 10.91 Tf
(n)Tj
/T1_2 7.97 Tf
12 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
5.8 1.64 Td
(+)Tj
1.0003 0 0 1.0003 72 769.82 Tm
455.92 -127.61 Td
(1)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 475 -131.67 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
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q 1 0 0 1 105.1 -131.87 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 0 -145.22 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 1.99 -145.22 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 22.5 -145.22 cm
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0 13.55 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 115.5722 628.6205 Tm
(Proto)Tj
1.0003 0 0 1.0003 72 769.82 Tm
70.715 -141.16 Td
(col)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 105.1 -145.22 cm
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S
Q
Q
BT
/T1_1 10.91 Tf
1.0003 0 0 1.0003 208.3082 628.6205 Tm
(U)Tj
/T1_2 7.97 Tf
5.72 -1.63 Td
(i;j)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 182.77 -145.22 cm
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S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 282.1988 628.6205 Tm
(3)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 242.96 -145.22 cm
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S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 328.5818 628.6205 Tm
(2)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 275.51 -145.22 cm
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S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 375.575 628.6205 Tm
(3)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 336.92 -145.22 cm
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S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 426.6193 628.6205 Tm
(1)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 377.58 -145.22 cm
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S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 464.97 628.6205 Tm
(2)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 413.59 -145.22 cm
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S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 513.6936 628.6205 Tm
(4)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 475 -145.22 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
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q 1 0 0 1 0 -145.42 cm
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476.99 0 l
S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 0 -147.41 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 0 -161.15 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 22.5 -161.15 cm
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S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 121.854 612.686 Tm
(Kim's)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 105.1 -161.15 cm
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S
Q
Q
BT
/T1_1 10.91 Tf
1.0003 0 0 1.0003 210.2987 612.686 Tm
(U)Tj
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5.72 -1.64 Td
(n)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 182.77 -161.15 cm
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S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 282.1988 612.686 Tm
(3)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 242.96 -161.15 cm
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S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 328.5818 612.686 Tm
(2)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 275.51 -161.15 cm
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0 13.54 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 361.391 612.686 Tm
(2)Tj
/T1_3 10.91 Tf
(m)Tj
/T1_0 10.91 Tf
17.45 0 Td
(+)Tj
1.0003 0 0 1.0003 72 769.82 Tm
317.67 -157.09 Td
(4)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 336.92 -161.15 cm
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S
Q
Q
BT
/T1_3 10.91 Tf
1.0003 0 0 1.0003 424.5587 612.686 Tm
(m)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 377.58 -161.15 cm
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S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 464.97 612.686 Tm
(2)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 413.59 -161.15 cm
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S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 499.5097 612.686 Tm
(2)Tj
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(m)Tj
/T1_0 10.91 Tf
17.45 0 Td
(+)Tj
1.0003 0 0 1.0003 72 769.82 Tm
455.75 -157.09 Td
(4)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 475 -161.15 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 476.99 -161.15 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 0 -174.7 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 22.5 -174.7 cm
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S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 116.2724 599.1322 Tm
([KLL04])Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 105.1 -174.7 cm
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S
Q
Q
BT
/T1_1 10.91 Tf
1.0003 0 0 1.0003 203.0967 599.1322 Tm
(U)Tj
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5.72 -1.63 Td
(1)Tj
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4.73 1.63 Td
(;)Tj
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4.85 0 Td
(U)Tj
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5.73 -1.63 Td
(2)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 182.77 -174.7 cm
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S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 282.1988 599.1322 Tm
(3)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 242.96 -174.7 cm
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0 13.55 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 328.5818 599.1322 Tm
(2)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 275.51 -174.7 cm
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S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 361.391 599.1322 Tm
(2)Tj
/T1_3 10.91 Tf
(m)Tj
/T1_0 10.91 Tf
17.45 0 Td
(+)Tj
1.0003 0 0 1.0003 72 769.82 Tm
317.67 -170.64 Td
(4)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 336.92 -174.7 cm
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S
Q
Q
BT
/T1_3 10.91 Tf
1.0003 0 0 1.0003 424.5587 599.1322 Tm
(m)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 377.58 -174.7 cm
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S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 464.97 599.1322 Tm
(2)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 413.59 -174.7 cm
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0 13.55 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 499.5097 599.1322 Tm
(2)Tj
/T1_3 10.91 Tf
(m)Tj
/T1_0 10.91 Tf
17.45 0 Td
(+)Tj
1.0003 0 0 1.0003 72 769.82 Tm
455.75 -170.64 Td
(4)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 475 -174.7 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 105.1 -174.9 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 0 -188.25 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 1.99 -188.25 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 22.5 -188.25 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 105.1 -188.25 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_1 10.91 Tf
1.0003 0 0 1.0003 192.9839 585.5884 Tm
(U)Tj
/T1_5 7.97 Tf
5.73 -1.64 Td
(3)Tj
/T1_4 10.91 Tf
7.15 1.64 Td
(\241)Tj
/T1_1 10.91 Tf
10.91 0 Td
(U)Tj
/T1_2 7.97 Tf
5.73 -1.64 Td
(n)Tj
/T1_6 7.97 Tf
5.13 0 Td
(\241)Tj
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6.59 0 Td
(1)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 182.77 -188.25 cm
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0 13.55 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 282.1988 585.5884 Tm
(2)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 242.96 -188.25 cm
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0 13.55 l
S
Q
Q
BT
/T1_4 10.91 Tf
1.0003 0 0 1.0003 327.0614 585.5884 Tm
(\241)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 275.51 -188.25 cm
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0 13.55 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 361.391 585.5884 Tm
(2)Tj
/T1_3 10.91 Tf
(m)Tj
/T1_0 10.91 Tf
17.45 0 Td
(+)Tj
1.0003 0 0 1.0003 72 769.82 Tm
317.67 -184.18 Td
(5)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 336.92 -188.25 cm
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0 13.55 l
S
Q
Q
BT
/T1_3 10.91 Tf
1.0003 0 0 1.0003 424.5587 585.5884 Tm
(m)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 377.58 -188.25 cm
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0 13.55 l
S
Q
Q
BT
/T1_4 10.91 Tf
1.0003 0 0 1.0003 463.4496 585.5884 Tm
(\241)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 413.59 -188.25 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 499.5097 585.5884 Tm
(2)Tj
/T1_3 10.91 Tf
(m)Tj
/T1_0 10.91 Tf
17.45 0 Td
(+)Tj
1.0003 0 0 1.0003 72 769.82 Tm
455.75 -184.18 Td
(5)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 475 -188.25 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
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371.89 0 l
S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 0 -201.79 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 1.99 -201.79 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 22.5 -201.79 cm
0 0 m
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 105.1 -201.79 cm
0 0 m
0 13.54 l
S
Q
Q
BT
/T1_1 10.91 Tf
1.0003 0 0 1.0003 199.5557 572.0346 Tm
(U)Tj
/T1_2 7.97 Tf
5.72 -1.63 Td
(j)Tj
/T1_4 10.91 Tf
7.41 1.63 Td
(2)Tj
1.0003 0 0 1.0003 72 769.82 Tm
150.949 -197.73 Td
(J)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 182.77 -201.79 cm
0 0 m
0 13.54 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 282.1988 572.0346 Tm
(3)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 242.96 -201.79 cm
0 0 m
0 13.54 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 328.5818 572.0346 Tm
(2)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 275.51 -201.79 cm
0 0 m
0 13.54 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 361.391 572.0346 Tm
(2)Tj
/T1_3 10.91 Tf
(m)Tj
/T1_0 10.91 Tf
17.45 0 Td
(+)Tj
1.0003 0 0 1.0003 72 769.82 Tm
317.67 -197.73 Td
(4)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 336.92 -201.79 cm
0 0 m
0 13.54 l
S
Q
Q
BT
/T1_3 10.91 Tf
1.0003 0 0 1.0003 415.1661 572.0346 Tm
(m)Tj
/T1_0 10.91 Tf
12 0 Td
(+)Tj
1.0003 0 0 1.0003 72 769.82 Tm
365.98 -197.73 Td
(2)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 377.58 -201.79 cm
0 0 m
0 13.54 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 464.97 572.0346 Tm
(2)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 413.59 -201.79 cm
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S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 499.5097 572.0346 Tm
(2)Tj
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(m)Tj
/T1_0 10.91 Tf
17.45 0 Td
(+)Tj
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ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
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Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
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S
Q
Q
q
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Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
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S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 81.4426 558.4908 Tm
(J)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
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S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 114.2318 558.4908 Tm
(NLKKW)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 105.1 -215.34 cm
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S
Q
Q
BT
/T1_1 10.91 Tf
1.0003 0 0 1.0003 213.1095 558.4908 Tm
(C)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 182.77 -215.34 cm
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S
Q
Q
BT
/T1_3 10.91 Tf
1.0003 0 0 1.0003 260.8029 558.4908 Tm
(n)Tj
/T1_0 10.91 Tf
8.97 0 Td
(+)Tj
/T1_3 10.91 Tf
10.9 0 Td
(m)Tj
/T1_0 10.91 Tf
12 0 Td
(+)Tj
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ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
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S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 328.5818 558.4908 Tm
(1)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
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S
Q
Q
BT
/T1_3 10.91 Tf
1.0003 0 0 1.0003 373.5144 558.4908 Tm
(m)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
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S
Q
Q
BT
/T1_3 10.91 Tf
1.0003 0 0 1.0003 424.5587 558.4908 Tm
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ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
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S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 464.97 558.4908 Tm
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ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
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S
Q
Q
BT
/T1_3 10.91 Tf
1.0003 0 0 1.0003 511.6231 558.4908 Tm
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ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
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Q
Q
q
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Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
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S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 80.0122 544.9371 Tm
(O)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
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S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 112.0512 544.9371 Tm
([NLK)Tj
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26.51 3.96 Td
(+)Tj
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7.08 -3.96 Td
(04])Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
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S
Q
Q
BT
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(i)Tj
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6.41 1.63 Td
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(=)Tj
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(C)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
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S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 282.1988 544.9371 Tm
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ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 242.96 -228.88 cm
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S
Q
Q
BT
/T1_4 10.91 Tf
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ET
q
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S
Q
Q
BT
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ET
q
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S
Q
Q
BT
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ET
q
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S
Q
Q
BT
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ET
q
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S
Q
Q
BT
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ET
q
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Q
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q
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Q
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q
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Q
Q
q
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S
Q
Q
BT
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ET
q
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Q
Q
q
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S
Q
Q
BT
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ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
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S
Q
Q
BT
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ET
q
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S
Q
Q
BT
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ET
q
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S
Q
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BT
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ET
q
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Q
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BT
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ET
q
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S
Q
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BT
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ET
q
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S
Q
Q
BT
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ET
q
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Q
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Q
Q
q
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Q
Q
q
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Q
Q
q
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S
Q
Q
BT
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(N)Tj
ET
q
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S
Q
Q
BT
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ET
q
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S
Q
Q
BT
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ET
q
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S
Q
Q
BT
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6.58 1.64 Td
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ET
q
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S
Q
Q
BT
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ET
q
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S
Q
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BT
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ET
q
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S
Q
Q
BT
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ET
q
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S
Q
Q
BT
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ET
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Q
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BT
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ET
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Q
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Q
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q
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Q
Q
q
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Q
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Q
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q
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S
Q
Q
BT
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(Join)Tj
ET
q
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S
Q
Q
BT
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1.0003 0 0 1.0003 210.1787 504.2957 Tm
(S)Tj
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(J)Tj
ET
q
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S
Q
Q
BT
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(5)Tj
ET
q
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S
Q
Q
BT
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ET
q
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S
Q
Q
BT
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(m)Tj
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17.45 0 Td
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ET
q
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S
Q
Q
BT
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ET
q
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S
Q
Q
BT
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ET
q
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0.4 w
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S
Q
Q
BT
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1.0003 0 0 1.0003 499.5097 504.2957 Tm
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/T1_3 10.91 Tf
(m)Tj
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17.45 0 Td
(+)Tj
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ET
q
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S
Q
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Q
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S
Q
Q
q
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S
Q
Q
q
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S
Q
Q
q
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S
Q
Q
BT
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1.0003 0 0 1.0003 115.5722 490.7419 Tm
(Proto)Tj
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ET
q
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0.4 w
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S
Q
Q
BT
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1.0003 0 0 1.0003 198.3554 490.7419 Tm
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5.72 -1.64 Td
(i)Tj
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6.41 1.64 Td
(6)Tj
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(=)Tj
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ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
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S
Q
Q
BT
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ET
q
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S
Q
Q
BT
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ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
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S
Q
Q
BT
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ET
q
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Q
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BT
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ET
q
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S
Q
Q
BT
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ET
q
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S
Q
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BT
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ET
q
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Q
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q
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BT
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ET
q
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Q
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BT
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ET
q
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BT
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ET
q
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Q
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BT
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ET
q
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ET
q
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Q
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BT
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ET
q
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BT
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ET
q
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Q
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q
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Q
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BT
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ET
q
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Q
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BT
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ET
q
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Q
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BT
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ET
q
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Q
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BT
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ET
q
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Q
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BT
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ET
q
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Q
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BT
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ET
q
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BT
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ET
q
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Q
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q
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Q
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BT
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ET
q
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Q
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BT
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ET
q
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S
Q
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BT
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ET
q
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S
Q
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BT
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ET
q
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Q
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BT
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ET
q
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S
Q
Q
BT
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ET
q
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Q
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BT
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ET
q
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Q
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S
Q
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q
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S
Q
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BT
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16.69 0 Td
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ET
q
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S
Q
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BT
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ET
q
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S
Q
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BT
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ET
q
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S
Q
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BT
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ET
q
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Q
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BT
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ET
q
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Q
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BT
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ET
q
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S
Q
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BT
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Q
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S
Q
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BT
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ET
q
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S
Q
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BT
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ET
q
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S
Q
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BT
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ET
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Q
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BT
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ET
q
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S
Q
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BT
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ET
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S
Q
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BT
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ET
q
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S
Q
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BT
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ET
q
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S
Q
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BT
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S
Q
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BT
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([KLL04])Tj
ET
q
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S
Q
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BT
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ET
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S
Q
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BT
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ET
q
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S
Q
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BT
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ET
q
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S
Q
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BT
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(n)Tj
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8.97 0 Td
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10.9 0 Td
(`)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
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S
Q
Q
BT
/T1_4 10.91 Tf
1.0003 0 0 1.0003 425.1088 407.0585 Tm
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ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
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S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 464.97 407.0585 Tm
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ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 413.59 -366.73 cm
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S
Q
Q
BT
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1.0003 0 0 1.0003 504.201 407.0585 Tm
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8.97 0 Td
(+)Tj
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10.91 0 Td
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ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
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1.0002747 0 0 1.0002747 72 769.8200073 cm
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Q
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q
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Q
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q
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Q
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q
1.0002747 0 0 1.0002747 72 769.8200073 cm
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Q
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q
1.0002747 0 0 1.0002747 72 769.8200073 cm
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S
Q
Q
BT
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1.0003 0 0 1.0003 183.1111 393.5047 Tm
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5.72 -1.63 Td
(i)Tj
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(6)Tj
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(=)Tj
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(00)Tj
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ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
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S
Q
Q
BT
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ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
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S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 328.5818 393.5047 Tm
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ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 275.51 -380.27 cm
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S
Q
Q
BT
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1.0003 0 0 1.0003 366.0923 393.5047 Tm
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8.97 0 Td
(+)Tj
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10.9 0 Td
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ET
q
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S
Q
Q
BT
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ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
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S
Q
Q
BT
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ET
q
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0.4 w
q 1 0 0 1 413.59 -380.27 cm
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S
Q
Q
BT
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(n)Tj
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10.91 0 Td
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ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
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Q
Q
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Q
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q
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Q
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q
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
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q 1 0 0 1 1.99 -393.82 cm
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S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 80.8425 379.9609 Tm
(L)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 22.5 -393.82 cm
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S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 114.2318 379.9609 Tm
(NLKKW)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 105.1 -393.82 cm
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S
Q
Q
BT
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1.0003 0 0 1.0003 213.1095 379.9609 Tm
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ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 182.77 -393.82 cm
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S
Q
Q
BT
/T1_3 10.91 Tf
1.0003 0 0 1.0003 263.3136 379.9609 Tm
(n)Tj
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8.97 0 Td
(\241)Tj
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10.91 0 Td
(`)Tj
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6.97 0 Td
(+)Tj
1.0003 0 0 1.0003 72 769.82 Tm
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ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
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S
Q
Q
BT
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ET
q
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S
Q
Q
BT
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ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
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S
Q
Q
BT
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ET
q
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S
Q
Q
BT
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ET
q
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S
Q
Q
BT
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1.0003 0 0 1.0003 512.1732 379.9609 Tm
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ET
q
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Q
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q
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Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
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Q
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q
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Q
Q
q
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S
Q
Q
BT
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ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
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S
Q
Q
BT
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([NLK)Tj
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26.51 3.96 Td
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(04])Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
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S
Q
Q
BT
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ET
q
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S
Q
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BT
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ET
q
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S
Q
Q
BT
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ET
q
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Q
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BT
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ET
q
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S
Q
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BT
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ET
q
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S
Q
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BT
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ET
q
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S
Q
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BT
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ET
q
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Q
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q
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Q
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Q
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q
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S
Q
Q
BT
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ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
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S
Q
Q
BT
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ET
q
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S
Q
Q
BT
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ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
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S
Q
Q
BT
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ET
q
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S
Q
Q
BT
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ET
q
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S
Q
Q
BT
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ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
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S
Q
Q
BT
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ET
q
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0.4 w
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S
Q
Q
BT
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ET
q
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S
Q
Q
BT
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ET
q
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Q
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Q
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q
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S
Q
Q
q
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S
Q
Q
q
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S
Q
Q
BT
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1.0003 0 0 1.0003 80.1623 339.3095 Tm
(V)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
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S
Q
Q
BT
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1.0003 0 0 1.0003 122.2541 339.3095 Tm
(Lea)Tj
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[(v)28(e)]TJ
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
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S
Q
Q
BT
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1.0003 0 0 1.0003 209.9886 339.3095 Tm
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ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
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S
Q
Q
BT
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ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
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S
Q
Q
BT
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1.0003 0 0 1.0003 328.5818 339.3095 Tm
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ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 275.51 -434.45 cm
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S
Q
Q
BT
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1.0003 0 0 1.0003 353.5688 339.3095 Tm
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6.54 -1.69 Td
(L)Tj
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8.68 1.69 Td
(+)Tj
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10.91 0 Td
(`)Tj
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6.97 0 Td
(+)Tj
1.0003 0 0 1.0003 72 769.82 Tm
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ET
q
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0.4 w
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S
Q
Q
BT
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1.0003 0 0 1.0003 425.1088 339.3095 Tm
(\241)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 377.58 -434.45 cm
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S
Q
Q
BT
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1.0003 0 0 1.0003 464.97 339.3095 Tm
(5)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 413.59 -434.45 cm
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0 13.54 l
S
Q
Q
BT
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1.0003 0 0 1.0003 491.6775 339.3095 Tm
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(L)Tj
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8.68 1.69 Td
(+)Tj
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10.9 0 Td
(`)Tj
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6.97 0 Td
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ET
q
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Q
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q
1.0002747 0 0 1.0002747 72 769.8200073 cm
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S
Q
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q
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 1.99 -448 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 80.5424 325.7557 Tm
(E)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 22.5 -448 cm
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0 13.55 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 115.5722 325.7557 Tm
(Proto)Tj
1.0003 0 0 1.0003 72 769.82 Tm
70.715 -443.94 Td
(col)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 105.1 -448 cm
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S
Q
Q
BT
/T1_1 10.91 Tf
1.0003 0 0 1.0003 198.1553 325.7557 Tm
(S)Tj
/T1_2 7.97 Tf
5.73 -1.63 Td
(i)Tj
/T1_4 10.91 Tf
6.41 1.63 Td
(6)Tj
/T1_0 10.91 Tf
(=)Tj
/T1_1 10.91 Tf
11.51 0 Td
(S)Tj
/T1_2 7.97 Tf
5.73 -1.68 Td
(L)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 182.77 -448 cm
0 0 m
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S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 282.1988 325.7557 Tm
(1)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 242.96 -448 cm
0 0 m
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S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 328.5818 325.7557 Tm
(1)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 275.51 -448 cm
0 0 m
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S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 375.575 325.7557 Tm
(1)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 336.92 -448 cm
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S
Q
Q
BT
/T1_4 10.91 Tf
1.0003 0 0 1.0003 425.1088 325.7557 Tm
(\241)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 377.58 -448 cm
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S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 464.97 325.7557 Tm
(1)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 413.59 -448 cm
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S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 513.6936 325.7557 Tm
(1)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 475 -448 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 476.99 -448 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 105.1 -448.2 cm
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371.89 0 l
S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 0 -461.54 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 1.99 -461.54 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 22.5 -461.54 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 105.1 -461.54 cm
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S
Q
Q
BT
/T1_1 10.91 Tf
1.0003 0 0 1.0003 185.6918 312.2119 Tm
(V)Tj
/T1_2 7.97 Tf
5.72 -1.78 Td
(L;k)Tj
/T1_4 10.91 Tf
16.26 1.78 Td
(2)Tj
1.0003 0 0 1.0003 72 769.82 Tm
145.939 -457.48 Td
(N)Tj
/T1_0 10.91 Tf
10.551 0 Td
(\()Tj
/T1_4 10.91 Tf
(R)Tj
/T1_0 10.91 Tf
(\))Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 182.77 -461.54 cm
0 0 m
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S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 282.1988 312.2119 Tm
(3)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 242.96 -461.54 cm
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S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 328.5818 312.2119 Tm
(2)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 275.51 -461.54 cm
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S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 375.575 312.2119 Tm
(3)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 336.92 -461.54 cm
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S
Q
Q
BT
/T1_4 10.91 Tf
1.0003 0 0 1.0003 425.1088 312.2119 Tm
(\241)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 377.58 -461.54 cm
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S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 464.97 312.2119 Tm
(2)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 413.59 -461.54 cm
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S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 513.6936 312.2119 Tm
(4)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 475 -461.54 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 1.99 -475.09 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 22.5 -475.09 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 105.1 -475.09 cm
0 0 m
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S
Q
Q
BT
/T1_1 10.91 Tf
1.0003 0 0 1.0003 186.0519 298.6581 Tm
(V)Tj
/T1_2 7.97 Tf
5.73 -1.68 Td
(L;j)Tj
/T1_3 10.91 Tf
16.73 1.68 Td
(=)Tj
/T1_4 10.91 Tf
-1.21 0 Td
(2)Tj
1.0003 0 0 1.0003 72 769.82 Tm
145.569 -471.03 Td
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10.551 0 Td
(\()Tj
/T1_4 10.91 Tf
4.25 0 Td
(R)Tj
/T1_0 10.91 Tf
9.24 0 Td
(\))Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 182.77 -475.09 cm
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S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 275.2269 298.6581 Tm
(1\(0\))Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 242.96 -475.09 cm
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S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 328.5818 298.6581 Tm
(1)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 275.51 -475.09 cm
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S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 375.575 298.6581 Tm
(3)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 336.92 -475.09 cm
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S
Q
Q
BT
/T1_4 10.91 Tf
1.0003 0 0 1.0003 425.1088 298.6581 Tm
(\241)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 377.58 -475.09 cm
0 0 m
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S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 464.97 298.6581 Tm
(1)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 413.59 -475.09 cm
0 0 m
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S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 513.6936 298.6581 Tm
(4)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 475 -475.09 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 105.1 -475.29 cm
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371.89 0 l
S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 0 -488.64 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 1.99 -488.64 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 22.5 -488.64 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 105.1 -488.64 cm
0 0 m
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S
Q
Q
BT
/T1_1 10.91 Tf
1.0003 0 0 1.0003 185.2717 285.1143 Tm
(U)Tj
/T1_2 7.97 Tf
5.73 -1.64 Td
(i;j)Tj
/T1_0 10.91 Tf
13.25 1.64 Td
(for)Tj
/T1_3 10.91 Tf
16.69 0 Td
(i)Tj
/T1_4 10.91 Tf
6.79 0 Td
(6)Tj
/T1_0 10.91 Tf
(=)Tj
/T1_3 10.91 Tf
11.51 0 Td
(L)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 182.77 -488.64 cm
0 0 m
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S
Q
Q
BT
/T1_4 10.91 Tf
1.0003 0 0 1.0003 280.6784 285.1143 Tm
(\241)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 242.96 -488.64 cm
0 0 m
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S
Q
Q
BT
/T1_4 10.91 Tf
1.0003 0 0 1.0003 327.0614 285.1143 Tm
(\241)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 275.51 -488.64 cm
0 0 m
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S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 375.575 285.1143 Tm
(1)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 336.92 -488.64 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_4 10.91 Tf
1.0003 0 0 1.0003 425.1088 285.1143 Tm
(\241)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 377.58 -488.64 cm
0 0 m
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S
Q
Q
BT
/T1_4 10.91 Tf
1.0003 0 0 1.0003 463.4496 285.1143 Tm
(\241)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 413.59 -488.64 cm
0 0 m
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S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 513.6936 285.1143 Tm
(1)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 475 -488.64 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 476.99 -488.64 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 0 -488.83 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 0 -490.83 cm
0 0 m
476.99 0 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 72 257.5266 Tm
(Note:)Tj
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30.6 0 Td
(S)Tj
/T1_2 7.97 Tf
5.72 -1.69 Td
(L)Tj
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9.89 1.69 Td
(p)Tj
1.0003 0 0 1.0003 72 769.82 Tm
52.581 -512.15 Td
[(erforms)-333(5)-333(mo)-28(d.)-445(exp.)-444(if)]TJ
/T1_1 10.91 Tf
111.599 0 Td
(S)Tj
/T1_2 7.97 Tf
5.73 -1.69 Td
(L)Tj
/T1_4 10.91 Tf
9.28 1.69 Td
[(2)-277(N)]TJ
/T1_0 10.91 Tf
20.86 0 Td
(\()Tj
/T1_4 10.91 Tf
(R)Tj
/T1_0 10.91 Tf
13.48 0 Td
[(\),)-333(otherwise)]TJ
/T1_1 10.91 Tf
59.47 0 Td
(S)Tj
/T1_2 7.97 Tf
5.73 -1.69 Td
(L)Tj
/T1_0 10.91 Tf
9.89 1.69 Td
[(p)-27(erforms)-333(2)-334(mo)-27(d.)-445(exp.)-444(if)]TJ
/T1_1 10.91 Tf
117.96 0 Td
(S)Tj
/T1_2 7.97 Tf
5.73 -1.69 Td
(L)Tj
/T1_3 10.91 Tf
10.5 1.69 Td
(=)Tj
/T1_4 10.91 Tf
-1.22 0 Td
[(2)-278(N)]TJ
/T1_0 10.91 Tf
20.86 0 Td
(\()Tj
/T1_4 10.91 Tf
(R)Tj
/T1_0 10.91 Tf
13.48 0 Td
(\).)Tj
-455.93 -13.55 Td
(Only)Tj
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27.98 0 Td
(V)Tj
/T1_2 7.97 Tf
5.73 -1.69 Td
(L;j)Tj
/T1_3 10.91 Tf
18.44 1.69 Td
(=)Tj
/T1_4 10.91 Tf
-1.22 0 Td
[(2)-434(N)]TJ
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22.56 0 Td
(\()Tj
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(R)Tj
/T1_0 10.91 Tf
[(\),)-450(who)-427(are)-427(left)-427(or)-427(righ)27(t)-426(neigh)26(b)-26(or)-427(of)]TJ
/T1_1 10.91 Tf
190.18 0 Td
(V)Tj
/T1_2 7.97 Tf
5.72 -1.78 Td
(L;k)Tj
/T1_4 10.91 Tf
17.97 1.78 Td
[(2)-433(N)]TJ
/T1_0 10.91 Tf
22.56 0 Td
(\()Tj
/T1_4 10.91 Tf
(R)Tj
/T1_0 10.91 Tf
13.48 0 Td
[(\),)-450(p)-28(erforms)-427(1)-427(exp.,)-450(otherwise,)]TJ
/T1_1 10.91 Tf
-323.4 -13.54 Td
(V)Tj
/T1_2 7.97 Tf
5.73 -1.69 Td
(L;j)Tj
/T1_3 10.91 Tf
16.73 1.69 Td
(=)Tj
/T1_4 10.91 Tf
-1.21 0 Td
[(2)-277(N)]TJ
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20.85 0 Td
(\()Tj
/T1_4 10.91 Tf
(R)Tj
/T1_0 10.91 Tf
13.48 0 Td
[(\))-333(do)-334(not)-333(need)-333(to)-334(p)-27(erform)-334(an)27(y)-332(exp.)]TJ
-55.58 -34.12 Td
[(Proto)-27(col)-320(and)-320(NLKKW)-320(Join)-320(Proto)-28(col)-320(need)-320(to)-320(p)-28(erform)-320(mo)-28(dular)-320(exp)-28(onen)27(tiations.)-439(F)83(urthermore,)]TJ
/T1_1 10.91 Tf
450.98 0 Td
(U)Tj
/T1_2 7.97 Tf
5.73 -1.69 Td
[(J)24(;j)]TJ
/T1_0 10.91 Tf
-456.71 -20.22 Td
[(for)-292(2)]TJ
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24.73 0 Td
(\267)Tj
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11.51 0 Td
(j)Tj
/T1_4 10.91 Tf
8.15 0 Td
(\267)Tj
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11.51 0 Td
(n)Tj
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6.55 -1.69 Td
(J)Tj
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7.4 1.69 Td
(\241)Tj
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10.02 0 Td
[(1)-292(only)-292(has)-293(to)-292(receiv)26(e)-291(2)-293(messages)-292(and)-293(v)27(erify)-292(1)-292(message)-293(while)]TJ
/T1_1 10.91 Tf
282.58 0 Td
(U)Tj
/T1_2 7.97 Tf
5.73 -1.64 Td
(i;j)Tj
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12.8 1.64 Td
[(for)-292(1)]TJ
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24.73 0 Td
(\267)Tj
/T1_3 10.91 Tf
11.51 0 Td
(i)Tj
/T1_4 10.91 Tf
6.79 0 Td
(6)Tj
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(=)Tj
/T1_3 10.91 Tf
11.51 0 Td
(J)Tj
/T1_4 10.91 Tf
10.13 0 Td
(\267)Tj
/T1_3 10.91 Tf
11.51 0 Td
(n)Tj
/T1_2 7.97 Tf
6.55 -1.64 Td
(c)Tj
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-463.71 -20.28 Td
[(and)-268(2)]TJ
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28.98 0 Td
(\267)Tj
/T1_3 10.91 Tf
11.51 0 Td
(j)Tj
/T1_4 10.91 Tf
8.15 0 Td
(\267)Tj
/T1_3 10.91 Tf
11.51 0 Td
(n)Tj
/T1_2 7.97 Tf
6.55 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
6.3 1.64 Td
[(only)-268(has)-269(to)-268(receiv)27(e)-268(and)-268(v)27(erify)-268(1)-268(message.)-423(In)-268(comparison,)]TJ
/T1_1 10.91 Tf
267.13 0 Td
(U)Tj
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5.72 -1.64 Td
(1)Tj
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4.73 1.64 Td
(,)Tj
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6.1 0 Td
(U)Tj
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5.73 -1.64 Td
(2)Tj
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7.65 1.64 Td
(and)Tj
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20.5 0 Td
(U)Tj
/T1_2 7.97 Tf
5.73 -1.64 Td
(n)Tj
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8.56 1.64 Td
[(in)-268(Kim's)-268(Join)]TJ
-404.85 -21.92 Td
[(proto)-27(col)-339(has)-340(to)-339(p)-28(erform)-339(3)-339(exp)-28(onen)27(tiations,)-339(receiv)26(e)-338(2)]TJ
/T1_3 10.91 Tf
249.12 0 Td
(m)Tj
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[(e\261cien)27(t)-336(for)-336(di\256eren)26(t)-335(n)27(um)27(b)-26(er)-337(of)-337(user)-336(no)-28(des.)-454(F)82(urthermore,)-336(the)-337(prop)-28(osed)-336(proto)-28(col)-337(is)-336(also)-337(the)]TJ
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T*
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ET
q
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S
Q
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ET
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ET
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ET
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ET
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ET
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ET
q
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S
Q
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ET
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ET
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ET
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Q
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BT
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[(2)-277(J)]TJ
ET
q
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BT
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ET
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q
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BT
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T*
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T*
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T*
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[(b)-27(et)27(w)27(een)-431(the)-432(con)27(trollers)-431(and)-433(users)-432(as)-432(compared)-432(to)-432(a)-432(common)-432(passw)26(ord)-431(shared)-432(b)-28(et)27(w)28(een)-431(users)-432(or)]TJ
T*
[(b)-27(et)27(w)27(een)-244(users)-246(and)-245(serv)27(er/con)27(troller.)-414(If)-245(a)-246(common)-245(passw)27(ord)-245(is)-245(shared)-246(b)27(y)-245(all)-245(users,)-263(then)-246(the)-245(passw)27(ord)]TJ
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[(has)-339(to)-339(b)-28(e)-339(c)27(hanged)-338(and)-339(up)-28(dated)-339(securely)-339(if)-339(an)26(y)-338(user)-339(lost)-339(the)-339(passw)27(ord.)-461(F)82(urthermore,)-339(users)-339(lea)26(ving)]TJ
0 -21.92 TD
[(the)-385(group)-385(will)-385(still)-385(kno)26(w)-384(the)-385(common)-385(passw)26(ord)-384(and)-385(this)-385(mak)26(es)-384(it)-385(di\261cult)-385(to)-386(securely)-385(up)-28(date)-385(all)]TJ
T*
[(remaining)-465(users)-466(with)-466(the)-465(new)-466(passw)27(ord.)-841(Although)-466(Byun)-466(et)-465(al's)-466(EKE-D)-466(proto)-28(col)-465(in)-466([BLLH06])]TJ
0 -21.91 TD
[(also)-370(uses)-370(di\256eren)27(t)-369(passw)27(ords,)-378(their)-370(proto)-28(col)-370(do)-28(es)-370(not)-370(pro)27(vide)-369(protection)-370(against)-370(DoS)-370(attac)27(ks)-369(and)]TJ
0 -21.92 TD
[(on-line)-377(passw)27(ord)-376(guessing)-377(attac)26(ks.)-575(Our)-377(passw)27(ord-based)-377(GKA)-377(proto)-28(col)-377(pro)27(vides)-376(a)-377(b)-28(etter)-378(solution)]TJ
T*
[(against)-459(DoS)-459(attac)27(ks)-458(as)-460(the)-459(no)-28(des)-459(need)-459(not)-460(p)-27(erform)-460(computationally)-459(in)27(tensiv)28(e)-459(digital)-459(signature)]TJ
0 -21.91 TD
[(v)27(eri\257cations)-376(on)-378(in)27(v)55(alid)-377(messages)-377(sen)26(t)-376(b)26(y)-376(attac)26(k)28(ers.)-577(This)-377(is)-378(b)-28(ecause)-378(the)-378(prop)-27(osed)-378(passw)27(ord-based)]TJ
0 -21.92 TD
[(GKA)-228(proto)-28(col)-229(uses)-229(symmetric)-229(k)27(ey)-228(encryption,)-250(message)-229(authen)27(tication)-228(co)-28(de)-229(and)-229(hash)-229(function)-229(whic)27(h)]TJ
T*
[(ha)27(v)28(e)-354(v)27(ery)-354(lo)26(w)-354(computation)-355(time)-355(as)-355(compare)-355(to)-355(mo)-28(dular)-355(exp)-28(onen)27(tiations)-354(used)-356(in)-355(digital)-355(signature)]TJ
0 -21.91 TD
[(sc)27(hemes)-289(\(e.g.)-430(DSA\).)-290(W)82(e)-289(p)-27(erform)-291(a)-290(complexit)27(y)-289(and)-290(energy)-290(analysis)-290(of)-290(the)-290(prop)-28(osed)-290(passw)27(ord-based)]TJ
0 -21.92 TD
[(Initial)-456(GKA)-457(proto)-28(col)-456(with)-457(t)27(w)28(o)-456(curren)27(t)-456(passw)27(ord-based)-456(GKA)-457(proto)-27(cols,)-488(namely)-457(Ab)-27(dalla)-457(et)-457(al's)]TJ
0 -21.91 TD
[(proto)-27(col)-379([ABCP06])-379(and)-379(Byun)-378(et)-379(al's)-379(EKE-D)-379(proto)-27(col)-379([BLLH06],)-390(and)-379(sho)27(w)-378(that)-379(ev)27(en)-378(though)-378(the)]TJ
0 -21.92 TD
[(prop)-27(osed)-355(proto)-28(col)-354(pro)26(vides)-353(protection)-355(against)-355(DoS)-354(attac)26(ks)-353(and)-355(is)-355(secure)-354(against)-355(b)-28(oth)-355(on-line)-354(and)]TJ
T*
[(o\256-line)-311(passw)26(ord)-310(guessing)-312(attac)27(ks,)-316(the)-311(prop)-28(osed)-312(proto)-28(col)-312(is)-312(still)-311(more)-312(energy)-312(e\261cien)27(t)-311(and)-312(scalable.)]TJ
225.76 -109.1 Td
(235)Tj
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[(Securit)30(y)-374(Analysis)-375(and)-375(Impro)30(v)31(emen)32(t)-374(of)-375(a)-375(DoS-Resistan)30(t)]TJ
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[(and)-376(only)-376(authorized)-376(users)-376(\(legitimate)-376(clien)27(ts\))-375(are)-376(allo)27(w)27(ed)-375(to)-376(access)-376(the)-376(wireless)-376(net)27(w)28(ork)-375(services.)]TJ
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[(Hence,)-407(there)-392(is)-393(a)-393(need)-392(to)-393(pro)27(vide)-392(secure)-392(authen)27(tication)-392(and)-393(k)27(ey)-391(exc)26(hange)-391(mec)26(hanism)-391(to)-393(prev)27(en)28(t)]TJ
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[(unauthorized)-427(users)-427(from)-427(gaining)-427(access)-428(to)-427(the)-427(net)27(w)28(ork.)-726(Priv)55(acy)-426(problems)-427(can)-428(o)-27(ccur)-428(in)-427(wireless)]TJ
T*
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[(trac)27(k)-236(do)27(wn)-236(his/her)-237(mo)27(v)28(emen)27(t.)-411(Hence,)-256(con\257den)26(tialit)28(y)-236(protection)-237(of)-237(the)-237(clien)27(t's)-236(iden)27(tit)27(y)-236(is)-237(imp)-27(ortan)26(t.)]TJ
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[(ev)27(er,)-393(most)-381(P)82(AKE)-381(proto)-28(cols)-381(do)-382(not)-382(pro)27(vide)-381(clien)27(t)-381(anon)27(ymit)28(y)-381(and)-382(DoS-resistance)-381(for)-382(wireless)-382(net-)]TJ
T*
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T*
[(wireless)-328(net)27(w)28(orks.)-442(The)-328(Lancaster)-329(proto)-27(col)-329(uses)-328(passw)27(ord-based)-327(authen)26(tication)-327(and)-328(pro)27(vides)-328(clien)27(t)]TJ
T*
[(anon)27(ymit)28(y)83(.)-425(Ho)26(w)28(ev)28(er,)-290(W)82(an)-279(et)-281(al)-280([WDBA05])-281(p)-27(oin)26(ted)-279(out)-281(the)-280(securit)27(y)-280(w)27(eaknesses)-279(and)-281(design)-280(\260a)27(ws)-280(in)]TJ
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[(the)-291(Lancaster)-292(proto)-28(col)-292(and)-292(prop)-28(osed)-292(a)-292(DoS-Resistan)27(t)-291(anon)27(ymous)-291(authen)27(tication)-291(and)-292(k)27(ey)-291(exc)27(hange)]TJ
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[(proto)-27(col,)-489(whic)27(h)-456(also)-458(uses)-457(passw)27(ords.)-816(In)-457(the)-458(next)-457(section,)-489(w)27(e)-456(sho)26(w)-456(three)-457(di\256eren)26(t)-456(DoS)-457(attac)26(ks)]TJ
T*
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0 -21.91 TD
[(scrib)-27(ed)-370(in)-370(Section)-370(2.5.3)-369(of)-370(Chapter)-370(2.)-553(Next,)-379(w)27(e)-369(prop)-28(ose)-370(a)-369(new)-370(DoS-Resistan)27(t)-369(authen)27(tication)-369(and)]TJ
0 -21.92 TD
[(k)27(ey)-269(exc)26(hange)-269(proto)-28(col)-270(that)-271(is)-271(free)-270(from)-271(the)-270(\260a)26(ws)-269(in)-271(W)83(an)-270(et)-271(al's)-270(proto)-28(col.)-423(A)-271(securit)27(y)-270(and)-270(complexit)26(y)]TJ
T*
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[(exc)27(hange)-332(in)-333(wireless)-334(net)27(w)28(orks.)]TJ
/T1_0 11.95 Tf
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[(and)-333(Key)-333(Exc)27(hange)-333(Proto)-27(col)-334([WDBA05])-333(as)-333(follo)26(ws:)]TJ
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8.76 -1.63 Td
(s)Tj
/T1_6 10.91 Tf
4.42 1.63 Td
(h)Tj
/T1_1 10.91 Tf
(b)Tj
/T1_0 10.91 Tf
11.78 0 Td
[(+)-261(1)]TJ
/T1_1 10.91 Tf
[(;)-166(L)]TJ
/T1_6 10.91 Tf
(i)Tj
/T1_0 10.91 Tf
[(.)-623(Finally)]TJ
/T1_2 10.91 Tf
80.89 0 Td
(S)Tj
/T1_0 10.91 Tf
10.35 0 Td
(sends)Tj
/T1_6 10.91 Tf
29.85 0 Td
(f)Tj
/T1_2 10.91 Tf
(S)Tj
/T1_1 10.91 Tf
11.52 0 Td
[(;)-166(N)]TJ
/T1_4 7.97 Tf
13.61 -1.63 Td
(s)Tj
/T1_6 10.91 Tf
4.41 1.63 Td
(h)Tj
/T1_1 10.91 Tf
(b)Tj
/T1_0 10.91 Tf
11.78 0 Td
(+)Tj
-459.39 -21.91 Td
(1)Tj
/T1_1 10.91 Tf
[(;)-166(L)]TJ
/T1_6 10.91 Tf
(i)Tj
/T1_1 10.91 Tf
[(;)-166(\270;)-167(b)]TJ
/T1_6 10.91 Tf
(g)Tj
/T1_0 10.91 Tf
51.79 0 Td
(to)Tj
/T1_2 10.91 Tf
13.33 0 Td
(C)Tj
/T1_0 10.91 Tf
10.6 0 Td
[(and)-333(sets)-333(an)-334(expiry)-333(time)-333(for)]TJ
/T1_2 10.91 Tf
132.57 0 Td
(C)Tj
/T1_0 10.91 Tf
10.6 0 Td
[(to)-333(resp)-28(ond.)]TJ
-218.89 -21.92 Td
[(Round)-333(3)]TJ
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 0 -165.9 cm
0 0 m
40.75 0 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 112.7614 605.404 Tm
(:)Tj
/T1_2 10.91 Tf
9.64 0 Td
(C)Tj
/T1_0 10.91 Tf
11.49 0 Td
(computes)Tj
1.0003 0 0 1.0003 72 769.82 Tm
111.313 -164.37 Td
[(b)27(y)-414(brute)-414(force)-415(the)]TJ
/T1_1 10.91 Tf
92.957 0 Td
(b)Tj
/T1_0 10.91 Tf
[(-bits)-414(string)]TJ
/T1_1 10.91 Tf
62.34 0 Td
(N)Tj
/T1_7 7.97 Tf
9.95 3.96 Td
(0)Tj
/T1_4 7.97 Tf
-1.19 -6.66 Td
(s)Tj
/T1_6 10.91 Tf
4.42 2.7 Td
(h)Tj
/T1_0 10.91 Tf
(1)Tj
/T1_1 10.91 Tf
[(;)-166(b)]TJ
/T1_6 10.91 Tf
19.22 0 Td
(i)Tj
/T1_0 10.91 Tf
8.76 0 Td
[(whic)27(h)-413(satis\257es)-415(the)-414(hash)-414(equation)]TJ
/T1_1 10.91 Tf
-307.77 -21.92 Td
(\270)Tj
/T1_0 10.91 Tf
11.79 0 Td
(=)Tj
/T1_2 10.91 Tf
13.92 0 Td
(H)Tj
/T1_5 7.97 Tf
7.73 -1.63 Td
(1)Tj
/T1_0 10.91 Tf
4.73 1.63 Td
(\()Tj
/T1_2 10.91 Tf
(S)Tj
/T1_1 10.91 Tf
10.3 0 Td
[(;)-166(N)]TJ
/T1_7 7.97 Tf
14.8 3.96 Td
(0)Tj
/T1_4 7.97 Tf
-1.19 -6.65 Td
(s)Tj
/T1_6 10.91 Tf
4.41 2.69 Td
(h)Tj
/T1_0 10.91 Tf
(1)Tj
/T1_1 10.91 Tf
[(;)-166(b)]TJ
/T1_6 10.91 Tf
19.22 0 Td
(i)Tj
/T1_1 10.91 Tf
[(;)-166(N)]TJ
/T1_4 7.97 Tf
17.85 -1.63 Td
(s)Tj
/T1_6 10.91 Tf
4.42 1.63 Td
(h)Tj
/T1_1 10.91 Tf
(b)Tj
/T1_0 10.91 Tf
12.3 0 Td
[(+)-310(1)]TJ
/T1_1 10.91 Tf
[(;)-166(L)]TJ
/T1_6 10.91 Tf
(i)Tj
/T1_0 10.91 Tf
[(\).)-841(Next,)]TJ
/T1_2 10.91 Tf
81.77 0 Td
(C)Tj
/T1_0 10.91 Tf
12.04 0 Td
[(selects)-465(a)]TJ
/T1_1 10.91 Tf
46.03 0 Td
(L)Tj
/T1_0 10.91 Tf
7.42 0 Td
[(-bits)-465(random)-466(nonce)]TJ
/T1_1 10.91 Tf
100.15 0 Td
(N)Tj
/T1_4 7.97 Tf
8.76 -1.63 Td
(c)Tj
/T1_0 10.91 Tf
4.17 1.63 Td
[(,)-498(random)]TJ
/T1_1 10.91 Tf
49.92 0 Td
(x)Tj
/T1_6 10.91 Tf
11.67 0 Td
(2)Tj
/T1_1 10.91 Tf
12.7 0 Td
(Z)Tj
/T1_7 7.97 Tf
8.23 3.96 Td
(\244)Tj
/T1_4 7.97 Tf
-0.78 -6.65 Td
(q)Tj
/T1_0 10.91 Tf
-462.36 -19.22 Td
[(and)-389(computes)]TJ
/T1_1 10.91 Tf
70.96 0 Td
(z)Tj
/T1_4 7.97 Tf
5.07 -1.64 Td
(c)Tj
/T1_0 10.91 Tf
8.21 1.64 Td
(=)Tj
/T1_1 10.91 Tf
12.53 0 Td
(g)Tj
/T1_4 7.97 Tf
5.59 3.95 Td
(x)Tj
/T1_0 10.91 Tf
8.29 -3.95 Td
[(mo)-28(d)]TJ
/T1_1 10.91 Tf
23.94 0 Td
(p)Tj
/T1_0 10.91 Tf
9.73 0 Td
(and)Tj
/T1_1 10.91 Tf
21.81 0 Td
(\271)Tj
/T1_4 7.97 Tf
6.58 -1.64 Td
(c)Tj
/T1_0 10.91 Tf
8.21 1.64 Td
(=)Tj
/T1_6 10.91 Tf
12.52 0 Td
(M)Tj
/T1_4 7.97 Tf
13.1 -1.64 Td
(\267)Tj
/T1_0 10.91 Tf
5.38 1.64 Td
(\()Tj
/T1_1 10.91 Tf
(z)Tj
/T1_4 7.97 Tf
9.31 -1.64 Td
(c)Tj
/T1_1 10.91 Tf
4.16 1.64 Td
[(;)-167(N)]TJ
/T1_4 7.97 Tf
13.61 -1.64 Td
(c)Tj
/T1_1 10.91 Tf
4.17 1.64 Td
[(;)-166(N)]TJ
/T1_4 7.97 Tf
13.61 -1.64 Td
(s)Tj
/T1_1 10.91 Tf
4.41 1.64 Td
(;)Tj
/T1_2 10.91 Tf
4.85 0 Td
(C)Tj
/T1_1 10.91 Tf
(;)Tj
/T1_2 10.91 Tf
11.81 0 Td
(S)Tj
/T1_1 10.91 Tf
6.06 0 Td
(;)Tj
/T1_0 10.91 Tf
4.85 0 Td
[(00\),)-403(where)]TJ
/T1_1 10.91 Tf
54.72 0 Td
(\267)Tj
/T1_0 10.91 Tf
10.53 0 Td
[(is)-389(the)-389(secret)-389(k)27(ey)-388(shared)]TJ
-354.01 -21.92 Td
[(b)-27(et)27(w)27(een)]TJ
/T1_2 10.91 Tf
41.56 0 Td
(C)Tj
/T1_0 10.91 Tf
10.06 0 Td
(and)Tj
/T1_2 10.91 Tf
20.66 0 Td
(S)Tj
/T1_0 10.91 Tf
6.06 0 Td
(.)Tj
/T1_2 10.91 Tf
7.7 0 Td
(C)Tj
/T1_0 10.91 Tf
10.05 0 Td
[(then)-283(encrypts)]TJ
/T1_6 10.91 Tf
67.77 0 Td
(f)Tj
/T1_2 10.91 Tf
(C)Tj
/T1_1 10.91 Tf
12.42 0 Td
(;)Tj
/T1_3 10.91 Tf
4.85 0 Td
(MAC)Tj
/T1_8 7.97 Tf
17.18 -1.64 Td
(C)Tj
/T1_1 10.91 Tf
4.73 1.64 Td
(;)Tj
/T1_2 10.91 Tf
4.85 0 Td
[(p)28(w)]TJ
/T1_1 10.91 Tf
12.93 0 Td
(;)Tj
/T1_2 10.91 Tf
4.85 0 Td
(S)Tj
/T1_1 10.91 Tf
6.06 0 Td
[(;)-166(N)]TJ
/T1_4 7.97 Tf
13.61 -1.64 Td
(c)Tj
/T1_1 10.91 Tf
4.16 1.64 Td
[(;)-166(N)]TJ
/T1_7 7.97 Tf
14.8 3.96 Td
(0)Tj
/T1_4 7.97 Tf
-1.19 -6.66 Td
(s)Tj
/T1_6 10.91 Tf
4.41 2.7 Td
(h)Tj
/T1_0 10.91 Tf
4.25 0 Td
(1)Tj
/T1_1 10.91 Tf
[(;)-166(b)]TJ
/T1_6 10.91 Tf
14.98 0 Td
(i)Tj
/T1_1 10.91 Tf
[(;)-166(N)]TJ
/T1_4 7.97 Tf
17.85 -1.64 Td
(s)Tj
/T1_6 10.91 Tf
4.41 1.64 Td
(h)Tj
/T1_1 10.91 Tf
(b)Tj
/T1_0 10.91 Tf
10.25 0 Td
[(+)-122(1)]TJ
/T1_1 10.91 Tf
[(;)-166(L)]TJ
/T1_6 10.91 Tf
(i)Tj
/T1_1 10.91 Tf
[(;)-166(\271)]TJ
/T1_4 7.97 Tf
43.2 -1.64 Td
(c)Tj
/T1_6 10.91 Tf
4.17 1.64 Td
(g)Tj
/T1_0 10.91 Tf
8.54 0 Td
(using)Tj
/T1_2 10.91 Tf
27.99 0 Td
(S)Tj
/T1_0 10.91 Tf
6.06 0 Td
[('s)-283(public)-283(k)27(ey)]TJ
/T1_1 10.91 Tf
-409.22 -21.92 Td
(p\267)Tj
/T1_0 10.91 Tf
16 0 Td
[(and)-386(obtains)-388(ciphertext)]TJ
/T1_3 10.91 Tf
113.03 0 Td
(c)Tj
/T1_4 7.97 Tf
5.73 -1.63 Td
(s)Tj
/T1_0 10.91 Tf
8.42 1.63 Td
[(=)-368(E)]TJ
/T1_4 7.97 Tf
19.92 -1.63 Td
(p\267)Tj
/T1_0 10.91 Tf
9.64 1.63 Td
(\()Tj
/T1_2 10.91 Tf
(C)Tj
/T1_1 10.91 Tf
(;)Tj
/T1_3 10.91 Tf
16.05 0 Td
(MAC)Tj
/T1_8 7.97 Tf
17.18 -1.63 Td
(C)Tj
/T1_1 10.91 Tf
4.73 1.63 Td
(;)Tj
/T1_2 10.91 Tf
4.85 0 Td
[(p)27(w)]TJ
/T1_1 10.91 Tf
12.93 0 Td
(;)Tj
/T1_2 10.91 Tf
4.85 0 Td
(S)Tj
/T1_1 10.91 Tf
6.06 0 Td
[(;)-166(N)]TJ
/T1_4 7.97 Tf
13.61 -1.63 Td
(c)Tj
/T1_1 10.91 Tf
4.17 1.63 Td
[(;)-166(N)]TJ
/T1_7 7.97 Tf
14.79 3.96 Td
(0)Tj
/T1_4 7.97 Tf
-1.18 -6.65 Td
(s)Tj
/T1_6 10.91 Tf
4.41 2.69 Td
(h)Tj
/T1_0 10.91 Tf
(1)Tj
/T1_1 10.91 Tf
[(;)-166(b)]TJ
/T1_6 10.91 Tf
19.22 0 Td
(i)Tj
/T1_1 10.91 Tf
[(;)-166(N)]TJ
/T1_4 7.97 Tf
17.85 -1.63 Td
(s)Tj
/T1_6 10.91 Tf
4.41 1.63 Td
(h)Tj
/T1_1 10.91 Tf
4.25 0 Td
(b)Tj
/T1_0 10.91 Tf
7.49 0 Td
[(+)-258(1)]TJ
/T1_1 10.91 Tf
16.75 0 Td
[(;)-166(L)]TJ
/T1_6 10.91 Tf
(i)Tj
/T1_1 10.91 Tf
[(;)-167(\271)]TJ
/T1_4 7.97 Tf
27.93 -1.63 Td
(c)Tj
/T1_0 10.91 Tf
4.17 1.63 Td
[(\).)-606(Finally)83(,)]TJ
/T1_2 10.91 Tf
53.85 0 Td
(C)Tj
/T1_0 10.91 Tf
11.19 0 Td
(sends)Tj
/T1_6 10.91 Tf
-442.3 -21.91 Td
(f)Tj
/T1_1 10.91 Tf
(z)Tj
/T1_4 7.97 Tf
10.52 -1.64 Td
(c)Tj
/T1_1 10.91 Tf
4.17 1.64 Td
[(;)-166(N)]TJ
/T1_7 7.97 Tf
14.8 3.95 Td
(0)Tj
/T1_4 7.97 Tf
-1.19 -6.65 Td
(s)Tj
/T1_6 10.91 Tf
4.41 2.7 Td
(h)Tj
/T1_0 10.91 Tf
(1)Tj
/T1_1 10.91 Tf
[(;)-166(b)]TJ
/T1_6 10.91 Tf
(i)Tj
/T1_1 10.91 Tf
23.47 0 Td
[(;)-166(N)]TJ
/T1_4 7.97 Tf
13.61 -1.64 Td
(s)Tj
/T1_6 10.91 Tf
4.41 1.64 Td
(h)Tj
/T1_1 10.91 Tf
(b)Tj
/T1_0 10.91 Tf
11.34 0 Td
[(+)-222(1)]TJ
/T1_1 10.91 Tf
[(;)-166(L)]TJ
/T1_6 10.91 Tf
(i)Tj
/T1_1 10.91 Tf
(;)Tj
/T1_3 10.91 Tf
37.72 0 Td
(c)Tj
/T1_4 7.97 Tf
5.73 -1.64 Td
(s)Tj
/T1_6 10.91 Tf
4.41 1.64 Td
(g)Tj
/T1_0 10.91 Tf
9.09 0 Td
(to)Tj
/T1_2 10.91 Tf
13.33 0 Td
(S)Tj
/T1_0 10.91 Tf
6.06 0 Td
(.)Tj
-161.88 -21.92 Td
[(Round)-333(4)]TJ
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 0 -297.4 cm
0 0 m
40.75 0 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 112.7614 473.8672 Tm
(:)Tj
/T1_2 10.91 Tf
9.58 0 Td
(S)Tj
/T1_0 10.91 Tf
10.54 0 Td
(\257rst)Tj
1.0003 0 0 1.0003 72 769.82 Tm
84.239 -295.87 Td
[(c)27(hec)28(ks)-411(if)]TJ
/T1_2 10.91 Tf
45.381 0 Td
(C)Tj
/T1_0 10.91 Tf
11.45 0 Td
[(has)-411(resp)-28(onded)-411(b)-28(efore)-411(the)-412(expiry)-411(time.)-679(If)-411(the)-412(expiry)-411(time)-411(has)-412(past,)]TJ
/T1_2 10.91 Tf
-141.07 -21.92 Td
(S)Tj
/T1_0 10.91 Tf
10.46 0 Td
(ignores)Tj
/T1_2 10.91 Tf
37.81 0 Td
(C)Tj
/T1_0 10.91 Tf
[(.)-654(Otherwise,)]TJ
/T1_2 10.91 Tf
72.71 0 Td
(S)Tj
/T1_0 10.91 Tf
10.46 0 Td
[(c)27(hec)28(ks)-402(if)]TJ
/T1_2 10.91 Tf
45.21 0 Td
(C)Tj
/T1_0 10.91 Tf
11.37 0 Td
[(has)-402(computed)-404(the)-403(correct)]TJ
/T1_1 10.91 Tf
127.98 0 Td
(N)Tj
/T1_4 7.97 Tf
8.77 -1.63 Td
(s)Tj
/T1_6 10.91 Tf
4.41 1.63 Td
(h)Tj
/T1_0 10.91 Tf
(1)Tj
/T1_1 10.91 Tf
[(;)-167(b)]TJ
/T1_6 10.91 Tf
(i)Tj
/T1_0 10.91 Tf
[(.)-654(If)]TJ
/T1_1 10.91 Tf
45.3 0 Td
(N)Tj
/T1_4 7.97 Tf
8.76 -1.63 Td
(s)Tj
/T1_6 10.91 Tf
4.41 1.63 Td
(h)Tj
/T1_0 10.91 Tf
4.25 0 Td
(1)Tj
/T1_1 10.91 Tf
[(;)-166(b)]TJ
/T1_6 10.91 Tf
14.98 0 Td
[(i)-394(6)]TJ
/T1_0 10.91 Tf
(=)Tj
/T1_1 10.91 Tf
21.32 0 Td
(N)Tj
/T1_7 7.97 Tf
9.95 3.96 Td
(0)Tj
/T1_4 7.97 Tf
-1.18 -6.65 Td
(s)Tj
/T1_6 10.91 Tf
4.41 2.69 Td
(h)Tj
/T1_0 10.91 Tf
(1)Tj
/T1_1 10.91 Tf
[(;)-166(b)]TJ
/T1_6 10.91 Tf
19.22 0 Td
(i)Tj
/T1_0 10.91 Tf
(,)Tj
/T1_2 10.91 Tf
-460.6 -21.91 Td
(S)Tj
/T1_0 10.91 Tf
10.93 0 Td
[(blo)-28(c)27(ks)-446(malicious)]TJ
/T1_2 10.91 Tf
83.49 0 Td
(C)Tj
/T1_0 10.91 Tf
[(.)-785(Otherwise,)]TJ
/T1_2 10.91 Tf
74.74 0 Td
(S)Tj
/T1_0 10.91 Tf
10.93 0 Td
[(uses)-447(its)-447(priv)55(ate)-447(k)27(ey)]TJ
/T1_1 10.91 Tf
99.7 0 Td
(s\267)Tj
/T1_0 10.91 Tf
16.27 0 Td
[(to)-446(decrypt)-447(ciphertext)]TJ
/T1_3 10.91 Tf
108.6 0 Td
(c)Tj
/T1_4 7.97 Tf
5.73 -1.64 Td
(s)Tj
/T1_0 10.91 Tf
9.28 1.64 Td
[(and)-447(c)27(hec)28(k)]TJ
-419.67 -21.92 Td
(if)Tj
/T1_2 10.91 Tf
11.67 0 Td
(C)Tj
/T1_1 10.91 Tf
(;)Tj
/T1_3 10.91 Tf
11.82 0 Td
(MAC)Tj
/T1_8 7.97 Tf
17.17 -1.64 Td
(C)Tj
/T1_0 10.91 Tf
4.74 1.64 Td
(,)Tj
/T1_2 10.91 Tf
8.75 0 Td
(S)Tj
/T1_0 10.91 Tf
6.06 0 Td
(,)Tj
/T1_2 10.91 Tf
8.76 0 Td
[(p)27(w)]TJ
/T1_0 10.91 Tf
18.25 0 Td
(and)Tj
/T1_1 10.91 Tf
22.88 0 Td
(N)Tj
/T1_4 7.97 Tf
8.76 -1.64 Td
(s)Tj
/T1_0 10.91 Tf
9.73 1.64 Td
(in)Tj
/T1_3 10.91 Tf
14.4 0 Td
(c)Tj
/T1_4 7.97 Tf
5.72 -1.64 Td
(s)Tj
/T1_0 10.91 Tf
9.73 1.64 Td
[(are)-486(decrypted)-487(correctly)82(.)-904(If)-487(passw)27(ord)]TJ
/T1_2 10.91 Tf
187.1 0 Td
[(p)27(w)]TJ
/T1_0 10.91 Tf
18.25 0 Td
[(is)-486(incorrect,)]TJ
/T1_2 10.91 Tf
63.26 0 Td
(S)Tj
/T1_0 10.91 Tf
11.37 0 Td
[(blo)-28(c)27(ks)]TJ
-438.42 -21.92 Td
(malicious)Tj
/T1_2 10.91 Tf
48.73 0 Td
(C)Tj
/T1_0 10.91 Tf
6.96 0 Td
[(.)-665(Otherwise,)]TJ
/T1_2 10.91 Tf
65.91 0 Td
(S)Tj
/T1_0 10.91 Tf
10.49 0 Td
(obtains)Tj
/T1_1 10.91 Tf
39.03 0 Td
(N)Tj
/T1_4 7.97 Tf
8.77 -1.63 Td
(c)Tj
/T1_0 10.91 Tf
8.6 1.63 Td
(and)Tj
/T1_1 10.91 Tf
22 0 Td
(\271)Tj
/T1_4 7.97 Tf
6.58 -1.63 Td
(c)Tj
/T1_0 10.91 Tf
4.16 1.63 Td
[(.)-664(Next,)]TJ
/T1_2 10.91 Tf
40.97 0 Td
(S)Tj
/T1_0 10.91 Tf
10.49 0 Td
(uses)Tj
/T1_1 10.91 Tf
23.95 0 Td
(\267)Tj
/T1_0 10.91 Tf
10.72 0 Td
[(to)-406(v)26(erify)]TJ
/T1_1 10.91 Tf
45.26 0 Td
(\271)Tj
/T1_4 7.97 Tf
6.57 -1.63 Td
(c)Tj
/T1_0 10.91 Tf
4.16 1.63 Td
[(.)-664(If)]TJ
/T1_1 10.91 Tf
21.99 0 Td
(\271)Tj
/T1_4 7.97 Tf
6.57 -1.63 Td
(c)Tj
/T1_0 10.91 Tf
8.6 1.63 Td
[(is)-406(incorrect,)]TJ
/T1_2 10.91 Tf
61.3 0 Td
(S)Tj
/T1_0 10.91 Tf
-461.81 -21.91 Td
[(blo)-27(c)27(ks)-434(malicious)]TJ
/T1_2 10.91 Tf
83.21 0 Td
(C)Tj
/T1_0 10.91 Tf
[(.)-747(Otherwise,)]TJ
/T1_2 10.91 Tf
74.16 0 Td
(S)Tj
/T1_0 10.91 Tf
10.79 0 Td
[(selects)-434(random)]TJ
/T1_1 10.91 Tf
76.28 0 Td
(y)Tj
/T1_6 10.91 Tf
10.6 0 Td
(2)Tj
/T1_1 10.91 Tf
12.14 0 Td
(Z)Tj
/T1_7 7.97 Tf
8.23 3.96 Td
(\244)Tj
/T1_4 7.97 Tf
-0.78 -6.66 Td
(q)Tj
/T1_0 10.91 Tf
10.25 2.7 Td
[(and)-434(computes)]TJ
/T1_1 10.91 Tf
71.94 0 Td
(z)Tj
/T1_4 7.97 Tf
5.07 -1.64 Td
(s)Tj
/T1_0 10.91 Tf
9.28 1.64 Td
(=)Tj
/T1_1 10.91 Tf
13.35 0 Td
(g)Tj
/T1_4 7.97 Tf
5.6 3.96 Td
(y)Tj
/T1_0 10.91 Tf
7.99 -3.96 Td
[(mo)-28(d)]TJ
/T1_1 10.91 Tf
23.94 0 Td
(p)Tj
/T1_0 10.91 Tf
5.48 0 Td
[(,)-460(session)]TJ
-427.53 -21.92 Td
[(k)27(ey)]TJ
/T1_1 10.91 Tf
21.07 0 Td
(k)Tj
/T1_0 10.91 Tf
11.34 0 Td
(=)Tj
/T1_2 10.91 Tf
13.8 0 Td
(H)Tj
/T1_5 7.97 Tf
7.73 -1.63 Td
(2)Tj
/T1_0 10.91 Tf
4.73 1.63 Td
(\()Tj
/T1_2 10.91 Tf
(C)Tj
/T1_1 10.91 Tf
(;)Tj
/T1_2 10.91 Tf
16.06 0 Td
(S)Tj
/T1_1 10.91 Tf
6.05 0 Td
[(;)-167(N)]TJ
/T1_4 7.97 Tf
13.61 -1.63 Td
(c)Tj
/T1_1 10.91 Tf
4.17 1.63 Td
[(;)-166(N)]TJ
/T1_4 7.97 Tf
13.61 -1.63 Td
(s)Tj
/T1_1 10.91 Tf
4.41 1.63 Td
[(;)-166(z)]TJ
/T1_4 7.97 Tf
10.4 5.31 Td
(y)Tj
-0.48 -6.73 Td
(c)Tj
/T1_0 10.91 Tf
5.45 1.42 Td
[(\),)-490(k)26(ey)-458(con\257rmation)-459(co)-28(de)]TJ
/T1_1 10.91 Tf
125.24 0 Td
(\265)Tj
/T1_4 7.97 Tf
5.12 -1.63 Td
(s)Tj
/T1_0 10.91 Tf
9.73 1.63 Td
(=)Tj
/T1_2 10.91 Tf
13.8 0 Td
(H)Tj
/T1_5 7.97 Tf
7.73 -1.63 Td
(1)Tj
/T1_0 10.91 Tf
4.73 1.63 Td
(\()Tj
/T1_2 10.91 Tf
(S)Tj
/T1_1 10.91 Tf
10.3 0 Td
(;)Tj
/T1_2 10.91 Tf
4.85 0 Td
(C)Tj
/T1_1 10.91 Tf
6.96 0 Td
[(;)-167(N)]TJ
/T1_4 7.97 Tf
13.61 -1.63 Td
(s)Tj
/T1_1 10.91 Tf
4.42 1.63 Td
[(;)-166(N)]TJ
/T1_4 7.97 Tf
13.61 -1.63 Td
(c)Tj
/T1_1 10.91 Tf
4.16 1.63 Td
[(;)-166(k)-32(;)-166(z)]TJ
/T1_4 7.97 Tf
20.79 -1.63 Td
(s)Tj
/T1_1 10.91 Tf
4.41 1.63 Td
[(;)-166(z)]TJ
/T1_4 7.97 Tf
9.92 -1.63 Td
(c)Tj
/T1_1 10.91 Tf
4.17 1.63 Td
(;)Tj
/T1_0 10.91 Tf
4.84 0 Td
[(01\))-459(and)]TJ
/T1_1 10.91 Tf
42.74 0 Td
(\271)Tj
/T1_4 7.97 Tf
6.57 -1.63 Td
(s)Tj
/T1_0 10.91 Tf
9.74 1.63 Td
(=)Tj
/T1_6 10.91 Tf
-459.39 -21.92 Td
(M)Tj
/T1_4 7.97 Tf
13.1 -1.63 Td
(\267)Tj
/T1_0 10.91 Tf
5.37 1.63 Td
(\()Tj
/T1_1 10.91 Tf
(z)Tj
/T1_4 7.97 Tf
9.32 -1.63 Td
(s)Tj
/T1_1 10.91 Tf
4.41 1.63 Td
[(;)-166(\265)]TJ
/T1_4 7.97 Tf
9.97 -1.63 Td
(s)Tj
/T1_1 10.91 Tf
4.41 1.63 Td
[(;)-166(N)]TJ
/T1_4 7.97 Tf
13.61 -1.63 Td
(s)Tj
/T1_1 10.91 Tf
4.41 1.63 Td
[(;)-166(N)]TJ
/T1_4 7.97 Tf
13.61 -1.63 Td
(c)Tj
/T1_1 10.91 Tf
4.17 1.63 Td
(;)Tj
/T1_2 10.91 Tf
4.84 0 Td
(S)Tj
/T1_1 10.91 Tf
6.06 0 Td
(;)Tj
/T1_2 10.91 Tf
4.85 0 Td
(C)Tj
/T1_1 10.91 Tf
(;)Tj
/T1_0 10.91 Tf
11.81 0 Td
(10\).)Tj
/T1_2 10.91 Tf
27.4 0 Td
(S)Tj
/T1_0 10.91 Tf
11.15 0 Td
[(then)-467(encrypts)]TJ
/T1_6 10.91 Tf
71.78 0 Td
(f)Tj
/T1_2 10.91 Tf
(C)Tj
/T1_1 10.91 Tf
(;)Tj
/T1_2 10.91 Tf
17.26 0 Td
(S)Tj
/T1_1 10.91 Tf
6.06 0 Td
(;)Tj
/T1_3 10.91 Tf
4.85 0 Td
(IP)Tj
/T1_8 7.97 Tf
11.45 -1.63 Td
(C)Tj
/T1_1 10.91 Tf
4.73 1.63 Td
[(;)-166(N)]TJ
/T1_4 7.97 Tf
13.61 -1.63 Td
(c)Tj
/T1_1 10.91 Tf
4.17 1.63 Td
[(;)-166(N)]TJ
/T1_4 7.97 Tf
13.61 -1.63 Td
(s)Tj
/T1_6 10.91 Tf
4.41 1.63 Td
(g)Tj
/T1_0 10.91 Tf
10.55 0 Td
[(using)-466(session)-467(k)27(ey)]TJ
/T1_1 10.91 Tf
88.53 0 Td
(k)Tj
/T1_0 10.91 Tf
11.11 0 Td
[(and)-467(obtains)]TJ
/T1_3 10.91 Tf
-410.61 -21.91 Td
(c)Tj
/T1_7 7.97 Tf
5.73 3.96 Td
(0)Tj
/T1_4 7.97 Tf
0 -6.66 TD
(s)Tj
/T1_0 10.91 Tf
7.44 2.7 Td
(=)Tj
/T1_6 10.91 Tf
11.51 0 Td
(E)Tj
/T1_4 7.97 Tf
5.76 -1.78 Td
(k)Tj
/T1_0 10.91 Tf
5.11 1.78 Td
(\()Tj
/T1_2 10.91 Tf
4.25 0 Td
(C)Tj
/T1_1 10.91 Tf
6.96 0 Td
(;)Tj
/T1_2 10.91 Tf
4.85 0 Td
(S)Tj
/T1_1 10.91 Tf
6.06 0 Td
(;)Tj
/T1_3 10.91 Tf
4.85 0 Td
(IP)Tj
/T1_8 7.97 Tf
11.45 -1.64 Td
(C)Tj
/T1_1 10.91 Tf
4.73 1.64 Td
[(;)-166(N)]TJ
/T1_4 7.97 Tf
13.61 -1.64 Td
(c)Tj
/T1_1 10.91 Tf
4.16 1.64 Td
[(;)-166(N)]TJ
/T1_4 7.97 Tf
13.61 -1.64 Td
(s)Tj
/T1_0 10.91 Tf
4.42 1.64 Td
[(\))-332(and)-334(sends)]TJ
/T1_6 10.91 Tf
58.28 0 Td
(f)Tj
/T1_2 10.91 Tf
(S)Tj
/T1_1 10.91 Tf
11.51 0 Td
[(;)-167(z)]TJ
/T1_4 7.97 Tf
9.92 -1.64 Td
(s)Tj
/T1_1 10.91 Tf
4.42 1.64 Td
[(;)-166(\265)]TJ
/T1_4 7.97 Tf
9.96 -1.64 Td
(s)Tj
/T1_1 10.91 Tf
4.42 1.64 Td
[(;)-166(\271)]TJ
/T1_4 7.97 Tf
11.41 -1.64 Td
(s)Tj
/T1_1 10.91 Tf
4.42 1.64 Td
(;)Tj
/T1_3 10.91 Tf
4.84 0 Td
(c)Tj
/T1_7 7.97 Tf
5.73 3.96 Td
(0)Tj
/T1_4 7.97 Tf
T*
(s)Tj
/T1_6 10.91 Tf
4.41 2.7 Td
(g)Tj
/T1_0 10.91 Tf
9.09 0 Td
(to)Tj
/T1_2 10.91 Tf
13.33 0 Td
(C)Tj
/T1_0 10.91 Tf
(.)Tj
-266.24 -21.92 Td
[(Round)-333(5)]TJ
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 0 -494.64 cm
0 0 m
40.75 0 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 112.7614 276.5619 Tm
(:)Tj
/T1_2 10.91 Tf
9.46 0 Td
(C)Tj
/T1_0 10.91 Tf
11.39 0 Td
(c)Tj
1.0003 0 0 1.0003 72 769.82 Tm
66.149 -493.12 Td
[(hec)28(ks)-405(if)]TJ
/T1_1 10.91 Tf
40.721 0 Td
(\271)Tj
/T1_4 7.97 Tf
6.57 -1.63 Td
(s)Tj
/T1_0 10.91 Tf
8.84 1.63 Td
[(is)-405(v)54(alid.)-661(If)]TJ
/T1_1 10.91 Tf
56.43 0 Td
(\271)Tj
/T1_4 7.97 Tf
6.57 -1.63 Td
(s)Tj
/T1_0 10.91 Tf
8.84 1.63 Td
[(is)-405(not)-406(v)55(alid,)]TJ
/T1_2 10.91 Tf
62.31 0 Td
(C)Tj
/T1_0 10.91 Tf
11.39 0 Td
(rejects)Tj
/T1_2 10.91 Tf
35.12 0 Td
(S)Tj
/T1_0 10.91 Tf
6.06 0 Td
[(.)-661(Otherwise,)]TJ
/T1_2 10.91 Tf
65.86 0 Td
(C)Tj
/T1_0 10.91 Tf
11.39 0 Td
[(computes)-406(session)]TJ
-386.25 -21.91 Td
[(k)27(ey)]TJ
/T1_1 10.91 Tf
19.96 0 Td
(k)Tj
/T1_0 10.91 Tf
9.49 0 Td
(=)Tj
/T1_2 10.91 Tf
11.96 0 Td
(H)Tj
/T1_5 7.97 Tf
7.73 -1.64 Td
(2)Tj
/T1_0 10.91 Tf
4.73 1.64 Td
(\()Tj
/T1_2 10.91 Tf
(C)Tj
/T1_1 10.91 Tf
(;)Tj
/T1_2 10.91 Tf
16.05 0 Td
(S)Tj
/T1_1 10.91 Tf
6.06 0 Td
[(;)-166(N)]TJ
/T1_4 7.97 Tf
13.61 -1.64 Td
(c)Tj
/T1_1 10.91 Tf
4.17 1.64 Td
[(;)-166(N)]TJ
/T1_4 7.97 Tf
13.61 -1.64 Td
(s)Tj
/T1_1 10.91 Tf
4.41 1.64 Td
[(;)-166(z)]TJ
/T1_4 7.97 Tf
10.4 3.95 Td
(x)Tj
-0.48 -6.65 Td
(s)Tj
/T1_0 10.91 Tf
5.74 2.7 Td
[(\))-357(and)-358(v)27(eri\257es)]TJ
/T1_1 10.91 Tf
66.33 0 Td
(\265)Tj
/T1_4 7.97 Tf
5.12 -1.64 Td
(s)Tj
/T1_0 10.91 Tf
4.41 1.64 Td
[(.)-517(If)]TJ
/T1_1 10.91 Tf
19.85 0 Td
(\265)Tj
/T1_4 7.97 Tf
5.12 -1.64 Td
(s)Tj
/T1_0 10.91 Tf
8.32 1.64 Td
[(is)-357(not)-358(correct,)]TJ
/T1_2 10.91 Tf
70.66 0 Td
(C)Tj
/T1_0 10.91 Tf
10.87 0 Td
(rejects)Tj
/T1_2 10.91 Tf
34.59 0 Td
(S)Tj
/T1_0 10.91 Tf
6.06 0 Td
[(.)-518(Otherwise,)]TJ
/T1_2 10.91 Tf
63.63 0 Td
(C)Tj
/T1_0 10.91 Tf
10.87 0 Td
(accepts)Tj
/T1_1 10.91 Tf
-433.27 -21.92 Td
(k)Tj
/T1_0 10.91 Tf
10.45 0 Td
[(and)-405(decrypts)-406(ciphertext)]TJ
/T1_3 10.91 Tf
119.43 0 Td
(c)Tj
/T1_7 7.97 Tf
5.73 3.96 Td
(0)Tj
/T1_4 7.97 Tf
T*
(s)Tj
/T1_0 10.91 Tf
4.41 2.7 Td
(.)Tj
/T1_2 10.91 Tf
10.25 0 Td
(C)Tj
/T1_0 10.91 Tf
11.4 0 Td
[(then)-405(c)26(hec)28(ks)-405(if)-406(the)-406(iden)27(tities)]TJ
/T1_2 10.91 Tf
138.28 0 Td
(C)Tj
/T1_0 10.91 Tf
11.4 0 Td
(and)Tj
/T1_2 10.91 Tf
22 0 Td
(S)Tj
/T1_0 10.91 Tf
10.48 0 Td
[(and)-406(nonces)]TJ
/T1_1 10.91 Tf
58 0 Td
(N)Tj
/T1_4 7.97 Tf
8.76 -1.64 Td
(c)Tj
/T1_0 10.91 Tf
8.59 1.64 Td
(and)Tj
/T1_1 10.91 Tf
22 0 Td
(N)Tj
/T1_4 7.97 Tf
8.76 -1.64 Td
(s)Tj
/T1_0 10.91 Tf
8.84 1.64 Td
(in)Tj
/T1_3 10.91 Tf
-458.78 -21.92 Td
(c)Tj
/T1_7 7.97 Tf
5.73 3.96 Td
(0)Tj
/T1_4 7.97 Tf
0 -6.65 TD
(s)Tj
/T1_0 10.91 Tf
9.13 2.69 Td
[(are)-432(decrypted)-432(correctly)82(.)-741(If)-432(y)27(es,)]TJ
/T1_2 10.91 Tf
157.37 0 Td
(C)Tj
/T1_0 10.91 Tf
11.69 0 Td
[(accepts)-432(the)-432(assigned)-433(IP)-432(address)]TJ
/T1_3 10.91 Tf
159.48 0 Td
(IP)Tj
/T1_8 7.97 Tf
11.45 -1.63 Td
(C)Tj
/T1_0 10.91 Tf
4.73 1.63 Td
[(.)-742(Finally)82(,)]TJ
/T1_2 10.91 Tf
51.71 0 Td
(C)Tj
/T1_0 10.91 Tf
11.68 0 Td
(computes)Tj
/T1_1 10.91 Tf
-422.97 -21.91 Td
(\265)Tj
/T1_4 7.97 Tf
5.12 -1.64 Td
(c)Tj
/T1_0 10.91 Tf
7.19 1.64 Td
(=)Tj
/T1_2 10.91 Tf
11.52 0 Td
(H)Tj
/T1_5 7.97 Tf
7.72 -1.64 Td
(1)Tj
/T1_0 10.91 Tf
4.73 1.64 Td
(\()Tj
/T1_2 10.91 Tf
(C)Tj
/T1_1 10.91 Tf
(;)Tj
/T1_2 10.91 Tf
16.06 0 Td
(S)Tj
/T1_1 10.91 Tf
6.06 0 Td
[(;)-166(N)]TJ
/T1_4 7.97 Tf
13.61 -1.64 Td
(c)Tj
/T1_1 10.91 Tf
4.16 1.64 Td
[(;)-166(N)]TJ
/T1_4 7.97 Tf
13.61 -1.64 Td
(s)Tj
/T1_1 10.91 Tf
4.41 1.64 Td
(;)Tj
/T1_3 10.91 Tf
4.85 0 Td
(IP)Tj
/T1_8 7.97 Tf
11.45 -1.64 Td
(C)Tj
/T1_1 10.91 Tf
4.73 1.64 Td
[(;)-167(k)-31(;)-167(z)]TJ
/T1_4 7.97 Tf
20.79 -1.64 Td
(c)Tj
/T1_1 10.91 Tf
4.17 1.64 Td
[(;)-166(z)]TJ
/T1_4 7.97 Tf
9.91 -1.64 Td
(s)Tj
/T1_1 10.91 Tf
4.42 1.64 Td
(;)Tj
/T1_0 10.91 Tf
4.84 0 Td
[(11\))-333(and)-334(sends)]TJ
/T1_1 10.91 Tf
69.2 0 Td
(\265)Tj
/T1_4 7.97 Tf
5.12 -1.64 Td
(c)Tj
/T1_0 10.91 Tf
7.8 1.64 Td
(to)Tj
/T1_2 10.91 Tf
13.33 0 Td
(S)Tj
/T1_0 10.91 Tf
6.06 0 Td
(.)Tj
-260.86 -21.92 Td
[(Round)-333(6)]TJ
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 0 -604.23 cm
0 0 m
40.75 0 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 112.7614 166.9512 Tm
(:)Tj
/T1_2 10.91 Tf
8.73 0 Td
(S)Tj
/T1_0 10.91 Tf
10.12 0 Td
(c)Tj
1.0003 0 0 1.0003 72 769.82 Tm
64.139 -602.7 Td
[(hec)27(ks)-371(if)]TJ
/T1_1 10.91 Tf
39.991 0 Td
(\265)Tj
/T1_4 7.97 Tf
5.12 -1.64 Td
(c)Tj
/T1_0 10.91 Tf
8.23 1.64 Td
[(is)-372(v)54(alid.)-560(If)]TJ
/T1_1 10.91 Tf
54.6 0 Td
(\265)Tj
/T1_4 7.97 Tf
5.12 -1.64 Td
(c)Tj
/T1_0 10.91 Tf
8.23 1.64 Td
[(is)-372(not)-372(v)54(alid,)]TJ
/T1_2 10.91 Tf
61.13 0 Td
(S)Tj
/T1_0 10.91 Tf
10.12 0 Td
(rejects)Tj
/T1_2 10.91 Tf
34.75 0 Td
(C)Tj
/T1_0 10.91 Tf
[(.)-561(Otherwise,)]TJ
/T1_2 10.91 Tf
71.28 0 Td
(S)Tj
/T1_0 10.91 Tf
10.12 0 Td
[(con\257rms)-372(that)]TJ
/T1_2 10.91 Tf
68.2 0 Td
(C)Tj
/T1_0 10.91 Tf
11.03 0 Td
(has)Tj
-452.06 -21.92 Td
[(receiv)27(ed)-352(the)-354(correct)-353(session)-354(k)27(ey)]TJ
/T1_1 10.91 Tf
153.76 0 Td
(k)Tj
/T1_0 10.91 Tf
9.87 0 Td
[(and)-353(IP)-354(address)]TJ
/T1_3 10.91 Tf
75.8 0 Td
(IP)Tj
/T1_8 7.97 Tf
11.45 -1.63 Td
(C)Tj
/T1_0 10.91 Tf
4.73 1.63 Td
[(.)-504(Next,)]TJ
/T1_2 10.91 Tf
38.5 0 Td
(S)Tj
/T1_0 10.91 Tf
9.91 0 Td
(sends)Tj
/T1_6 10.91 Tf
29.43 0 Td
(f)Tj
/T1_1 10.91 Tf
[(k)-31(;)]TJ
/T1_3 10.91 Tf
16.32 0 Td
(MAC)Tj
/T1_8 7.97 Tf
17.18 -1.63 Td
(C)Tj
/T1_1 10.91 Tf
4.73 1.63 Td
(;)Tj
/T1_3 10.91 Tf
4.84 0 Td
(IP)Tj
/T1_8 7.97 Tf
11.46 -1.63 Td
(C)Tj
/T1_6 10.91 Tf
4.73 1.63 Td
(g)Tj
/T1_0 10.91 Tf
9.31 0 Td
(to)Tj
/T1_2 10.91 Tf
13.55 0 Td
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[(for)-270(1)]TJ
/T1_6 10.91 Tf
24.49 0 Td
(\267)Tj
/T1_4 10.91 Tf
11.51 0 Td
(i)Tj
/T1_6 10.91 Tf
6.79 0 Td
(\267)Tj
/T1_4 10.91 Tf
11.51 0 Td
(n)Tj
/T1_2 7.97 Tf
6.55 -1.63 Td
(c)Tj
/T1_0 10.91 Tf
7.12 1.63 Td
[(randomly)-270(selects)]TJ
/T1_4 10.91 Tf
81.49 0 Td
(\277)Tj
/T1_2 7.97 Tf
4.77 -1.63 Td
(i)Tj
/T1_6 10.91 Tf
6.41 1.63 Td
(2)Tj
/T1_4 10.91 Tf
10.3 0 Td
(Z)Tj
/T1_7 7.97 Tf
8.22 3.96 Td
(\244)Tj
/T1_2 7.97 Tf
-0.78 -6.65 Td
(q)Tj
/T1_0 10.91 Tf
5.52 2.69 Td
(,)Tj
/T1_4 10.91 Tf
6.12 0 Td
(\277)Tj
/T1_2 7.97 Tf
4.76 -1.63 Td
(i;j)Tj
/T1_6 10.91 Tf
12.65 1.63 Td
(2)Tj
/T1_4 10.91 Tf
10.3 0 Td
(Z)Tj
/T1_7 7.97 Tf
8.22 3.96 Td
(\244)Tj
/T1_2 7.97 Tf
-0.78 -6.65 Td
(q)Tj
/T1_0 10.91 Tf
8.47 2.69 Td
[(for)-270(1)]TJ
/T1_6 10.91 Tf
24.49 0 Td
(\267)Tj
/T1_4 10.91 Tf
11.51 0 Td
(j)Tj
/T1_6 10.91 Tf
8.15 0 Td
(\267)Tj
/T1_4 10.91 Tf
-459.39 -21.91 Td
(n)Tj
/T1_2 7.97 Tf
6.55 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
6.98 1.64 Td
[(and)-329(session)-330(iden)27(tit)28(y)]TJ
/T1_1 10.91 Tf
97.31 0 Td
(SID)Tj
/T1_2 7.97 Tf
17.18 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
3.38 1.64 Td
[(,)-330(encrypts)]TJ
/T1_4 10.91 Tf
50.62 0 Td
(\277)Tj
/T1_2 7.97 Tf
4.76 -1.64 Td
(i)Tj
/T1_6 10.91 Tf
3.38 1.64 Td
(jj)Tj
/T1_4 10.91 Tf
6.06 0 Td
(\277)Tj
/T1_2 7.97 Tf
4.77 -1.64 Td
(i;j)Tj
/T1_6 10.91 Tf
9.62 1.64 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(S)Tj
/T1_2 7.97 Tf
5.72 -1.64 Td
(i)Tj
/T1_6 10.91 Tf
3.38 1.64 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(U)Tj
/T1_2 7.97 Tf
5.73 -1.64 Td
(i;j)Tj
/T1_6 10.91 Tf
9.61 1.64 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(SID)Tj
/T1_2 7.97 Tf
17.18 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
6.98 1.64 Td
(using)Tj
/T1_4 10.91 Tf
28.5 0 Td
(ek)Tj
/T1_2 7.97 Tf
10.75 -1.64 Td
(i;j)Tj
/T1_0 10.91 Tf
13.22 1.64 Td
[(and)-329(obtains)-330(ciphertext)]TJ
/T1_1 10.91 Tf
111.16 0 Td
(c)Tj
/T1_2 7.97 Tf
5.72 -1.64 Td
(i;j)Tj
/T1_0 10.91 Tf
12.65 1.64 Td
(=)Tj
/T1_6 10.91 Tf
-459.39 -21.92 Td
(E)Tj
/T1_2 7.97 Tf
5.76 -1.78 Td
(ek)Tj
/T1_8 5.98 Tf
8.33 -1.21 Td
(i;j)Tj
/T1_0 10.91 Tf
9.33 2.99 Td
(\()Tj
/T1_4 10.91 Tf
(\277)Tj
/T1_2 7.97 Tf
9.01 -1.63 Td
(i)Tj
/T1_6 10.91 Tf
3.38 1.63 Td
(jj)Tj
/T1_4 10.91 Tf
6.06 0 Td
(\277)Tj
/T1_2 7.97 Tf
4.77 -1.63 Td
(i;j)Tj
/T1_6 10.91 Tf
9.61 1.63 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(S)Tj
/T1_2 7.97 Tf
5.73 -1.63 Td
(i)Tj
/T1_6 10.91 Tf
3.38 1.63 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(U)Tj
/T1_2 7.97 Tf
5.72 -1.63 Td
(i;j)Tj
/T1_6 10.91 Tf
9.62 1.63 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(SID)Tj
/T1_2 7.97 Tf
17.17 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
3.38 1.63 Td
[(\))-383(and)-384(computes)]TJ
/T1_4 10.91 Tf
79.26 0 Td
(v)Tj
/T1_2 7.97 Tf
5.28 -1.63 Td
(i;j)Tj
/T1_0 10.91 Tf
13.56 1.63 Td
(=)Tj
/T1_3 10.91 Tf
12.42 0 Td
(H)Tj
/T1_9 7.97 Tf
7.72 -1.63 Td
(1)Tj
/T1_0 10.91 Tf
4.73 1.63 Td
(\()Tj
/T1_3 10.91 Tf
4.25 0 Td
[(p)28(w)]TJ
/T1_2 7.97 Tf
12.93 -2.62 Td
(i;j)Tj
/T1_6 10.91 Tf
9.62 2.62 Td
(jj)Tj
/T1_4 10.91 Tf
6.06 0 Td
(\277)Tj
/T1_2 7.97 Tf
4.76 -1.63 Td
(i)Tj
/T1_6 10.91 Tf
3.38 1.63 Td
(jj)Tj
/T1_4 10.91 Tf
6.06 0 Td
(\277)Tj
/T1_2 7.97 Tf
4.77 -1.63 Td
(i;j)Tj
/T1_6 10.91 Tf
9.61 1.63 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(SID)Tj
/T1_2 7.97 Tf
17.18 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
3.38 1.63 Td
[(\))-383(for)-383(1)]TJ
/T1_6 10.91 Tf
35.05 0 Td
(\267)Tj
/T1_4 10.91 Tf
12.42 0 Td
(j)Tj
/T1_6 10.91 Tf
9.06 0 Td
(\267)Tj
/T1_4 10.91 Tf
12.42 0 Td
(n)Tj
/T1_2 7.97 Tf
6.55 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
3.38 1.63 Td
[(.)-594(Finally)83(,)]TJ
/T1_1 10.91 Tf
49.42 0 Td
(S)Tj
/T1_2 7.97 Tf
5.73 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
-464.49 -20.29 Td
(broadcasts)Tj
/T1_6 10.91 Tf
54.08 0 Td
(f)Tj
/T1_1 10.91 Tf
(SID)Tj
/T1_2 7.97 Tf
22.63 -1.63 Td
(i)Tj
/T1_6 10.91 Tf
3.38 1.63 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(S)Tj
/T1_2 7.97 Tf
5.72 -1.63 Td
(i)Tj
/T1_6 10.91 Tf
3.38 1.63 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(c)Tj
/T1_2 7.97 Tf
5.73 -1.63 Td
(i;j)Tj
/T1_6 10.91 Tf
9.61 1.63 Td
(jj)Tj
/T1_4 10.91 Tf
6.06 0 Td
(v)Tj
/T1_2 7.97 Tf
5.29 -1.63 Td
(i;j)Tj
/T1_6 10.91 Tf
9.61 1.63 Td
(g)Tj
/T1_0 10.91 Tf
9.09 0 Td
[(for)-333(1)]TJ
/T1_6 10.91 Tf
25.17 0 Td
(\267)Tj
/T1_4 10.91 Tf
11.52 0 Td
(j)Tj
/T1_6 10.91 Tf
8.14 0 Td
(\267)Tj
/T1_4 10.91 Tf
11.51 0 Td
(n)Tj
/T1_2 7.97 Tf
6.55 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
7.01 1.63 Td
[(to)-333(subgroup)]TJ
/T1_6 10.91 Tf
60.69 0 Td
(G)Tj
/T1_2 7.97 Tf
6.48 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
3.38 1.63 Td
(.)Tj
-287.15 -21.91 Td
[(Round)-333(2)]TJ
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 0 -309.35 cm
0 0 m
40.75 0 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 112.7614 461.9138 Tm
(:)Tj
1.0003 0 0 1.0003 72 769.82 Tm
48.376 -307.82 Td
[(Eac)26(h)-288(subgroup)-288(mem)26(b)-26(er)]TJ
/T1_1 10.91 Tf
114.854 0 Td
(U)Tj
/T1_2 7.97 Tf
5.72 -1.64 Td
(i;j)Tj
/T1_0 10.91 Tf
12.77 1.64 Td
[(for)-288(1)]TJ
/T1_6 10.91 Tf
24.69 0 Td
(\267)Tj
/T1_4 10.91 Tf
11.51 0 Td
(i)Tj
/T1_6 10.91 Tf
6.79 0 Td
(\267)Tj
/T1_4 10.91 Tf
11.51 0 Td
(n)Tj
/T1_2 7.97 Tf
6.55 -1.64 Td
(c)Tj
/T1_0 10.91 Tf
7.31 1.64 Td
[(and)-289(1)]TJ
/T1_6 10.91 Tf
29.21 0 Td
(\267)Tj
/T1_4 10.91 Tf
11.51 0 Td
(j)Tj
/T1_6 10.91 Tf
8.14 0 Td
(\267)Tj
/T1_4 10.91 Tf
11.52 0 Td
(n)Tj
/T1_2 7.97 Tf
6.54 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
6.53 1.64 Td
[(\257rst)-289(decrypts)]TJ
/T1_1 10.91 Tf
65.56 0 Td
(c)Tj
/T1_2 7.97 Tf
5.73 -1.64 Td
(i;j)Tj
/T1_0 10.91 Tf
12.76 1.64 Td
[(and)-289(c)27(hec)28(ks)-288(if)]TJ
-407.58 -21.92 Td
[(the)-339(iden)27(tities)]TJ
/T1_1 10.91 Tf
65.92 0 Td
(S)Tj
/T1_2 7.97 Tf
5.73 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
3.38 1.63 Td
(,)Tj
/T1_1 10.91 Tf
6.74 0 Td
(U)Tj
/T1_2 7.97 Tf
5.73 -1.63 Td
(i;j)Tj
/T1_0 10.91 Tf
13.31 1.63 Td
(and)Tj
/T1_1 10.91 Tf
21.27 0 Td
(SID)Tj
/T1_2 7.97 Tf
17.18 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
7.08 1.63 Td
[(are)-338(decrypted)-339(correctly)82(.)-460(If)-339(the)-340(iden)27(tities)-338(are)-339(not)-339(correct,)]TJ
/T1_1 10.91 Tf
271.8 0 Td
(U)Tj
/T1_2 7.97 Tf
5.73 -1.63 Td
(i;j)Tj
/T1_0 10.91 Tf
13.31 1.63 Td
(rejects)Tj
/T1_1 10.91 Tf
-437.18 -21.91 Td
(S)Tj
/T1_2 7.97 Tf
5.73 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
3.38 1.64 Td
[(.)-435(Otherwise,)]TJ
/T1_1 10.91 Tf
62.19 0 Td
(U)Tj
/T1_2 7.97 Tf
5.72 -1.64 Td
(i;j)Tj
/T1_0 10.91 Tf
12.98 1.64 Td
[(uses)-308(passw)26(ord)]TJ
/T1_3 10.91 Tf
69.72 0 Td
[(p)27(w)]TJ
/T1_2 7.97 Tf
12.93 -2.62 Td
(i;j)Tj
/T1_0 10.91 Tf
12.98 2.62 Td
[(to)-308(c)26(hec)28(k)-307(the)-309(v)55(alidit)27(y)-307(of)]TJ
/T1_4 10.91 Tf
111.65 0 Td
(v)Tj
/T1_2 7.97 Tf
5.29 -1.64 Td
(i;j)Tj
/T1_0 10.91 Tf
12.64 1.64 Td
(=)Tj
/T1_3 10.91 Tf
11.52 0 Td
(H)Tj
/T1_9 7.97 Tf
7.72 -1.64 Td
(1)Tj
/T1_0 10.91 Tf
4.73 1.64 Td
(\()Tj
/T1_3 10.91 Tf
[(p)27(w)]TJ
/T1_2 7.97 Tf
17.18 -2.62 Td
(i;j)Tj
/T1_6 10.91 Tf
9.61 2.62 Td
(jj)Tj
/T1_4 10.91 Tf
6.06 0 Td
(\277)Tj
/T1_2 7.97 Tf
4.77 -1.64 Td
(i)Tj
/T1_6 10.91 Tf
3.38 1.64 Td
(jj)Tj
/T1_4 10.91 Tf
6.06 0 Td
(\277)Tj
/T1_2 7.97 Tf
4.77 -1.64 Td
(i;j)Tj
/T1_6 10.91 Tf
9.61 1.64 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(SID)Tj
/T1_2 7.97 Tf
17.18 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
3.38 1.64 Td
[(\).)-436(If)-308(it)-309(is)]TJ
-427.24 -21.92 Td
(incorrect,)Tj
/T1_1 10.91 Tf
48.53 0 Td
(U)Tj
/T1_2 7.97 Tf
5.73 -1.64 Td
(i;j)Tj
/T1_0 10.91 Tf
13.25 1.64 Td
(rejects)Tj
/T1_1 10.91 Tf
34.32 0 Td
(S)Tj
/T1_2 7.97 Tf
5.73 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
3.38 1.64 Td
[(.)-444(Otherwise,)]TJ
/T1_1 10.91 Tf
62.5 0 Td
(U)Tj
/T1_2 7.97 Tf
5.72 -1.64 Td
(i;j)Tj
/T1_0 10.91 Tf
13.25 1.64 Td
[(randomly)-333(selects)]TJ
/T1_4 10.91 Tf
82.86 0 Td
(r)Tj
/T1_2 7.97 Tf
4.92 -1.64 Td
(i;j)Tj
/T1_6 10.91 Tf
12.64 1.64 Td
(2)Tj
/T1_4 10.91 Tf
10.3 0 Td
(Z)Tj
/T1_7 7.97 Tf
8.23 3.96 Td
(\244)Tj
/T1_2 7.97 Tf
-0.78 -6.66 Td
(q)Tj
/T1_0 10.91 Tf
9.14 2.7 Td
[(and)-333(computes)]TJ
/T1_4 10.91 Tf
-230.69 -39.64 Td
(z)Tj
/T1_2 7.97 Tf
5.07 -1.64 Td
(i;j)Tj
/T1_0 10.91 Tf
12.65 1.64 Td
(=)Tj
/T1_4 10.91 Tf
11.51 0 Td
(g)Tj
/T1_2 7.97 Tf
5.59 4.5 Td
(r)Tj
/T1_8 5.98 Tf
3.82 -1.22 Td
(i;j)Tj
/T1_0 10.91 Tf
12.36 -3.28 Td
[(mo)-28(d)]TJ
/T1_4 10.91 Tf
23.94 0 Td
(p)Tj
/T1_0 10.91 Tf
11.95 0 Td
(,)Tj
/T1_4 10.91 Tf
9.5 0 Td
(z)Tj
/T1_7 7.97 Tf
5.55 4.5 Td
(\244)Tj
/T1_2 7.97 Tf
-0.48 -7.2 Td
(i;j)Tj
/T1_0 10.91 Tf
12.65 2.7 Td
(=)Tj
/T1_4 10.91 Tf
11.51 0 Td
(z)Tj
/T1_2 7.97 Tf
5.07 -1.64 Td
(i;j)Tj
/T1_6 10.91 Tf
12.04 1.64 Td
(\242)Tj
/T1_4 10.91 Tf
5.45 0 Td
(h)Tj
/T1_10 7.97 Tf
6.29 4.5 Td
(H)Tj
/T1_11 5.98 Tf
5.97 -1.11 Td
(1)Tj
/T1_9 7.97 Tf
4.15 1.11 Td
(\()Tj
/T1_12 7.97 Tf
(SID)Tj
/T1_8 5.98 Tf
15.99 -1.22 Td
(i)Tj
/T1_7 7.97 Tf
3.16 1.22 Td
(jj)Tj
/T1_12 7.97 Tf
4.71 0 Td
(U)Tj
/T1_8 5.98 Tf
4.23 -1.22 Td
(i;j)Tj
/T1_7 7.97 Tf
8.83 1.22 Td
(jj)Tj
/T1_12 7.97 Tf
4.71 0 Td
(S)Tj
/T1_8 5.98 Tf
4.23 -1.22 Td
(i)Tj
/T1_7 7.97 Tf
3.16 1.22 Td
(jj)Tj
/T1_10 7.97 Tf
[(p)28(w)]TJ
/T1_8 5.98 Tf
14.74 -2.05 Td
(i;j)Tj
/T1_7 7.97 Tf
8.83 2.05 Td
(jj)Tj
/T1_2 7.97 Tf
4.71 0 Td
(\277)Tj
/T1_8 5.98 Tf
3.75 -1.22 Td
(i)Tj
/T1_7 7.97 Tf
3.17 1.22 Td
(jj)Tj
/T1_2 7.97 Tf
(\277)Tj
/T1_8 5.98 Tf
8.46 -1.22 Td
(i;j)Tj
/T1_9 7.97 Tf
8.83 1.22 Td
(\))Tj
/T1_4 10.91 Tf
-206.62 -29.41 Td
(\271)Tj
/T1_2 7.97 Tf
6.58 -1.63 Td
(i;j)Tj
/T1_0 10.91 Tf
12.64 1.63 Td
(=)Tj
/T1_3 10.91 Tf
11.51 0 Td
[(MA)27(C)]TJ
/T1_2 7.97 Tf
23.48 -1.78 Td
(ak)Tj
/T1_8 5.98 Tf
8.9 -1.21 Td
(i;j)Tj
/T1_0 10.91 Tf
9.34 2.99 Td
(\()Tj
/T1_4 10.91 Tf
(\277)Tj
/T1_2 7.97 Tf
9 -1.63 Td
(i)Tj
/T1_6 10.91 Tf
3.39 1.63 Td
(jj)Tj
/T1_4 10.91 Tf
6.05 0 Td
(\277)Tj
/T1_2 7.97 Tf
4.77 -1.63 Td
(i;j)Tj
/T1_6 10.91 Tf
9.62 1.63 Td
(jj)Tj
/T1_4 10.91 Tf
6.06 0 Td
(z)Tj
/T1_7 7.97 Tf
5.55 4.5 Td
(\244)Tj
/T1_2 7.97 Tf
-0.48 -7.19 Td
(i;j)Tj
/T1_6 10.91 Tf
9.61 2.69 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(SID)Tj
/T1_2 7.97 Tf
17.18 -1.63 Td
(i)Tj
/T1_6 10.91 Tf
3.38 1.63 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(U)Tj
/T1_2 7.97 Tf
5.72 -1.63 Td
(i;j)Tj
/T1_6 10.91 Tf
9.62 1.63 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(S)Tj
/T1_2 7.97 Tf
5.72 -1.63 Td
(i)Tj
/T1_6 10.91 Tf
3.38 1.63 Td
(jj)Tj
/T1_0 10.91 Tf
6.06 0 Td
(00\))Tj
-194.39 -24.9 Td
(\271)Tj
/T1_4 10.91 Tf
-0.87 0 Td
(\271)Tj
/T1_2 7.97 Tf
6.58 -1.64 Td
(i;j)Tj
/T1_0 10.91 Tf
12.64 1.64 Td
(=)Tj
/T1_3 10.91 Tf
11.51 0 Td
[(MA)27(C)]TJ
/T1_2 7.97 Tf
23.48 -1.78 Td
(ak)Tj
/T1_8 5.98 Tf
8.9 -1.21 Td
(i;j)Tj
/T1_0 10.91 Tf
9.34 2.99 Td
(\()Tj
/T1_4 10.91 Tf
(\277)Tj
/T1_2 7.97 Tf
9 -1.64 Td
(i)Tj
/T1_6 10.91 Tf
3.39 1.64 Td
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(\277)Tj
/T1_2 7.97 Tf
4.77 -1.63 Td
(i)Tj
/T1_6 10.91 Tf
3.38 1.63 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(C)Tj
/T1_6 10.91 Tf
5.72 0 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(S)Tj
/T1_2 7.97 Tf
5.73 -1.63 Td
(i)Tj
/T1_6 10.91 Tf
3.38 1.63 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(SID)Tj
/T1_9 7.97 Tf
17.17 -1.63 Td
(c)Tj
/T1_0 10.91 Tf
10.06 1.63 Td
(using)Tj
/T1_3 10.91 Tf
30.22 0 Td
(ek)Tj
/T1_2 7.97 Tf
10.76 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
8.7 1.63 Td
[(to)-487(obtain)]TJ
/T1_1 10.91 Tf
50.63 0 Td
(c)Tj
/T1_2 7.97 Tf
5.72 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
9.22 1.63 Td
(=)Tj
/T1_6 10.91 Tf
14.33 0 Td
(E)Tj
/T1_2 7.97 Tf
5.75 -1.77 Td
(ek)Tj
/T1_4 5.98 Tf
8.34 -1.22 Td
(i)Tj
/T1_0 10.91 Tf
3.66 2.99 Td
(\()Tj
/T1_3 10.91 Tf
(\277)Tj
/T1_9 7.97 Tf
9.01 -1.63 Td
(C)Tj
/T1_6 10.91 Tf
4.73 1.63 Td
(jj)Tj
/T1_0 10.91 Tf
6.63 0 Td
(\271)Tj
/T1_3 10.91 Tf
-0.57 0 Td
(\277)Tj
/T1_2 7.97 Tf
4.76 -1.63 Td
(i)Tj
/T1_6 10.91 Tf
3.38 1.63 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(C)Tj
/T1_6 10.91 Tf
(jj)Tj
/T1_1 10.91 Tf
11.79 0 Td
(S)Tj
/T1_2 7.97 Tf
5.72 -1.63 Td
(i)Tj
/T1_6 10.91 Tf
3.38 1.63 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(SID)Tj
/T1_9 7.97 Tf
17.18 -1.63 Td
(c)Tj
/T1_0 10.91 Tf
4.73 1.63 Td
[(\))-487(and)-488(computes)]TJ
/T1_3 10.91 Tf
-390.52 -21.91 Td
(v)Tj
/T1_2 7.97 Tf
5.29 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
7.16 1.64 Td
(=)Tj
/T1_11 10.91 Tf
12.27 0 Td
(H)Tj
/T1_7 7.97 Tf
7.72 -1.64 Td
(1)Tj
/T1_0 10.91 Tf
4.73 1.64 Td
(\()Tj
/T1_11 10.91 Tf
4.25 0 Td
[(p)28(w)]TJ
/T1_2 7.97 Tf
12.93 -2.62 Td
(i)Tj
/T1_6 10.91 Tf
3.38 2.62 Td
(jj)Tj
/T1_3 10.91 Tf
6.06 0 Td
(\277)Tj
/T1_9 7.97 Tf
4.77 -1.64 Td
(C)Tj
/T1_6 10.91 Tf
4.73 1.64 Td
(jj)Tj
/T1_0 10.91 Tf
6.64 0 Td
(\271)Tj
/T1_3 10.91 Tf
-0.58 0 Td
(\277)Tj
/T1_2 7.97 Tf
4.77 -1.64 Td
(i)Tj
/T1_6 10.91 Tf
3.38 1.64 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(SID)Tj
/T1_9 7.97 Tf
17.17 -1.64 Td
(c)Tj
/T1_0 10.91 Tf
4.73 1.64 Td
[(\))-375(for)-375(1)]TJ
/T1_6 10.91 Tf
34.72 0 Td
(\267)Tj
/T1_3 10.91 Tf
12.26 0 Td
(i)Tj
/T1_6 10.91 Tf
7.55 0 Td
(\267)Tj
/T1_3 10.91 Tf
12.26 0 Td
(n)Tj
/T1_2 7.97 Tf
6.55 -1.64 Td
(c)Tj
/T1_0 10.91 Tf
4.16 1.64 Td
[(.)-569(Finally)82(,)]TJ
/T1_1 10.91 Tf
49.04 0 Td
(C)Tj
/T1_0 10.91 Tf
9.81 0 Td
(broadcasts)Tj
/T1_6 10.91 Tf
54.53 0 Td
(f)Tj
/T1_1 10.91 Tf
(SID)Tj
/T1_9 7.97 Tf
22.63 -1.64 Td
(c)Tj
/T1_6 10.91 Tf
4.73 1.64 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(C)Tj
/T1_6 10.91 Tf
(jj)Tj
/T1_1 10.91 Tf
11.78 0 Td
(c)Tj
/T1_2 7.97 Tf
5.73 -1.64 Td
(i)Tj
/T1_6 10.91 Tf
3.38 1.64 Td
(jj)Tj
/T1_3 10.91 Tf
6.06 0 Td
(v)Tj
/T1_2 7.97 Tf
5.29 -1.64 Td
(i)Tj
/T1_6 10.91 Tf
3.38 1.64 Td
(g)Tj
/T1_0 10.91 Tf
9.54 0 Td
[(for)-374(1)]TJ
/T1_6 10.91 Tf
26.38 0 Td
(\267)Tj
/T1_3 10.91 Tf
12.27 0 Td
(i)Tj
/T1_6 10.91 Tf
7.54 0 Td
(\267)Tj
/T1_3 10.91 Tf
12.27 0 Td
(n)Tj
/T1_2 7.97 Tf
6.54 -1.64 Td
(c)Tj
/T1_0 10.91 Tf
8.26 1.64 Td
(to)Tj
-458.18 -21.92 Td
[(subgroup)-333(con)27(trollers)]TJ
/T1_1 10.91 Tf
100.49 0 Td
(S)Tj
/T1_2 7.97 Tf
5.72 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
3.38 1.64 Td
(.)Tj
-109.59 -21.92 Td
[(Round)-333(2)]TJ
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 0 -248.28 cm
0 0 m
40.75 0 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 112.7614 522.9909 Tm
(:)Tj
1.0003 0 0 1.0003 72 769.82 Tm
49.325 -246.76 Td
[(Eac)27(h)-364(subgroup)-365(con)26(troller)]TJ
/T1_1 10.91 Tf
124.335 0 Td
(S)Tj
/T1_2 7.97 Tf
5.73 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
7.36 1.63 Td
[(for)-365(1)]TJ
/T1_6 10.91 Tf
26.11 0 Td
(\267)Tj
/T1_3 10.91 Tf
12.09 0 Td
(i)Tj
/T1_6 10.91 Tf
7.37 0 Td
(\267)Tj
/T1_3 10.91 Tf
12.09 0 Td
(n)Tj
/T1_2 7.97 Tf
6.55 -1.63 Td
(c)Tj
/T1_0 10.91 Tf
8.15 1.63 Td
[(\257rst)-364(decrypts)]TJ
/T1_1 10.91 Tf
67.22 0 Td
(c)Tj
/T1_2 7.97 Tf
5.73 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
7.36 1.63 Td
[(and)-365(c)27(hec)28(ks)-365(if)-365(the)-365(iden)27(tities)]TJ
/T1_1 10.91 Tf
-339.42 -21.91 Td
(C)Tj
/T1_0 10.91 Tf
(,)Tj
/T1_1 10.91 Tf
13.2 0 Td
(S)Tj
/T1_2 7.97 Tf
5.72 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
7.66 1.64 Td
(and)Tj
/T1_1 10.91 Tf
21.86 0 Td
(SID)Tj
/T1_9 7.97 Tf
17.17 -1.64 Td
(c)Tj
/T1_0 10.91 Tf
9.01 1.64 Td
[(are)-392(decrypted)-393(correctly)82(.)-620(If)-393(the)-392(iden)26(tities)-391(are)-393(not)-392(correct,)]TJ
/T1_1 10.91 Tf
278.37 0 Td
(S)Tj
/T1_2 7.97 Tf
5.73 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
7.66 1.64 Td
(rejects)Tj
/T1_1 10.91 Tf
34.97 0 Td
(C)Tj
/T1_0 10.91 Tf
5.72 0 Td
[(.)-622(Otherwise,)]TJ
/T1_1 10.91 Tf
-407.07 -21.92 Td
(S)Tj
/T1_2 7.97 Tf
5.73 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
7.58 1.64 Td
[(uses)-385(passw)26(ord)]TJ
/T1_11 10.91 Tf
71.4 0 Td
[(p)28(w)]TJ
/T1_2 7.97 Tf
12.93 -2.62 Td
(i)Tj
/T1_0 10.91 Tf
7.59 2.62 Td
[(to)-385(c)27(hec)27(k)-384(if)]TJ
/T1_3 10.91 Tf
54.42 0 Td
(v)Tj
/T1_2 7.97 Tf
5.29 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
7.36 1.64 Td
(=)Tj
/T1_11 10.91 Tf
12.46 0 Td
(H)Tj
/T1_7 7.97 Tf
7.73 -1.64 Td
(1)Tj
/T1_0 10.91 Tf
4.73 1.64 Td
(\()Tj
/T1_11 10.91 Tf
[(p)27(w)]TJ
/T1_2 7.97 Tf
17.18 -2.62 Td
(i)Tj
/T1_6 10.91 Tf
3.38 2.62 Td
(jj)Tj
/T1_3 10.91 Tf
6.06 0 Td
(\277)Tj
/T1_9 7.97 Tf
4.76 -1.64 Td
(C)Tj
/T1_6 10.91 Tf
4.74 1.64 Td
(jj)Tj
/T1_0 10.91 Tf
6.63 0 Td
(\271)Tj
/T1_3 10.91 Tf
-0.58 0 Td
(\277)Tj
/T1_2 7.97 Tf
4.77 -1.64 Td
(i)Tj
/T1_6 10.91 Tf
3.38 1.64 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(SID)Tj
/T1_9 7.97 Tf
17.18 -1.64 Td
(c)Tj
/T1_0 10.91 Tf
4.73 1.64 Td
[(\).)-601(If)-386(the)-385(c)27(hec)27(k)-384(is)-386(incorrect,)]TJ
/T1_1 10.91 Tf
135.4 0 Td
(S)Tj
/T1_2 7.97 Tf
5.72 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
7.59 1.64 Td
(rejects)Tj
/T1_1 10.91 Tf
34.9 0 Td
(C)Tj
/T1_0 10.91 Tf
5.72 0 Td
(.)Tj
-464.84 -21.92 Td
(Otherwise,)Tj
/T1_1 10.91 Tf
54.62 0 Td
(S)Tj
/T1_2 7.97 Tf
5.73 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
7.01 1.63 Td
[(uses)-333(the)-333(subgroup)-334(k)27(ey)]TJ
/T1_3 10.91 Tf
108.97 0 Td
(K)Tj
/T1_2 7.97 Tf
9.27 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
7.01 1.63 Td
[(computed)-333(in)-333(Phase)-334(1)-333(Round)-333(3)-334(to)-333(compute:)]TJ
/T1_3 10.91 Tf
-93.11 -39.64 Td
(y)Tj
/T1_2 7.97 Tf
5.34 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
6.41 1.64 Td
(=)Tj
/T1_3 10.91 Tf
11.52 0 Td
(g)Tj
/T1_12 7.97 Tf
5.59 4.5 Td
(H)Tj
/T1_13 5.98 Tf
5.98 -1.1 Td
(2)Tj
/T1_7 7.97 Tf
4.15 1.1 Td
(\()Tj
/T1_2 7.97 Tf
(K)Tj
/T1_4 5.98 Tf
10.43 -1.21 Td
(i)Tj
/T1_7 7.97 Tf
3.16 1.21 Td
(\))Tj
/T1_0 10.91 Tf
6.82 -4.5 Td
[(mo)-27(d)]TJ
/T1_3 10.91 Tf
23.93 0 Td
(p)Tj
/T1_0 10.91 Tf
11.96 0 Td
(,)Tj
/T1_3 10.91 Tf
9.5 0 Td
(y)Tj
/T1_10 7.97 Tf
5.73 4.5 Td
(\244)Tj
/T1_2 7.97 Tf
-0.39 -7.2 Td
(i)Tj
/T1_0 10.91 Tf
8.15 2.7 Td
(=)Tj
/T1_3 10.91 Tf
11.52 0 Td
(y)Tj
/T1_2 7.97 Tf
5.34 -1.64 Td
(i)Tj
/T1_6 10.91 Tf
5.81 1.64 Td
(\242)Tj
/T1_3 10.91 Tf
5.45 0 Td
(h)Tj
/T1_12 7.97 Tf
6.28 4.5 Td
(H)Tj
/T1_13 5.98 Tf
5.98 -1.1 Td
(1)Tj
/T1_7 7.97 Tf
4.15 1.1 Td
(\()Tj
/T1_9 7.97 Tf
(SID)Tj
/T1_9 5.98 Tf
15.99 -0.99 Td
(c)Tj
/T1_10 7.97 Tf
3.67 0.99 Td
(jj)Tj
/T1_9 7.97 Tf
4.71 0 Td
(S)Tj
/T1_4 5.98 Tf
4.23 -1.21 Td
(i)Tj
/T1_10 7.97 Tf
3.16 1.21 Td
(jj)Tj
/T1_9 7.97 Tf
(C)Tj
/T1_10 7.97 Tf
8.94 0 Td
(jj)Tj
/T1_12 7.97 Tf
[(p)29(w)]TJ
/T1_4 5.98 Tf
14.74 -2.04 Td
(i)Tj
/T1_10 7.97 Tf
3.16 2.04 Td
(jj)Tj
/T1_2 7.97 Tf
(\277)Tj
/T1_9 5.98 Tf
8.46 -0.99 Td
(C)Tj
/T1_10 7.97 Tf
3.67 0.99 Td
(jj)Tj
/T1_7 7.97 Tf
5.16 0 Td
(\271)Tj
/T1_2 7.97 Tf
-0.46 0 Td
(\277)Tj
/T1_4 5.98 Tf
3.76 -1.21 Td
(i)Tj
/T1_7 7.97 Tf
3.16 1.21 Td
(\))Tj
/T1_3 10.91 Tf
-177.34 -29.4 Td
(\271)Tj
/T1_2 7.97 Tf
6.57 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
6.41 1.64 Td
(=)Tj
/T1_11 10.91 Tf
11.51 0 Td
[(MA)27(C)]TJ
/T1_2 7.97 Tf
23.48 -1.78 Td
(ak)Tj
/T1_4 5.98 Tf
8.91 -1.22 Td
(i)Tj
/T1_0 10.91 Tf
3.66 3 Td
(\()Tj
/T1_3 10.91 Tf
(\277)Tj
/T1_9 7.97 Tf
9 -1.64 Td
(C)Tj
/T1_6 10.91 Tf
4.74 1.64 Td
(jj)Tj
/T1_0 10.91 Tf
6.63 0 Td
(\271)Tj
/T1_3 10.91 Tf
-0.58 0 Td
(\277)Tj
/T1_2 7.97 Tf
4.77 -1.64 Td
(i)Tj
/T1_6 10.91 Tf
3.38 1.64 Td
(jj)Tj
/T1_3 10.91 Tf
6.06 0 Td
(y)Tj
/T1_10 7.97 Tf
5.74 4.5 Td
(\244)Tj
/T1_2 7.97 Tf
-0.39 -7.2 Td
(i)Tj
/T1_6 10.91 Tf
5.12 2.7 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(SID)Tj
/T1_9 7.97 Tf
17.18 -1.64 Td
(c)Tj
/T1_6 10.91 Tf
4.73 1.64 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(S)Tj
/T1_2 7.97 Tf
5.72 -1.64 Td
(i)Tj
/T1_6 10.91 Tf
3.38 1.64 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(C)Tj
/T1_6 10.91 Tf
(jj)Tj
/T1_0 10.91 Tf
11.79 0 Td
(00\))Tj
-163.39 -24.91 Td
(\271)Tj
/T1_3 10.91 Tf
-0.86 0 Td
(\271)Tj
/T1_2 7.97 Tf
6.57 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
6.41 1.63 Td
(=)Tj
/T1_11 10.91 Tf
11.51 0 Td
[(MA)27(C)]TJ
/T1_2 7.97 Tf
23.48 -1.78 Td
(ak)Tj
/T1_4 5.98 Tf
8.91 -1.21 Td
(i)Tj
/T1_0 10.91 Tf
3.66 2.99 Td
(\()Tj
/T1_3 10.91 Tf
(\277)Tj
/T1_9 7.97 Tf
9.01 -1.63 Td
(C)Tj
/T1_6 10.91 Tf
4.73 1.63 Td
(jj)Tj
/T1_0 10.91 Tf
6.63 0 Td
(\271)Tj
/T1_3 10.91 Tf
-0.57 0 Td
(\277)Tj
/T1_2 7.97 Tf
4.76 -1.63 Td
(i)Tj
/T1_6 10.91 Tf
3.38 1.63 Td
(jj)Tj
/T1_3 10.91 Tf
6.06 0 Td
(y)Tj
/T1_2 7.97 Tf
5.35 -1.63 Td
(i)Tj
/T1_6 10.91 Tf
3.38 1.63 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(SID)Tj
/T1_9 7.97 Tf
17.18 -1.63 Td
(c)Tj
/T1_6 10.91 Tf
4.73 1.63 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(S)Tj
/T1_2 7.97 Tf
5.72 -1.63 Td
(i)Tj
/T1_6 10.91 Tf
3.38 1.63 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(C)Tj
/T1_6 10.91 Tf
(jj)Tj
/T1_0 10.91 Tf
11.79 0 Td
(01\))Tj
-333.31 -39.64 Td
[(Finally)83(,)]TJ
/T1_1 10.91 Tf
39.23 0 Td
(S)Tj
/T1_2 7.97 Tf
5.73 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
7.01 1.64 Td
(sends)Tj
/T1_6 10.91 Tf
29.21 0 Td
(f)Tj
/T1_1 10.91 Tf
(SID)Tj
/T1_9 7.97 Tf
22.63 -1.64 Td
(c)Tj
/T1_6 10.91 Tf
4.73 1.64 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(S)Tj
/T1_2 7.97 Tf
5.72 -1.64 Td
(i)Tj
/T1_6 10.91 Tf
3.38 1.64 Td
(jj)Tj
/T1_3 10.91 Tf
6.06 0 Td
(y)Tj
/T1_10 7.97 Tf
5.74 3.96 Td
(\244)Tj
/T1_2 7.97 Tf
-0.39 -7.02 Td
(i)Tj
/T1_6 10.91 Tf
5.12 3.06 Td
(jj)Tj
/T1_3 10.91 Tf
6.06 0 Td
(\271)Tj
/T1_2 7.97 Tf
6.57 -1.64 Td
(i)Tj
/T1_6 10.91 Tf
3.38 1.64 Td
(jj)Tj
/T1_0 10.91 Tf
6.92 0 Td
(\271)Tj
/T1_3 10.91 Tf
-0.86 0 Td
(\271)Tj
/T1_2 7.97 Tf
6.57 -1.64 Td
(i)Tj
/T1_6 10.91 Tf
3.38 1.64 Td
(g)Tj
/T1_0 10.91 Tf
9.09 0 Td
(to)Tj
/T1_1 10.91 Tf
13.33 0 Td
(C)Tj
/T1_0 10.91 Tf
(.)Tj
-194.67 -21.92 Td
[(Round)-333(3)]TJ
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 0 -465.04 cm
0 0 m
40.75 0 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 112.7614 306.1702 Tm
(:)Tj
1.0003 0 0 1.0003 72 769.82 Tm
51.889 -463.52 Td
[(Main)-483(con)26(troller)]TJ
/T1_1 10.91 Tf
80.281 0 Td
(C)Tj
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10.99 0 Td
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22.63 -1.64 Td
(c)Tj
/T1_5 10.91 Tf
4.73 1.64 Td
(jj)Tj
/T1_8 10.91 Tf
6.06 0 Td
(UID)Tj
/T1_2 7.97 Tf
18.4 -1.64 Td
(C)Tj
/T1_5 10.91 Tf
4.73 1.64 Td
(jj)Tj
/T1_9 10.91 Tf
6.06 0 Td
(C)Tj
/T1_5 10.91 Tf
(jj)Tj
/T1_1 10.91 Tf
11.79 0 Td
(y)Tj
/T1_2 7.97 Tf
5.35 -1.64 Td
(C)Tj
/T1_5 10.91 Tf
4.73 1.64 Td
(jj)Tj
/T1_0 10.91 Tf
6.92 0 Td
(^)Tj
/T1_1 10.91 Tf
-0.86 0 Td
(\271)Tj
/T1_3 7.97 Tf
6.57 -1.64 Td
(i)Tj
/T1_5 10.91 Tf
3.38 1.64 Td
(jj)Tj
/T1_0 10.91 Tf
6.19 0 Td
(^)Tj
/T1_9 10.91 Tf
-0.13 0 Td
(c)Tj
/T1_3 7.97 Tf
5.72 -1.64 Td
(i)Tj
/T1_5 10.91 Tf
3.38 1.64 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(\265)Tj
/T1_2 7.97 Tf
5.12 -1.64 Td
(C)Tj
/T1_5 10.91 Tf
4.73 1.64 Td
(g)Tj
/T1_0 10.91 Tf
9.09 0 Td
[(for)-333(1)]TJ
/T1_5 10.91 Tf
25.17 0 Td
(\267)Tj
/T1_1 10.91 Tf
11.52 0 Td
(i)Tj
/T1_5 10.91 Tf
6.78 0 Td
(\267)Tj
/T1_1 10.91 Tf
11.52 0 Td
(n)Tj
/T1_3 7.97 Tf
6.54 -1.64 Td
(c)Tj
/T1_0 10.91 Tf
4.17 1.64 Td
(.)Tj
/T1_10 10.91 Tf
-378.29 -27.9 Td
[(Phase)-383(3:)-511(Key)-383(Distribution)]TJ
/T1_0 10.91 Tf
0 -27.89 TD
[(Round)-333(1)]TJ
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 0 -247.31 cm
0 0 m
40.75 0 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 112.7614 523.9612 Tm
(:)Tj
1.0003 0 0 1.0003 72 769.82 Tm
48.452 -245.79 Td
[(Eac)27(h)]TJ
/T1_9 10.91 Tf
26.778 0 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
6.68 1.63 Td
[(for)-302(1)]TJ
/T1_5 10.91 Tf
24.84 0 Td
(\267)Tj
/T1_1 10.91 Tf
11.51 0 Td
(i)Tj
/T1_5 10.91 Tf
6.78 0 Td
(\267)Tj
/T1_1 10.91 Tf
11.52 0 Td
(n)Tj
/T1_3 7.97 Tf
6.54 -1.63 Td
(c)Tj
/T1_0 10.91 Tf
7.47 1.63 Td
[(\257rst)-302(c)27(hec)28(ks)-302(if)-381(^)]TJ
/T1_1 10.91 Tf
65.18 0 Td
(\271)Tj
/T1_3 7.97 Tf
6.57 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
6.41 1.63 Td
(=)Tj
/T1_8 10.91 Tf
11.51 0 Td
[(MA)27(C)]TJ
/T1_3 7.97 Tf
23.48 -1.77 Td
(ak)Tj
/T1_6 5.98 Tf
8.91 -1.22 Td
(i)Tj
/T1_0 10.91 Tf
3.66 2.99 Td
(\()Tj
/T1_1 10.91 Tf
(\277)Tj
/T1_2 7.97 Tf
9.01 -1.63 Td
(C)Tj
/T1_5 10.91 Tf
4.73 1.63 Td
(jj)Tj
/T1_0 10.91 Tf
6.63 0 Td
(\271)Tj
/T1_1 10.91 Tf
-0.57 0 Td
(\277)Tj
/T1_3 7.97 Tf
4.76 -1.63 Td
(i)Tj
/T1_5 10.91 Tf
3.38 1.63 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(y)Tj
/T1_2 7.97 Tf
5.35 -1.63 Td
(C)Tj
/T1_5 10.91 Tf
4.73 1.63 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(\265)Tj
/T1_2 7.97 Tf
5.12 -1.63 Td
(C)Tj
/T1_5 10.91 Tf
4.73 1.63 Td
(jj)Tj
/T1_9 10.91 Tf
6.06 0 Td
(SID)Tj
/T1_2 7.97 Tf
17.18 -1.63 Td
(c)Tj
/T1_5 10.91 Tf
4.73 1.63 Td
(jj)Tj
/T1_9 10.91 Tf
6.06 0 Td
(C)Tj
/T1_5 10.91 Tf
5.72 0 Td
(jj)Tj
/T1_9 10.91 Tf
6.06 0 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.63 Td
(i)Tj
/T1_5 10.91 Tf
3.38 1.63 Td
(jj)Tj
/T1_0 10.91 Tf
6.06 0 Td
[(11\))-302(is)-302(correct.)]TJ
-402.99 -21.91 Td
[(If)-407(the)-408(equation)-408(is)-407(incorrect,)]TJ
/T1_9 10.91 Tf
137.98 0 Td
(S)Tj
/T1_3 7.97 Tf
5.72 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
7.83 1.64 Td
[(rejects)-407(malicious)-408(main)-408(con)27(troller)]TJ
/T1_9 10.91 Tf
161.59 0 Td
(C)Tj
/T1_0 10.91 Tf
[(.)-667(Otherwise,)]TJ
/T1_9 10.91 Tf
71.67 0 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
7.83 1.64 Td
(computes)Tj
/T1_1 10.91 Tf
49.34 0 Td
(t)Tj
/T1_3 7.97 Tf
3.94 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
7.76 1.64 Td
(=)Tj
/T1_1 10.91 Tf
-459.39 -21.92 Td
(y)Tj
/T1_11 7.97 Tf
5.74 5.75 Td
(H)Tj
/T1_12 5.98 Tf
5.97 -1.11 Td
(2)Tj
/T1_7 7.97 Tf
4.15 1.11 Td
(\()Tj
/T1_3 7.97 Tf
3.3 0 Td
(K)Tj
/T1_6 5.98 Tf
7.14 -1.22 Td
(i)Tj
/T1_7 7.97 Tf
3.16 1.22 Td
(\))Tj
/T1_2 7.97 Tf
-24.11 -8.61 Td
(C)Tj
/T1_0 10.91 Tf
30.93 2.86 Td
[(mo)-27(d)]TJ
/T1_1 10.91 Tf
23.93 0 Td
(p)Tj
/T1_0 10.91 Tf
8.92 0 Td
[(and)-315(uses)]TJ
/T1_1 10.91 Tf
43.95 0 Td
(t)Tj
/T1_3 7.97 Tf
3.94 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
6.82 1.64 Td
[(to)-314(decrypt)-327(^)]TJ
/T1_9 10.91 Tf
52.64 0 Td
(c)Tj
/T1_3 7.97 Tf
5.73 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
6.81 1.64 Td
[(and)-315(obtains)-314(the)-315(\257nal)-315(group)-315(k)26(ey)]TJ
/T1_1 10.91 Tf
151.88 0 Td
(K)Tj
/T1_0 10.91 Tf
10.04 0 Td
[(,)-318(iden)27(tit)27(y)]TJ
/T1_9 10.91 Tf
46.6 0 Td
(C)Tj
/T1_0 10.91 Tf
5.72 0 Td
(,)Tj
/T1_1 10.91 Tf
6.51 0 Td
(y)Tj
/T1_3 7.97 Tf
5.34 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
6.82 1.64 Td
(and)Tj
/T1_9 10.91 Tf
21 0 Td
(SID)Tj
/T1_2 7.97 Tf
17.18 -1.64 Td
(c)Tj
/T1_0 10.91 Tf
4.73 1.64 Td
(.)Tj
-464.84 -21.92 Td
[(If)-301(the)-301(iden)27(tit)27(y)]TJ
/T1_9 10.91 Tf
68.94 0 Td
(C)Tj
/T1_0 10.91 Tf
5.72 0 Td
(,)Tj
/T1_1 10.91 Tf
6.39 0 Td
(y)Tj
/T1_3 7.97 Tf
5.34 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
6.67 1.63 Td
(and)Tj
/T1_9 10.91 Tf
20.86 0 Td
(SID)Tj
/T1_2 7.97 Tf
17.18 -1.63 Td
(c)Tj
/T1_0 10.91 Tf
8.01 1.63 Td
[(are)-301(not)-302(decrypted)-301(correctly)82(,)-306(then)]TJ
/T1_9 10.91 Tf
158.71 0 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
6.66 1.63 Td
[(rejects)-314(^)]TJ
/T1_9 10.91 Tf
33.98 0 Td
(c)Tj
/T1_3 7.97 Tf
5.72 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
3.39 1.63 Td
[(.)-433(Otherwise,)]TJ
/T1_9 10.91 Tf
62.1 0 Td
(S)Tj
/T1_3 7.97 Tf
5.72 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
6.67 1.63 Td
(con\257rms)Tj
-427.79 -21.91 Td
[(and)-450(accepts)-451(the)-450(\257nal)-451(group)-451(k)27(ey)]TJ
/T1_1 10.91 Tf
160.76 0 Td
(K)Tj
/T1_0 10.91 Tf
14.95 0 Td
[(if)-451(the)-450(k)27(ey)-450(con\257rmation)-451(co)-27(de)]TJ
/T1_1 10.91 Tf
143.67 0 Td
(\265)Tj
/T1_2 7.97 Tf
5.12 -1.64 Td
(C)Tj
/T1_0 10.91 Tf
9.89 1.64 Td
(=)Tj
/T1_8 10.91 Tf
13.64 0 Td
(H)Tj
/T1_7 7.97 Tf
7.73 -1.64 Td
(1)Tj
/T1_0 10.91 Tf
4.73 1.64 Td
(\()Tj
/T1_9 10.91 Tf
(SID)Tj
/T1_2 7.97 Tf
21.42 -1.64 Td
(c)Tj
/T1_5 10.91 Tf
4.73 1.64 Td
(jj)Tj
/T1_8 10.91 Tf
6.06 0 Td
(UID)Tj
/T1_2 7.97 Tf
18.4 -1.64 Td
(C)Tj
/T1_5 10.91 Tf
4.73 1.64 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(K)Tj
/T1_5 10.91 Tf
10.04 0 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(\277)Tj
/T1_2 7.97 Tf
4.77 -1.64 Td
(C)Tj
/T1_5 10.91 Tf
4.73 1.64 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(y)Tj
/T1_2 7.97 Tf
5.35 -1.64 Td
(C)Tj
/T1_0 10.91 Tf
4.73 1.64 Td
(\))Tj
-463.63 -21.92 Td
[(holds.)-459(Next,)]TJ
/T1_9 10.91 Tf
62.7 0 Td
(S)Tj
/T1_3 7.97 Tf
5.72 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
7.07 1.64 Td
(encrypts)Tj
/T1_1 10.91 Tf
44.08 0 Td
(K)Tj
/T1_3 7.97 Tf
9.26 -1.64 Td
(i)Tj
/T1_5 10.91 Tf
3.38 1.64 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(K)Tj
/T1_5 10.91 Tf
10.04 0 Td
(jj)Tj
/T1_9 10.91 Tf
6.06 0 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.64 Td
(i)Tj
/T1_5 10.91 Tf
3.38 1.64 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(z)Tj
/T1_3 7.97 Tf
5.07 -1.64 Td
(i;j)Tj
/T1_5 10.91 Tf
9.61 1.64 Td
(jj)Tj
/T1_9 10.91 Tf
6.06 0 Td
(SID)Tj
/T1_3 7.97 Tf
17.18 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
7.07 1.64 Td
(using)Tj
/T1_1 10.91 Tf
28.59 0 Td
(t)Tj
/T1_3 7.97 Tf
3.94 -1.64 Td
(i;j)Tj
/T1_0 10.91 Tf
13.3 1.64 Td
[(and)-338(obtains)-351(^)]TJ
/T1_9 10.91 Tf
59.55 0 Td
(c)Tj
/T1_3 7.97 Tf
5.73 -1.64 Td
(i;j)Tj
/T1_0 10.91 Tf
12.73 1.64 Td
(=)Tj
/T1_5 10.91 Tf
11.6 0 Td
(E)Tj
/T1_3 7.97 Tf
5.76 -1.64 Td
(t)Tj
/T1_6 5.98 Tf
3.06 -1.21 Td
(i;j)Tj
/T1_0 10.91 Tf
9.33 2.85 Td
(\()Tj
/T1_1 10.91 Tf
(K)Tj
/T1_3 7.97 Tf
13.5 -1.64 Td
(i)Tj
/T1_5 10.91 Tf
3.38 1.64 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(K)Tj
/T1_5 10.91 Tf
10.04 0 Td
(jj)Tj
/T1_9 10.91 Tf
6.06 0 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.64 Td
(i)Tj
/T1_5 10.91 Tf
3.38 1.64 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(z)Tj
/T1_3 7.97 Tf
5.07 -1.64 Td
(i;j)Tj
/T1_5 10.91 Tf
9.61 1.64 Td
(jj)Tj
/T1_9 10.91 Tf
6.06 0 Td
(SID)Tj
/T1_3 7.97 Tf
17.18 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
3.38 1.64 Td
(\))Tj
-463.63 -21.92 Td
[(for)-333(1)]TJ
/T1_5 10.91 Tf
25.17 0 Td
(\267)Tj
/T1_1 10.91 Tf
11.52 0 Td
(j)Tj
/T1_5 10.91 Tf
8.14 0 Td
(\267)Tj
/T1_1 10.91 Tf
11.51 0 Td
(n)Tj
/T1_3 7.97 Tf
6.55 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
3.38 1.63 Td
(.)Tj
/T1_9 10.91 Tf
7.88 0 Td
(S)Tj
/T1_3 7.97 Tf
5.72 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
7.02 1.63 Td
[(then)-333(computes)-333(the)-333(k)26(ey)-332(con\257rmation)-333(co)-28(de)]TJ
/T1_1 10.91 Tf
200.64 0 Td
(\265)Tj
/T1_3 7.97 Tf
5.12 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
7.02 1.63 Td
[(and)-411(^)]TJ
/T1_1 10.91 Tf
21.2 0 Td
(\271)Tj
/T1_3 7.97 Tf
6.57 -1.63 Td
(i;j)Tj
/T1_0 10.91 Tf
13.25 1.63 Td
[(for)-333(1)]TJ
/T1_5 10.91 Tf
25.18 0 Td
(\267)Tj
/T1_1 10.91 Tf
11.51 0 Td
(j)Tj
/T1_5 10.91 Tf
8.15 0 Td
(\267)Tj
/T1_1 10.91 Tf
11.51 0 Td
(n)Tj
/T1_3 7.97 Tf
6.54 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
3.38 1.63 Td
(:)Tj
/T1_1 10.91 Tf
-281.63 -39.64 Td
(\265)Tj
/T1_3 7.97 Tf
5.12 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
13.34 1.64 Td
(=)Tj
/T1_8 10.91 Tf
18.44 0 Td
(H)Tj
/T1_7 7.97 Tf
7.72 -1.64 Td
(1)Tj
/T1_0 10.91 Tf
4.73 1.64 Td
(\()Tj
/T1_9 10.91 Tf
4.25 0 Td
(SID)Tj
/T1_3 7.97 Tf
17.17 -1.64 Td
(i)Tj
/T1_5 10.91 Tf
3.38 1.64 Td
(jj)Tj
/T1_9 10.91 Tf
6.06 0 Td
(UID)Tj
/T1_3 7.97 Tf
17.18 -1.64 Td
(i)Tj
/T1_5 10.91 Tf
3.38 1.64 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(K)Tj
/T1_3 7.97 Tf
9.26 -1.64 Td
(i)Tj
/T1_5 10.91 Tf
3.38 1.64 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(K)Tj
/T1_5 10.91 Tf
10.04 0 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(\277)Tj
/T1_3 7.97 Tf
4.77 -1.64 Td
(i)Tj
/T1_5 10.91 Tf
3.38 1.64 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(z)Tj
/T1_3 7.97 Tf
5.07 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
3.38 1.64 Td
(\))Tj
-171.12 -24.9 Td
(^)Tj
/T1_1 10.91 Tf
-0.86 0 Td
(\271)Tj
/T1_3 7.97 Tf
6.57 -1.64 Td
(i;j)Tj
/T1_0 10.91 Tf
19.58 1.64 Td
(=)Tj
/T1_8 10.91 Tf
18.44 0 Td
[(MA)27(C)]TJ
/T1_3 7.97 Tf
23.48 -1.78 Td
(ak)Tj
/T1_6 5.98 Tf
8.9 -1.22 Td
(i;j)Tj
/T1_0 10.91 Tf
9.33 3 Td
(\()Tj
/T1_1 10.91 Tf
(\277)Tj
/T1_3 7.97 Tf
9.01 -1.64 Td
(i)Tj
/T1_5 10.91 Tf
3.38 1.64 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(\277)Tj
/T1_3 7.97 Tf
4.77 -1.64 Td
(i;j)Tj
/T1_5 10.91 Tf
9.61 1.64 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(z)Tj
/T1_3 7.97 Tf
5.07 -1.64 Td
(i)Tj
/T1_5 10.91 Tf
3.38 1.64 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(\265)Tj
/T1_3 7.97 Tf
5.12 -1.64 Td
(i)Tj
/T1_5 10.91 Tf
3.38 1.64 Td
(jj)Tj
/T1_9 10.91 Tf
6.06 0 Td
(SID)Tj
/T1_3 7.97 Tf
17.18 -1.64 Td
(i)Tj
/T1_5 10.91 Tf
3.38 1.64 Td
(jj)Tj
/T1_9 10.91 Tf
6.06 0 Td
(S)Tj
/T1_3 7.97 Tf
5.72 -1.64 Td
(i)Tj
/T1_5 10.91 Tf
3.38 1.64 Td
(jj)Tj
/T1_9 10.91 Tf
6.06 0 Td
(U)Tj
/T1_3 7.97 Tf
5.73 -1.64 Td
(i;j)Tj
/T1_5 10.91 Tf
9.61 1.64 Td
(jj)Tj
/T1_0 10.91 Tf
6.06 0 Td
(11\))Tj
-335.08 -39.65 Td
(where)Tj
/T1_9 10.91 Tf
32.06 0 Td
(UID)Tj
/T1_3 7.97 Tf
17.18 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
7.29 1.63 Td
(=)Tj
/T1_9 10.91 Tf
12.39 0 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.63 Td
(i)Tj
/T1_5 10.91 Tf
3.38 1.63 Td
(jj)Tj
/T1_9 10.91 Tf
6.06 0 Td
(U)Tj
/T1_3 7.97 Tf
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(+)Tj
/T1_2 10.91 Tf
8.85 0 Td
(m)Tj
/T1_1 10.91 Tf
-458.29 -21.92 Td
[(are)-302(the)-303(new)-302(users,)-309(and)-302(new)-303(\257nal)-302(group)-303(k)27(ey)]TJ
/T1_2 10.91 Tf
205.38 0 Td
(K)Tj
/T1_8 7.97 Tf
10.04 3.96 Td
(0)Tj
/T1_1 10.91 Tf
6.09 -3.96 Td
[(for)-302(all)-303(users)-302(in)-303(the)-302(net)26(w)28(ork)-301(to)-303(prev)27(en)28(t)-302(the)-302(new)-303(users)]TJ
-221.51 -21.91 Td
[(from)-270(kno)27(wing)-269(previous)-270(group)-270(comm)26(unications.)-422(W)82(e)-269(assume)-270(that)-270(eac)27(h)-269(new)-271(user)]TJ
/T1_4 10.91 Tf
370.78 0 Td
(U)Tj
/T1_5 7.97 Tf
5.72 -1.78 Td
[(J)23(;k)]TJ
/T1_1 10.91 Tf
14.85 1.78 Td
(for)Tj
/T1_2 10.91 Tf
16 0 Td
(n)Tj
/T1_5 7.97 Tf
6.55 -1.69 Td
(J)Tj
/T1_1 10.91 Tf
6.92 1.69 Td
[(+)-95(1)]TJ
/T1_3 10.91 Tf
18.01 0 Td
(\267)Tj
/T1_2 10.91 Tf
11.51 0 Td
(k)Tj
/T1_3 10.91 Tf
9.05 0 Td
(\267)Tj
/T1_2 10.91 Tf
-459.39 -21.92 Td
(n)Tj
/T1_5 7.97 Tf
6.55 -1.69 Td
(J)Tj
/T1_1 10.91 Tf
7.31 1.69 Td
(+)Tj
/T1_2 10.91 Tf
9.93 0 Td
(m)Tj
/T1_1 10.91 Tf
12.73 0 Td
[(shares)-288(passw)27(ord)]TJ
/T1_10 10.91 Tf
79 0 Td
[(p)27(w)]TJ
/T1_5 7.97 Tf
12.94 -2.62 Td
[(J)24(;k)]TJ
/T1_1 10.91 Tf
15.05 2.62 Td
[(with)-288(subgroup)-288(con)27(troller)]TJ
/T1_4 10.91 Tf
119.56 0 Td
(S)Tj
/T1_5 7.97 Tf
5.72 -1.69 Td
(J)Tj
/T1_1 10.91 Tf
5.88 1.69 Td
[(.)-429(W)83(e)-288(also)-288(assume)-289(that)]TJ
/T1_4 10.91 Tf
107.73 0 Td
(U)Tj
/T1_5 7.97 Tf
5.72 -1.77 Td
[(J)23(;k)]TJ
/T1_1 10.91 Tf
15.05 1.77 Td
(and)Tj
/T1_4 10.91 Tf
20.72 0 Td
(S)Tj
/T1_5 7.97 Tf
5.73 -1.69 Td
(J)Tj
/T1_1 10.91 Tf
9.02 1.69 Td
(shares)Tj
-438.64 -21.91 Td
[(pairwise)-395(secret)-395(k)26(ey)]TJ
/T1_2 10.91 Tf
95.22 0 Td
(\267)Tj
/T1_5 7.97 Tf
6.28 -1.78 Td
[(J)23(;k)]TJ
/T1_1 10.91 Tf
11.9 1.78 Td
[(,)-411(whic)27(h)-394(is)-396(used)-395(to)-396(deriv)27(e)-394(authen)26(tication)-394(k)27(ey)]TJ
/T1_2 10.91 Tf
216.9 0 Td
(ak)Tj
/T1_5 7.97 Tf
11.44 -1.78 Td
[(J)24(;k)]TJ
/T1_1 10.91 Tf
16.06 1.78 Td
(=)Tj
/T1_10 10.91 Tf
12.64 0 Td
(H)Tj
/T1_6 7.97 Tf
7.72 -1.64 Td
(2)Tj
/T1_1 10.91 Tf
4.74 1.64 Td
(\()Tj
/T1_2 10.91 Tf
(\267)Tj
/T1_5 7.97 Tf
10.52 -1.78 Td
[(J)24(;k)]TJ
/T1_3 10.91 Tf
11.9 1.78 Td
(jj)Tj
/T1_4 10.91 Tf
6.06 0 Td
(U)Tj
/T1_5 7.97 Tf
5.73 -1.78 Td
[(J)24(;k)]TJ
/T1_3 10.91 Tf
11.9 1.78 Td
(jj)Tj
/T1_4 10.91 Tf
6.06 0 Td
(S)Tj
/T1_5 7.97 Tf
5.72 -1.69 Td
(J)Tj
/T1_3 10.91 Tf
5.87 1.69 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(01\))Tj
-452.72 -21.92 Td
[(and)-332(the)-332(encryption)-332(k)26(ey)]TJ
/T1_2 10.91 Tf
113.89 0 Td
(ek)Tj
/T1_5 7.97 Tf
10.76 -1.78 Td
[(J)24(;k)]TJ
/T1_1 10.91 Tf
14.93 1.78 Td
(=)Tj
/T1_10 10.91 Tf
11.51 0 Td
(H)Tj
/T1_6 7.97 Tf
7.73 -1.64 Td
(2)Tj
/T1_1 10.91 Tf
4.73 1.64 Td
(\()Tj
/T1_2 10.91 Tf
(\267)Tj
/T1_5 7.97 Tf
10.52 -1.78 Td
[(J)23(;k)]TJ
/T1_3 10.91 Tf
11.91 1.78 Td
(jj)Tj
/T1_4 10.91 Tf
6.05 0 Td
(U)Tj
/T1_5 7.97 Tf
5.73 -1.78 Td
[(J)24(;k)]TJ
/T1_3 10.91 Tf
11.9 1.78 Td
(jj)Tj
/T1_4 10.91 Tf
6.06 0 Td
(S)Tj
/T1_5 7.97 Tf
5.73 -1.69 Td
(J)Tj
/T1_3 10.91 Tf
5.87 1.69 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
[(10\).)-443(Eac)26(h)]TJ
/T1_4 10.91 Tf
50.12 0 Td
(U)Tj
/T1_5 7.97 Tf
5.72 -1.78 Td
[(J)23(;k)]TJ
/T1_1 10.91 Tf
15.53 1.78 Td
(and)Tj
/T1_4 10.91 Tf
21.2 0 Td
(S)Tj
/T1_5 7.97 Tf
5.72 -1.69 Td
(J)Tj
/T1_1 10.91 Tf
9.5 1.69 Td
(stores)Tj
/T1_2 10.91 Tf
31.04 0 Td
(\267)Tj
/T1_5 7.97 Tf
6.28 -1.78 Td
[(J)24(;k)]TJ
/T1_1 10.91 Tf
11.9 1.78 Td
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/T1_2 10.91 Tf
6.66 0 Td
(ak)Tj
/T1_5 7.97 Tf
11.44 -1.78 Td
[(J)23(;k)]TJ
/T1_1 10.91 Tf
15.53 1.78 Td
(and)Tj
/T1_2 10.91 Tf
21.19 0 Td
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/T1_5 7.97 Tf
10.76 -1.78 Td
[(J)24(;k)]TJ
/T1_1 10.91 Tf
-455.97 -20.14 Td
[(securely)-333(in)-333(tamp)-28(er-pro)-28(of)-333(devices.)]TJ
16.93 -21.91 Td
[(The)-400(Join)-400(Proto)-28(col)-400(consists)-400(of)-400(3)-400(phases.)-644(During)-400(Phase)-400(1,)-417(subgroup)-400(con)27(troller)]TJ
/T1_4 10.91 Tf
378.12 0 Td
(S)Tj
/T1_5 7.97 Tf
5.72 -1.69 Td
(J)Tj
/T1_1 10.91 Tf
10.24 1.69 Td
[(of)-399(subgroup)]TJ
/T1_3 10.91 Tf
-411.01 -21.92 Td
(G)Tj
/T1_8 7.97 Tf
7.13 3.96 Td
(0)Tj
/T1_5 7.97 Tf
-0.64 -7.19 Td
(J)Tj
/T1_1 10.91 Tf
9.79 3.23 Td
[(and)-359(new)-359(users)]TJ
/T1_4 10.91 Tf
71.9 0 Td
(U)Tj
/T1_5 7.97 Tf
5.72 -1.78 Td
[(J)24(;k)]TJ
/T1_1 10.91 Tf
15.82 1.78 Td
(for)Tj
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16.98 0 Td
(n)Tj
/T1_5 7.97 Tf
6.55 -1.69 Td
(J)Tj
/T1_1 10.91 Tf
8.48 1.69 Td
[(+)-239(1)]TJ
/T1_3 10.91 Tf
20.06 0 Td
(\267)Tj
/T1_2 10.91 Tf
11.98 0 Td
(k)Tj
/T1_3 10.91 Tf
9.53 0 Td
(\267)Tj
/T1_2 10.91 Tf
11.99 0 Td
(n)Tj
/T1_5 7.97 Tf
6.54 -1.69 Td
(J)Tj
/T1_1 10.91 Tf
8.49 1.69 Td
(+)Tj
/T1_2 10.91 Tf
11.09 0 Td
(m)Tj
/T1_1 10.91 Tf
13.5 0 Td
[(will)-359(in)27(teract)-359(and)-359(compute)-359(the)-360(new)-359(subgroup)-360(k)27(ey)]TJ
/T1_2 10.91 Tf
-234.91 -21.92 Td
(K)Tj
/T1_8 7.97 Tf
10.04 3.96 Td
(0)Tj
/T1_5 7.97 Tf
-0.78 -7.19 Td
(J)Tj
/T1_1 10.91 Tf
5.87 3.23 Td
[(.)-444(Next)-331(in)-331(Phase)-331(2,)]TJ
/T1_2 10.91 Tf
91 0 Td
(S)Tj
/T1_5 7.97 Tf
6.69 -1.69 Td
(J)Tj
/T1_1 10.91 Tf
9.48 1.69 Td
(uses)Tj
/T1_2 10.91 Tf
23.13 0 Td
(K)Tj
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10.04 3.96 Td
(0)Tj
/T1_5 7.97 Tf
-0.78 -7.19 Td
(J)Tj
/T1_1 10.91 Tf
9.48 3.23 Td
[(to)-331(in)27(teract)-330(with)-332(main)-331(con)27(troller)]TJ
/T1_4 10.91 Tf
154.48 0 Td
(C)Tj
/T1_1 10.91 Tf
9.34 0 Td
[(in)-331(order)-331(for)]TJ
/T1_4 10.91 Tf
57.88 0 Td
(C)Tj
/T1_1 10.91 Tf
9.34 0 Td
[(to)-331(compute)-331(the)]TJ
-395.21 -21.91 Td
[(new)-345(\257nal)-346(group)-346(k)26(ey)]TJ
/T1_2 10.91 Tf
97.83 0 Td
(K)Tj
/T1_8 7.97 Tf
10.04 3.95 Td
(0)Tj
/T1_1 10.91 Tf
2.79 -3.95 Td
[(.)-482(Finally)-346(in)-346(Phase)-346(3,)-349(the)-346(new)-346(\257nal)-346(group)-346(k)27(ey)]TJ
/T1_2 10.91 Tf
219.3 0 Td
(K)Tj
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10.04 3.95 Td
(0)Tj
/T1_1 10.91 Tf
6.57 -3.95 Td
[(is)-345(disseminated)-346(from)]TJ
/T1_4 10.91 Tf
102.11 0 Td
(C)Tj
/T1_1 10.91 Tf
9.5 0 Td
(to)Tj
-458.18 -21.92 Td
[(all)-333(user)-334(no)-28(des)-334(via)-334(subgroup)-334(con)27(trollers)]TJ
/T1_4 10.91 Tf
187.32 0 Td
(S)Tj
/T1_5 7.97 Tf
5.73 -1.64 Td
(i)Tj
/T1_1 10.91 Tf
7.02 1.64 Td
[(for)-333(1)]TJ
/T1_3 10.91 Tf
25.19 0 Td
(\267)Tj
/T1_2 10.91 Tf
11.52 0 Td
(i)Tj
/T1_3 10.91 Tf
6.8 0 Td
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11.52 0 Td
(n)Tj
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6.55 -1.64 Td
(c)Tj
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7.81 1.64 Td
(\(including)Tj
/T1_4 10.91 Tf
51.5 0 Td
(S)Tj
/T1_5 7.97 Tf
5.73 -1.69 Td
(J)Tj
/T1_1 10.91 Tf
5.87 1.69 Td
(\).)Tj
/T1_4 10.91 Tf
12.14 0 Td
(S)Tj
/T1_5 7.97 Tf
5.72 -1.69 Td
(J)Tj
/T1_1 10.91 Tf
9.52 1.69 Td
[(will)-333(then)-334(send)-334(the)-334(new)]TJ
-359.94 -21.92 Td
[(subgroup)-326(k)27(ey)]TJ
/T1_2 10.91 Tf
66.9 0 Td
(K)Tj
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10.04 3.96 Td
(0)Tj
/T1_5 7.97 Tf
-0.78 -7.19 Td
(J)Tj
/T1_1 10.91 Tf
9.43 3.23 Td
[(and)-327(new)-326(\257nal)-327(group)-327(k)27(ey)]TJ
/T1_2 10.91 Tf
118.13 0 Td
(K)Tj
/T1_8 7.97 Tf
10.04 3.96 Td
(0)Tj
/T1_1 10.91 Tf
6.36 -3.96 Td
[(securely)-326(to)-326(all)-327(existing)-327(users)]TJ
/T1_4 10.91 Tf
137.47 0 Td
(U)Tj
/T1_5 7.97 Tf
5.73 -1.68 Td
[(J)24(;j)]TJ
/T1_1 10.91 Tf
14.73 1.68 Td
[(for)-326(1)]TJ
/T1_3 10.91 Tf
25.1 0 Td
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11.51 0 Td
(j)Tj
/T1_3 10.91 Tf
8.15 0 Td
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/T1_2 10.91 Tf
11.51 0 Td
(n)Tj
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6.55 -1.68 Td
(J)Tj
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9.43 1.68 Td
(and)Tj
-450.3 -21.91 Td
[(new)-343(users)]TJ
/T1_4 10.91 Tf
50.07 0 Td
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5.72 -1.78 Td
[(J)23(;k)]TJ
/T1_1 10.91 Tf
15.66 1.78 Td
(for)Tj
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16.8 0 Td
(n)Tj
/T1_5 7.97 Tf
6.55 -1.69 Td
(J)Tj
/T1_1 10.91 Tf
8.37 1.69 Td
[(+)-229(1)]TJ
/T1_3 10.91 Tf
19.66 0 Td
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11.7 0 Td
(k)Tj
/T1_3 10.91 Tf
9.25 0 Td
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11.7 0 Td
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6.55 -1.69 Td
(J)Tj
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8.37 1.69 Td
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10.98 0 Td
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(.)Tj
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17.8 0 Td
(S)Tj
/T1_5 7.97 Tf
5.73 -1.64 Td
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7.13 1.64 Td
[(for)-343(1)]TJ
/T1_3 10.91 Tf
25.48 0 Td
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/T1_2 10.91 Tf
11.71 0 Td
(i)Tj
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6.98 0 Td
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11.7 0 Td
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10.32 0 Td
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11.71 0 Td
(n)Tj
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6.54 -1.64 Td
(c)Tj
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7.92 1.64 Td
[(will)-343(also)-344(up)-28(date)-344(its)-344(subgroup)-344(with)]TJ
-304.4 -21.92 Td
[(the)-285(new)-285(\257nal)-285(group)-285(k)27(ey)]TJ
/T1_2 10.91 Tf
113.43 0 Td
(K)Tj
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10.05 3.96 Td
(0)Tj
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2.79 -3.96 Td
[(.)-428(Key)-285(con\257rmation)-285(messages)-286(are)-285(also)-285(sen)27(t)-284(together)-286(to)-285(v)27(erify)-284(and)-285(con\257rm)]TJ
-126.27 -21.92 Td
[(the)-333(new)-333(subgroup)-333(k)26(ey)]TJ
/T1_2 10.91 Tf
108.24 0 Td
(K)Tj
/T1_8 7.97 Tf
10.05 3.96 Td
(0)Tj
/T1_5 7.97 Tf
-0.78 -7.19 Td
(J)Tj
/T1_1 10.91 Tf
9.5 3.23 Td
[(and)-333(the)-333(new)-334(\257nal)-333(group)-333(k)26(ey)]TJ
/T1_2 10.91 Tf
137.27 0 Td
(K)Tj
/T1_8 7.97 Tf
10.04 3.96 Td
(0)Tj
/T1_1 10.91 Tf
2.79 -3.96 Td
[(.)-444(The)-334(Join)-333(Proto)-28(col)-333(is)-333(describ)-28(ed)-334(b)-27(elo)26(w:)]TJ
/T1_0 10.91 Tf
-277.11 -21.91 Td
[(Phase)-383(1:)-511(Subgroup)-383(Key)-384(Generation)]TJ
/T1_1 10.91 Tf
0 -21.92 TD
[(Round)-333(1)]TJ
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 0 -457.86 cm
0 0 m
40.75 0 l
S
Q
Q
BT
/T1_1 10.91 Tf
1.0003 0 0 1.0003 112.7614 313.3622 Tm
(:)Tj
1.0003 0 0 1.0003 72 769.82 Tm
48.398 -456.33 Td
[(Subgroup)-293(con)27(troller)]TJ
/T1_4 10.91 Tf
97.052 0 Td
(S)Tj
/T1_5 7.97 Tf
5.73 -1.69 Td
(J)Tj
/T1_1 10.91 Tf
9.06 1.69 Td
[(randomly)-292(selects)-293(new)]TJ
/T1_2 10.91 Tf
103.94 0 Td
(\277)Tj
/T1_8 7.97 Tf
6 3.96 Td
(0)Tj
/T1_5 7.97 Tf
-1.23 -7.19 Td
(J)Tj
/T1_3 10.91 Tf
8.9 3.23 Td
(2)Tj
/T1_2 10.91 Tf
10.3 0 Td
(Z)Tj
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8.22 3.96 Td
(\244)Tj
/T1_5 7.97 Tf
-0.78 -6.65 Td
(q)Tj
/T1_1 10.91 Tf
5.51 2.69 Td
(,)Tj
/T1_2 10.91 Tf
6.31 0 Td
(\277)Tj
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6 3.96 Td
(0)Tj
/T1_5 7.97 Tf
-1.23 -7.28 Td
[(J)24(;k)]TJ
/T1_3 10.91 Tf
14.93 3.32 Td
(2)Tj
/T1_2 10.91 Tf
10.3 0 Td
(Z)Tj
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8.23 3.96 Td
(\244)Tj
/T1_5 7.97 Tf
-0.78 -6.65 Td
(q)Tj
/T1_1 10.91 Tf
8.7 2.69 Td
(for)Tj
/T1_2 10.91 Tf
16.24 0 Td
(n)Tj
/T1_5 7.97 Tf
6.55 -1.69 Td
(J)Tj
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7.41 1.69 Td
[(+)-140(1)]TJ
/T1_3 10.91 Tf
18.49 0 Td
(\267)Tj
/T1_2 10.91 Tf
11.52 0 Td
(k)Tj
/T1_3 10.91 Tf
9.05 0 Td
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11.51 0 Td
(n)Tj
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6.54 -1.69 Td
(J)Tj
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7.41 1.69 Td
(+)Tj
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10.01 0 Td
(m)Tj
/T1_1 10.91 Tf
-458.29 -21.91 Td
[(and)-282(session)-283(iden)27(tit)28(y)]TJ
/T1_4 10.91 Tf
95.77 0 Td
(SID)Tj
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17.17 3.95 Td
(0)Tj
/T1_5 7.97 Tf
0 -7.19 TD
(J)Tj
/T1_1 10.91 Tf
5.87 3.24 Td
[(,)-293(encrypts)]TJ
/T1_2 10.91 Tf
49.69 0 Td
(\277)Tj
/T1_8 7.97 Tf
6 3.95 Td
(0)Tj
/T1_5 7.97 Tf
-1.23 -7.19 Td
(J)Tj
/T1_3 10.91 Tf
5.87 3.24 Td
(jj)Tj
/T1_2 10.91 Tf
6.06 0 Td
(\277)Tj
/T1_8 7.97 Tf
6 3.95 Td
(0)Tj
/T1_5 7.97 Tf
-1.24 -7.28 Td
[(J)23(;k)]TJ
/T1_3 10.91 Tf
11.91 3.33 Td
(jj)Tj
/T1_4 10.91 Tf
6.06 0 Td
(S)Tj
/T1_5 7.97 Tf
5.72 -1.69 Td
(J)Tj
/T1_3 10.91 Tf
5.87 1.69 Td
(jj)Tj
/T1_4 10.91 Tf
6.06 0 Td
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(00\))Tj
-212.89 -24.91 Td
(\271)Tj
/T1_3 10.91 Tf
-0.86 0 Td
(\271)Tj
/T1_4 7.97 Tf
6.57 4.51 Td
(0)Tj
/T1_2 7.97 Tf
0 -7.28 TD
[(J)24(;k)]TJ
/T1_0 10.91 Tf
14.93 2.77 Td
(=)Tj
/T1_12 10.91 Tf
11.51 0 Td
[(MA)27(C)]TJ
/T1_2 7.97 Tf
23.48 -1.77 Td
(ak)Tj
/T1_7 5.98 Tf
8.9 -1.41 Td
[(J)34(;k)]TJ
/T1_0 10.91 Tf
11.21 3.18 Td
(\()Tj
/T1_3 10.91 Tf
(\277)Tj
/T1_4 7.97 Tf
10.24 4.51 Td
(0)Tj
/T1_2 7.97 Tf
-1.23 -7.2 Td
(J)Tj
/T1_5 10.91 Tf
5.87 2.69 Td
(jj)Tj
/T1_3 10.91 Tf
6.06 0 Td
(\277)Tj
/T1_4 7.97 Tf
6 4.51 Td
(0)Tj
/T1_2 7.97 Tf
-1.24 -7.28 Td
[(J)23(;k)]TJ
/T1_5 10.91 Tf
11.91 2.77 Td
(jj)Tj
/T1_3 10.91 Tf
6.05 0 Td
(z)Tj
/T1_4 7.97 Tf
5.56 4.51 Td
(0)Tj
/T1_2 7.97 Tf
-0.48 -7.28 Td
[(J)24(;k)]TJ
/T1_5 10.91 Tf
11.9 2.77 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(SID)Tj
/T1_4 7.97 Tf
17.17 4.51 Td
(0)Tj
/T1_2 7.97 Tf
0 -7.2 TD
(J)Tj
/T1_5 10.91 Tf
5.88 2.69 Td
(jj)Tj
/T1_1 10.91 Tf
6.05 0 Td
(U)Tj
/T1_2 7.97 Tf
5.73 -1.77 Td
[(J)24(;k)]TJ
/T1_5 10.91 Tf
11.9 1.77 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(S)Tj
/T1_2 7.97 Tf
5.73 -1.69 Td
(J)Tj
/T1_5 10.91 Tf
5.87 1.69 Td
(jj)Tj
/T1_0 10.91 Tf
6.06 0 Td
(01\))Tj
-359.55 -39.64 Td
[(Finally)83(,)]TJ
/T1_1 10.91 Tf
39.23 0 Td
(U)Tj
/T1_2 7.97 Tf
5.73 -1.78 Td
[(J)24(;k)]TJ
/T1_0 10.91 Tf
15.53 1.78 Td
(sends)Tj
/T1_5 10.91 Tf
29.21 0 Td
(f)Tj
/T1_1 10.91 Tf
(SID)Tj
/T1_4 7.97 Tf
22.63 3.96 Td
(0)Tj
/T1_2 7.97 Tf
0 -7.19 TD
(J)Tj
/T1_5 10.91 Tf
5.87 3.23 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(U)Tj
/T1_2 7.97 Tf
5.72 -1.78 Td
[(J)23(;k)]TJ
/T1_5 10.91 Tf
11.91 1.78 Td
(jj)Tj
/T1_0 10.91 Tf
6.06 0 Td
(\()Tj
/T1_3 10.91 Tf
(z)Tj
/T1_4 7.97 Tf
9.79 3.96 Td
(\244)Tj
/T1_2 7.97 Tf
-0.48 -7.28 Td
[(J)24(;k)]TJ
/T1_0 10.91 Tf
11.9 3.32 Td
(\))Tj
/T1_4 7.97 Tf
4.24 3.96 Td
(0)Tj
/T1_5 10.91 Tf
2.8 -3.96 Td
(jj)Tj
/T1_3 10.91 Tf
6.06 0 Td
(\271)Tj
/T1_4 7.97 Tf
6.57 3.96 Td
(0)Tj
/T1_2 7.97 Tf
0 -7.28 TD
[(J)24(;k)]TJ
/T1_5 10.91 Tf
11.9 3.32 Td
(jj)Tj
/T1_0 10.91 Tf
6.92 0 Td
(\271)Tj
/T1_3 10.91 Tf
-0.86 0 Td
(\271)Tj
/T1_4 7.97 Tf
6.57 3.96 Td
(0)Tj
/T1_2 7.97 Tf
T*
[(J)24(;k)]TJ
/T1_5 10.91 Tf
11.9 3.32 Td
(g)Tj
/T1_0 10.91 Tf
9.09 0 Td
(to)Tj
/T1_1 10.91 Tf
13.33 0 Td
(S)Tj
/T1_2 7.97 Tf
5.73 -1.69 Td
(J)Tj
/T1_0 10.91 Tf
5.87 1.69 Td
(.)Tj
-259.28 -21.92 Td
[(Round)-333(3)]TJ
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 0 -163.49 cm
0 0 m
40.75 0 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 112.7614 607.8046 Tm
(:)Tj
/T1_1 10.91 Tf
8.44 0 Td
(S)Tj
/T1_2 7.97 Tf
5.73 -1.69 Td
(J)Tj
/T1_0 10.91 Tf
9.79 1.69 Td
(c)Tj
1.0003 0 0 1.0003 72 769.82 Tm
69.259 -161.97 Td
[(hec)28(ks)-358(if)]TJ
/T1_3 10.91 Tf
39.701 0 Td
(\271)Tj
/T1_4 7.97 Tf
6.57 3.96 Td
(0)Tj
/T1_2 7.97 Tf
T*
[(J)23(;k)]TJ
/T1_0 10.91 Tf
15.41 3.32 Td
(=)Tj
/T1_12 10.91 Tf
11.98 0 Td
[(MA)27(C)]TJ
/T1_2 7.97 Tf
23.48 -1.77 Td
(ak)Tj
/T1_7 5.98 Tf
8.91 -1.41 Td
[(J)35(;k)]TJ
/T1_0 10.91 Tf
11.2 3.18 Td
(\()Tj
/T1_3 10.91 Tf
(\277)Tj
/T1_4 7.97 Tf
10.24 3.96 Td
(0)Tj
/T1_2 7.97 Tf
-1.23 -7.19 Td
(J)Tj
/T1_5 10.91 Tf
5.87 3.23 Td
(jj)Tj
/T1_3 10.91 Tf
6.06 0 Td
(\277)Tj
/T1_4 7.97 Tf
6 3.96 Td
(0)Tj
/T1_2 7.97 Tf
-1.23 -7.28 Td
[(J)24(;k)]TJ
/T1_5 10.91 Tf
11.9 3.32 Td
(jj)Tj
/T1_0 10.91 Tf
6.06 0 Td
(\()Tj
/T1_3 10.91 Tf
(z)Tj
/T1_4 7.97 Tf
9.79 3.96 Td
(\244)Tj
/T1_2 7.97 Tf
-0.48 -7.28 Td
[(J)24(;k)]TJ
/T1_0 10.91 Tf
11.9 3.32 Td
(\))Tj
/T1_4 7.97 Tf
4.24 3.96 Td
(0)Tj
/T1_5 10.91 Tf
2.8 -3.96 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(SID)Tj
/T1_4 7.97 Tf
17.17 3.96 Td
(0)Tj
/T1_2 7.97 Tf
0 -7.19 TD
(J)Tj
/T1_5 10.91 Tf
5.87 3.23 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(U)Tj
/T1_2 7.97 Tf
5.73 -1.77 Td
[(J)24(;k)]TJ
/T1_5 10.91 Tf
11.9 1.77 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(S)Tj
/T1_2 7.97 Tf
5.73 -1.69 Td
(J)Tj
/T1_5 10.91 Tf
5.87 1.69 Td
(jj)Tj
/T1_0 10.91 Tf
6.06 0 Td
[(00\).)-522(If)-359(the)-360(c)27(hec)28(k)-358(is)-360(not)-359(cor-)]TJ
-334.94 -21.91 Td
(rect,)Tj
/T1_1 10.91 Tf
23.9 0 Td
(S)Tj
/T1_2 7.97 Tf
5.73 -1.69 Td
(J)Tj
/T1_0 10.91 Tf
8.29 1.69 Td
[(blo)-28(c)27(ks)-221(malicious)-222(user)]TJ
/T1_1 10.91 Tf
100.49 0 Td
(U)Tj
/T1_2 7.97 Tf
5.73 -1.78 Td
[(J)24(;k)]TJ
/T1_0 10.91 Tf
11.9 1.78 Td
[(.)-407(Otherwise,)]TJ
/T1_1 10.91 Tf
61.12 0 Td
(S)Tj
/T1_2 7.97 Tf
5.73 -1.69 Td
(J)Tj
/T1_0 10.91 Tf
8.29 1.69 Td
(obtains)Tj
/T1_3 10.91 Tf
37.02 0 Td
(z)Tj
/T1_4 7.97 Tf
5.55 3.95 Td
(0)Tj
/T1_2 7.97 Tf
-0.48 -7.27 Td
[(J)23(;k)]TJ
/T1_0 10.91 Tf
14.94 3.32 Td
[(=)-277(\()]TJ
/T1_3 10.91 Tf
(z)Tj
/T1_4 7.97 Tf
21.3 3.95 Td
(\244)Tj
/T1_2 7.97 Tf
-0.48 -7.27 Td
[(J)23(;k)]TJ
/T1_0 10.91 Tf
11.9 3.32 Td
(\))Tj
/T1_4 7.97 Tf
4.24 3.95 Td
(0)Tj
/T1_5 10.91 Tf
2.8 -3.95 Td
(\242)Tj
/T1_3 10.91 Tf
(h)Tj
/T1_4 7.97 Tf
9.31 5.1 Td
(\241)Tj
/T1_8 7.97 Tf
6.59 0 Td
(H)Tj
/T1_9 5.98 Tf
5.97 -1.1 Td
(1)Tj
/T1_10 7.97 Tf
4.15 1.1 Td
(\()Tj
/T1_11 7.97 Tf
3.3 0 Td
(SID)Tj
/T1_6 5.98 Tf
12.69 2.82 Td
(0)Tj
/T1_7 5.98 Tf
0 -5.52 TD
(J)Tj
/T1_4 7.97 Tf
5.14 2.7 Td
(jj)Tj
/T1_11 7.97 Tf
(U)Tj
/T1_7 5.98 Tf
8.94 -1.4 Td
[(J)35(;k)]TJ
/T1_4 7.97 Tf
10.7 1.4 Td
(jj)Tj
/T1_11 7.97 Tf
(S)Tj
/T1_7 5.98 Tf
8.94 -1.33 Td
(J)Tj
/T1_4 7.97 Tf
5.13 1.33 Td
(jj)Tj
/T1_8 7.97 Tf
4.71 0 Td
[(p)29(w)]TJ
/T1_7 5.98 Tf
10.03 -2.04 Td
[(J)34(;k)]TJ
/T1_4 7.97 Tf
10.71 2.04 Td
(jj)Tj
/T1_2 7.97 Tf
(\277)Tj
/T1_6 5.98 Tf
9.38 2.82 Td
(0)Tj
/T1_7 5.98 Tf
-0.92 -5.52 Td
(J)Tj
/T1_4 7.97 Tf
5.13 2.7 Td
(jj)Tj
/T1_2 7.97 Tf
4.71 0 Td
(\277)Tj
/T1_6 5.98 Tf
4.67 2.82 Td
(0)Tj
/T1_7 5.98 Tf
-0.92 -5.59 Td
[(J)34(;k)]TJ
/T1_10 7.97 Tf
10.71 2.77 Td
(\))Tj
/T1_0 10.91 Tf
-467.04 -27.02 Td
[(and)-414(c)27(hec)27(ks)-493(\271)]TJ
/T1_3 10.91 Tf
56.67 0 Td
(\271)Tj
/T1_4 7.97 Tf
6.57 3.96 Td
(0)Tj
/T1_2 7.97 Tf
0 -7.28 TD
[(J)23(;k)]TJ
/T1_0 10.91 Tf
16.41 3.32 Td
(=)Tj
/T1_12 10.91 Tf
13 0 Td
[(MA)28(C)]TJ
/T1_2 7.97 Tf
23.47 -1.78 Td
(ak)Tj
/T1_7 5.98 Tf
8.91 -1.4 Td
[(J)35(;k)]TJ
/T1_0 10.91 Tf
11.2 3.18 Td
(\()Tj
/T1_3 10.91 Tf
(\277)Tj
/T1_4 7.97 Tf
10.24 3.96 Td
(0)Tj
/T1_2 7.97 Tf
-1.23 -7.19 Td
(J)Tj
/T1_5 10.91 Tf
5.87 3.23 Td
(jj)Tj
/T1_3 10.91 Tf
6.06 0 Td
(\277)Tj
/T1_4 7.97 Tf
6 3.96 Td
(0)Tj
/T1_2 7.97 Tf
-1.23 -7.28 Td
[(J)24(;k)]TJ
/T1_5 10.91 Tf
11.9 3.32 Td
(jj)Tj
/T1_3 10.91 Tf
6.06 0 Td
(z)Tj
/T1_4 7.97 Tf
5.55 3.96 Td
(0)Tj
/T1_2 7.97 Tf
-0.48 -7.28 Td
[(J)24(;k)]TJ
/T1_5 10.91 Tf
11.9 3.32 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(SID)Tj
/T1_4 7.97 Tf
17.18 3.96 Td
(0)Tj
/T1_2 7.97 Tf
0 -7.19 TD
(J)Tj
/T1_5 10.91 Tf
5.87 3.23 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(U)Tj
/T1_2 7.97 Tf
5.72 -1.78 Td
[(J)23(;k)]TJ
/T1_5 10.91 Tf
11.91 1.78 Td
(jj)Tj
/T1_1 10.91 Tf
6.05 0 Td
(S)Tj
/T1_2 7.97 Tf
5.73 -1.69 Td
(J)Tj
/T1_5 10.91 Tf
5.87 1.69 Td
(jj)Tj
/T1_0 10.91 Tf
6.06 0 Td
[(01\).)-688(If)-415(the)-415(c)27(hec)28(k)-414(is)-415(incorrect,)]TJ
/T1_1 10.91 Tf
148.92 0 Td
(S)Tj
/T1_2 7.97 Tf
5.73 -1.69 Td
(J)Tj
/T1_0 10.91 Tf
10.39 1.69 Td
[(blo)-28(c)27(ks)]TJ
-438.42 -21.92 Td
[(malicious)-418(user)]TJ
/T1_1 10.91 Tf
72.9 0 Td
(U)Tj
/T1_2 7.97 Tf
5.73 -1.77 Td
[(J)24(;k)]TJ
/T1_0 10.91 Tf
11.9 1.77 Td
[(.)-700(Otherwise,)]TJ
/T1_1 10.91 Tf
66.45 0 Td
(S)Tj
/T1_2 7.97 Tf
5.72 -1.68 Td
(J)Tj
/T1_0 10.91 Tf
10.44 1.68 Td
[(selects)-418(new)-419(random)]TJ
/T1_3 10.91 Tf
99.28 0 Td
(r)Tj
/T1_4 7.97 Tf
5.22 3.96 Td
(0)Tj
/T1_2 7.97 Tf
-0.3 -7.19 Td
(J)Tj
/T1_5 10.91 Tf
10.45 3.23 Td
(2)Tj
/T1_3 10.91 Tf
11.85 0 Td
(Z)Tj
/T1_4 7.97 Tf
8.23 3.96 Td
(\244)Tj
/T1_2 7.97 Tf
-0.78 -6.65 Td
(q)Tj
/T1_0 10.91 Tf
10.07 2.69 Td
[(and)-418(computes)]TJ
/T1_3 10.91 Tf
71.6 0 Td
(z)Tj
/T1_4 7.97 Tf
5.55 3.96 Td
(0)Tj
/T1_2 7.97 Tf
-0.48 -7.19 Td
(J)Tj
/T1_0 10.91 Tf
10.45 3.23 Td
(=)Tj
/T1_3 10.91 Tf
13.06 0 Td
(g)Tj
/T1_2 7.97 Tf
5.6 3.96 Td
(r)Tj
/T1_6 5.98 Tf
4.05 2.81 Td
(0)Tj
/T1_7 5.98 Tf
-0.23 -5.51 Td
(J)Tj
/T1_0 10.91 Tf
8.66 -1.26 Td
[(mo)-27(d)]TJ
/T1_3 10.91 Tf
23.93 0 Td
(p)Tj
/T1_0 10.91 Tf
(.)Tj
-459.35 -21.91 Td
(Next,)Tj
/T1_1 10.91 Tf
29.75 0 Td
(S)Tj
/T1_2 7.97 Tf
5.72 -1.69 Td
(J)Tj
/T1_0 10.91 Tf
9.55 1.69 Td
[(computes)-337(DH)-338(k)27(eys)]TJ
/T1_3 10.91 Tf
92.81 0 Td
(t)Tj
/T1_4 7.97 Tf
3.94 3.95 Td
(0)Tj
/T1_2 7.97 Tf
0 -7.27 TD
[(J)23(;k)]TJ
/T1_0 10.91 Tf
15.59 3.32 Td
(for)Tj
/T1_3 10.91 Tf
16.73 0 Td
(n)Tj
/T1_2 7.97 Tf
6.55 -1.69 Td
(J)Tj
/T1_0 10.91 Tf
8.33 1.69 Td
[(+)-224(1)]TJ
/T1_5 10.91 Tf
19.49 0 Td
(\267)Tj
/T1_3 10.91 Tf
11.59 0 Td
(k)Tj
/T1_5 10.91 Tf
9.13 0 Td
(\267)Tj
/T1_3 10.91 Tf
11.59 0 Td
(n)Tj
/T1_2 7.97 Tf
6.54 -1.69 Td
(J)Tj
/T1_0 10.91 Tf
8.33 1.69 Td
(+)Tj
/T1_3 10.91 Tf
10.93 0 Td
(m)Tj
/T1_0 10.91 Tf
13.26 0 Td
[(shared)-337(with)]TJ
/T1_1 10.91 Tf
59.56 0 Td
(U)Tj
/T1_2 7.97 Tf
5.73 -1.78 Td
[(J)24(;k)]TJ
/T1_0 10.91 Tf
15.58 1.78 Td
[(and)-337(new)-338(subgroup)-337(k)26(ey)]TJ
/T1_3 10.91 Tf
-360.7 -21.92 Td
(K)Tj
/T1_4 7.97 Tf
10.04 3.96 Td
(0)Tj
/T1_2 7.97 Tf
-0.78 -7.19 Td
(J)Tj
/T1_0 10.91 Tf
9.51 3.23 Td
(:)Tj
/T1_3 10.91 Tf
107.28 -39.64 Td
(t)Tj
/T1_4 7.97 Tf
3.94 4.5 Td
(0)Tj
/T1_2 7.97 Tf
0 -7.28 TD
[(J)24(;k)]TJ
/T1_0 10.91 Tf
21.86 2.78 Td
[(=)-913(\()]TJ
/T1_3 10.91 Tf
22.68 0 Td
(z)Tj
/T1_4 7.97 Tf
5.56 4.5 Td
(0)Tj
/T1_2 7.97 Tf
-0.48 -7.28 Td
[(J)24(;k)]TJ
/T1_0 10.91 Tf
11.9 2.78 Td
(\))Tj
/T1_2 7.97 Tf
4.24 4.5 Td
(r)Tj
/T1_6 5.98 Tf
4.05 2.81 Td
(0)Tj
/T1_7 5.98 Tf
-0.23 -5.52 Td
(J)Tj
/T1_0 10.91 Tf
8.66 -1.79 Td
[(mo)-28(d)]TJ
/T1_3 10.91 Tf
23.94 0 Td
(p)Tj
-105.41 -33.65 Td
(K)Tj
/T1_4 7.97 Tf
10.04 4.51 Td
(0)Tj
/T1_2 7.97 Tf
-0.78 -7.2 Td
(J)Tj
/T1_0 10.91 Tf
15.83 2.69 Td
(=)Tj
/T1_13 10.91 Tf
18.44 21.92 Td
(0)Tj
0 -19.63 TD
(@)Tj
/T1_3 10.91 Tf
9.55 -2.29 Td
(z)Tj
/T1_4 7.97 Tf
5.55 4.51 Td
(0)Tj
/T1_2 7.97 Tf
-0.48 -7.2 Td
(J)Tj
/T1_5 10.91 Tf
8.29 2.69 Td
(\242)Tj
/T1_2 7.97 Tf
7.67 14.01 Td
(n)Tj
/T1_7 5.98 Tf
5.14 -1.34 Td
(J)Tj
/T1_13 10.91 Tf
-6.97 -2.31 Td
(Y)Tj
/T1_2 7.97 Tf
-0.39 -23.44 Td
(j)Tj
/T1_10 7.97 Tf
3.89 0 Td
(=1)Tj
/T1_3 10.91 Tf
12.63 13.08 Td
(z)Tj
/T1_2 7.97 Tf
5.07 -1.68 Td
[(J)23(;j)]TJ
/T1_5 10.91 Tf
13.59 1.68 Td
(\242)Tj
/T1_2 7.97 Tf
9.43 14.01 Td
(n)Tj
/T1_7 5.98 Tf
5.14 -1.34 Td
(J)Tj
/T1_10 7.97 Tf
5.13 1.34 Td
(+)Tj
/T1_2 7.97 Tf
6.59 0 Td
(m)Tj
/T1_13 10.91 Tf
-11.65 -3.65 Td
(Y)Tj
/T1_2 7.97 Tf
-9.18 -23.71 Td
(k)Tj
/T1_10 7.97 Tf
4.62 0 Td
(=)Tj
/T1_2 7.97 Tf
(n)Tj
/T1_7 5.98 Tf
11.72 -1.33 Td
(J)Tj
/T1_10 7.97 Tf
5.13 1.33 Td
(+1)Tj
/T1_3 10.91 Tf
12.64 13.35 Td
(z)Tj
/T1_4 7.97 Tf
5.55 4.51 Td
(0)Tj
/T1_2 7.97 Tf
-0.48 -7.28 Td
[(J)23(;k)]TJ
/T1_13 10.91 Tf
11.9 24.69 Td
(1)Tj
T*
(A)Tj
/T1_2 7.97 Tf
9.55 16.92 Td
(r)Tj
/T1_6 5.98 Tf
4.05 2.81 Td
(0)Tj
/T1_7 5.98 Tf
-0.23 -5.52 Td
(J)Tj
/T1_0 10.91 Tf
8.66 -16.5 Td
[(mo)-27(d)]TJ
/T1_3 10.91 Tf
23.93 0 Td
(p)Tj
/T1_14 10.91 Tf
-336.33 -49.17 Td
[(Phase)-383(2:)-511(Final)-383(Key)-384(Generation)]TJ
/T1_0 10.91 Tf
0 -27.9 TD
[(Round)-333(1)]TJ
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 0 -423.43 cm
0 0 m
40.75 0 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 112.7614 347.7919 Tm
(:)Tj
1.0003 0 0 1.0003 72 769.82 Tm
50.198 -421.91 Td
[(Main)-405(con)27(troller)]TJ
/T1_1 10.91 Tf
78.572 0 Td
(C)Tj
/T1_0 10.91 Tf
10.15 0 Td
[(selects)-405(random)]TJ
/T1_3 10.91 Tf
75.64 0 Td
(\277)Tj
/T1_4 7.97 Tf
6 3.96 Td
(0)Tj
/T1_11 7.97 Tf
-1.23 -6.65 Td
(C)Tj
/T1_5 10.91 Tf
9.06 2.69 Td
(2)Tj
/T1_3 10.91 Tf
11.61 0 Td
(Z)Tj
/T1_4 7.97 Tf
8.23 3.96 Td
(\244)Tj
/T1_2 7.97 Tf
-0.78 -6.65 Td
(q)Tj
/T1_0 10.91 Tf
5.51 2.69 Td
[(,)-476(\271)]TJ
/T1_3 10.91 Tf
7.65 0 Td
(\277)Tj
/T1_4 7.97 Tf
6 3.96 Td
(0)Tj
/T1_2 7.97 Tf
-1.24 -7.19 Td
(J)Tj
/T1_5 10.91 Tf
10.21 3.23 Td
(2)Tj
/T1_3 10.91 Tf
11.61 0 Td
(Z)Tj
/T1_4 7.97 Tf
8.22 3.96 Td
(\244)Tj
/T1_2 7.97 Tf
-0.78 -6.65 Td
(q)Tj
/T1_0 10.91 Tf
5.52 2.69 Td
[(,)-475(\271)]TJ
/T1_3 10.91 Tf
7.64 0 Td
(\277)Tj
/T1_4 7.97 Tf
6 3.96 Td
(0)Tj
/T1_2 7.97 Tf
-1.23 -7.01 Td
(i)Tj
/T1_5 10.91 Tf
8.37 3.05 Td
(2)Tj
/T1_3 10.91 Tf
11.6 0 Td
(Z)Tj
/T1_4 7.97 Tf
8.23 3.96 Td
(\244)Tj
/T1_2 7.97 Tf
-0.78 -6.65 Td
(q)Tj
/T1_0 10.91 Tf
9.93 2.69 Td
[(for)-405(1)]TJ
/T1_5 10.91 Tf
27.27 0 Td
(\267)Tj
/T1_3 10.91 Tf
12.82 0 Td
(i)Tj
/T1_5 10.91 Tf
8.09 0 Td
(6)Tj
/T1_0 10.91 Tf
(=)Tj
/T1_3 10.91 Tf
12.82 0 Td
(J)Tj
/T1_5 10.91 Tf
11.44 0 Td
(\267)Tj
/T1_3 10.91 Tf
12.82 0 Td
(n)Tj
/T1_2 7.97 Tf
6.54 -1.63 Td
(c)Tj
/T1_0 10.91 Tf
8.59 1.63 Td
(and)Tj
-450.3 -21.91 Td
[(session)-247(iden)27(tit)27(y)]TJ
/T1_1 10.91 Tf
74.35 0 Td
(SID)Tj
/T1_4 7.97 Tf
17.18 3.96 Td
(0)Tj
/T1_11 7.97 Tf
0 -6.66 TD
(c)Tj
/T1_0 10.91 Tf
4.73 2.7 Td
[(,)-264(encrypts)]TJ
/T1_3 10.91 Tf
49 0 Td
(\277)Tj
/T1_4 7.97 Tf
6 3.96 Td
(0)Tj
/T1_11 7.97 Tf
-1.23 -6.66 Td
(C)Tj
/T1_5 10.91 Tf
4.73 2.7 Td
(jj)Tj
/T1_0 10.91 Tf
6.64 0 Td
(\271)Tj
/T1_3 10.91 Tf
-0.58 0 Td
(\277)Tj
/T1_4 7.97 Tf
6 3.96 Td
(0)Tj
/T1_2 7.97 Tf
-1.23 -7.19 Td
(J)Tj
/T1_5 10.91 Tf
5.87 3.23 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(C)Tj
/T1_5 10.91 Tf
5.72 0 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(S)Tj
/T1_2 7.97 Tf
5.73 -1.69 Td
(J)Tj
/T1_5 10.91 Tf
5.87 1.69 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(SID)Tj
/T1_4 7.97 Tf
17.17 3.96 Td
(0)Tj
/T1_11 7.97 Tf
T*
(c)Tj
/T1_0 10.91 Tf
7.44 2.7 Td
(using)Tj
/T1_3 10.91 Tf
27.6 0 Td
(ek)Tj
/T1_2 7.97 Tf
10.75 -1.69 Td
(J)Tj
/T1_0 10.91 Tf
8.58 1.69 Td
(and)Tj
/T1_3 10.91 Tf
20.27 0 Td
(\277)Tj
/T1_4 7.97 Tf
6 3.96 Td
(0)Tj
/T1_11 7.97 Tf
-1.23 -6.66 Td
(C)Tj
/T1_5 10.91 Tf
4.73 2.7 Td
(jj)Tj
/T1_0 10.91 Tf
6.63 0 Td
(\271)Tj
/T1_3 10.91 Tf
-0.57 0 Td
(\277)Tj
/T1_4 7.97 Tf
6 3.96 Td
(0)Tj
/T1_2 7.97 Tf
-1.24 -7.02 Td
(i)Tj
/T1_5 10.91 Tf
4.03 3.06 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(C)Tj
/T1_5 10.91 Tf
(jj)Tj
/T1_1 10.91 Tf
11.79 0 Td
(S)Tj
/T1_2 7.97 Tf
5.72 -1.64 Td
(i)Tj
/T1_5 10.91 Tf
3.38 1.64 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(SID)Tj
/T1_4 7.97 Tf
17.18 3.96 Td
(0)Tj
/T1_11 7.97 Tf
T*
(c)Tj
/T1_0 10.91 Tf
7.43 2.7 Td
(using)Tj
/T1_3 10.91 Tf
27.6 0 Td
(ek)Tj
/T1_2 7.97 Tf
10.76 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
6.08 1.64 Td
[(to)-247(obtain)]TJ
/T1_1 10.91 Tf
-425.18 -21.92 Td
(c)Tj
/T1_4 7.97 Tf
5.73 3.96 Td
(0)Tj
/T1_2 7.97 Tf
0 -7.19 TD
(J)Tj
/T1_0 10.91 Tf
10.69 3.23 Td
(=)Tj
/T1_5 10.91 Tf
13.31 0 Td
(E)Tj
/T1_2 7.97 Tf
5.76 -1.78 Td
(ek)Tj
/T1_7 5.98 Tf
8.33 -1.33 Td
(J)Tj
/T1_0 10.91 Tf
5.64 3.11 Td
(\()Tj
/T1_3 10.91 Tf
(\277)Tj
/T1_4 7.97 Tf
10.24 3.96 Td
(0)Tj
/T1_11 7.97 Tf
-1.23 -6.65 Td
(C)Tj
/T1_5 10.91 Tf
4.73 2.69 Td
(jj)Tj
/T1_0 10.91 Tf
6.64 0 Td
(\271)Tj
/T1_3 10.91 Tf
-0.58 0 Td
(\277)Tj
/T1_4 7.97 Tf
6 3.96 Td
(0)Tj
/T1_2 7.97 Tf
-1.23 -7.19 Td
(J)Tj
/T1_5 10.91 Tf
5.87 3.23 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(C)Tj
/T1_5 10.91 Tf
5.72 0 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(S)Tj
/T1_2 7.97 Tf
5.73 -1.69 Td
(J)Tj
/T1_5 10.91 Tf
5.87 1.69 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(SID)Tj
/T1_4 7.97 Tf
17.17 3.96 Td
(0)Tj
/T1_11 7.97 Tf
0 -6.65 TD
(c)Tj
/T1_0 10.91 Tf
4.73 2.69 Td
[(\))-432(and)]TJ
/T1_1 10.91 Tf
31.24 0 Td
(c)Tj
/T1_4 7.97 Tf
5.73 3.96 Td
(0)Tj
/T1_2 7.97 Tf
0 -7.01 TD
(i)Tj
/T1_0 10.91 Tf
8.21 3.05 Td
(=)Tj
/T1_5 10.91 Tf
13.31 0 Td
(E)Tj
/T1_2 7.97 Tf
5.75 -1.78 Td
(ek)Tj
/T1_7 5.98 Tf
8.34 -1.21 Td
(i)Tj
/T1_0 10.91 Tf
3.66 2.99 Td
(\()Tj
/T1_3 10.91 Tf
(\277)Tj
/T1_4 7.97 Tf
10.24 3.96 Td
(0)Tj
/T1_11 7.97 Tf
-1.23 -6.65 Td
(C)Tj
/T1_5 10.91 Tf
4.73 2.69 Td
(jj)Tj
/T1_0 10.91 Tf
6.63 0 Td
(\271)Tj
/T1_3 10.91 Tf
-0.57 0 Td
(\277)Tj
/T1_4 7.97 Tf
6 3.96 Td
(0)Tj
/T1_2 7.97 Tf
-1.24 -7.01 Td
(i)Tj
/T1_5 10.91 Tf
4.03 3.05 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(C)Tj
/T1_5 10.91 Tf
(jj)Tj
/T1_1 10.91 Tf
11.79 0 Td
(S)Tj
/T1_2 7.97 Tf
5.72 -1.63 Td
(i)Tj
/T1_5 10.91 Tf
3.38 1.63 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(SID)Tj
/T1_4 7.97 Tf
17.18 3.96 Td
(0)Tj
/T1_11 7.97 Tf
0 -6.65 TD
(c)Tj
/T1_0 10.91 Tf
4.73 2.69 Td
[(\))-432(for)-432(1)]TJ
/T1_5 10.91 Tf
37 0 Td
(\267)Tj
/T1_3 10.91 Tf
13.31 0 Td
(i)Tj
/T1_5 10.91 Tf
8.59 0 Td
(6)Tj
/T1_0 10.91 Tf
(=)Tj
/T1_3 10.91 Tf
13.31 0 Td
(J)Tj
/T1_5 10.91 Tf
11.92 0 Td
(\267)Tj
/T1_3 10.91 Tf
13.31 0 Td
(n)Tj
/T1_2 7.97 Tf
6.55 -1.63 Td
(c)Tj
/T1_0 10.91 Tf
8.88 1.63 Td
[(resp)-27(ectiv)27(ely)83(.)]TJ
-409.92 -21.92 Td
(Next,)Tj
/T1_1 10.91 Tf
30.73 0 Td
(C)Tj
/T1_0 10.91 Tf
10.2 0 Td
(computes)Tj
/T1_3 10.91 Tf
49.37 0 Td
(v)Tj
/T1_4 7.97 Tf
5.67 3.96 Td
(0)Tj
/T1_2 7.97 Tf
-0.39 -7.19 Td
(J)Tj
/T1_0 10.91 Tf
10.29 3.23 Td
(=)Tj
/T1_12 10.91 Tf
12.91 0 Td
(H)Tj
/T1_10 7.97 Tf
7.72 -1.63 Td
(1)Tj
/T1_0 10.91 Tf
4.73 1.63 Td
(\()Tj
/T1_12 10.91 Tf
[(p)27(w)]TJ
/T1_2 7.97 Tf
17.18 -2.61 Td
(J)Tj
/T1_5 10.91 Tf
5.87 2.61 Td
(jj)Tj
/T1_3 10.91 Tf
6.06 0 Td
(\277)Tj
/T1_4 7.97 Tf
6 3.96 Td
(0)Tj
/T1_11 7.97 Tf
-1.23 -6.65 Td
(C)Tj
/T1_5 10.91 Tf
4.73 2.69 Td
(jj)Tj
/T1_0 10.91 Tf
6.64 0 Td
(\271)Tj
/T1_3 10.91 Tf
-0.58 0 Td
(\277)Tj
/T1_4 7.97 Tf
6 3.96 Td
(0)Tj
/T1_2 7.97 Tf
-1.23 -7.19 Td
(J)Tj
/T1_5 10.91 Tf
5.87 3.23 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(SID)Tj
/T1_4 7.97 Tf
17.17 3.96 Td
(0)Tj
/T1_11 7.97 Tf
T*
(c)Tj
/T1_0 10.91 Tf
4.73 2.69 Td
[(\))-410(and)]TJ
/T1_3 10.91 Tf
30.76 0 Td
(v)Tj
/T1_4 7.97 Tf
5.67 3.96 Td
(0)Tj
/T1_2 7.97 Tf
-0.39 -7.01 Td
(i)Tj
/T1_0 10.91 Tf
7.8 3.05 Td
(=)Tj
/T1_12 10.91 Tf
12.91 0 Td
(H)Tj
/T1_10 7.97 Tf
7.72 -1.63 Td
(1)Tj
/T1_0 10.91 Tf
4.73 1.63 Td
(\()Tj
/T1_12 10.91 Tf
[(p)27(w)]TJ
/T1_2 7.97 Tf
17.18 -2.61 Td
(i)Tj
/T1_5 10.91 Tf
3.38 2.61 Td
(jj)Tj
/T1_3 10.91 Tf
6.06 0 Td
(\277)Tj
/T1_4 7.97 Tf
6 3.96 Td
(0)Tj
/T1_11 7.97 Tf
-1.23 -6.65 Td
(C)Tj
/T1_5 10.91 Tf
4.73 2.69 Td
(jj)Tj
/T1_0 10.91 Tf
6.63 0 Td
(\271)Tj
/T1_3 10.91 Tf
-0.57 0 Td
(\277)Tj
/T1_4 7.97 Tf
6 3.96 Td
(0)Tj
/T1_2 7.97 Tf
-1.24 -7.01 Td
(i)Tj
/T1_5 10.91 Tf
4.03 3.05 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(SID)Tj
/T1_4 7.97 Tf
17.18 3.96 Td
(0)Tj
/T1_11 7.97 Tf
T*
(c)Tj
/T1_0 10.91 Tf
4.73 2.69 Td
[(\))-409(for)-410(1)]TJ
/T1_5 10.91 Tf
36.11 0 Td
(\267)Tj
/T1_3 10.91 Tf
12.91 0 Td
(i)Tj
/T1_5 10.91 Tf
8.18 0 Td
(6)Tj
/T1_0 10.91 Tf
(=)Tj
/T1_3 10.91 Tf
12.9 0 Td
(J)Tj
/T1_5 10.91 Tf
11.52 0 Td
(\267)Tj
/T1_3 10.91 Tf
12.9 0 Td
(n)Tj
/T1_2 7.97 Tf
6.55 -1.63 Td
(c)Tj
/T1_0 10.91 Tf
-463.71 -20.28 Td
[(and)-496(sends)]TJ
/T1_5 10.91 Tf
53.98 0 Td
(f)Tj
/T1_1 10.91 Tf
(SID)Tj
/T1_4 7.97 Tf
22.63 3.96 Td
(0)Tj
/T1_11 7.97 Tf
0 -6.66 TD
(c)Tj
/T1_5 10.91 Tf
4.73 2.7 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(C)Tj
/T1_5 10.91 Tf
5.72 0 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(c)Tj
/T1_4 7.97 Tf
5.73 3.96 Td
(0)Tj
/T1_2 7.97 Tf
0 -7.19 TD
(J)Tj
/T1_5 10.91 Tf
5.87 3.23 Td
(jj)Tj
/T1_3 10.91 Tf
6.06 0 Td
(v)Tj
/T1_4 7.97 Tf
5.67 3.96 Td
(0)Tj
/T1_2 7.97 Tf
-0.39 -7.19 Td
(J)Tj
/T1_5 10.91 Tf
5.87 3.23 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(c)Tj
/T1_4 7.97 Tf
5.73 3.96 Td
(0)Tj
/T1_2 7.97 Tf
0 -7.02 TD
(i)Tj
/T1_5 10.91 Tf
3.38 3.06 Td
(jj)Tj
/T1_3 10.91 Tf
6.06 0 Td
(v)Tj
/T1_4 7.97 Tf
5.67 3.96 Td
(0)Tj
/T1_2 7.97 Tf
-0.39 -7.02 Td
(i)Tj
/T1_5 10.91 Tf
3.38 3.06 Td
(g)Tj
/T1_0 10.91 Tf
10.88 0 Td
[(for)-496(1)]TJ
/T1_5 10.91 Tf
29.92 0 Td
(\267)Tj
/T1_3 10.91 Tf
14.49 0 Td
(i)Tj
/T1_5 10.91 Tf
9.76 0 Td
(6)Tj
/T1_0 10.91 Tf
(=)Tj
/T1_3 10.91 Tf
14.48 0 Td
(J)Tj
/T1_5 10.91 Tf
13.1 0 Td
(\267)Tj
/T1_3 10.91 Tf
14.48 0 Td
(n)Tj
/T1_2 7.97 Tf
6.55 -1.64 Td
(c)Tj
/T1_0 10.91 Tf
9.58 1.64 Td
[(to)-496(subgroup)-497(con)27(trollers)]TJ
/T1_1 10.91 Tf
119.17 0 Td
(S)Tj
/T1_2 7.97 Tf
5.72 -1.69 Td
(J)Tj
/T1_0 10.91 Tf
11.29 1.69 Td
(and)Tj
/T1_1 10.91 Tf
22.99 0 Td
(S)Tj
/T1_2 7.97 Tf
5.73 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
8.79 1.64 Td
(for)Tj
-454.81 -21.92 Td
(1)Tj
/T1_5 10.91 Tf
8.48 0 Td
(\267)Tj
/T1_3 10.91 Tf
11.51 0 Td
(i)Tj
/T1_5 10.91 Tf
6.79 0 Td
(6)Tj
/T1_0 10.91 Tf
(=)Tj
/T1_3 10.91 Tf
11.51 0 Td
(J)Tj
/T1_5 10.91 Tf
10.13 0 Td
(\267)Tj
/T1_3 10.91 Tf
11.51 0 Td
(n)Tj
/T1_2 7.97 Tf
6.55 -1.63 Td
(c)Tj
/T1_0 10.91 Tf
4.16 1.63 Td
(.)Tj
-70.64 -21.91 Td
[(Round)-333(2)]TJ
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 0 -554.93 cm
0 0 m
40.75 0 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 112.7614 216.265 Tm
(:)Tj
-40.75 -21.92 Td
(\()Tj
/T1_3 10.91 Tf
(i)Tj
/T1_0 10.91 Tf
(\))Tj
1.0003 0 0 1.0003 72 769.82 Tm
16.848 -575.32 Td
[(The)-422(subgroup)-423(con)27(troller)]TJ
/T1_1 10.91 Tf
121.522 0 Td
(S)Tj
/T1_2 7.97 Tf
5.72 -1.69 Td
(J)Tj
/T1_0 10.91 Tf
10.48 1.69 Td
[(\257rst)-422(decrypts)]TJ
/T1_1 10.91 Tf
68.47 0 Td
(c)Tj
/T1_4 7.97 Tf
5.73 3.96 Td
(0)Tj
/T1_2 7.97 Tf
0 -7.19 TD
(J)Tj
/T1_0 10.91 Tf
10.48 3.23 Td
[(and)-422(c)27(hec)28(ks)-421(if)-423(the)-422(iden)26(tities)]TJ
/T1_1 10.91 Tf
135.55 0 Td
(C)Tj
/T1_0 10.91 Tf
5.72 0 Td
(,)Tj
/T1_1 10.91 Tf
7.88 0 Td
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4.73 2.69 Td
[(,)-386(\271)]TJ
/T1_3 10.91 Tf
6.67 0 Td
(\277)Tj
/T1_4 7.97 Tf
6 3.96 Td
(0)Tj
/T1_1 7.97 Tf
-1.23 -7.01 Td
(i)Tj
/T1_2 10.91 Tf
7.66 3.05 Td
(and)Tj
/T1_0 10.91 Tf
21.21 0 Td
(SID)Tj
/T1_4 7.97 Tf
17.17 3.96 Td
(0)Tj
/T1_11 7.97 Tf
0 -6.65 TD
(c)Tj
/T1_2 10.91 Tf
8.37 2.69 Td
[(for)-333(later)-333(computation.)]TJ
-173.76 -21.91 Td
[(Round)-333(3)]TJ
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 0 -251.16 cm
0 0 m
40.75 0 l
S
Q
Q
BT
/T1_2 10.91 Tf
1.0003 0 0 1.0003 112.7614 520.1201 Tm
(:)Tj
1.0003 0 0 1.0003 72 769.82 Tm
52.555 -249.63 Td
[(Main)-514(con)27(troller)]TJ
/T1_0 10.91 Tf
80.945 0 Td
(C)Tj
/T1_2 10.91 Tf
11.32 0 Td
[(\257rst)-513(c)26(hec)28(ks)-513(if)]TJ
/T1_3 10.91 Tf
72.1 0 Td
(\271)Tj
/T1_4 7.97 Tf
6.57 3.95 Td
(0)Tj
/T1_1 7.97 Tf
0 -7.18 TD
(J)Tj
/T1_2 10.91 Tf
12.18 3.23 Td
(=)Tj
/T1_12 10.91 Tf
14.78 0 Td
[(MA)27(C)]TJ
/T1_1 7.97 Tf
23.48 -1.78 Td
(ak)Tj
/T1_9 5.98 Tf
8.91 -1.34 Td
(J)Tj
/T1_2 10.91 Tf
5.63 3.12 Td
(\()Tj
/T1_3 10.91 Tf
(\277)Tj
/T1_4 7.97 Tf
10.25 3.95 Td
(0)Tj
/T1_11 7.97 Tf
-1.24 -6.65 Td
(C)Tj
/T1_10 10.91 Tf
4.73 2.7 Td
(jj)Tj
/T1_2 10.91 Tf
6.64 0 Td
(\271)Tj
/T1_3 10.91 Tf
-0.58 0 Td
(\277)Tj
/T1_4 7.97 Tf
6 3.95 Td
(0)Tj
/T1_1 7.97 Tf
-1.23 -7.18 Td
(J)Tj
/T1_10 10.91 Tf
5.87 3.23 Td
(jj)Tj
/T1_2 10.91 Tf
6.06 0 Td
(\()Tj
/T1_3 10.91 Tf
(y)Tj
/T1_4 7.97 Tf
9.98 3.95 Td
(\244)Tj
/T1_1 7.97 Tf
-0.39 -7.18 Td
(J)Tj
/T1_2 10.91 Tf
5.87 3.23 Td
(\))Tj
/T1_4 7.97 Tf
4.24 3.95 Td
(0)Tj
/T1_10 10.91 Tf
2.79 -3.95 Td
(jj)Tj
/T1_0 10.91 Tf
6.06 0 Td
(SID)Tj
/T1_4 7.97 Tf
17.18 3.95 Td
(0)Tj
/T1_11 7.97 Tf
0 -6.65 TD
(c)Tj
/T1_10 10.91 Tf
4.73 2.7 Td
(jj)Tj
/T1_0 10.91 Tf
6.06 0 Td
(S)Tj
/T1_1 7.97 Tf
5.72 -1.69 Td
(J)Tj
/T1_10 10.91 Tf
5.87 1.69 Td
(jj)Tj
/T1_0 10.91 Tf
6.06 0 Td
(C)Tj
/T1_10 10.91 Tf
(jj)Tj
/T1_2 10.91 Tf
11.79 0 Td
[(00\).)-985(If)-513(the)]TJ
-410.93 -21.92 Td
[(c)27(hec)28(k)-534(is)-534(not)-535(correct,)]TJ
/T1_0 10.91 Tf
108.52 0 Td
(C)Tj
/T1_2 10.91 Tf
11.56 0 Td
[(blo)-27(c)27(ks)-534(malicious)-535(subgroup)-535(con)27(troller)]TJ
/T1_0 10.91 Tf
185.98 0 Td
(S)Tj
/T1_1 7.97 Tf
5.73 -1.69 Td
(J)Tj
/T1_2 10.91 Tf
5.87 1.69 Td
[(.)-1048(Otherwise,)]TJ
/T1_0 10.91 Tf
71.83 0 Td
(C)Tj
/T1_2 10.91 Tf
11.56 0 Td
(obtains)Tj
/T1_3 10.91 Tf
40.43 0 Td
(y)Tj
/T1_4 7.97 Tf
5.74 3.96 Td
(0)Tj
/T1_1 7.97 Tf
-0.39 -7.19 Td
(J)Tj
/T1_2 10.91 Tf
12.56 3.23 Td
(=)Tj
-459.39 -21.92 Td
(\()Tj
/T1_3 10.91 Tf
(y)Tj
/T1_4 7.97 Tf
9.98 3.96 Td
(\244)Tj
/T1_1 7.97 Tf
-0.39 -7.19 Td
(J)Tj
/T1_2 10.91 Tf
5.87 3.23 Td
(\))Tj
/T1_4 7.97 Tf
4.24 3.96 Td
(0)Tj
/T1_10 10.91 Tf
4.89 -3.96 Td
(\242)Tj
/T1_3 10.91 Tf
5.12 0 Td
(h)Tj
/T1_4 7.97 Tf
6.29 3.96 Td
(\241)Tj
/T1_5 7.97 Tf
(H)Tj
/T1_6 5.98 Tf
12.56 -1.1 Td
(1)Tj
/T1_7 7.97 Tf
4.15 1.1 Td
(\()Tj
/T1_11 7.97 Tf
(SID)Tj
/T1_8 5.98 Tf
15.99 2.81 Td
(0)Tj
/T1_11 5.98 Tf
0 -4.8 TD
(c)Tj
/T1_4 7.97 Tf
3.67 1.99 Td
(jj)Tj
/T1_11 7.97 Tf
(S)Tj
/T1_9 5.98 Tf
8.94 -1.34 Td
(J)Tj
/T1_4 7.97 Tf
5.13 1.34 Td
(jj)Tj
/T1_11 7.97 Tf
4.71 0 Td
(C)Tj
/T1_4 7.97 Tf
(jj)Tj
/T1_5 7.97 Tf
[(p)29(w)]TJ
/T1_9 5.98 Tf
18.97 -2.05 Td
(J)Tj
/T1_4 7.97 Tf
5.13 2.05 Td
(jj)Tj
/T1_1 7.97 Tf
4.71 0 Td
(\277)Tj
/T1_8 5.98 Tf
4.67 2.81 Td
(0)Tj
/T1_11 5.98 Tf
-0.92 -5.08 Td
(C)Tj
/T1_4 7.97 Tf
3.68 2.27 Td
(jj)Tj
/T1_7 7.97 Tf
5.16 0 Td
(\271)Tj
/T1_1 7.97 Tf
-0.46 0 Td
(\277)Tj
/T1_8 5.98 Tf
4.68 2.81 Td
(0)Tj
/T1_9 5.98 Tf
-0.92 -5.51 Td
(J)Tj
/T1_7 7.97 Tf
5.13 2.7 Td
(\))Tj
/T1_2 10.91 Tf
7.27 -3.96 Td
[(and)-317(c)27(hec)27(ks)-396(\271)]TJ
/T1_3 10.91 Tf
54.56 0 Td
(\271)Tj
/T1_4 7.97 Tf
6.57 3.96 Td
(0)Tj
/T1_1 7.97 Tf
0 -7.19 TD
(J)Tj
/T1_2 10.91 Tf
8.9 3.23 Td
(=)Tj
/T1_12 10.91 Tf
11.51 0 Td
[(MA)27(C)]TJ
/T1_1 7.97 Tf
23.48 -1.77 Td
(ak)Tj
/T1_9 5.98 Tf
8.91 -1.34 Td
(J)Tj
/T1_2 10.91 Tf
5.63 3.11 Td
(\()Tj
/T1_3 10.91 Tf
(\277)Tj
/T1_4 7.97 Tf
10.24 3.96 Td
(0)Tj
/T1_11 7.97 Tf
-1.23 -6.65 Td
(C)Tj
/T1_10 10.91 Tf
4.73 2.69 Td
(jj)Tj
/T1_2 10.91 Tf
6.64 0 Td
(\271)Tj
/T1_3 10.91 Tf
-0.58 0 Td
(\277)Tj
/T1_4 7.97 Tf
6 3.96 Td
(0)Tj
/T1_1 7.97 Tf
-1.23 -7.19 Td
(J)Tj
/T1_10 10.91 Tf
5.87 3.23 Td
(jj)Tj
/T1_3 10.91 Tf
6.06 0 Td
(y)Tj
/T1_4 7.97 Tf
5.74 3.96 Td
(0)Tj
/T1_1 7.97 Tf
-0.4 -7.19 Td
(J)Tj
/T1_10 10.91 Tf
5.87 3.23 Td
(jj)Tj
/T1_0 10.91 Tf
6.06 0 Td
(SID)Tj
/T1_4 7.97 Tf
17.18 3.96 Td
(0)Tj
/T1_11 7.97 Tf
0 -6.65 TD
(c)Tj
/T1_10 10.91 Tf
4.73 2.69 Td
(jj)Tj
/T1_0 10.91 Tf
6.06 0 Td
(S)Tj
/T1_1 7.97 Tf
5.73 -1.68 Td
(J)Tj
/T1_10 10.91 Tf
5.87 1.68 Td
(jj)Tj
/T1_0 10.91 Tf
6.06 0 Td
(C)Tj
/T1_10 10.91 Tf
5.72 0 Td
(jj)Tj
/T1_2 10.91 Tf
6.06 0 Td
[(01\).)-439(If)-318(the)-318(c)26(hec)28(k)-317(is)]TJ
-378.99 -21.91 Td
(incorrect,)Tj
/T1_0 10.91 Tf
48.24 0 Td
(C)Tj
/T1_2 10.91 Tf
9 0 Td
[(blo)-28(c)27(ks)-299(malicious)-300(subgroup)-301(con)27(troller)]TJ
/T1_0 10.91 Tf
175.76 0 Td
(S)Tj
/T1_1 7.97 Tf
5.72 -1.69 Td
(J)Tj
/T1_2 10.91 Tf
5.87 1.69 Td
[(.)-433(Otherwise,)]TJ
/T1_0 10.91 Tf
62.09 0 Td
(C)Tj
/T1_2 10.91 Tf
9 0 Td
[(selects)-300(new)-300(random)]TJ
/T1_3 10.91 Tf
95.41 0 Td
(r)Tj
/T1_4 7.97 Tf
5.22 3.96 Td
(0)Tj
/T1_11 7.97 Tf
-0.3 -6.66 Td
(C)Tj
/T1_10 10.91 Tf
7.76 2.7 Td
(2)Tj
/T1_3 10.91 Tf
10.3 0 Td
(Z)Tj
/T1_4 7.97 Tf
8.22 3.96 Td
(\244)Tj
/T1_1 7.97 Tf
-0.78 -6.66 Td
(q)Tj
/T1_2 10.91 Tf
8.79 2.7 Td
(and)Tj
-450.3 -21.92 Td
(computes)Tj
/T1_3 10.91 Tf
48.36 0 Td
(y)Tj
/T1_4 7.97 Tf
5.74 3.96 Td
(0)Tj
/T1_11 7.97 Tf
-0.39 -6.66 Td
(C)Tj
/T1_2 10.91 Tf
7.76 2.7 Td
(=)Tj
/T1_3 10.91 Tf
11.51 0 Td
(g)Tj
/T1_1 7.97 Tf
5.59 3.96 Td
(r)Tj
/T1_8 5.98 Tf
4.06 2.81 Td
(0)Tj
/T1_11 5.98 Tf
-0.24 -5.09 Td
(C)Tj
/T1_2 10.91 Tf
7.2 -1.68 Td
[(mo)-28(d)]TJ
/T1_3 10.91 Tf
23.94 0 Td
(p)Tj
/T1_2 10.91 Tf
5.48 0 Td
[(.)-439(Next,)]TJ
/T1_0 10.91 Tf
37.37 0 Td
(C)Tj
/T1_2 10.91 Tf
9.19 0 Td
[(computes)-317(the)-318(new)-318(DH)-317(k)27(eys)]TJ
/T1_3 10.91 Tf
133.02 0 Td
(t)Tj
/T1_4 7.97 Tf
3.94 3.96 Td
(0)Tj
/T1_1 7.97 Tf
0 -7.19 TD
(J)Tj
/T1_2 10.91 Tf
9.33 3.23 Td
(and)Tj
/T1_3 10.91 Tf
21.04 0 Td
(t)Tj
/T1_4 7.97 Tf
3.93 3.96 Td
(0)Tj
/T1_1 7.97 Tf
0 -7.01 TD
(i)Tj
/T1_2 10.91 Tf
6.85 3.05 Td
[(that)-317(it)-318(shares)-317(with)]TJ
/T1_0 10.91 Tf
91.56 0 Td
(S)Tj
/T1_1 7.97 Tf
5.73 -1.69 Td
(J)Tj
/T1_2 10.91 Tf
9.33 1.69 Td
(and)Tj
/T1_0 10.91 Tf
-450.3 -21.92 Td
(S)Tj
/T1_1 7.97 Tf
5.73 -1.63 Td
(i)Tj
/T1_2 10.91 Tf
7.01 1.63 Td
[(for)-333(1)]TJ
/T1_10 10.91 Tf
25.18 0 Td
(\267)Tj
/T1_3 10.91 Tf
11.51 0 Td
(i)Tj
/T1_10 10.91 Tf
6.78 0 Td
(6)Tj
/T1_2 10.91 Tf
(=)Tj
/T1_3 10.91 Tf
11.52 0 Td
(J)Tj
/T1_10 10.91 Tf
10.12 0 Td
(\267)Tj
/T1_3 10.91 Tf
11.51 0 Td
(n)Tj
/T1_1 7.97 Tf
6.55 -1.63 Td
(c)Tj
/T1_2 10.91 Tf
7.8 1.63 Td
[(resp)-27(ectiv)26(ely)84(,)-333(the)-333(new)-333(\257nal)-334(group)-333(k)27(ey)]TJ
/T1_3 10.91 Tf
177.65 0 Td
(K)Tj
/T1_4 7.97 Tf
10.04 3.96 Td
(0)Tj
/T1_2 10.91 Tf
2.8 -3.96 Td
(,)Tj
/T1_3 10.91 Tf
6.66 0 Td
(\265)Tj
/T1_4 7.97 Tf
5.42 3.96 Td
(0)Tj
/T1_11 7.97 Tf
-0.3 -6.65 Td
(C)Tj
/T1_2 10.91 Tf
4.73 2.69 Td
[(,)-412(^)]TJ
/T1_3 10.91 Tf
6.67 0 Td
(\271)Tj
/T1_4 7.97 Tf
6.57 3.96 Td
(0)Tj
/T1_1 7.97 Tf
0 -7.19 TD
(J)Tj
/T1_2 10.91 Tf
9.5 3.23 Td
[(and)-412(^)]TJ
/T1_3 10.91 Tf
21.21 0 Td
(\271)Tj
/T1_4 7.97 Tf
6.57 3.96 Td
(0)Tj
/T1_1 7.97 Tf
0 -7.01 TD
(i)Tj
/T1_2 10.91 Tf
7.02 3.05 Td
[(for)-333(1)]TJ
/T1_10 10.91 Tf
25.17 0 Td
(\267)Tj
/T1_3 10.91 Tf
11.51 0 Td
(i)Tj
/T1_10 10.91 Tf
6.79 0 Td
(6)Tj
/T1_2 10.91 Tf
(=)Tj
/T1_3 10.91 Tf
11.51 0 Td
(J)Tj
/T1_10 10.91 Tf
10.13 0 Td
(\267)Tj
/T1_3 10.91 Tf
11.51 0 Td
(n)Tj
/T1_1 7.97 Tf
6.55 -1.63 Td
(c)Tj
/T1_2 10.91 Tf
4.16 1.63 Td
(:)Tj
/T1_3 10.91 Tf
-328.79 -39.64 Td
(t)Tj
/T1_4 7.97 Tf
3.93 4.5 Td
(0)Tj
/T1_1 7.97 Tf
0 -7.19 TD
(J)Tj
/T1_2 10.91 Tf
15.84 2.69 Td
[(=)-912(\()]TJ
/T1_3 10.91 Tf
(y)Tj
/T1_4 7.97 Tf
28.42 4.5 Td
(0)Tj
/T1_1 7.97 Tf
-0.39 -7.19 Td
(J)Tj
/T1_2 10.91 Tf
5.87 2.69 Td
(\))Tj
/T1_1 7.97 Tf
4.24 4.5 Td
(r)Tj
/T1_8 5.98 Tf
4.05 2.82 Td
(0)Tj
/T1_11 5.98 Tf
-0.23 -5.09 Td
(C)Tj
/T1_2 10.91 Tf
7.2 -2.23 Td
[(mo)-27(d)]TJ
/T1_3 10.91 Tf
23.93 0 Td
[(p)-1039(;)-1206(t)]TJ
/T1_4 7.97 Tf
36.94 4.5 Td
(0)Tj
/T1_1 7.97 Tf
T*
(i)Tj
/T1_2 10.91 Tf
12.08 2.69 Td
(=)Tj
/T1_3 10.91 Tf
17.18 0 Td
(y)Tj
/T1_1 7.97 Tf
5.74 6.03 Td
(r)Tj
/T1_8 5.98 Tf
4.05 2.81 Td
(0)Tj
/T1_11 5.98 Tf
-0.23 -5.08 Td
(C)Tj
/T1_1 7.97 Tf
-4.21 -7.01 Td
(i)Tj
/T1_2 10.91 Tf
11.41 3.25 Td
[(mo)-27(d)]TJ
/T1_3 10.91 Tf
23.93 0 Td
(p)Tj
-202.78 -32.57 Td
(K)Tj
/T1_4 7.97 Tf
10.04 4.5 Td
(0)Tj
/T1_2 10.91 Tf
12.76 -4.5 Td
(=)Tj
/T1_13 10.91 Tf
18.44 21.92 Td
(0)Tj
0 -19.63 TD
(@)Tj
/T1_3 10.91 Tf
9.54 -2.29 Td
(y)Tj
/T1_4 7.97 Tf
5.74 4.5 Td
(0)Tj
/T1_11 7.97 Tf
-0.39 -7.2 Td
(C)Tj
/T1_10 10.91 Tf
7.15 2.7 Td
(\242)Tj
/T1_3 10.91 Tf
5.45 0 Td
(y)Tj
/T1_4 7.97 Tf
5.74 4.5 Td
(0)Tj
/T1_1 7.97 Tf
-0.39 -7.2 Td
(J)Tj
/T1_10 10.91 Tf
8.3 2.7 Td
(\242)Tj
/T1_1 7.97 Tf
16.41 13.66 Td
(n)Tj
/T1_9 5.98 Tf
5.13 -1 Td
(c)Tj
/T1_13 10.91 Tf
-7.61 -2.3 Td
(Y)Tj
/T1_1 7.97 Tf
-8.48 -23.71 Td
(i)Tj
/T1_7 7.97 Tf
2.88 0 Td
(=1)Tj
/T1_1 7.97 Tf
(;i)Tj
/T1_4 7.97 Tf
16.05 0 Td
(6)Tj
/T1_7 7.97 Tf
(=)Tj
/T1_1 7.97 Tf
6.59 0 Td
(J)Tj
/T1_3 10.91 Tf
7.19 13.35 Td
(y)Tj
/T1_1 7.97 Tf
5.35 -1.64 Td
(i)Tj
/T1_13 10.91 Tf
3.38 23.56 Td
(1)Tj
T*
(A)Tj
/T1_1 7.97 Tf
9.54 16.91 Td
(r)Tj
/T1_8 5.98 Tf
4.05 2.81 Td
(0)Tj
/T1_11 5.98 Tf
-0.23 -5.08 Td
(C)Tj
/T1_2 10.91 Tf
7.2 -16.93 Td
[(mo)-27(d)]TJ
/T1_3 10.91 Tf
23.93 0 Td
(p)Tj
-170.78 -29.82 Td
(\265)Tj
/T1_4 7.97 Tf
5.43 4.5 Td
(0)Tj
/T1_11 7.97 Tf
-0.31 -7.2 Td
(C)Tj
/T1_2 10.91 Tf
14.7 2.7 Td
(=)Tj
/T1_12 10.91 Tf
18.44 0 Td
(H)Tj
/T1_7 7.97 Tf
7.72 -1.64 Td
(1)Tj
/T1_2 10.91 Tf
4.73 1.64 Td
(\()Tj
/T1_0 10.91 Tf
(SID)Tj
/T1_4 7.97 Tf
21.42 4.5 Td
(0)Tj
/T1_11 7.97 Tf
0 -7.2 TD
(c)Tj
/T1_10 10.91 Tf
4.73 2.7 Td
(jj)Tj
/T1_12 10.91 Tf
6.06 0 Td
(UID)Tj
/T1_11 7.97 Tf
18.41 -1.64 Td
(C)Tj
/T1_10 10.91 Tf
4.73 1.64 Td
(jj)Tj
/T1_3 10.91 Tf
6.06 0 Td
(K)Tj
/T1_4 7.97 Tf
10.04 4.5 Td
(0)Tj
/T1_10 10.91 Tf
2.79 -4.5 Td
(jj)Tj
/T1_3 10.91 Tf
6.06 0 Td
(\277)Tj
/T1_4 7.97 Tf
6 4.5 Td
(0)Tj
/T1_11 7.97 Tf
-1.23 -7.2 Td
(C)Tj
/T1_10 10.91 Tf
4.73 2.7 Td
(jj)Tj
/T1_3 10.91 Tf
6.06 0 Td
(y)Tj
/T1_4 7.97 Tf
5.74 4.5 Td
(0)Tj
/T1_11 7.97 Tf
-0.39 -7.2 Td
(C)Tj
/T1_2 10.91 Tf
4.73 2.7 Td
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5.73 -1.69 Td
(J)Tj
/T1_0 10.91 Tf
10.5 1.69 Td
(rejects)Tj
/T1_2 10.91 Tf
35.32 0 Td
(C)Tj
/T1_0 10.91 Tf
[(.)-719(Otherwise,)]TJ
/T1_2 10.91 Tf
72.47 0 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.69 Td
(J)Tj
/T1_0 10.91 Tf
10.5 1.69 Td
(computes)Tj
/T1_1 10.91 Tf
49.53 0 Td
(t)Tj
/T1_4 7.97 Tf
3.94 3.96 Td
(0)Tj
/T1_3 7.97 Tf
0 -7.19 TD
(J)Tj
/T1_0 10.91 Tf
10.57 3.23 Td
[(=)-429(\()]TJ
/T1_1 10.91 Tf
(y)Tj
/T1_4 7.97 Tf
23.15 3.96 Td
(0)Tj
/T1_7 7.97 Tf
-0.39 -6.66 Td
(C)Tj
/T1_0 10.91 Tf
4.73 2.7 Td
(\))Tj
/T1_9 7.97 Tf
4.24 3.96 Td
(H)Tj
/T1_10 5.98 Tf
5.98 -1.11 Td
(2)Tj
/T1_11 7.97 Tf
4.15 1.11 Td
(\()Tj
/T1_3 7.97 Tf
(K)Tj
/T1_12 5.98 Tf
10.99 2.81 Td
(0)Tj
/T1_6 5.98 Tf
-0.56 -5.52 Td
(J)Tj
/T1_11 7.97 Tf
5.14 2.71 Td
(\))Tj
/T1_0 10.91 Tf
6.82 -3.96 Td
[(mo)-27(d)]TJ
/T1_1 10.91 Tf
23.93 0 Td
(p)Tj
/T1_0 10.91 Tf
10.12 0 Td
[(and)-424(uses)]TJ
/T1_1 10.91 Tf
46.35 0 Td
(t)Tj
/T1_4 7.97 Tf
3.94 3.96 Td
(0)Tj
/T1_3 7.97 Tf
T*
(J)Tj
/T1_0 10.91 Tf
10.5 3.23 Td
[(to)-424(de-)]TJ
-439 -21.92 Td
[(crypt)-487(^)]TJ
/T1_2 10.91 Tf
30.35 0 Td
(c)Tj
/T1_4 7.97 Tf
5.73 3.96 Td
(0)Tj
/T1_3 7.97 Tf
T*
(J)Tj
/T1_0 10.91 Tf
11.04 3.23 Td
[(and)-474(obtains)-475(the)-474(new)-475(\257nal)-474(group)-475(k)27(ey)]TJ
/T1_1 10.91 Tf
186.28 0 Td
(K)Tj
/T1_4 7.97 Tf
10.04 3.96 Td
(0)Tj
/T1_0 10.91 Tf
2.8 -3.96 Td
[(,)-509(iden)27(tit)28(y)]TJ
/T1_2 10.91 Tf
50.42 0 Td
(C)Tj
/T1_0 10.91 Tf
5.72 0 Td
(,)Tj
/T1_1 10.91 Tf
8.59 0 Td
(y)Tj
/T1_4 7.97 Tf
5.74 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.39 -7.19 Td
(J)Tj
/T1_0 10.91 Tf
11.05 3.23 Td
(and)Tj
/T1_2 10.91 Tf
22.74 0 Td
(SID)Tj
/T1_4 7.97 Tf
17.18 3.96 Td
(0)Tj
/T1_7 7.97 Tf
0 -6.65 TD
(c)Tj
/T1_0 10.91 Tf
4.73 2.69 Td
[(.)-867(If)-475(the)-474(iden)26(tit)28(y)]TJ
/T1_2 10.91 Tf
87.1 0 Td
(C)Tj
/T1_0 10.91 Tf
5.72 0 Td
(,)Tj
/T1_1 10.91 Tf
-464.84 -21.92 Td
(y)Tj
/T1_4 7.97 Tf
5.74 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.39 -7.19 Td
(J)Tj
/T1_0 10.91 Tf
11.46 3.23 Td
(and)Tj
/T1_2 10.91 Tf
23.17 0 Td
(SID)Tj
/T1_4 7.97 Tf
17.18 3.96 Td
(0)Tj
/T1_7 7.97 Tf
T*
(c)Tj
/T1_0 10.91 Tf
10.32 2.69 Td
[(are)-513(not)-513(decrypted)-513(correctly)83(,)]TJ
/T1_2 10.91 Tf
143.87 0 Td
(S)Tj
/T1_3 7.97 Tf
5.72 -1.68 Td
(J)Tj
/T1_0 10.91 Tf
11.47 1.68 Td
[(rejects)-525(^)]TJ
/T1_2 10.91 Tf
36.28 0 Td
(c)Tj
/T1_4 7.97 Tf
5.73 3.96 Td
(0)Tj
/T1_3 7.97 Tf
0 -7.19 TD
(J)Tj
/T1_0 10.91 Tf
5.87 3.23 Td
[(.)-983(Otherwise,)]TJ
/T1_2 10.91 Tf
70.82 0 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.68 Td
(J)Tj
/T1_0 10.91 Tf
11.46 1.68 Td
[(con\257rms)-513(and)-513(accepts)]TJ
-364.43 -21.91 Td
[(the)-449(new)-450(\257nal)-450(group)-450(k)27(ey)]TJ
/T1_1 10.91 Tf
122.41 0 Td
(K)Tj
/T1_4 7.97 Tf
10.05 3.96 Td
(0)Tj
/T1_0 10.91 Tf
7.7 -3.96 Td
[(if)-449(the)-450(k)27(ey)-449(con\257rmation)-450(co)-27(de)]TJ
/T1_1 10.91 Tf
143.61 0 Td
(\265)Tj
/T1_4 7.97 Tf
5.43 3.96 Td
(0)Tj
/T1_7 7.97 Tf
-0.31 -6.66 Td
(C)Tj
/T1_0 10.91 Tf
9.88 2.7 Td
(=)Tj
/T1_5 10.91 Tf
13.63 0 Td
(H)Tj
/T1_11 7.97 Tf
7.73 -1.64 Td
(1)Tj
/T1_0 10.91 Tf
4.73 1.64 Td
(\()Tj
/T1_2 10.91 Tf
(SID)Tj
/T1_4 7.97 Tf
21.42 3.96 Td
(0)Tj
/T1_7 7.97 Tf
0 -6.66 TD
(c)Tj
/T1_8 10.91 Tf
4.73 2.7 Td
(jj)Tj
/T1_5 10.91 Tf
6.06 0 Td
(UID)Tj
/T1_7 7.97 Tf
18.4 -1.64 Td
(C)Tj
/T1_8 10.91 Tf
4.73 1.64 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(K)Tj
/T1_4 7.97 Tf
10.04 3.96 Td
(0)Tj
/T1_8 10.91 Tf
2.8 -3.96 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(\277)Tj
/T1_4 7.97 Tf
6 3.96 Td
(0)Tj
/T1_7 7.97 Tf
-1.24 -6.66 Td
(C)Tj
/T1_8 10.91 Tf
4.73 2.7 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(y)Tj
/T1_4 7.97 Tf
5.74 3.96 Td
(0)Tj
/T1_7 7.97 Tf
-0.39 -6.66 Td
(C)Tj
/T1_0 10.91 Tf
4.73 2.7 Td
[(\))-449(holds.)]TJ
-430.79 -21.92 Td
(Next,)Tj
/T1_2 10.91 Tf
31.17 0 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.69 Td
(J)Tj
/T1_0 10.91 Tf
10.69 1.69 Td
(encrypts)Tj
/T1_1 10.91 Tf
45.21 0 Td
(K)Tj
/T1_4 7.97 Tf
10.04 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.78 -7.19 Td
(J)Tj
/T1_8 10.91 Tf
5.88 3.23 Td
(jj)Tj
/T1_1 10.91 Tf
6.05 0 Td
(K)Tj
/T1_4 7.97 Tf
10.05 3.96 Td
(0)Tj
/T1_8 10.91 Tf
2.79 -3.96 Td
(jj)Tj
/T1_2 10.91 Tf
6.06 0 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.69 Td
(J)Tj
/T1_8 10.91 Tf
5.87 1.69 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(z)Tj
/T1_4 7.97 Tf
5.55 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.48 -7.28 Td
[(J)24(;k)]TJ
/T1_8 10.91 Tf
11.9 3.32 Td
(jj)Tj
/T1_2 10.91 Tf
6.06 0 Td
(SID)Tj
/T1_4 7.97 Tf
17.18 3.96 Td
(0)Tj
/T1_3 7.97 Tf
0 -7.19 TD
(J)Tj
/T1_0 10.91 Tf
10.69 3.23 Td
(using)Tj
/T1_1 10.91 Tf
29.73 0 Td
(t)Tj
/T1_4 7.97 Tf
3.93 3.96 Td
(0)Tj
/T1_3 7.97 Tf
0 -7.28 TD
[(J)23(;k)]TJ
/T1_0 10.91 Tf
16.73 3.32 Td
(and)Tj
/T1_1 10.91 Tf
22.4 0 Td
(K)Tj
/T1_4 7.97 Tf
10.04 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.78 -7.19 Td
(J)Tj
/T1_8 10.91 Tf
5.87 3.23 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(K)Tj
/T1_4 7.97 Tf
10.04 3.96 Td
(0)Tj
/T1_8 10.91 Tf
2.79 -3.96 Td
(jj)Tj
/T1_2 10.91 Tf
6.06 0 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.69 Td
(J)Tj
/T1_8 10.91 Tf
5.87 1.69 Td
(jj)Tj
/T1_2 10.91 Tf
6.06 0 Td
(SID)Tj
/T1_4 7.97 Tf
17.18 3.96 Td
(0)Tj
/T1_3 7.97 Tf
0 -7.19 TD
(J)Tj
/T1_8 10.91 Tf
5.87 3.23 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(\277)Tj
/T1_4 7.97 Tf
6 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-1.24 -7.19 Td
(J)Tj
/T1_0 10.91 Tf
10.7 3.23 Td
[(using)-442(existing)-442(sub-)]TJ
-376.55 -21.91 Td
[(group)-472(k)27(ey)]TJ
/T1_1 10.91 Tf
53.66 0 Td
(K)Tj
/T1_3 7.97 Tf
9.26 -1.69 Td
(J)Tj
/T1_0 10.91 Tf
11.03 1.69 Td
[(and)-472(obtains)-485(^)]TJ
/T1_2 10.91 Tf
62.47 0 Td
(c)Tj
/T1_4 7.97 Tf
5.73 3.95 Td
(0)Tj
/T1_3 7.97 Tf
0 -7.28 TD
[(J)24(;k)]TJ
/T1_0 10.91 Tf
17.46 3.33 Td
(=)Tj
/T1_8 10.91 Tf
14.05 0 Td
(E)Tj
/T1_3 7.97 Tf
5.75 -2.31 Td
(t)Tj
/T1_12 5.98 Tf
3.06 2.74 Td
(0)Tj
/T1_6 5.98 Tf
0 -5.58 TD
[(J)35(;k)]TJ
/T1_0 10.91 Tf
11.2 5.15 Td
(\()Tj
/T1_1 10.91 Tf
(K)Tj
/T1_4 7.97 Tf
14.29 3.95 Td
(0)Tj
/T1_3 7.97 Tf
-0.78 -7.19 Td
(J)Tj
/T1_8 10.91 Tf
5.87 3.24 Td
(jj)Tj
/T1_1 10.91 Tf
6.05 0 Td
(K)Tj
/T1_4 7.97 Tf
10.05 3.95 Td
(0)Tj
/T1_8 10.91 Tf
2.79 -3.95 Td
(jj)Tj
/T1_2 10.91 Tf
6.06 0 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.69 Td
(J)Tj
/T1_8 10.91 Tf
5.87 1.69 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(z)Tj
/T1_4 7.97 Tf
5.55 3.95 Td
(0)Tj
/T1_3 7.97 Tf
-0.48 -7.28 Td
[(J)24(;k)]TJ
/T1_8 10.91 Tf
11.9 3.33 Td
(jj)Tj
/T1_2 10.91 Tf
6.06 0 Td
(SID)Tj
/T1_4 7.97 Tf
17.18 3.95 Td
(0)Tj
/T1_3 7.97 Tf
0 -7.19 TD
(J)Tj
/T1_0 10.91 Tf
5.87 3.24 Td
[(\))-472(for)]TJ
/T1_1 10.91 Tf
27.6 0 Td
(n)Tj
/T1_3 7.97 Tf
6.55 -1.69 Td
(J)Tj
/T1_0 10.91 Tf
9.31 1.69 Td
[(+)-314(1)]TJ
/T1_8 10.91 Tf
22.93 0 Td
(\267)Tj
/T1_1 10.91 Tf
14.04 0 Td
(k)Tj
/T1_8 10.91 Tf
11.58 0 Td
(\267)Tj
/T1_1 10.91 Tf
14.05 0 Td
(n)Tj
/T1_3 7.97 Tf
6.54 -1.69 Td
(J)Tj
/T1_0 10.91 Tf
9.31 1.69 Td
(+)Tj
/T1_1 10.91 Tf
11.92 0 Td
(m)Tj
/T1_0 10.91 Tf
14.73 0 Td
(and)Tj
-450.16 -21.92 Td
(^)Tj
/T1_2 10.91 Tf
-0.14 0 Td
(c)Tj
/T1_4 7.97 Tf
5.73 3.96 Td
(00)Tj
/T1_3 7.97 Tf
T*
(J)Tj
/T1_0 10.91 Tf
11.19 3.23 Td
(=)Tj
/T1_8 10.91 Tf
13.81 0 Td
(E)Tj
/T1_3 7.97 Tf
5.75 -1.69 Td
(K)Tj
/T1_6 5.98 Tf
7.14 -1.34 Td
(J)Tj
/T1_0 10.91 Tf
5.64 3.03 Td
(\()Tj
/T1_1 10.91 Tf
(K)Tj
/T1_4 7.97 Tf
14.28 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.78 -7.19 Td
(J)Tj
/T1_8 10.91 Tf
5.87 3.23 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(K)Tj
/T1_4 7.97 Tf
10.04 3.96 Td
(0)Tj
/T1_8 10.91 Tf
2.8 -3.96 Td
(jj)Tj
/T1_2 10.91 Tf
6.06 0 Td
(S)Tj
/T1_3 7.97 Tf
5.72 -1.69 Td
(J)Tj
/T1_8 10.91 Tf
5.87 1.69 Td
(jj)Tj
/T1_2 10.91 Tf
6.06 0 Td
(SID)Tj
/T1_4 7.97 Tf
17.18 3.96 Td
(0)Tj
/T1_3 7.97 Tf
T*
(J)Tj
/T1_8 10.91 Tf
5.87 3.23 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(\277)Tj
/T1_4 7.97 Tf
6 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-1.23 -7.19 Td
(J)Tj
/T1_0 10.91 Tf
5.87 3.23 Td
(\).)Tj
/T1_2 10.91 Tf
16.24 0 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.69 Td
(J)Tj
/T1_0 10.91 Tf
10.88 1.69 Td
[(then)-459(computes)-460(the)-459(k)26(ey)-458(con\257rmation)-460(co)-27(de)]TJ
/T1_1 10.91 Tf
208.9 0 Td
(\265)Tj
/T1_4 7.97 Tf
5.43 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.31 -7.19 Td
(J)Tj
/T1_0 10.91 Tf
10.89 3.23 Td
[(and)-538(^)]TJ
/T1_1 10.91 Tf
22.58 0 Td
(\271)Tj
/T1_4 7.97 Tf
6.57 3.96 Td
(0)Tj
/T1_3 7.97 Tf
0 -7.28 TD
[(J)24(;k)]TJ
/T1_0 10.91 Tf
16.91 3.32 Td
(for)Tj
/T1_1 10.91 Tf
-454.81 -21.92 Td
(n)Tj
/T1_3 7.97 Tf
6.55 -1.69 Td
(J)Tj
/T1_0 10.91 Tf
8.29 1.69 Td
[(+)-222(1)]TJ
/T1_8 10.91 Tf
19.39 0 Td
(\267)Tj
/T1_1 10.91 Tf
11.51 0 Td
(k)Tj
/T1_8 10.91 Tf
9.05 0 Td
(\267)Tj
/T1_1 10.91 Tf
11.51 0 Td
(n)Tj
/T1_3 7.97 Tf
6.55 -1.69 Td
(J)Tj
/T1_0 10.91 Tf
8.29 1.69 Td
(+)Tj
/T1_1 10.91 Tf
10.91 0 Td
(m)Tj
/T1_0 10.91 Tf
(:)Tj
/T1_1 10.91 Tf
22.48 -39.64 Td
(\265)Tj
/T1_4 7.97 Tf
5.42 4.5 Td
(0)Tj
/T1_3 7.97 Tf
-0.3 -7.2 Td
(J)Tj
/T1_0 10.91 Tf
15.83 2.7 Td
(=)Tj
/T1_5 10.91 Tf
18.44 0 Td
(H)Tj
/T1_11 7.97 Tf
7.73 -1.64 Td
(1)Tj
/T1_0 10.91 Tf
4.73 1.64 Td
(\()Tj
/T1_2 10.91 Tf
(SID)Tj
/T1_4 7.97 Tf
21.42 4.5 Td
(0)Tj
/T1_3 7.97 Tf
0 -7.2 TD
(J)Tj
/T1_8 10.91 Tf
5.87 2.7 Td
(jj)Tj
/T1_2 10.91 Tf
6.06 0 Td
(UID)Tj
/T1_4 7.97 Tf
17.17 4.5 Td
(0)Tj
/T1_3 7.97 Tf
T*
(J)Tj
/T1_8 10.91 Tf
5.87 2.7 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(K)Tj
/T1_4 7.97 Tf
10.05 4.5 Td
(0)Tj
/T1_3 7.97 Tf
-0.78 -7.2 Td
(J)Tj
/T1_8 10.91 Tf
5.87 2.7 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(K)Tj
/T1_4 7.97 Tf
10.04 4.5 Td
(0)Tj
/T1_8 10.91 Tf
2.79 -4.5 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(\277)Tj
/T1_4 7.97 Tf
6 4.5 Td
(0)Tj
/T1_3 7.97 Tf
-1.23 -7.2 Td
(J)Tj
/T1_8 10.91 Tf
5.87 2.7 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(z)Tj
/T1_4 7.97 Tf
5.55 4.5 Td
(0)Tj
/T1_3 7.97 Tf
-0.48 -7.2 Td
(J)Tj
/T1_0 10.91 Tf
5.87 2.7 Td
(\))Tj
-188.65 -24.9 Td
(^)Tj
/T1_1 10.91 Tf
-0.86 0 Td
(\271)Tj
/T1_4 7.97 Tf
6.57 4.5 Td
(0)Tj
/T1_3 7.97 Tf
0 -7.28 TD
[(J)24(;k)]TJ
/T1_0 10.91 Tf
21.86 2.78 Td
(=)Tj
/T1_5 10.91 Tf
18.44 0 Td
[(MA)27(C)]TJ
/T1_3 7.97 Tf
23.48 -1.78 Td
(ak)Tj
/T1_6 5.98 Tf
8.91 -1.41 Td
[(J)35(;k)]TJ
/T1_0 10.91 Tf
11.2 3.19 Td
(\()Tj
/T1_1 10.91 Tf
(\277)Tj
/T1_4 7.97 Tf
10.24 4.5 Td
(0)Tj
/T1_3 7.97 Tf
-1.23 -7.2 Td
(J)Tj
/T1_8 10.91 Tf
5.87 2.7 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(\277)Tj
/T1_4 7.97 Tf
6 4.5 Td
(0)Tj
/T1_3 7.97 Tf
-1.24 -7.28 Td
[(J)23(;k)]TJ
/T1_8 10.91 Tf
11.91 2.78 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(z)Tj
/T1_4 7.97 Tf
5.55 4.5 Td
(0)Tj
/T1_3 7.97 Tf
-0.48 -7.2 Td
(J)Tj
/T1_8 10.91 Tf
5.87 2.7 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(\265)Tj
/T1_4 7.97 Tf
5.42 4.5 Td
(0)Tj
/T1_3 7.97 Tf
-0.3 -7.2 Td
(J)Tj
/T1_8 10.91 Tf
5.87 2.7 Td
(jj)Tj
/T1_2 10.91 Tf
6.06 0 Td
(SID)Tj
/T1_4 7.97 Tf
17.17 4.5 Td
(0)Tj
/T1_3 7.97 Tf
0 -7.2 TD
(J)Tj
/T1_8 10.91 Tf
5.87 2.7 Td
(jj)Tj
/T1_2 10.91 Tf
6.06 0 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.69 Td
(J)Tj
/T1_8 10.91 Tf
5.87 1.69 Td
(jj)Tj
/T1_2 10.91 Tf
6.06 0 Td
(U)Tj
/T1_3 7.97 Tf
5.72 -1.78 Td
[(J)23(;k)]TJ
/T1_8 10.91 Tf
11.91 1.78 Td
(jj)Tj
/T1_0 10.91 Tf
6.06 0 Td
(11\))Tj
-345.68 -39.65 Td
(where)Tj
/T1_2 10.91 Tf
30.33 0 Td
(UID)Tj
/T1_4 7.97 Tf
17.17 3.96 Td
(0)Tj
/T1_3 7.97 Tf
0 -7.19 TD
(J)Tj
/T1_0 10.91 Tf
8.9 3.23 Td
(=)Tj
/T1_2 10.91 Tf
11.51 0 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.69 Td
(J)Tj
/T1_8 10.91 Tf
5.87 1.69 Td
(jj)Tj
/T1_2 10.91 Tf
6.06 0 Td
(U)Tj
/T1_3 7.97 Tf
5.73 -1.69 Td
[(J)24(;)]TJ
/T1_11 7.97 Tf
(1)Tj
/T1_8 10.91 Tf
11.51 1.69 Td
(jj)Tj
/T1_2 10.91 Tf
6.06 0 Td
(U)Tj
/T1_3 7.97 Tf
5.72 -1.69 Td
[(J)23(;)]TJ
/T1_11 7.97 Tf
(2)Tj
/T1_8 10.91 Tf
11.52 1.69 Td
[(jj)-166(\242)-167(\242)-166(\242)-167(jj)]TJ
/T1_2 10.91 Tf
28.48 0 Td
(U)Tj
/T1_3 7.97 Tf
5.72 -1.69 Td
[(J)23(;n)]TJ
/T1_6 5.98 Tf
11.92 -1.34 Td
(J)Tj
/T1_11 7.97 Tf
5.14 1.34 Td
(+)Tj
/T1_3 7.97 Tf
(m)Tj
/T1_0 10.91 Tf
14.57 1.69 Td
[(.)-407(Next,)]TJ
/T1_2 10.91 Tf
36.19 0 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.69 Td
(J)Tj
/T1_0 10.91 Tf
8.29 1.69 Td
(broadcast)Tj
/T1_8 10.91 Tf
48.56 0 Td
(f)Tj
/T1_2 10.91 Tf
(SID)Tj
/T1_4 7.97 Tf
22.63 3.96 Td
(0)Tj
/T1_3 7.97 Tf
T*
(J)Tj
/T1_8 10.91 Tf
5.88 3.23 Td
(jj)Tj
/T1_2 10.91 Tf
6.05 0 Td
(UID)Tj
/T1_4 7.97 Tf
17.18 3.96 Td
(0)Tj
/T1_3 7.97 Tf
T*
(J)Tj
/T1_8 10.91 Tf
5.87 3.23 Td
(jj)Tj
/T1_2 10.91 Tf
6.06 0 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.69 Td
(J)Tj
/T1_8 10.91 Tf
5.87 1.69 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(z)Tj
/T1_4 7.97 Tf
5.55 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.48 -7.19 Td
(J)Tj
/T1_8 10.91 Tf
5.87 3.23 Td
(jj)Tj
/T1_0 10.91 Tf
6.92 0 Td
(^)Tj
/T1_1 10.91 Tf
-0.86 0 Td
(\271)Tj
/T1_4 7.97 Tf
6.57 3.96 Td
(0)Tj
/T1_3 7.97 Tf
0 -7.28 TD
[(J)24(;k)]TJ
/T1_8 10.91 Tf
11.9 3.32 Td
(jj)Tj
/T1_0 10.91 Tf
6.2 0 Td
(^)Tj
/T1_2 10.91 Tf
-0.14 0 Td
(c)Tj
/T1_4 7.97 Tf
5.73 3.96 Td
(0)Tj
/T1_3 7.97 Tf
T*
[(J)24(;k)]TJ
/T1_8 10.91 Tf
11.9 3.32 Td
(jj)Tj
/T1_0 10.91 Tf
6.19 0 Td
(^)Tj
/T1_2 10.91 Tf
-0.13 0 Td
(c)Tj
/T1_4 7.97 Tf
5.72 3.96 Td
(00)Tj
/T1_3 7.97 Tf
0 -7.19 TD
(J)Tj
/T1_8 10.91 Tf
5.87 3.23 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(\265)Tj
/T1_4 7.97 Tf
5.43 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.31 -7.19 Td
(J)Tj
/T1_8 10.91 Tf
5.87 3.23 Td
(g)Tj
/T1_0 10.91 Tf
-465.9 -21.91 Td
(for)Tj
/T1_1 10.91 Tf
16.69 0 Td
(n)Tj
/T1_3 7.97 Tf
6.55 -1.69 Td
(J)Tj
/T1_0 10.91 Tf
8.29 1.69 Td
[(+)-222(1)]TJ
/T1_8 10.91 Tf
19.39 0 Td
(\267)Tj
/T1_1 10.91 Tf
11.51 0 Td
(k)Tj
/T1_8 10.91 Tf
9.05 0 Td
(\267)Tj
/T1_1 10.91 Tf
11.52 0 Td
(n)Tj
/T1_3 7.97 Tf
6.54 -1.69 Td
(J)Tj
/T1_0 10.91 Tf
8.3 1.69 Td
(+)Tj
/T1_1 10.91 Tf
10.9 0 Td
(m)Tj
/T1_0 10.91 Tf
13.21 0 Td
[(to)-333(subgroup)]TJ
/T1_8 10.91 Tf
60.68 0 Td
(G)Tj
/T1_4 7.97 Tf
7.14 3.95 Td
(0)Tj
/T1_3 7.97 Tf
-0.65 -7.19 Td
(J)Tj
/T1_0 10.91 Tf
5.87 3.24 Td
(.)Tj
-194.99 -21.92 Td
(\()Tj
/T1_1 10.91 Tf
(ii)Tj
/T1_0 10.91 Tf
[(\))-346(Eac)27(h)]TJ
/T1_2 10.91 Tf
47.05 0 Td
(S)Tj
/T1_3 7.97 Tf
5.72 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
7.17 1.64 Td
[(for)-347(1)]TJ
/T1_8 10.91 Tf
25.57 0 Td
(\267)Tj
/T1_1 10.91 Tf
11.77 0 Td
(i)Tj
/T1_8 10.91 Tf
7.03 0 Td
(6)Tj
/T1_0 10.91 Tf
(=)Tj
/T1_1 10.91 Tf
11.77 0 Td
(J)Tj
/T1_8 10.91 Tf
10.37 0 Td
(\267)Tj
/T1_1 10.91 Tf
11.77 0 Td
(n)Tj
/T1_3 7.97 Tf
6.54 -1.64 Td
(c)Tj
/T1_0 10.91 Tf
7.95 1.64 Td
[(\257rst)-347(c)27(hec)28(ks)-346(if)-427(^)]TJ
/T1_1 10.91 Tf
66.65 0 Td
(\271)Tj
/T1_4 7.97 Tf
6.57 3.96 Td
(0)Tj
/T1_3 7.97 Tf
0 -7.02 TD
(i)Tj
/T1_0 10.91 Tf
6.66 3.06 Td
(=)Tj
/T1_5 10.91 Tf
11.76 0 Td
[(MA)27(C)]TJ
/T1_3 7.97 Tf
23.48 -1.78 Td
(ak)Tj
/T1_6 5.98 Tf
8.91 -1.21 Td
(i)Tj
/T1_0 10.91 Tf
3.65 2.99 Td
(\()Tj
/T1_1 10.91 Tf
4.25 0 Td
(\277)Tj
/T1_4 7.97 Tf
6 3.96 Td
(0)Tj
/T1_7 7.97 Tf
-1.24 -6.66 Td
(C)Tj
/T1_8 10.91 Tf
4.73 2.7 Td
(jj)Tj
/T1_0 10.91 Tf
6.64 0 Td
(\271)Tj
/T1_1 10.91 Tf
-0.58 0 Td
(\277)Tj
/T1_4 7.97 Tf
6.01 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-1.24 -7.02 Td
(i)Tj
/T1_8 10.91 Tf
4.03 3.06 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(y)Tj
/T1_4 7.97 Tf
5.74 3.96 Td
(0)Tj
/T1_7 7.97 Tf
-0.39 -6.66 Td
(C)Tj
/T1_8 10.91 Tf
4.73 2.7 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(\265)Tj
/T1_4 7.97 Tf
5.42 3.96 Td
(0)Tj
/T1_7 7.97 Tf
-0.3 -6.66 Td
(C)Tj
/T1_8 10.91 Tf
4.73 2.7 Td
(jj)Tj
/T1_2 10.91 Tf
6.06 0 Td
(SID)Tj
/T1_4 7.97 Tf
17.17 3.96 Td
(0)Tj
/T1_7 7.97 Tf
0 -6.66 TD
(c)Tj
/T1_8 10.91 Tf
4.73 2.7 Td
(jj)Tj
/T1_2 10.91 Tf
6.06 0 Td
(C)Tj
/T1_8 10.91 Tf
(jj)Tj
/T1_2 10.91 Tf
11.79 0 Td
(S)Tj
/T1_3 7.97 Tf
5.72 -1.64 Td
(i)Tj
/T1_8 10.91 Tf
3.38 1.64 Td
(jj)Tj
/T1_0 10.91 Tf
6.06 0 Td
[(11\))-347(is)-347(correct.)]TJ
-402.01 -21.92 Td
[(If)-395(the)-396(equation)-396(is)-396(incorrect,)]TJ
/T1_2 10.91 Tf
137.3 0 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
7.7 1.63 Td
(rejects)Tj
/T1_2 10.91 Tf
35.01 0 Td
(C)Tj
/T1_0 10.91 Tf
5.72 0 Td
[(.)-632(Otherwise,)]TJ
/T1_2 10.91 Tf
65.4 0 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
7.69 1.63 Td
(computes)Tj
/T1_1 10.91 Tf
49.22 0 Td
(t)Tj
/T1_4 7.97 Tf
3.94 3.96 Td
(0)Tj
/T1_3 7.97 Tf
0 -7.01 TD
(i)Tj
/T1_0 10.91 Tf
7.55 3.05 Td
[(=)-381(\()]TJ
/T1_1 10.91 Tf
(y)Tj
/T1_4 7.97 Tf
22.62 3.96 Td
(0)Tj
/T1_7 7.97 Tf
-0.39 -6.65 Td
(C)Tj
/T1_0 10.91 Tf
4.73 2.69 Td
(\))Tj
/T1_9 7.97 Tf
4.25 3.96 Td
(H)Tj
/T1_10 5.98 Tf
5.97 -1.11 Td
(2)Tj
/T1_11 7.97 Tf
4.15 1.11 Td
(\()Tj
/T1_3 7.97 Tf
(K)Tj
/T1_6 5.98 Tf
10.43 -1.21 Td
(i)Tj
/T1_11 7.97 Tf
3.16 1.21 Td
(\))Tj
/T1_0 10.91 Tf
6.82 -3.96 Td
[(mo)-28(d)]TJ
/T1_1 10.91 Tf
23.94 0 Td
(p)Tj
/T1_0 10.91 Tf
9.8 0 Td
[(and)-396(uses)]TJ
/T1_1 10.91 Tf
-426.47 -21.91 Td
(t)Tj
/T1_4 7.97 Tf
3.94 3.95 Td
(0)Tj
/T1_3 7.97 Tf
T*
(i)Tj
/T1_0 10.91 Tf
7.65 3.06 Td
[(to)-392(decrypt)-404(^)]TJ
/T1_2 10.91 Tf
54.33 0 Td
(c)Tj
/T1_4 7.97 Tf
5.72 3.95 Td
(0)Tj
/T1_3 7.97 Tf
T*
(i)Tj
/T1_0 10.91 Tf
7.66 3.06 Td
[(and)-391(obtains)-392(the)-392(new)-392(\257nal)-392(group)-392(k)27(ey)]TJ
/T1_1 10.91 Tf
179.97 0 Td
(K)Tj
/T1_4 7.97 Tf
10.05 3.95 Td
(0)Tj
/T1_0 10.91 Tf
2.79 -3.95 Td
[(,)-406(iden)27(tit)27(y)]TJ
/T1_2 10.91 Tf
48.4 0 Td
(C)Tj
/T1_0 10.91 Tf
5.72 0 Td
(,)Tj
/T1_1 10.91 Tf
7.47 0 Td
(y)Tj
/T1_3 7.97 Tf
5.34 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
7.66 1.64 Td
(and)Tj
/T1_2 10.91 Tf
21.84 0 Td
(SID)Tj
/T1_4 7.97 Tf
17.18 3.95 Td
(0)Tj
/T1_7 7.97 Tf
0 -6.65 TD
(c)Tj
/T1_0 10.91 Tf
4.73 2.7 Td
[(.)-620(If)-392(the)-392(iden)27(tit)28(y)]TJ
/T1_2 10.91 Tf
-390.45 -21.92 Td
(C)Tj
/T1_0 10.91 Tf
(,)Tj
/T1_1 10.91 Tf
13.13 0 Td
(y)Tj
/T1_3 7.97 Tf
5.35 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
7.61 1.64 Td
(and)Tj
/T1_2 10.91 Tf
21.8 0 Td
(SID)Tj
/T1_4 7.97 Tf
17.17 3.96 Td
(0)Tj
/T1_7 7.97 Tf
0 -6.66 TD
(c)Tj
/T1_0 10.91 Tf
8.96 2.7 Td
[(are)-387(not)-388(decrypted)-388(correctly)82(,)]TJ
/T1_2 10.91 Tf
138.06 0 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
7.61 1.64 Td
[(rejects)-399(^)]TJ
/T1_2 10.91 Tf
34.91 0 Td
(c)Tj
/T1_4 7.97 Tf
5.73 3.96 Td
(0)Tj
/T1_3 7.97 Tf
0 -7.01 TD
(i)Tj
/T1_0 10.91 Tf
3.38 3.05 Td
[(.)-607(Otherwise,)]TJ
/T1_2 10.91 Tf
65.02 0 Td
(S)Tj
/T1_3 7.97 Tf
5.72 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
7.61 1.64 Td
[(con\257rms)-387(and)-388(accepts)-388(the)]TJ
-347.79 -21.92 Td
[(\257nal)-422(group)-422(k)27(ey)]TJ
/T1_1 10.91 Tf
77.77 0 Td
(K)Tj
/T1_4 7.97 Tf
10.04 3.96 Td
(0)Tj
/T1_0 10.91 Tf
7.4 -3.96 Td
[(if)-421(the)-423(k)27(ey)-421(con\257rmation)-422(co)-28(de)]TJ
/T1_1 10.91 Tf
142.11 0 Td
(\265)Tj
/T1_4 7.97 Tf
5.42 3.96 Td
(0)Tj
/T1_7 7.97 Tf
-0.3 -6.65 Td
(C)Tj
/T1_0 10.91 Tf
9.37 2.69 Td
(=)Tj
/T1_5 10.91 Tf
13.13 0 Td
(H)Tj
/T1_11 7.97 Tf
7.73 -1.63 Td
(1)Tj
/T1_0 10.91 Tf
4.73 1.63 Td
(\()Tj
/T1_2 10.91 Tf
(SID)Tj
/T1_4 7.97 Tf
21.42 3.96 Td
(0)Tj
/T1_7 7.97 Tf
0 -6.65 TD
(c)Tj
/T1_8 10.91 Tf
4.73 2.69 Td
(jj)Tj
/T1_5 10.91 Tf
6.06 0 Td
(UID)Tj
/T1_7 7.97 Tf
18.4 -1.63 Td
(C)Tj
/T1_8 10.91 Tf
4.73 1.63 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(K)Tj
/T1_4 7.97 Tf
10.04 3.96 Td
(0)Tj
/T1_8 10.91 Tf
2.8 -3.96 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(\277)Tj
/T1_4 7.97 Tf
6 3.96 Td
(0)Tj
/T1_7 7.97 Tf
-1.24 -6.65 Td
(C)Tj
/T1_8 10.91 Tf
4.73 2.69 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(y)Tj
/T1_4 7.97 Tf
5.74 3.96 Td
(0)Tj
/T1_7 7.97 Tf
-0.39 -6.65 Td
(C)Tj
/T1_0 10.91 Tf
4.73 2.69 Td
[(\))-422(holds.)-711(Next,)]TJ
/T1_2 10.91 Tf
75.43 0 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
-464.49 -20.28 Td
(selects)Tj
/T1_1 10.91 Tf
34.53 0 Td
(\277)Tj
/T1_4 7.97 Tf
6 3.95 Td
(0)Tj
/T1_3 7.97 Tf
-1.24 -7.01 Td
(i)Tj
/T1_8 10.91 Tf
7.86 3.06 Td
(2)Tj
/T1_1 10.91 Tf
11.09 0 Td
(Z)Tj
/T1_4 7.97 Tf
8.22 3.95 Td
(\244)Tj
/T1_3 7.97 Tf
-0.78 -6.65 Td
(q)Tj
/T1_0 10.91 Tf
9.63 2.7 Td
[(and)-376(session)-377(iden)27(tit)27(y)]TJ
/T1_2 10.91 Tf
98.85 0 Td
(SID)Tj
/T1_4 7.97 Tf
17.18 3.95 Td
(0)Tj
/T1_3 7.97 Tf
0 -7.01 TD
(i)Tj
/T1_0 10.91 Tf
7.49 3.06 Td
[(and)-377(encrypts)]TJ
/T1_1 10.91 Tf
66.18 0 Td
(K)Tj
/T1_4 7.97 Tf
10.04 3.95 Td
(0)Tj
/T1_8 10.91 Tf
2.79 -3.95 Td
(jj)Tj
/T1_2 10.91 Tf
6.06 0 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.64 Td
(i)Tj
/T1_8 10.91 Tf
3.38 1.64 Td
(jj)Tj
/T1_2 10.91 Tf
6.06 0 Td
(SID)Tj
/T1_4 7.97 Tf
17.17 3.95 Td
(0)Tj
/T1_3 7.97 Tf
T*
(i)Tj
/T1_8 10.91 Tf
3.39 3.06 Td
(jj)Tj
/T1_1 10.91 Tf
6.05 0 Td
(\277)Tj
/T1_4 7.97 Tf
6.01 3.95 Td
(0)Tj
/T1_3 7.97 Tf
-1.24 -7.01 Td
(i)Tj
/T1_0 10.91 Tf
8.14 3.06 Td
(using)Tj
/T1_1 10.91 Tf
29.02 0 Td
(K)Tj
/T1_3 7.97 Tf
9.26 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
7.49 1.64 Td
[(and)-376(obtains)-390(^)]TJ
/T1_2 10.91 Tf
60.39 0 Td
(c)Tj
/T1_4 7.97 Tf
5.73 3.95 Td
(00)Tj
/T1_3 7.97 Tf
T*
(i)Tj
/T1_0 10.91 Tf
8.91 3.06 Td
(=)Tj
/T1_8 10.91 Tf
-459.39 -21.92 Td
(E)Tj
/T1_3 7.97 Tf
5.76 -1.69 Td
(K)Tj
/T1_6 5.98 Tf
7.14 -1.21 Td
(i)Tj
/T1_0 10.91 Tf
3.65 2.9 Td
(\()Tj
/T1_1 10.91 Tf
4.25 0 Td
(K)Tj
/T1_4 7.97 Tf
10.04 3.96 Td
(0)Tj
/T1_8 10.91 Tf
2.79 -3.96 Td
(jj)Tj
/T1_2 10.91 Tf
6.06 0 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.64 Td
(i)Tj
/T1_8 10.91 Tf
3.38 1.64 Td
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[(and)-283(obtains)]TJ
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[(new)-257(subgroup)-258(k)26(ey)]TJ
/T1_0 10.91 Tf
86.99 0 Td
(K)Tj
/T1_1 7.97 Tf
10.04 3.96 Td
(0)Tj
/T1_2 7.97 Tf
-0.78 -7.19 Td
(J)Tj
/T1_3 10.91 Tf
5.88 3.23 Td
[(,)-272(new)-258(\257nal)-258(group)-258(k)27(ey)]TJ
/T1_0 10.91 Tf
99.99 0 Td
(K)Tj
/T1_1 7.97 Tf
10.04 3.96 Td
(0)Tj
/T1_3 10.91 Tf
2.79 -3.96 Td
[(,)-273(iden)27(tit)28(y)]TJ
/T1_6 10.91 Tf
45.48 0 Td
(S)Tj
/T1_2 7.97 Tf
5.73 -1.69 Td
(J)Tj
/T1_3 10.91 Tf
5.87 1.69 Td
(,)Tj
/T1_6 10.91 Tf
6 0 Td
(SID)Tj
/T1_1 7.97 Tf
17.18 3.96 Td
(0)Tj
/T1_2 7.97 Tf
T*
(J)Tj
/T1_3 10.91 Tf
8.68 3.23 Td
(and)Tj
/T1_0 10.91 Tf
20.39 0 Td
(\277)Tj
/T1_1 7.97 Tf
6 3.96 Td
(0)Tj
/T1_2 7.97 Tf
-1.24 -7.19 Td
(J)Tj
/T1_3 10.91 Tf
5.88 3.23 Td
[(.)-418(If)-258(the)-258(iden)27(tit)27(y)]TJ
/T1_6 10.91 Tf
75.11 0 Td
(S)Tj
/T1_2 7.97 Tf
5.73 -1.69 Td
(J)Tj
/T1_3 10.91 Tf
8.68 1.69 Td
(and)Tj
/T1_6 10.91 Tf
20.38 0 Td
(SID)Tj
/T1_1 7.97 Tf
17.18 3.96 Td
(0)Tj
/T1_2 7.97 Tf
T*
(J)Tj
/T1_3 10.91 Tf
-462 -18.69 Td
[(are)-289(not)-290(decrypted)-290(correctly)82(,)]TJ
/T1_6 10.91 Tf
133.74 0 Td
(U)Tj
/T1_2 7.97 Tf
5.73 -1.68 Td
[(J)24(;j)]TJ
/T1_3 10.91 Tf
14.32 1.68 Td
[(rejects)-302(^)]TJ
/T1_6 10.91 Tf
33.86 0 Td
(c)Tj
/T1_1 7.97 Tf
5.72 3.96 Td
(00)Tj
/T1_2 7.97 Tf
T*
(J)Tj
/T1_3 10.91 Tf
5.87 3.23 Td
[(.)-430(Otherwise,)]TJ
/T1_6 10.91 Tf
61.96 0 Td
(U)Tj
/T1_2 7.97 Tf
5.73 -1.68 Td
[(J)24(;j)]TJ
/T1_3 10.91 Tf
14.33 1.68 Td
[(con\257rms)-289(and)-290(accepts)-290(new)-290(subgroup)-290(k)27(ey)]TJ
/T1_0 10.91 Tf
-281.26 -21.91 Td
(K)Tj
/T1_1 7.97 Tf
10.04 3.96 Td
(0)Tj
/T1_2 7.97 Tf
-0.78 -7.19 Td
(J)Tj
/T1_3 10.91 Tf
9.51 3.23 Td
[(and)-333(new)-333(\257nal)-333(group)-334(k)27(ey)]TJ
/T1_0 10.91 Tf
118.48 0 Td
(K)Tj
/T1_1 7.97 Tf
10.04 3.96 Td
(0)Tj
/T1_3 10.91 Tf
6.43 -3.96 Td
(if)Tj
/T1_0 10.91 Tf
10 0 Td
(\265)Tj
/T1_1 7.97 Tf
5.42 3.96 Td
(0)Tj
/T1_2 7.97 Tf
-0.3 -7.19 Td
(J)Tj
/T1_3 10.91 Tf
8.9 3.23 Td
(=)Tj
/T1_4 10.91 Tf
11.51 0 Td
(H)Tj
/T1_5 7.97 Tf
7.73 -1.64 Td
(1)Tj
/T1_3 10.91 Tf
4.73 1.64 Td
(\()Tj
/T1_6 10.91 Tf
(SID)Tj
/T1_1 7.97 Tf
21.42 3.96 Td
(0)Tj
/T1_2 7.97 Tf
T*
(J)Tj
/T1_7 10.91 Tf
5.87 3.23 Td
(jj)Tj
/T1_6 10.91 Tf
6.06 0 Td
(UID)Tj
/T1_1 7.97 Tf
17.17 3.96 Td
(0)Tj
/T1_2 7.97 Tf
T*
(J)Tj
/T1_7 10.91 Tf
5.87 3.23 Td
(jj)Tj
/T1_0 10.91 Tf
6.06 0 Td
(K)Tj
/T1_1 7.97 Tf
10.05 3.96 Td
(0)Tj
/T1_2 7.97 Tf
-0.78 -7.19 Td
(J)Tj
/T1_7 10.91 Tf
5.87 3.23 Td
(jj)Tj
/T1_0 10.91 Tf
6.06 0 Td
(K)Tj
/T1_1 7.97 Tf
10.04 3.96 Td
(0)Tj
/T1_7 10.91 Tf
2.79 -3.96 Td
(jj)Tj
/T1_0 10.91 Tf
6.06 0 Td
(\277)Tj
/T1_1 7.97 Tf
6 3.96 Td
(0)Tj
/T1_2 7.97 Tf
-1.23 -7.19 Td
(J)Tj
/T1_7 10.91 Tf
5.87 3.23 Td
(jj)Tj
/T1_0 10.91 Tf
6.06 0 Td
(z)Tj
/T1_1 7.97 Tf
5.55 3.96 Td
(0)Tj
/T1_2 7.97 Tf
-0.48 -7.19 Td
(J)Tj
/T1_3 10.91 Tf
5.87 3.23 Td
[(\))-333(holds.)]TJ
-331.89 -21.92 Td
(\()Tj
/T1_0 10.91 Tf
(iii)Tj
/T1_3 10.91 Tf
15.51 0 Td
[(\))-291(Eac)27(h)]TJ
/T1_6 10.91 Tf
34.08 0 Td
(U)Tj
/T1_2 7.97 Tf
5.73 -1.63 Td
(i;j)Tj
/T1_3 10.91 Tf
12.79 1.63 Td
[(for)-291(1)]TJ
/T1_7 10.91 Tf
24.72 0 Td
(\267)Tj
/T1_0 10.91 Tf
11.51 0 Td
(i)Tj
/T1_7 10.91 Tf
6.79 0 Td
(6)Tj
/T1_3 10.91 Tf
(=)Tj
/T1_0 10.91 Tf
11.51 0 Td
(J)Tj
/T1_7 10.91 Tf
10.12 0 Td
(\267)Tj
/T1_0 10.91 Tf
11.52 0 Td
(n)Tj
/T1_2 7.97 Tf
6.54 -1.63 Td
(c)Tj
/T1_3 10.91 Tf
7.35 1.63 Td
[(and)-291(1)]TJ
/T1_7 10.91 Tf
29.23 0 Td
(\267)Tj
/T1_0 10.91 Tf
11.51 0 Td
(j)Tj
/T1_7 10.91 Tf
8.14 0 Td
(\267)Tj
/T1_0 10.91 Tf
11.52 0 Td
(n)Tj
/T1_2 7.97 Tf
6.54 -1.63 Td
(i)Tj
/T1_3 10.91 Tf
6.56 1.63 Td
(uses)Tj
/T1_0 10.91 Tf
22.69 0 Td
(K)Tj
/T1_2 7.97 Tf
9.26 -1.63 Td
(i)Tj
/T1_3 10.91 Tf
6.56 1.63 Td
[(to)-291(decrypt)-304(^)]TJ
/T1_6 10.91 Tf
52.13 0 Td
(c)Tj
/T1_1 7.97 Tf
5.73 3.96 Td
(00)Tj
/T1_2 7.97 Tf
0 -7.01 TD
(i)Tj
/T1_3 10.91 Tf
8.27 3.05 Td
[(and)-291(obtains)-291(new)-292(\257nal)-291(group)]TJ
-336.31 -21.91 Td
[(k)27(ey)]TJ
/T1_0 10.91 Tf
19.53 0 Td
(K)Tj
/T1_1 7.97 Tf
10.04 3.95 Td
(0)Tj
/T1_3 10.91 Tf
2.79 -3.95 Td
[(,)-321(iden)27(tit)28(y)]TJ
/T1_6 10.91 Tf
46.66 0 Td
(S)Tj
/T1_2 7.97 Tf
5.73 -1.64 Td
(i)Tj
/T1_3 10.91 Tf
3.38 1.64 Td
(,)Tj
/T1_6 10.91 Tf
6.53 0 Td
(SID)Tj
/T1_1 7.97 Tf
17.17 3.95 Td
(0)Tj
/T1_2 7.97 Tf
T*
(i)Tj
/T1_3 10.91 Tf
6.85 3.06 Td
(and)Tj
/T1_0 10.91 Tf
21.04 0 Td
(\277)Tj
/T1_1 7.97 Tf
6.01 3.95 Td
(0)Tj
/T1_2 7.97 Tf
-1.24 -7.01 Td
(i)Tj
/T1_3 10.91 Tf
4.03 3.06 Td
[(.)-439(If)-318(the)-318(iden)27(tit)27(y)]TJ
/T1_6 10.91 Tf
77.3 0 Td
(S)Tj
/T1_2 7.97 Tf
5.73 -1.64 Td
(i)Tj
/T1_3 10.91 Tf
6.85 1.64 Td
(and)Tj
/T1_6 10.91 Tf
21.04 0 Td
(SID)Tj
/T1_1 7.97 Tf
17.18 3.95 Td
(0)Tj
/T1_2 7.97 Tf
T*
(i)Tj
/T1_3 10.91 Tf
6.85 3.06 Td
[(are)-317(not)-318(decrypted)-318(correctly)82(,)]TJ
/T1_6 10.91 Tf
134.9 0 Td
(U)Tj
/T1_2 7.97 Tf
5.73 -1.64 Td
(i;j)Tj
/T1_3 10.91 Tf
13.08 1.64 Td
(rejects)Tj
-437.04 -21.92 Td
(^)Tj
/T1_6 10.91 Tf
-0.14 0 Td
(c)Tj
/T1_1 7.97 Tf
5.73 3.96 Td
(00)Tj
/T1_2 7.97 Tf
0 -7.02 TD
(i)Tj
/T1_3 10.91 Tf
5.09 3.06 Td
[(.)-589(Otherwise,)]TJ
/T1_6 10.91 Tf
64.73 0 Td
(U)Tj
/T1_2 7.97 Tf
5.73 -1.64 Td
(i;j)Tj
/T1_3 10.91 Tf
13.78 1.64 Td
[(con\257rms)-381(and)-381(accepts)-382(new)-382(\257nal)-381(group)-382(k)27(ey)]TJ
/T1_0 10.91 Tf
204.11 0 Td
(K)Tj
/T1_1 7.97 Tf
10.05 3.96 Td
(0)Tj
/T1_3 10.91 Tf
6.95 -3.96 Td
(if)Tj
/T1_0 10.91 Tf
10.53 0 Td
(\265)Tj
/T1_1 7.97 Tf
5.42 3.96 Td
(0)Tj
/T1_2 7.97 Tf
-0.3 -7.02 Td
(i)Tj
/T1_3 10.91 Tf
7.29 3.06 Td
(=)Tj
/T1_4 10.91 Tf
12.39 0 Td
(H)Tj
/T1_5 7.97 Tf
7.72 -1.64 Td
(1)Tj
/T1_3 10.91 Tf
4.73 1.64 Td
(\()Tj
/T1_6 10.91 Tf
(SID)Tj
/T1_1 7.97 Tf
21.42 3.96 Td
(0)Tj
/T1_2 7.97 Tf
T*
(i)Tj
/T1_7 10.91 Tf
3.38 3.06 Td
(jj)Tj
/T1_6 10.91 Tf
6.06 0 Td
(UID)Tj
/T1_2 7.97 Tf
17.18 -1.64 Td
(i)Tj
/T1_7 10.91 Tf
3.38 1.64 Td
(jj)Tj
/T1_0 10.91 Tf
6.06 0 Td
(K)Tj
/T1_1 7.97 Tf
10.04 3.96 Td
(0)Tj
/T1_7 10.91 Tf
2.79 -3.96 Td
(jj)Tj
/T1_0 10.91 Tf
6.06 0 Td
(\277)Tj
/T1_1 7.97 Tf
6 3.96 Td
(0)Tj
/T1_2 7.97 Tf
-1.23 -7.02 Td
(i)Tj
/T1_7 10.91 Tf
4.03 3.06 Td
(jj)Tj
/T1_0 10.91 Tf
6.06 0 Td
(z)Tj
/T1_2 7.97 Tf
5.07 -1.64 Td
(i)Tj
/T1_3 10.91 Tf
3.38 1.64 Td
(\))Tj
-463.63 -21.92 Td
(holds.)Tj
/T1_8 10.91 Tf
0 -37.17 TD
[(Lea)31(v)32(e)-382(Proto)-32(col)]TJ
/T1_3 10.91 Tf
0 -28.96 TD
[(Supp)-27(ose)-369(a)-368(set)-369(of)]TJ
/T1_0 10.91 Tf
82.84 0 Td
(`)Tj
/T1_3 10.91 Tf
8.57 0 Td
(users)Tj
/T1_7 10.91 Tf
27.8 0 Td
(L)Tj
/T1_3 10.91 Tf
11.19 0 Td
(=)Tj
/T1_7 10.91 Tf
12.15 0 Td
(f)Tj
/T1_6 10.91 Tf
(U)Tj
/T1_2 7.97 Tf
11.18 -1.78 Td
(L;l)Tj
/T1_9 5.98 Tf
10.63 -1.11 Td
(1)Tj
/T1_0 10.91 Tf
4.65 2.89 Td
(;)Tj
/T1_7 10.91 Tf
4.85 0 Td
[(\242)-166(\242)-167(\242)]TJ
/T1_0 10.91 Tf
16.36 0 Td
(;)Tj
/T1_6 10.91 Tf
4.84 0 Td
(U)Tj
/T1_2 7.97 Tf
5.73 -1.78 Td
(L;l)Tj
/T1_10 5.98 Tf
10.63 -1.41 Td
(`)Tj
/T1_7 10.91 Tf
4.1 3.19 Td
(g)Tj
/T1_3 10.91 Tf
[(,)-377(with)-368(index)]TJ
/T1_7 10.91 Tf
67.59 0 Td
(f)Tj
/T1_0 10.91 Tf
(l)Tj
/T1_5 7.97 Tf
8.71 -1.64 Td
(1)Tj
/T1_0 10.91 Tf
4.73 1.64 Td
(;)Tj
/T1_7 10.91 Tf
4.85 0 Td
[(\242)-166(\242)-166(\242)]TJ
/T1_0 10.91 Tf
16.35 0 Td
[(;)-167(l)]TJ
/T1_2 7.97 Tf
8.11 -1.78 Td
(`)Tj
/T1_7 10.91 Tf
3.95 1.78 Td
[(g)-336(\275)-336(f)]TJ
/T1_3 10.91 Tf
(1)Tj
/T1_0 10.91 Tf
(;)Tj
/T1_3 10.91 Tf
37.03 0 Td
(2)Tj
/T1_0 10.91 Tf
(;)Tj
/T1_7 10.91 Tf
10.3 0 Td
[(\242)-166(\242)-167(\242)]TJ
/T1_0 10.91 Tf
16.36 0 Td
[(;)-166(n)]TJ
/T1_2 7.97 Tf
11.39 -1.69 Td
(L)Tj
/T1_7 10.91 Tf
6.26 1.69 Td
(g)Tj
/T1_3 10.91 Tf
[(,)-377(wishes)-368(to)]TJ
-411.15 -21.92 Td
[(lea)27(v)28(e)-288(subgroup)]TJ
/T1_7 10.91 Tf
73.35 0 Td
(G)Tj
/T1_2 7.97 Tf
6.49 -1.69 Td
(L)Tj
/T1_3 10.91 Tf
9.28 1.69 Td
(=)Tj
/T1_7 10.91 Tf
11.51 0 Td
(f)Tj
/T1_6 10.91 Tf
(U)Tj
/T1_2 7.97 Tf
11.18 -1.69 Td
(L;)Tj
/T1_5 7.97 Tf
(1)Tj
/T1_0 10.91 Tf
12.84 1.69 Td
(;)Tj
/T1_7 10.91 Tf
4.85 0 Td
[(\242)-166(\242)-167(\242)]TJ
/T1_0 10.91 Tf
16.36 0 Td
(;)Tj
/T1_6 10.91 Tf
4.85 0 Td
(U)Tj
/T1_2 7.97 Tf
5.72 -1.69 Td
(L;n)Tj
/T1_10 5.98 Tf
13.25 -1.34 Td
(L)Tj
/T1_7 10.91 Tf
6.05 3.03 Td
(g)Tj
/T1_3 10.91 Tf
[(,)-298(then)-289(the)-289(Lea)27(v)27(e)-288(Proto)-28(col)-289(will)-289(b)-28(e)-289(executed)-289(to)-289(establish)-289(a)-290(new)]TJ
-175.73 -21.92 Td
[(subgroup)-401(k)27(ey)]TJ
/T1_0 10.91 Tf
68.53 0 Td
(K)Tj
/T1_1 7.97 Tf
10.04 3.96 Td
(0)Tj
/T1_2 7.97 Tf
-0.78 -7.19 Td
(L)Tj
/T1_3 10.91 Tf
10.64 3.23 Td
[(and)-401(new)-401(\257nal)-402(group)-401(k)27(ey)]TJ
/T1_0 10.91 Tf
122.19 0 Td
(K)Tj
/T1_1 7.97 Tf
10.05 3.96 Td
(0)Tj
/T1_3 10.91 Tf
7.17 -3.96 Td
[(to)-401(protect)-401(future)-402(group)-401(comm)26(unications)-400(from)-402(the)]TJ
-227.84 -21.91 Td
[(lea)27(ving)-332(users.)-444(W)82(e)-332(re-index)-334(the)-333(remaining)-333(users)-334(in)-333(subgroup)]TJ
/T1_7 10.91 Tf
286.74 0 Td
(G)Tj
/T1_1 7.97 Tf
7.13 3.95 Td
(0)Tj
/T1_2 7.97 Tf
-0.64 -7.19 Td
(L)Tj
/T1_3 10.91 Tf
9.28 3.24 Td
(=)Tj
/T1_7 10.91 Tf
11.51 0 Td
(G)Tj
/T1_2 7.97 Tf
6.49 -1.69 Td
(L)Tj
/T1_7 10.91 Tf
8.68 1.69 Td
[(n)-222(L)]TJ
/T1_3 10.91 Tf
18.43 0 Td
(=)Tj
/T1_7 10.91 Tf
11.51 0 Td
(f)Tj
/T1_6 10.91 Tf
(V)Tj
/T1_2 7.97 Tf
11.18 -1.69 Td
(L;)Tj
/T1_5 7.97 Tf
(1)Tj
/T1_0 10.91 Tf
12.84 1.69 Td
(;)Tj
/T1_7 10.91 Tf
4.85 0 Td
[(\242)-166(\242)-166(\242)]TJ
/T1_0 10.91 Tf
16.36 0 Td
(;)Tj
/T1_6 10.91 Tf
4.84 0 Td
(V)Tj
/T1_2 7.97 Tf
5.73 -1.78 Td
(L;n)Tj
/T1_10 5.98 Tf
13.24 -1.34 Td
(L)Tj
/T1_1 7.97 Tf
5.56 1.34 Td
(\241)Tj
/T1_2 7.97 Tf
(`)Tj
/T1_7 10.91 Tf
10.54 1.78 Td
(g)Tj
/T1_3 10.91 Tf
(.)Tj
-427.34 -21.92 Td
[(The)-312(Lea)27(v)28(e)-311(Proto)-28(col)-312(consists)-311(of)-312(3)-312(phases.)-437(During)-312(Phase)-312(1,)-316(subgroup)-312(con)26(troller)]TJ
/T1_6 10.91 Tf
372.11 0 Td
(S)Tj
/T1_2 7.97 Tf
5.73 -1.69 Td
(L)Tj
/T1_3 10.91 Tf
9.66 1.69 Td
[(computes)-311(the)]TJ
-404.43 -21.92 Td
[(new)-389(subgroup)-389(k)27(ey)]TJ
/T1_0 10.91 Tf
91.28 0 Td
(K)Tj
/T1_1 7.97 Tf
10.05 3.96 Td
(0)Tj
/T1_2 7.97 Tf
-0.78 -7.19 Td
(L)Tj
/T1_3 10.91 Tf
6.25 3.23 Td
[(.)-611(Next)-389(in)-389(Phase)-389(2,)]TJ
/T1_6 10.91 Tf
95.5 0 Td
(S)Tj
/T1_2 7.97 Tf
5.73 -1.69 Td
(L)Tj
/T1_3 10.91 Tf
10.49 1.69 Td
(uses)Tj
/T1_0 10.91 Tf
23.76 0 Td
(K)Tj
/T1_1 7.97 Tf
10.04 3.96 Td
(0)Tj
/T1_2 7.97 Tf
-0.78 -7.19 Td
(L)Tj
/T1_3 10.91 Tf
10.5 3.23 Td
[(to)-388(in)26(teract)-388(with)-389(main)-389(con)27(troller)]TJ
/T1_6 10.91 Tf
157.63 0 Td
(C)Tj
/T1_3 10.91 Tf
9.97 0 Td
[(in)-388(order)]TJ
-429.64 -21.91 Td
(for)Tj
/T1_6 10.91 Tf
17.32 0 Td
(C)Tj
/T1_3 10.91 Tf
9.99 0 Td
[(to)-390(compute)-391(the)-391(new)-391(\257nal)-390(group)-391(k)27(ey)]TJ
/T1_0 10.91 Tf
178.01 0 Td
(K)Tj
/T1_1 7.97 Tf
10.04 3.95 Td
(0)Tj
/T1_3 10.91 Tf
2.79 -3.95 Td
[(.)-617(Finally)-390(in)-391(Phase)-391(3,)-405(the)-391(new)-391(\257nal)-391(group)-391(k)27(ey)]TJ
/T1_0 10.91 Tf
225.29 0 Td
(K)Tj
/T1_1 7.97 Tf
10.04 3.95 Td
(0)Tj
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-0.58 0 Td
(\277)Tj
/T1_2 7.97 Tf
6 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-1.23 -7.19 Td
(L)Tj
/T1_5 10.91 Tf
6.26 3.23 Td
(jj)Tj
/T1_4 10.91 Tf
6.05 0 Td
(C)Tj
/T1_5 10.91 Tf
(jj)Tj
/T1_4 10.91 Tf
11.79 0 Td
(S)Tj
/T1_3 7.97 Tf
5.72 -1.69 Td
(L)Tj
/T1_5 10.91 Tf
6.26 1.69 Td
(jj)Tj
/T1_4 10.91 Tf
6.06 0 Td
(SID)Tj
/T1_2 7.97 Tf
17.18 3.96 Td
(0)Tj
/T1_11 7.97 Tf
0 -6.65 TD
(c)Tj
/T1_0 10.91 Tf
4.73 2.69 Td
[(\))-428(and)]TJ
/T1_4 10.91 Tf
31.16 0 Td
(c)Tj
/T1_2 7.97 Tf
5.73 3.96 Td
(0)Tj
/T1_3 7.97 Tf
0 -7.01 TD
(i)Tj
/T1_0 10.91 Tf
8.15 3.05 Td
(=)Tj
/T1_5 10.91 Tf
13.25 0 Td
(E)Tj
/T1_3 7.97 Tf
5.75 -1.77 Td
(ek)Tj
/T1_7 5.98 Tf
8.34 -1.22 Td
(i)Tj
/T1_0 10.91 Tf
3.66 2.99 Td
(\()Tj
/T1_1 10.91 Tf
(\277)Tj
/T1_2 7.97 Tf
10.24 3.96 Td
(0)Tj
/T1_11 7.97 Tf
-1.23 -6.65 Td
(C)Tj
/T1_5 10.91 Tf
4.73 2.69 Td
(jj)Tj
/T1_0 10.91 Tf
6.63 0 Td
(\271)Tj
/T1_1 10.91 Tf
-0.57 0 Td
(\277)Tj
/T1_2 7.97 Tf
6 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-1.24 -7.01 Td
(i)Tj
/T1_5 10.91 Tf
4.03 3.05 Td
(jj)Tj
/T1_4 10.91 Tf
6.06 0 Td
(C)Tj
/T1_5 10.91 Tf
(jj)Tj
/T1_4 10.91 Tf
11.78 0 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.63 Td
(i)Tj
/T1_5 10.91 Tf
3.38 1.63 Td
(jj)Tj
/T1_4 10.91 Tf
6.06 0 Td
(SID)Tj
/T1_2 7.97 Tf
17.18 3.96 Td
(0)Tj
/T1_11 7.97 Tf
0 -6.65 TD
(c)Tj
/T1_0 10.91 Tf
4.73 2.69 Td
[(\))-428(for)-429(1)]TJ
/T1_5 10.91 Tf
36.87 0 Td
(\267)Tj
/T1_1 10.91 Tf
13.25 0 Td
(i)Tj
/T1_5 10.91 Tf
8.52 0 Td
(6)Tj
/T1_0 10.91 Tf
(=)Tj
/T1_1 10.91 Tf
13.25 0 Td
(L)Tj
/T1_5 10.91 Tf
12.19 0 Td
(\267)Tj
/T1_1 10.91 Tf
13.25 0 Td
(n)Tj
/T1_3 7.97 Tf
6.55 -1.63 Td
(c)Tj
/T1_0 10.91 Tf
-463.71 -20.28 Td
[(resp)-27(ectiv)27(ely)83(.)-587(Next,)]TJ
/T1_4 10.91 Tf
94.71 0 Td
(C)Tj
/T1_0 10.91 Tf
9.88 0 Td
(computes)Tj
/T1_1 10.91 Tf
49.05 0 Td
(v)Tj
/T1_2 7.97 Tf
5.68 3.95 Td
(0)Tj
/T1_3 7.97 Tf
-0.39 -7.19 Td
(L)Tj
/T1_0 10.91 Tf
10.15 3.24 Td
(=)Tj
/T1_12 10.91 Tf
12.38 0 Td
(H)Tj
/T1_9 7.97 Tf
7.73 -1.64 Td
(1)Tj
/T1_0 10.91 Tf
4.73 1.64 Td
(\()Tj
/T1_12 10.91 Tf
[(p)27(w)]TJ
/T1_3 7.97 Tf
17.18 -2.62 Td
(L)Tj
/T1_5 10.91 Tf
6.25 2.62 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(\277)Tj
/T1_2 7.97 Tf
6 3.95 Td
(0)Tj
/T1_11 7.97 Tf
-1.23 -6.65 Td
(C)Tj
/T1_5 10.91 Tf
4.73 2.7 Td
(jj)Tj
/T1_0 10.91 Tf
6.64 0 Td
(\271)Tj
/T1_1 10.91 Tf
-0.58 0 Td
(\277)Tj
/T1_2 7.97 Tf
6 3.95 Td
(0)Tj
/T1_3 7.97 Tf
-1.23 -7.19 Td
(L)Tj
/T1_5 10.91 Tf
6.25 3.24 Td
(jj)Tj
/T1_4 10.91 Tf
6.06 0 Td
(SID)Tj
/T1_2 7.97 Tf
17.18 3.95 Td
(0)Tj
/T1_11 7.97 Tf
T*
(c)Tj
/T1_0 10.91 Tf
4.73 2.7 Td
[(\))-381(and)]TJ
/T1_1 10.91 Tf
30.12 0 Td
(v)Tj
/T1_2 7.97 Tf
5.68 3.95 Td
(0)Tj
/T1_3 7.97 Tf
-0.39 -7.01 Td
(i)Tj
/T1_0 10.91 Tf
7.28 3.06 Td
(=)Tj
/T1_12 10.91 Tf
12.38 0 Td
(H)Tj
/T1_9 7.97 Tf
7.73 -1.64 Td
(1)Tj
/T1_0 10.91 Tf
4.73 1.64 Td
(\()Tj
/T1_12 10.91 Tf
[(p)27(w)]TJ
/T1_3 7.97 Tf
17.17 -2.62 Td
(i)Tj
/T1_5 10.91 Tf
3.38 2.62 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(\277)Tj
/T1_2 7.97 Tf
6.01 3.95 Td
(0)Tj
/T1_11 7.97 Tf
-1.24 -6.65 Td
(C)Tj
/T1_5 10.91 Tf
4.73 2.7 Td
(jj)Tj
/T1_0 10.91 Tf
6.64 0 Td
(\271)Tj
/T1_1 10.91 Tf
-0.58 0 Td
(\277)Tj
/T1_2 7.97 Tf
6 3.95 Td
(0)Tj
/T1_3 7.97 Tf
-1.23 -7.01 Td
(i)Tj
/T1_5 10.91 Tf
4.03 3.06 Td
(jj)Tj
/T1_4 10.91 Tf
6.06 0 Td
(SID)Tj
/T1_2 7.97 Tf
17.17 3.95 Td
(0)Tj
/T1_11 7.97 Tf
T*
(c)Tj
/T1_0 10.91 Tf
4.73 2.7 Td
[(\))-381(for)-381(1)]TJ
/T1_5 10.91 Tf
34.97 0 Td
(\267)Tj
/T1_1 10.91 Tf
-459.39 -21.92 Td
(i)Tj
/T1_5 10.91 Tf
6.79 0 Td
(6)Tj
/T1_0 10.91 Tf
(=)Tj
/T1_1 10.91 Tf
11.51 0 Td
(L)Tj
/T1_5 10.91 Tf
10.45 0 Td
(\267)Tj
/T1_1 10.91 Tf
11.51 0 Td
(n)Tj
/T1_3 7.97 Tf
6.55 -1.64 Td
(c)Tj
/T1_0 10.91 Tf
7.62 1.64 Td
[(and)-317(sends)]TJ
/T1_5 10.91 Tf
50.06 0 Td
(f)Tj
/T1_4 10.91 Tf
(SID)Tj
/T1_2 7.97 Tf
22.63 3.96 Td
(0)Tj
/T1_11 7.97 Tf
0 -6.66 TD
(c)Tj
/T1_5 10.91 Tf
4.73 2.7 Td
(jj)Tj
/T1_4 10.91 Tf
6.06 0 Td
(C)Tj
/T1_5 10.91 Tf
5.72 0 Td
(jj)Tj
/T1_4 10.91 Tf
6.06 0 Td
(c)Tj
/T1_2 7.97 Tf
5.73 3.96 Td
(0)Tj
/T1_3 7.97 Tf
0 -7.19 TD
(L)Tj
/T1_5 10.91 Tf
6.25 3.23 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(v)Tj
/T1_2 7.97 Tf
5.68 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.39 -7.19 Td
(L)Tj
/T1_5 10.91 Tf
6.25 3.23 Td
(jj)Tj
/T1_4 10.91 Tf
6.06 0 Td
(c)Tj
/T1_2 7.97 Tf
5.73 3.96 Td
(0)Tj
/T1_3 7.97 Tf
0 -7.02 TD
(i)Tj
/T1_5 10.91 Tf
3.38 3.06 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(v)Tj
/T1_2 7.97 Tf
5.67 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.39 -7.02 Td
(i)Tj
/T1_5 10.91 Tf
3.38 3.06 Td
(g)Tj
/T1_0 10.91 Tf
8.91 0 Td
[(for)-317(1)]TJ
/T1_5 10.91 Tf
25 0 Td
(\267)Tj
/T1_1 10.91 Tf
11.51 0 Td
(i)Tj
/T1_5 10.91 Tf
6.79 0 Td
(6)Tj
/T1_0 10.91 Tf
(=)Tj
/T1_1 10.91 Tf
11.51 0 Td
(L)Tj
/T1_5 10.91 Tf
10.45 0 Td
(\267)Tj
/T1_1 10.91 Tf
11.51 0 Td
(n)Tj
/T1_3 7.97 Tf
6.55 -1.64 Td
(c)Tj
/T1_0 10.91 Tf
7.62 1.64 Td
[(to)-317(subgroup)-317(con)27(trollers)]TJ
/T1_4 10.91 Tf
113.29 0 Td
(S)Tj
/T1_3 7.97 Tf
5.72 -1.69 Td
(L)Tj
/T1_0 10.91 Tf
9.72 1.69 Td
(and)Tj
/T1_4 10.91 Tf
21.02 0 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
-464.49 -20.28 Td
[(for)-333(1)]TJ
/T1_5 10.91 Tf
25.17 0 Td
(\267)Tj
/T1_1 10.91 Tf
11.52 0 Td
(i)Tj
/T1_5 10.91 Tf
6.78 0 Td
(6)Tj
/T1_0 10.91 Tf
(=)Tj
/T1_1 10.91 Tf
11.52 0 Td
(L)Tj
/T1_5 10.91 Tf
10.45 0 Td
(\267)Tj
/T1_1 10.91 Tf
11.51 0 Td
(n)Tj
/T1_3 7.97 Tf
6.55 -1.63 Td
(c)Tj
/T1_0 10.91 Tf
4.16 1.63 Td
(.)Tj
-87.66 -21.91 Td
[(Round)-333(2)]TJ
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 0 -304.96 cm
0 0 m
40.75 0 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 112.7614 466.305 Tm
(:)Tj
-40.75 -21.92 Td
(\()Tj
/T1_1 10.91 Tf
(i)Tj
/T1_0 10.91 Tf
(\))Tj
1.0003 0 0 1.0003 72 769.82 Tm
16.783 -325.35 Td
[(The)-416(subgroup)-416(con)26(troller)]TJ
/T1_4 10.91 Tf
121.317 0 Td
(S)Tj
/T1_3 7.97 Tf
5.72 -1.69 Td
(L)Tj
/T1_0 10.91 Tf
10.8 1.69 Td
[(\257rst)-416(decrypts)]TJ
/T1_4 10.91 Tf
68.34 0 Td
(c)Tj
/T1_2 7.97 Tf
5.72 3.96 Td
(0)Tj
/T1_3 7.97 Tf
0 -7.19 TD
(L)Tj
/T1_0 10.91 Tf
10.8 3.23 Td
[(and)-416(c)27(hec)28(ks)-416(if)-416(the)-416(iden)27(tities)]TJ
/T1_4 10.91 Tf
135.22 0 Td
(C)Tj
/T1_0 10.91 Tf
5.72 0 Td
(,)Tj
/T1_4 10.91 Tf
7.8 0 Td
(S)Tj
/T1_3 7.97 Tf
5.72 -1.69 Td
(L)Tj
/T1_0 10.91 Tf
10.8 1.69 Td
(and)Tj
/T1_4 10.91 Tf
22.11 0 Td
(SID)Tj
/T1_2 7.97 Tf
17.18 3.96 Td
(0)Tj
/T1_11 7.97 Tf
0 -6.66 TD
(c)Tj
/T1_0 10.91 Tf
9.27 2.7 Td
(are)Tj
-453.3 -21.92 Td
[(decrypted)-276(correctly)83(.)-425(If)-276(the)-276(iden)26(tities)-275(are)-276(not)-277(correct,)]TJ
/T1_4 10.91 Tf
248.46 0 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.68 Td
(L)Tj
/T1_0 10.91 Tf
9.27 1.68 Td
(rejects)Tj
/T1_4 10.91 Tf
33.7 0 Td
(C)Tj
/T1_0 10.91 Tf
5.72 0 Td
[(.)-425(Otherwise,)]TJ
/T1_4 10.91 Tf
61.8 0 Td
(S)Tj
/T1_3 7.97 Tf
5.72 -1.68 Td
(L)Tj
/T1_0 10.91 Tf
9.27 1.68 Td
[(uses)-276(passw)27(ord)]TJ
/T1_12 10.91 Tf
69.01 0 Td
[(p)27(w)]TJ
/T1_3 7.97 Tf
12.94 -2.61 Td
(L)Tj
/T1_0 10.91 Tf
-461.62 -19.3 Td
[(to)-333(c)27(hec)28(k)-332(if)]TJ
/T1_1 10.91 Tf
52.71 0 Td
(v)Tj
/T1_2 7.97 Tf
5.68 3.95 Td
(0)Tj
/T1_3 7.97 Tf
-0.4 -7.18 Td
(L)Tj
/T1_0 10.91 Tf
9.29 3.23 Td
(=)Tj
/T1_12 10.91 Tf
11.51 0 Td
(H)Tj
/T1_9 7.97 Tf
7.73 -1.64 Td
(1)Tj
/T1_0 10.91 Tf
4.73 1.64 Td
(\()Tj
/T1_12 10.91 Tf
[(p)27(w)]TJ
/T1_3 7.97 Tf
17.17 -2.62 Td
(L)Tj
/T1_5 10.91 Tf
6.26 2.62 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(\277)Tj
/T1_2 7.97 Tf
6 3.95 Td
(0)Tj
/T1_11 7.97 Tf
-1.23 -6.65 Td
(C)Tj
/T1_5 10.91 Tf
4.73 2.7 Td
(jj)Tj
/T1_0 10.91 Tf
6.63 0 Td
(\271)Tj
/T1_1 10.91 Tf
-0.57 0 Td
(\277)Tj
/T1_2 7.97 Tf
6 3.95 Td
(0)Tj
/T1_3 7.97 Tf
-1.24 -7.18 Td
(L)Tj
/T1_5 10.91 Tf
6.26 3.23 Td
(jj)Tj
/T1_4 10.91 Tf
6.06 0 Td
(SID)Tj
/T1_2 7.97 Tf
17.18 3.95 Td
(0)Tj
/T1_11 7.97 Tf
0 -6.65 TD
(c)Tj
/T1_0 10.91 Tf
4.73 2.7 Td
[(\))-332(is)-333(correct.)-445(If)-333(the)-333(c)27(hec)27(k)-332(is)-333(incorrect,)]TJ
/T1_4 10.91 Tf
178.06 0 Td
(S)Tj
/T1_3 7.97 Tf
5.72 -1.69 Td
(L)Tj
/T1_0 10.91 Tf
9.89 1.69 Td
(rejects)Tj
/T1_4 10.91 Tf
34.32 0 Td
(C)Tj
/T1_0 10.91 Tf
[(.)-444(Otherwise,)]TJ
/T1_4 10.91 Tf
-403.28 -21.92 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.69 Td
(L)Tj
/T1_0 10.91 Tf
9.89 1.69 Td
[(uses)-333(new)-333(subgroup)-333(k)27(ey)]TJ
/T1_1 10.91 Tf
112.6 0 Td
(K)Tj
/T1_2 7.97 Tf
10.04 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.78 -7.19 Td
(L)Tj
/T1_0 10.91 Tf
9.9 3.23 Td
[(computed)-332(in)-334(Phase)-333(1)-333(Round)-334(3)-333(to)-333(compute:)]TJ
/T1_1 10.91 Tf
-61.75 -39.64 Td
(y)Tj
/T1_2 7.97 Tf
5.74 4.5 Td
(0)Tj
/T1_3 7.97 Tf
-0.39 -7.2 Td
(L)Tj
/T1_0 10.91 Tf
9.28 2.7 Td
(=)Tj
/T1_1 10.91 Tf
11.51 0 Td
(g)Tj
/T1_13 7.97 Tf
5.6 4.5 Td
(H)Tj
/T1_14 5.98 Tf
5.97 -1.11 Td
(2)Tj
/T1_9 7.97 Tf
4.15 1.11 Td
(\()Tj
/T1_3 7.97 Tf
(K)Tj
/T1_6 5.98 Tf
11 2.81 Td
(0)Tj
/T1_7 5.98 Tf
-0.57 -5.51 Td
(L)Tj
/T1_9 7.97 Tf
5.56 2.7 Td
(\))Tj
/T1_0 10.91 Tf
6.82 -4.5 Td
[(mo)-27(d)]TJ
/T1_1 10.91 Tf
23.93 0 Td
(p)Tj
/T1_0 10.91 Tf
11.96 0 Td
[(,)-592(\()]TJ
/T1_1 10.91 Tf
(y)Tj
/T1_2 7.97 Tf
19.48 4.5 Td
(\244)Tj
/T1_3 7.97 Tf
-0.4 -7.2 Td
(L)Tj
/T1_0 10.91 Tf
6.26 2.7 Td
(\))Tj
/T1_2 7.97 Tf
4.24 4.5 Td
(0)Tj
/T1_0 10.91 Tf
5.83 -4.5 Td
(=)Tj
/T1_1 10.91 Tf
11.51 0 Td
(y)Tj
/T1_2 7.97 Tf
5.74 4.5 Td
(0)Tj
/T1_3 7.97 Tf
-0.4 -7.2 Td
(L)Tj
/T1_5 10.91 Tf
8.68 2.7 Td
(\242)Tj
/T1_1 10.91 Tf
5.46 0 Td
(h)Tj
/T1_13 7.97 Tf
6.28 4.5 Td
(H)Tj
/T1_14 5.98 Tf
5.98 -1.11 Td
(1)Tj
/T1_9 7.97 Tf
4.15 1.11 Td
(\()Tj
/T1_11 7.97 Tf
(SID)Tj
/T1_6 5.98 Tf
15.99 2.81 Td
(0)Tj
/T1_11 5.98 Tf
0 -4.8 TD
(c)Tj
/T1_2 7.97 Tf
3.67 1.99 Td
(jj)Tj
/T1_11 7.97 Tf
(S)Tj
/T1_7 5.98 Tf
8.94 -1.34 Td
(L)Tj
/T1_2 7.97 Tf
5.55 1.34 Td
(jj)Tj
/T1_11 7.97 Tf
(C)Tj
/T1_2 7.97 Tf
8.94 0 Td
(jj)Tj
/T1_13 7.97 Tf
[(p)29(w)]TJ
/T1_7 5.98 Tf
14.74 -2.05 Td
(L)Tj
/T1_2 7.97 Tf
5.55 2.05 Td
(jj)Tj
/T1_3 7.97 Tf
4.71 0 Td
(\277)Tj
/T1_6 5.98 Tf
4.67 2.81 Td
(0)Tj
/T1_11 5.98 Tf
-0.92 -5.08 Td
(C)Tj
/T1_2 7.97 Tf
3.68 2.27 Td
(jj)Tj
/T1_9 7.97 Tf
5.16 0 Td
(\271)Tj
/T1_3 7.97 Tf
-0.46 0 Td
(\277)Tj
/T1_6 5.98 Tf
4.68 2.81 Td
(0)Tj
/T1_7 5.98 Tf
-0.92 -5.51 Td
(L)Tj
/T1_9 7.97 Tf
5.55 2.7 Td
(\))Tj
/T1_1 10.91 Tf
-200.77 -29.41 Td
(\271)Tj
/T1_2 7.97 Tf
6.57 4.51 Td
(0)Tj
/T1_3 7.97 Tf
0 -7.2 TD
(L)Tj
/T1_0 10.91 Tf
9.29 2.69 Td
(=)Tj
/T1_12 10.91 Tf
11.51 0 Td
[(MA)28(C)]TJ
/T1_3 7.97 Tf
23.48 -1.77 Td
(ak)Tj
/T1_7 5.98 Tf
8.9 -1.34 Td
(L)Tj
/T1_0 10.91 Tf
6.05 3.11 Td
(\()Tj
/T1_1 10.91 Tf
4.25 0 Td
(\277)Tj
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/T1_2 7.97 Tf
-0.39 -7.19 Td
(L)Tj
/T1_5 10.91 Tf
6.25 3.23 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(SID)Tj
/T1_4 7.97 Tf
17.18 3.96 Td
(0)Tj
/T1_9 7.97 Tf
0 -6.66 TD
(c)Tj
/T1_5 10.91 Tf
4.73 2.7 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(S)Tj
/T1_2 7.97 Tf
5.72 -1.69 Td
(L)Tj
/T1_5 10.91 Tf
6.26 1.69 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(C)Tj
/T1_5 10.91 Tf
5.72 0 Td
(jj)Tj
/T1_0 10.91 Tf
6.06 0 Td
[(01\).)-567(If)-374(the)-375(c)27(hec)28(k)]TJ
-387.17 -21.92 Td
[(is)-453(incorrect,)-483(then)]TJ
/T1_1 10.91 Tf
88.59 0 Td
(C)Tj
/T1_0 10.91 Tf
10.67 0 Td
[(blo)-28(c)27(ks)-452(malicious)-453(subgroup)-454(con)27(troller)]TJ
/T1_1 10.91 Tf
182.43 0 Td
(S)Tj
/T1_2 7.97 Tf
5.73 -1.69 Td
(L)Tj
/T1_0 10.91 Tf
6.25 1.69 Td
[(.)-804(Otherwise,)]TJ
/T1_1 10.91 Tf
68.06 0 Td
(C)Tj
/T1_0 10.91 Tf
10.67 0 Td
[(selects)-453(new)-453(random)]TJ
/T1_3 10.91 Tf
-372.4 -21.92 Td
(r)Tj
/T1_4 7.97 Tf
5.22 3.96 Td
(0)Tj
/T1_9 7.97 Tf
-0.3 -6.65 Td
(C)Tj
/T1_5 10.91 Tf
7.87 2.69 Td
(2)Tj
/T1_3 10.91 Tf
10.41 0 Td
(Z)Tj
/T1_4 7.97 Tf
8.23 3.96 Td
(\244)Tj
/T1_2 7.97 Tf
-0.78 -6.65 Td
(q)Tj
/T1_0 10.91 Tf
9.21 2.69 Td
[(and)-339(computes)]TJ
/T1_3 10.91 Tf
69.87 0 Td
(y)Tj
/T1_4 7.97 Tf
5.74 3.96 Td
(0)Tj
/T1_9 7.97 Tf
-0.39 -6.65 Td
(C)Tj
/T1_0 10.91 Tf
7.87 2.69 Td
(=)Tj
/T1_3 10.91 Tf
11.62 0 Td
(g)Tj
/T1_2 7.97 Tf
5.59 3.96 Td
(r)Tj
/T1_10 5.98 Tf
4.06 2.81 Td
(0)Tj
/T1_9 5.98 Tf
-0.24 -5.08 Td
(C)Tj
/T1_0 10.91 Tf
7.2 -1.69 Td
[(mo)-28(d)]TJ
/T1_3 10.91 Tf
23.94 0 Td
(p)Tj
/T1_0 10.91 Tf
5.48 0 Td
[(.)-463(Next,)]TJ
/T1_1 10.91 Tf
37.85 0 Td
(C)Tj
/T1_0 10.91 Tf
9.43 0 Td
[(computes)-339(the)-339(new)-340(DH)-339(k)27(ey)]TJ
/T1_3 10.91 Tf
129.9 0 Td
(t)Tj
/T1_4 7.97 Tf
3.94 3.96 Td
(0)Tj
/T1_2 7.97 Tf
0 -7.19 TD
(L)Tj
/T1_0 10.91 Tf
9.96 3.23 Td
(and)Tj
/T1_3 10.91 Tf
21.27 0 Td
(t)Tj
/T1_4 7.97 Tf
3.94 3.96 Td
(0)Tj
/T1_2 7.97 Tf
0 -7.01 TD
(i)Tj
/T1_0 10.91 Tf
7.08 3.05 Td
[(that)-339(it)-339(shares)]TJ
-403.97 -21.91 Td
(with)Tj
/T1_1 10.91 Tf
25.71 0 Td
(S)Tj
/T1_2 7.97 Tf
5.73 -1.69 Td
(L)Tj
/T1_0 10.91 Tf
10.76 1.69 Td
(and)Tj
/T1_1 10.91 Tf
22.08 0 Td
(S)Tj
/T1_2 7.97 Tf
5.73 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
7.88 1.64 Td
[(for)-413(1)]TJ
/T1_5 10.91 Tf
27.5 0 Td
(\267)Tj
/T1_3 10.91 Tf
12.97 0 Td
(i)Tj
/T1_5 10.91 Tf
8.24 0 Td
(6)Tj
/T1_0 10.91 Tf
(=)Tj
/T1_3 10.91 Tf
12.96 0 Td
(L)Tj
/T1_5 10.91 Tf
11.91 0 Td
(\267)Tj
/T1_3 10.91 Tf
12.96 0 Td
(n)Tj
/T1_2 7.97 Tf
6.55 -1.64 Td
(c)Tj
/T1_0 10.91 Tf
8.67 1.64 Td
[(resp)-27(ectiv)27(ely)83(,)-432(the)-414(new)-413(\257nal)-413(group)-413(k)26(ey)]TJ
/T1_3 10.91 Tf
183.1 0 Td
(K)Tj
/T1_4 7.97 Tf
10.04 3.96 Td
(0)Tj
/T1_0 10.91 Tf
2.79 -3.96 Td
(,)Tj
/T1_3 10.91 Tf
7.76 0 Td
(\265)Tj
/T1_4 7.97 Tf
5.42 3.96 Td
(0)Tj
/T1_9 7.97 Tf
-0.3 -6.66 Td
(C)Tj
/T1_0 10.91 Tf
4.73 2.7 Td
[(,)-512(^)]TJ
/T1_3 10.91 Tf
7.75 0 Td
(\271)Tj
/T1_4 7.97 Tf
6.57 3.96 Td
(0)Tj
/T1_2 7.97 Tf
0 -7.19 TD
(L)Tj
/T1_0 10.91 Tf
10.77 3.23 Td
[(and)-492(^)]TJ
/T1_3 10.91 Tf
22.07 0 Td
(\271)Tj
/T1_4 7.97 Tf
6.58 3.96 Td
(0)Tj
/T1_2 7.97 Tf
0 -7.02 TD
(i)Tj
/T1_0 10.91 Tf
7.88 3.06 Td
(for)Tj
-454.81 -21.92 Td
(1)Tj
/T1_5 10.91 Tf
8.48 0 Td
(\267)Tj
/T1_3 10.91 Tf
11.51 0 Td
(i)Tj
/T1_5 10.91 Tf
6.79 0 Td
(6)Tj
/T1_0 10.91 Tf
(=)Tj
/T1_3 10.91 Tf
11.51 0 Td
(L)Tj
/T1_5 10.91 Tf
10.45 0 Td
(\267)Tj
/T1_3 10.91 Tf
11.52 0 Td
(n)Tj
/T1_2 7.97 Tf
6.54 -1.63 Td
(c)Tj
/T1_0 10.91 Tf
4.17 1.63 Td
(:)Tj
/T1_3 10.91 Tf
54.84 -39.64 Td
(t)Tj
/T1_4 7.97 Tf
3.94 4.5 Td
(0)Tj
/T1_2 7.97 Tf
0 -7.2 TD
(L)Tj
/T1_0 10.91 Tf
16.21 2.7 Td
[(=)-913(\()]TJ
/T1_3 10.91 Tf
22.68 0 Td
(y)Tj
/T1_4 7.97 Tf
5.74 4.5 Td
(0)Tj
/T1_2 7.97 Tf
-0.39 -7.2 Td
(L)Tj
/T1_0 10.91 Tf
6.26 2.7 Td
(\))Tj
/T1_2 7.97 Tf
4.24 4.5 Td
(r)Tj
/T1_10 5.98 Tf
4.05 2.81 Td
(0)Tj
/T1_9 5.98 Tf
-0.23 -5.08 Td
(C)Tj
/T1_0 10.91 Tf
7.2 -2.23 Td
[(mo)-27(d)]TJ
/T1_3 10.91 Tf
23.93 0 Td
[(p)-1039(;)-1206(t)]TJ
/T1_4 7.97 Tf
36.94 4.5 Td
(0)Tj
/T1_2 7.97 Tf
T*
(i)Tj
/T1_0 10.91 Tf
12.08 2.7 Td
(=)Tj
/T1_3 10.91 Tf
17.18 0 Td
(y)Tj
/T1_2 7.97 Tf
5.74 6.03 Td
(r)Tj
/T1_10 5.98 Tf
4.06 2.81 Td
(0)Tj
/T1_9 5.98 Tf
-0.24 -5.08 Td
(C)Tj
/T1_2 7.97 Tf
-4.21 -7.02 Td
(i)Tj
/T1_0 10.91 Tf
11.41 3.26 Td
[(mo)-27(d)]TJ
/T1_3 10.91 Tf
23.93 0 Td
(p)Tj
-203.17 -32.58 Td
(K)Tj
/T1_4 7.97 Tf
10.05 4.51 Td
(0)Tj
/T1_0 10.91 Tf
12.75 -4.51 Td
(=)Tj
/T1_13 10.91 Tf
18.44 21.92 Td
(0)Tj
0 -19.63 TD
(@)Tj
/T1_3 10.91 Tf
9.55 -2.29 Td
(y)Tj
/T1_4 7.97 Tf
5.73 4.51 Td
(0)Tj
/T1_9 7.97 Tf
-0.39 -7.2 Td
(C)Tj
/T1_5 10.91 Tf
7.16 2.69 Td
(\242)Tj
/T1_3 10.91 Tf
5.45 0 Td
(y)Tj
/T1_4 7.97 Tf
5.74 4.51 Td
(0)Tj
/T1_2 7.97 Tf
-0.39 -7.2 Td
(L)Tj
/T1_5 10.91 Tf
8.68 2.69 Td
(\242)Tj
/T1_2 7.97 Tf
16.6 13.66 Td
(n)Tj
/T1_11 5.98 Tf
5.14 -0.99 Td
(c)Tj
/T1_13 10.91 Tf
-7.62 -2.31 Td
(Y)Tj
/T1_2 7.97 Tf
-8.67 -23.71 Td
(i)Tj
/T1_8 7.97 Tf
2.88 0 Td
(=1)Tj
/T1_2 7.97 Tf
(;i)Tj
/T1_4 7.97 Tf
16.05 0 Td
(6)Tj
/T1_8 7.97 Tf
(=)Tj
/T1_2 7.97 Tf
6.59 0 Td
(L)Tj
/T1_3 10.91 Tf
7.57 13.35 Td
(y)Tj
/T1_2 7.97 Tf
5.35 -1.63 Td
(i)Tj
/T1_13 10.91 Tf
3.38 23.55 Td
(1)Tj
T*
(A)Tj
/T1_2 7.97 Tf
9.54 16.92 Td
(r)Tj
/T1_10 5.98 Tf
4.06 2.81 Td
(0)Tj
/T1_9 5.98 Tf
-0.24 -5.09 Td
(C)Tj
/T1_0 10.91 Tf
7.2 -16.93 Td
[(mo)-28(d)]TJ
/T1_3 10.91 Tf
23.94 0 Td
(p)Tj
-171.55 -29.81 Td
(\265)Tj
/T1_4 7.97 Tf
5.42 4.5 Td
(0)Tj
/T1_9 7.97 Tf
-0.3 -7.2 Td
(C)Tj
/T1_0 10.91 Tf
14.69 2.7 Td
(=)Tj
/T1_12 10.91 Tf
18.44 0 Td
(H)Tj
/T1_8 7.97 Tf
7.73 -1.64 Td
(1)Tj
/T1_0 10.91 Tf
4.73 1.64 Td
(\()Tj
/T1_1 10.91 Tf
(SID)Tj
/T1_4 7.97 Tf
21.42 4.5 Td
(0)Tj
/T1_9 7.97 Tf
0 -7.2 TD
(c)Tj
/T1_5 10.91 Tf
4.73 2.7 Td
(jj)Tj
/T1_12 10.91 Tf
6.06 0 Td
(UID)Tj
/T1_9 7.97 Tf
18.4 -1.64 Td
(C)Tj
/T1_5 10.91 Tf
4.73 1.64 Td
(jj)Tj
/T1_3 10.91 Tf
6.06 0 Td
(K)Tj
/T1_4 7.97 Tf
10.04 4.5 Td
(0)Tj
/T1_5 10.91 Tf
2.8 -4.5 Td
(jj)Tj
/T1_3 10.91 Tf
6.06 0 Td
(\277)Tj
/T1_4 7.97 Tf
6 4.5 Td
(0)Tj
/T1_9 7.97 Tf
-1.23 -7.2 Td
(C)Tj
/T1_5 10.91 Tf
4.73 2.7 Td
(jj)Tj
/T1_3 10.91 Tf
6.06 0 Td
(y)Tj
/T1_4 7.97 Tf
5.73 4.5 Td
(0)Tj
/T1_9 7.97 Tf
-0.39 -7.2 Td
(C)Tj
/T1_0 10.91 Tf
4.73 2.7 Td
(\))Tj
-158.75 -24.91 Td
(^)Tj
/T1_3 10.91 Tf
-0.87 0 Td
(\271)Tj
/T1_4 7.97 Tf
6.58 4.5 Td
(0)Tj
/T1_2 7.97 Tf
T*
(L)Tj
/T1_0 10.91 Tf
16.21 2.7 Td
(=)Tj
/T1_12 10.91 Tf
18.44 0 Td
[(MA)27(C)]TJ
/T1_2 7.97 Tf
23.48 -1.78 Td
(ak)Tj
/T1_11 5.98 Tf
8.91 -1.34 Td
(L)Tj
/T1_0 10.91 Tf
6.05 3.12 Td
(\()Tj
/T1_3 10.91 Tf
(\277)Tj
/T1_4 7.97 Tf
10.24 4.5 Td
(0)Tj
/T1_9 7.97 Tf
-1.23 -7.2 Td
(C)Tj
/T1_5 10.91 Tf
4.73 2.7 Td
(jj)Tj
/T1_0 10.91 Tf
6.64 0 Td
(\271)Tj
/T1_3 10.91 Tf
-0.58 0 Td
(\277)Tj
/T1_4 7.97 Tf
6 4.5 Td
(0)Tj
/T1_2 7.97 Tf
-1.23 -7.2 Td
(L)Tj
/T1_5 10.91 Tf
6.25 2.7 Td
(jj)Tj
/T1_3 10.91 Tf
6.06 0 Td
(y)Tj
/T1_4 7.97 Tf
5.74 4.5 Td
(0)Tj
/T1_9 7.97 Tf
-0.39 -7.2 Td
(C)Tj
/T1_5 10.91 Tf
4.73 2.7 Td
(jj)Tj
/T1_3 10.91 Tf
6.06 0 Td
(\265)Tj
/T1_4 7.97 Tf
5.42 4.5 Td
(0)Tj
/T1_9 7.97 Tf
-0.3 -7.2 Td
(C)Tj
/T1_5 10.91 Tf
4.73 2.7 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(SID)Tj
/T1_4 7.97 Tf
17.17 4.5 Td
(0)Tj
/T1_9 7.97 Tf
T*
(c)Tj
/T1_5 10.91 Tf
4.74 2.7 Td
(jj)Tj
/T1_1 10.91 Tf
6.05 0 Td
(C)Tj
/T1_5 10.91 Tf
(jj)Tj
/T1_1 10.91 Tf
11.79 0 Td
(S)Tj
/T1_2 7.97 Tf
5.72 -1.69 Td
(L)Tj
/T1_5 10.91 Tf
6.26 1.69 Td
(jj)Tj
/T1_0 10.91 Tf
6.06 0 Td
(11\))Tj
-202.65 -24.9 Td
(^)Tj
/T1_3 10.91 Tf
-0.86 0 Td
(\271)Tj
/T1_4 7.97 Tf
6.57 4.5 Td
(0)Tj
/T1_2 7.97 Tf
T*
(i)Tj
/T1_0 10.91 Tf
13.34 2.7 Td
(=)Tj
/T1_12 10.91 Tf
18.44 0 Td
[(MA)27(C)]TJ
/T1_2 7.97 Tf
23.48 -1.78 Td
(ak)Tj
/T1_11 5.98 Tf
8.91 -1.22 Td
(i)Tj
/T1_0 10.91 Tf
3.66 3 Td
(\()Tj
/T1_3 10.91 Tf
(\277)Tj
/T1_4 7.97 Tf
10.24 4.5 Td
(0)Tj
/T1_9 7.97 Tf
-1.24 -7.2 Td
(C)Tj
/T1_5 10.91 Tf
4.74 2.7 Td
(jj)Tj
/T1_0 10.91 Tf
6.63 0 Td
(\271)Tj
/T1_3 10.91 Tf
-0.58 0 Td
(\277)Tj
/T1_4 7.97 Tf
6.01 4.5 Td
(0)Tj
/T1_2 7.97 Tf
-1.24 -7.2 Td
(i)Tj
/T1_5 10.91 Tf
4.03 2.7 Td
(jj)Tj
/T1_3 10.91 Tf
6.06 0 Td
(y)Tj
/T1_4 7.97 Tf
5.74 4.5 Td
(0)Tj
/T1_9 7.97 Tf
-0.39 -7.2 Td
(C)Tj
/T1_5 10.91 Tf
4.73 2.7 Td
(jj)Tj
/T1_3 10.91 Tf
6.06 0 Td
(\265)Tj
/T1_4 7.97 Tf
5.42 4.5 Td
(0)Tj
/T1_9 7.97 Tf
-0.3 -7.2 Td
(C)Tj
/T1_5 10.91 Tf
4.73 2.7 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(SID)Tj
/T1_4 7.97 Tf
17.17 4.5 Td
(0)Tj
/T1_9 7.97 Tf
T*
(c)Tj
/T1_5 10.91 Tf
4.73 2.7 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(C)Tj
/T1_5 10.91 Tf
(jj)Tj
/T1_1 10.91 Tf
11.79 0 Td
(S)Tj
/T1_2 7.97 Tf
5.72 -1.64 Td
(i)Tj
/T1_5 10.91 Tf
3.38 1.64 Td
(jj)Tj
/T1_0 10.91 Tf
6.06 0 Td
(11\))Tj
-322.06 -39.65 Td
(where)Tj
/T1_12 10.91 Tf
32.23 0 Td
(UID)Tj
/T1_9 7.97 Tf
18.41 -1.63 Td
(C)Tj
/T1_0 10.91 Tf
8.91 1.63 Td
(=)Tj
/T1_1 10.91 Tf
12.67 0 Td
(C)Tj
/T1_5 10.91 Tf
(jj)Tj
/T1_1 10.91 Tf
11.79 0 Td
(S)Tj
/T1_8 7.97 Tf
5.72 -1.63 Td
(1)Tj
/T1_5 10.91 Tf
4.73 1.63 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(S)Tj
/T1_8 7.97 Tf
5.73 -1.63 Td
(2)Tj
/T1_5 10.91 Tf
4.73 1.63 Td
[(jj)-166(\242)-167(\242)-166(\242)-167(jj)]TJ
/T1_1 10.91 Tf
28.47 0 Td
(S)Tj
/T1_2 7.97 Tf
5.73 -1.63 Td
(n)Tj
/T1_11 5.98 Tf
5.14 -1 Td
(c)Tj
/T1_0 10.91 Tf
4.33 2.63 Td
(.)Tj
/T1_1 10.91 Tf
9.96 0 Td
(C)Tj
/T1_0 10.91 Tf
10.06 0 Td
(encrypts)Tj
/T1_3 10.91 Tf
44.71 0 Td
(K)Tj
/T1_4 7.97 Tf
10.04 3.96 Td
(0)Tj
/T1_5 10.91 Tf
2.8 -3.96 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(C)Tj
/T1_5 10.91 Tf
5.72 0 Td
(jj)Tj
/T1_3 10.91 Tf
6.06 0 Td
(y)Tj
/T1_4 7.97 Tf
5.74 3.96 Td
(0)Tj
/T1_2 7.97 Tf
-0.39 -7.19 Td
(L)Tj
/T1_5 10.91 Tf
6.25 3.23 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(SID)Tj
/T1_4 7.97 Tf
17.18 3.96 Td
(0)Tj
/T1_9 7.97 Tf
0 -6.65 TD
(c)Tj
/T1_0 10.91 Tf
9.06 2.69 Td
(using)Tj
/T1_3 10.91 Tf
29.23 0 Td
(t)Tj
/T1_4 7.97 Tf
3.94 3.96 Td
(0)Tj
/T1_2 7.97 Tf
0 -7.19 TD
(L)Tj
/T1_0 10.91 Tf
10.59 3.23 Td
(and)Tj
/T1_3 10.91 Tf
21.9 0 Td
(K)Tj
/T1_4 7.97 Tf
10.04 3.96 Td
(0)Tj
/T1_5 10.91 Tf
2.79 -3.96 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(C)Tj
/T1_5 10.91 Tf
(jj)Tj
/T1_3 10.91 Tf
11.79 0 Td
(y)Tj
/T1_2 7.97 Tf
5.34 -1.63 Td
(i)Tj
/T1_5 10.91 Tf
3.38 1.63 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(SID)Tj
/T1_4 7.97 Tf
17.18 3.96 Td
(0)Tj
/T1_9 7.97 Tf
0 -6.65 TD
(c)Tj
/T1_0 10.91 Tf
9.06 2.69 Td
(using)Tj
/T1_3 10.91 Tf
29.23 0 Td
(t)Tj
/T1_4 7.97 Tf
3.94 3.96 Td
(0)Tj
/T1_2 7.97 Tf
0 -7.01 TD
(i)Tj
/T1_0 10.91 Tf
-464.49 -18.86 Td
[(for)-347(1)]TJ
/T1_5 10.91 Tf
25.59 0 Td
(\267)Tj
/T1_3 10.91 Tf
11.77 0 Td
(i)Tj
/T1_5 10.91 Tf
7.05 0 Td
(6)Tj
/T1_0 10.91 Tf
(=)Tj
/T1_3 10.91 Tf
11.77 0 Td
(L)Tj
/T1_5 10.91 Tf
10.71 0 Td
(\267)Tj
/T1_3 10.91 Tf
11.77 0 Td
(n)Tj
/T1_2 7.97 Tf
6.54 -1.64 Td
(c)Tj
/T1_0 10.91 Tf
7.96 1.64 Td
[(and)-347(obtains)-360(^)]TJ
/T1_1 10.91 Tf
59.75 0 Td
(c)Tj
/T1_4 7.97 Tf
5.72 3.95 Td
(0)Tj
/T1_2 7.97 Tf
0 -7.19 TD
(L)Tj
/T1_0 10.91 Tf
9.55 3.24 Td
(=)Tj
/T1_5 10.91 Tf
11.77 0 Td
(E)Tj
/T1_2 7.97 Tf
5.75 -2.31 Td
(t)Tj
/T1_10 5.98 Tf
3.06 2.74 Td
(0)Tj
/T1_11 5.98 Tf
0 -5.51 TD
(L)Tj
/T1_0 10.91 Tf
6.05 5.08 Td
(\()Tj
/T1_3 10.91 Tf
4.25 0 Td
(K)Tj
/T1_4 7.97 Tf
10.04 3.95 Td
(0)Tj
/T1_5 10.91 Tf
2.79 -3.95 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(C)Tj
/T1_5 10.91 Tf
(jj)Tj
/T1_3 10.91 Tf
11.79 0 Td
(y)Tj
/T1_4 7.97 Tf
5.73 3.95 Td
(0)Tj
/T1_2 7.97 Tf
-0.39 -7.19 Td
(L)Tj
/T1_5 10.91 Tf
6.26 3.24 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(SID)Tj
/T1_4 7.97 Tf
17.17 3.95 Td
(0)Tj
/T1_9 7.97 Tf
0 -6.65 TD
(c)Tj
/T1_0 10.91 Tf
4.73 2.7 Td
[(\))-348(and)-360(^)]TJ
/T1_1 10.91 Tf
29.4 0 Td
(c)Tj
/T1_4 7.97 Tf
5.72 3.95 Td
(0)Tj
/T1_2 7.97 Tf
0 -7.01 TD
(i)Tj
/T1_0 10.91 Tf
6.67 3.06 Td
(=)Tj
/T1_5 10.91 Tf
11.77 0 Td
(E)Tj
/T1_2 7.97 Tf
5.76 -2.31 Td
(t)Tj
/T1_10 5.98 Tf
3.06 2.74 Td
(0)Tj
/T1_11 5.98 Tf
0 -5.39 TD
(i)Tj
/T1_0 10.91 Tf
3.66 4.96 Td
(\()Tj
/T1_3 10.91 Tf
(K)Tj
/T1_4 7.97 Tf
14.28 3.95 Td
(0)Tj
/T1_5 10.91 Tf
2.79 -3.95 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(C)Tj
/T1_5 10.91 Tf
(jj)Tj
/T1_3 10.91 Tf
11.79 0 Td
(y)Tj
/T1_2 7.97 Tf
5.34 -1.64 Td
(i)Tj
/T1_5 10.91 Tf
3.38 1.64 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(SID)Tj
/T1_4 7.97 Tf
17.18 3.95 Td
(0)Tj
/T1_9 7.97 Tf
0 -6.65 TD
(c)Tj
/T1_0 10.91 Tf
4.73 2.7 Td
[(\))-347(for)-348(1)]TJ
/T1_5 10.91 Tf
33.62 0 Td
(\267)Tj
/T1_3 10.91 Tf
11.77 0 Td
(i)Tj
/T1_5 10.91 Tf
7.05 0 Td
(6)Tj
/T1_0 10.91 Tf
(=)Tj
/T1_3 10.91 Tf
-459.39 -21.92 Td
(L)Tj
/T1_5 10.91 Tf
10.45 0 Td
(\267)Tj
/T1_3 10.91 Tf
11.51 0 Td
(n)Tj
/T1_2 7.97 Tf
6.55 -1.64 Td
(c)Tj
/T1_0 10.91 Tf
7.8 1.64 Td
[(resp)-27(ectiv)27(ely)83(.)]TJ
/T1_1 10.91 Tf
62.8 0 Td
(C)Tj
/T1_0 10.91 Tf
9.36 0 Td
[(then)-333(broadcast)]TJ
/T1_5 10.91 Tf
74.62 0 Td
(f)Tj
/T1_1 10.91 Tf
(SID)Tj
/T1_4 7.97 Tf
22.63 3.96 Td
(0)Tj
/T1_9 7.97 Tf
0 -6.66 TD
(c)Tj
/T1_5 10.91 Tf
4.73 2.7 Td
(jj)Tj
/T1_12 10.91 Tf
6.06 0 Td
(UID)Tj
/T1_9 7.97 Tf
18.4 -1.64 Td
(C)Tj
/T1_5 10.91 Tf
4.73 1.64 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(C)Tj
/T1_5 10.91 Tf
(jj)Tj
/T1_3 10.91 Tf
11.79 0 Td
(y)Tj
/T1_4 7.97 Tf
5.73 3.96 Td
(0)Tj
/T1_9 7.97 Tf
-0.39 -6.66 Td
(C)Tj
/T1_5 10.91 Tf
4.73 2.7 Td
(jj)Tj
/T1_0 10.91 Tf
6.93 0 Td
(^)Tj
/T1_3 10.91 Tf
-0.87 0 Td
(\271)Tj
/T1_4 7.97 Tf
6.57 3.96 Td
(0)Tj
/T1_2 7.97 Tf
0 -7.19 TD
(L)Tj
/T1_5 10.91 Tf
6.26 3.23 Td
(jj)Tj
/T1_0 10.91 Tf
6.92 0 Td
(^)Tj
/T1_3 10.91 Tf
-0.86 0 Td
(\271)Tj
/T1_4 7.97 Tf
6.57 3.96 Td
(0)Tj
/T1_2 7.97 Tf
0 -7.01 TD
(i)Tj
/T1_5 10.91 Tf
3.38 3.05 Td
(jj)Tj
/T1_0 10.91 Tf
6.2 0 Td
(^)Tj
/T1_1 10.91 Tf
-0.14 0 Td
(c)Tj
/T1_4 7.97 Tf
5.73 3.96 Td
(0)Tj
/T1_2 7.97 Tf
0 -7.19 TD
(L)Tj
/T1_5 10.91 Tf
6.25 3.23 Td
(jj)Tj
/T1_0 10.91 Tf
6.2 0 Td
(^)Tj
/T1_1 10.91 Tf
-0.14 0 Td
(c)Tj
/T1_4 7.97 Tf
5.73 3.96 Td
(0)Tj
/T1_2 7.97 Tf
0 -7.01 TD
(i)Tj
/T1_5 10.91 Tf
3.38 3.05 Td
(jj)Tj
/T1_3 10.91 Tf
6.05 0 Td
(\265)Tj
/T1_4 7.97 Tf
5.43 3.96 Td
(0)Tj
/T1_9 7.97 Tf
-0.31 -6.66 Td
(C)Tj
/T1_5 10.91 Tf
4.74 2.7 Td
(g)Tj
/T1_0 10.91 Tf
9.08 0 Td
[(for)-333(1)]TJ
/T1_5 10.91 Tf
25.18 0 Td
(\267)Tj
/T1_3 10.91 Tf
11.51 0 Td
(i)Tj
/T1_5 10.91 Tf
6.79 0 Td
(6)Tj
/T1_0 10.91 Tf
(=)Tj
/T1_3 10.91 Tf
11.51 0 Td
(L)Tj
/T1_5 10.91 Tf
10.45 0 Td
(\267)Tj
/T1_3 10.91 Tf
11.51 0 Td
(n)Tj
/T1_2 7.97 Tf
6.55 -1.64 Td
(c)Tj
/T1_0 10.91 Tf
4.16 1.64 Td
(.)Tj
/T1_14 10.91 Tf
-448.32 -21.92 Td
[(Phase)-383(3:)-511(Key)-383(Distribution)]TJ
/T1_0 10.91 Tf
0 -21.91 TD
[(Round)-333(1)]TJ
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 0 -401.22 cm
0 0 m
40.75 0 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 112.7614 370.0181 Tm
(:)Tj
-40.75 -21.92 Td
(\()Tj
/T1_3 10.91 Tf
(i)Tj
/T1_0 10.91 Tf
(\))Tj
/T1_1 10.91 Tf
17.45 0 Td
(S)Tj
/T1_2 7.97 Tf
5.72 -1.69 Td
(L)Tj
/T1_0 10.91 Tf
11.47 1.69 Td
(\257rst)Tj
1.0003 0 0 1.0003 72 769.82 Tm
58.729 -421.61 Td
[(c)27(hec)28(ks)-477(if)-557(^)]TJ
/T1_3 10.91 Tf
46.821 0 Td
(\271)Tj
/T1_4 7.97 Tf
6.58 3.96 Td
(0)Tj
/T1_2 7.97 Tf
0 -7.19 TD
(L)Tj
/T1_0 10.91 Tf
11.9 3.23 Td
(=)Tj
/T1_12 10.91 Tf
14.14 0 Td
[(MA)28(C)]TJ
/T1_2 7.97 Tf
23.48 -1.78 Td
(ak)Tj
/T1_11 5.98 Tf
8.9 -1.33 Td
(L)Tj
/T1_0 10.91 Tf
6.05 3.11 Td
(\()Tj
/T1_3 10.91 Tf
4.25 0 Td
(\277)Tj
/T1_4 7.97 Tf
6 3.96 Td
(0)Tj
/T1_9 7.97 Tf
-1.24 -6.66 Td
(C)Tj
/T1_5 10.91 Tf
4.73 2.7 Td
(jj)Tj
/T1_0 10.91 Tf
6.64 0 Td
(\271)Tj
/T1_3 10.91 Tf
-0.58 0 Td
(\277)Tj
/T1_4 7.97 Tf
6.01 3.96 Td
(0)Tj
/T1_2 7.97 Tf
-1.24 -7.19 Td
(L)Tj
/T1_5 10.91 Tf
6.26 3.23 Td
(jj)Tj
/T1_3 10.91 Tf
6.06 0 Td
(y)Tj
/T1_4 7.97 Tf
5.73 3.96 Td
(0)Tj
/T1_9 7.97 Tf
-0.39 -6.66 Td
(C)Tj
/T1_5 10.91 Tf
4.73 2.7 Td
(jj)Tj
/T1_3 10.91 Tf
6.06 0 Td
(\265)Tj
/T1_4 7.97 Tf
5.42 3.96 Td
(0)Tj
/T1_9 7.97 Tf
-0.3 -6.66 Td
(C)Tj
/T1_5 10.91 Tf
4.73 2.7 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(SID)Tj
/T1_4 7.97 Tf
17.18 3.96 Td
(0)Tj
/T1_9 7.97 Tf
0 -6.66 TD
(c)Tj
/T1_5 10.91 Tf
4.73 2.7 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(C)Tj
/T1_5 10.91 Tf
5.72 0 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(S)Tj
/T1_2 7.97 Tf
5.73 -1.69 Td
(L)Tj
/T1_5 10.91 Tf
6.25 1.69 Td
(jj)Tj
/T1_0 10.91 Tf
6.06 0 Td
[(11\))-477(is)-478(correct.)-877(If)-478(the)-478(equation)-477(is)]TJ
-303.32 -21.92 Td
(incorrect,)Tj
/T1_1 10.91 Tf
49.94 0 Td
(S)Tj
/T1_2 7.97 Tf
5.73 -1.68 Td
(L)Tj
/T1_0 10.91 Tf
11.02 1.68 Td
(rejects)Tj
/T1_1 10.91 Tf
35.45 0 Td
(C)Tj
/T1_0 10.91 Tf
[(.)-755(Otherwise,)]TJ
/T1_1 10.91 Tf
73.03 0 Td
(S)Tj
/T1_2 7.97 Tf
5.73 -1.68 Td
(L)Tj
/T1_0 10.91 Tf
11.02 1.68 Td
(computes)Tj
/T1_3 10.91 Tf
49.66 0 Td
(t)Tj
/T1_4 7.97 Tf
3.94 3.96 Td
(0)Tj
/T1_2 7.97 Tf
0 -7.19 TD
(L)Tj
/T1_0 10.91 Tf
11.17 3.23 Td
[(=)-450(\()]TJ
/T1_3 10.91 Tf
17.63 0 Td
(y)Tj
/T1_4 7.97 Tf
5.74 3.96 Td
(0)Tj
/T1_9 7.97 Tf
-0.39 -6.65 Td
(C)Tj
/T1_0 10.91 Tf
4.73 2.69 Td
(\))Tj
/T1_6 7.97 Tf
4.24 3.96 Td
(H)Tj
/T1_7 5.98 Tf
5.98 -1.1 Td
(2)Tj
/T1_8 7.97 Tf
4.15 1.1 Td
(\()Tj
/T1_2 7.97 Tf
(K)Tj
/T1_10 5.98 Tf
10.99 2.81 Td
(0)Tj
/T1_11 5.98 Tf
-0.56 -5.51 Td
(L)Tj
/T1_8 7.97 Tf
5.55 2.7 Td
(\))Tj
/T1_0 10.91 Tf
6.82 -3.96 Td
[(mo)-28(d)]TJ
/T1_3 10.91 Tf
23.94 0 Td
(p)Tj
/T1_0 10.91 Tf
10.25 0 Td
[(and)-436(uses)]TJ
/T1_3 10.91 Tf
46.61 0 Td
(t)Tj
/T1_4 7.97 Tf
3.94 3.96 Td
(0)Tj
/T1_2 7.97 Tf
T*
(L)Tj
/T1_0 10.91 Tf
11.02 3.23 Td
[(to)-436(decrypt)]TJ
-417.19 -21.91 Td
(^)Tj
/T1_1 10.91 Tf
-0.14 0 Td
(c)Tj
/T1_4 7.97 Tf
5.73 3.96 Td
(0)Tj
/T1_2 7.97 Tf
T*
(L)Tj
/T1_0 10.91 Tf
10.95 3.23 Td
[(and)-431(obtains)-431(the)-431(new)-431(\257nal)-431(group)-431(k)27(ey)]TJ
/T1_3 10.91 Tf
182.95 0 Td
(K)Tj
/T1_4 7.97 Tf
10.05 3.96 Td
(0)Tj
/T1_0 10.91 Tf
2.79 -3.96 Td
[(,)-455(iden)27(tit)28(y)]TJ
/T1_1 10.91 Tf
49.35 0 Td
(C)Tj
/T1_0 10.91 Tf
(,)Tj
/T1_3 10.91 Tf
13.73 0 Td
(y)Tj
/T1_4 7.97 Tf
5.73 3.96 Td
(0)Tj
/T1_2 7.97 Tf
-0.39 -7.19 Td
(L)Tj
/T1_0 10.91 Tf
10.96 3.23 Td
(and)Tj
/T1_1 10.91 Tf
22.27 0 Td
(SID)Tj
/T1_4 7.97 Tf
17.18 3.96 Td
(0)Tj
/T1_9 7.97 Tf
0 -6.66 TD
(c)Tj
/T1_0 10.91 Tf
4.73 2.7 Td
[(.)-737(If)-431(the)-431(iden)27(tit)28(y)]TJ
/T1_1 10.91 Tf
84.25 0 Td
(C)Tj
/T1_0 10.91 Tf
5.72 0 Td
(,)Tj
/T1_3 10.91 Tf
8 0 Td
(y)Tj
/T1_4 7.97 Tf
5.74 3.96 Td
(0)Tj
/T1_2 7.97 Tf
-0.4 -7.19 Td
(L)Tj
/T1_0 10.91 Tf
10.96 3.23 Td
(and)Tj
/T1_1 10.91 Tf
-450.3 -21.92 Td
(SID)Tj
/T1_4 7.97 Tf
17.18 3.96 Td
(0)Tj
/T1_9 7.97 Tf
0 -6.65 TD
(c)Tj
/T1_0 10.91 Tf
9.94 2.69 Td
[(are)-478(not)-478(decrypted)-478(correctly)83(,)]TJ
/T1_1 10.91 Tf
142.25 0 Td
(S)Tj
/T1_2 7.97 Tf
5.72 -1.69 Td
(L)Tj
/T1_0 10.91 Tf
11.47 1.69 Td
[(rejects)-490(^)]TJ
/T1_1 10.91 Tf
35.9 0 Td
(c)Tj
/T1_4 7.97 Tf
5.73 3.96 Td
(0)Tj
/T1_2 7.97 Tf
0 -7.19 TD
(L)Tj
/T1_0 10.91 Tf
6.25 3.23 Td
[(.)-878(Otherwise,)]TJ
/T1_1 10.91 Tf
69.21 0 Td
(S)Tj
/T1_2 7.97 Tf
5.72 -1.69 Td
(L)Tj
/T1_0 10.91 Tf
11.47 1.69 Td
[(con\257rms)-478(and)-478(accepts)-478(the)-478(new)]TJ
-320.84 -21.91 Td
[(\257nal)-407(group)-407(k)27(ey)]TJ
/T1_3 10.91 Tf
77.28 0 Td
(K)Tj
/T1_4 7.97 Tf
10.04 3.95 Td
(0)Tj
/T1_0 10.91 Tf
7.23 -3.95 Td
[(if)-407(the)-407(k)27(ey)-407(con\257rmation)-407(co)-28(de)]TJ
/T1_3 10.91 Tf
141.3 0 Td
(\265)Tj
/T1_4 7.97 Tf
5.42 3.95 Td
(0)Tj
/T1_9 7.97 Tf
-0.3 -6.65 Td
(C)Tj
/T1_0 10.91 Tf
9.1 2.7 Td
(=)Tj
/T1_12 10.91 Tf
12.86 0 Td
(H)Tj
/T1_8 7.97 Tf
7.72 -1.64 Td
(1)Tj
/T1_0 10.91 Tf
4.73 1.64 Td
(\()Tj
/T1_1 10.91 Tf
(SID)Tj
/T1_4 7.97 Tf
21.42 3.95 Td
(0)Tj
/T1_9 7.97 Tf
0 -6.65 TD
(c)Tj
/T1_5 10.91 Tf
4.73 2.7 Td
(jj)Tj
/T1_12 10.91 Tf
6.06 0 Td
(UID)Tj
/T1_9 7.97 Tf
18.4 -1.64 Td
(C)Tj
/T1_5 10.91 Tf
4.73 1.64 Td
(jj)Tj
/T1_3 10.91 Tf
6.06 0 Td
(K)Tj
/T1_4 7.97 Tf
10.05 3.95 Td
(0)Tj
/T1_5 10.91 Tf
2.79 -3.95 Td
(jj)Tj
/T1_3 10.91 Tf
6.06 0 Td
(\277)Tj
/T1_4 7.97 Tf
6 3.95 Td
(0)Tj
/T1_9 7.97 Tf
-1.23 -6.65 Td
(C)Tj
/T1_5 10.91 Tf
4.73 2.7 Td
(jj)Tj
/T1_3 10.91 Tf
6.06 0 Td
(y)Tj
/T1_4 7.97 Tf
5.74 3.95 Td
(0)Tj
/T1_9 7.97 Tf
-0.4 -6.65 Td
(C)Tj
/T1_0 10.91 Tf
4.74 2.7 Td
[(\))-406(holds.)-666(Next,)]TJ
/T1_1 10.91 Tf
74.57 0 Td
(S)Tj
/T1_2 7.97 Tf
5.73 -1.69 Td
(L)Tj
/T1_0 10.91 Tf
-461.62 -20.23 Td
[(selects)-409(new)-409(random)]TJ
/T1_3 10.91 Tf
98.97 0 Td
(\277)Tj
/T1_4 7.97 Tf
6.01 3.96 Td
(0)Tj
/T1_2 7.97 Tf
-1.24 -7.19 Td
(L)Tj
/T1_5 10.91 Tf
10.67 3.23 Td
(2)Tj
/T1_3 10.91 Tf
11.68 0 Td
(Z)Tj
/T1_4 7.97 Tf
8.22 3.96 Td
(\244)Tj
/T1_2 7.97 Tf
-0.78 -6.66 Td
(q)Tj
/T1_0 10.91 Tf
5.51 2.7 Td
(,)Tj
/T1_3 10.91 Tf
7.7 0 Td
(\277)Tj
/T1_4 7.97 Tf
6 3.96 Td
(0)Tj
/T1_2 7.97 Tf
-1.23 -7.19 Td
(L;j)Tj
/T1_5 10.91 Tf
16.9 3.23 Td
(2)Tj
/T1_3 10.91 Tf
11.68 0 Td
(Z)Tj
/T1_4 7.97 Tf
8.22 3.96 Td
(\244)Tj
/T1_2 7.97 Tf
-0.78 -6.66 Td
(q)Tj
/T1_0 10.91 Tf
9.98 2.7 Td
[(for)-409(1)]TJ
/T1_5 10.91 Tf
27.38 0 Td
(\267)Tj
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/T1_2 10.91 Tf
6.06 0 Td
(v)Tj
/T1_5 7.97 Tf
5.68 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.39 -7.19 Td
(L;j)Tj
/T1_1 10.91 Tf
12.49 3.23 Td
(jj)Tj
/T1_2 10.91 Tf
6.05 0 Td
(z)Tj
/T1_5 7.97 Tf
5.56 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.48 -7.19 Td
(L)Tj
/T1_1 10.91 Tf
6.25 3.23 Td
(jj)Tj
/T1_0 10.91 Tf
-460.95 -21.91 Td
(^)Tj
/T1_2 10.91 Tf
-0.86 0 Td
(\271)Tj
/T1_5 7.97 Tf
6.57 3.95 Td
(0)Tj
/T1_3 7.97 Tf
0 -7.18 TD
(L;j)Tj
/T1_1 10.91 Tf
12.49 3.23 Td
(jj)Tj
/T1_0 10.91 Tf
6.2 0 Td
(^)Tj
/T1_4 10.91 Tf
-0.14 0 Td
(c)Tj
/T1_5 7.97 Tf
5.73 3.95 Td
(0)Tj
/T1_3 7.97 Tf
T*
(L;j)Tj
/T1_1 10.91 Tf
12.49 3.23 Td
(jj)Tj
/T1_2 10.91 Tf
6.06 0 Td
(\265)Tj
/T1_5 7.97 Tf
5.42 3.95 Td
(0)Tj
/T1_3 7.97 Tf
-0.31 -7.18 Td
(L)Tj
/T1_1 10.91 Tf
6.26 3.23 Td
(g)Tj
/T1_0 10.91 Tf
9.09 0 Td
[(for)-333(1)]TJ
/T1_1 10.91 Tf
25.17 0 Td
(\267)Tj
/T1_2 10.91 Tf
11.52 0 Td
(j)Tj
/T1_1 10.91 Tf
8.14 0 Td
(\267)Tj
/T1_2 10.91 Tf
11.51 0 Td
(n)Tj
/T1_3 7.97 Tf
6.55 -1.69 Td
(L)Tj
/T1_1 10.91 Tf
8.68 1.69 Td
(\241)Tj
/T1_2 10.91 Tf
10.9 0 Td
(`)Tj
/T1_0 10.91 Tf
8.18 0 Td
[(to)-333(remaining)-333(users)]TJ
/T1_4 10.91 Tf
91.67 0 Td
(V)Tj
/T1_3 7.97 Tf
5.73 -1.69 Td
(L;j)Tj
/T1_0 10.91 Tf
16.13 1.69 Td
[(for)-332(1)]TJ
/T1_1 10.91 Tf
25.17 0 Td
(\267)Tj
/T1_2 10.91 Tf
11.51 0 Td
(j)Tj
/T1_1 10.91 Tf
8.15 0 Td
(\267)Tj
/T1_2 10.91 Tf
11.51 0 Td
(n)Tj
/T1_3 7.97 Tf
6.55 -1.69 Td
(L)Tj
/T1_1 10.91 Tf
8.67 1.69 Td
(\241)Tj
/T1_2 10.91 Tf
10.91 0 Td
(`)Tj
/T1_0 10.91 Tf
4.54 0 Td
(.)Tj
-361.05 -21.92 Td
(\()Tj
/T1_2 10.91 Tf
(ii)Tj
/T1_0 10.91 Tf
[(\))-345(Eac)27(h)]TJ
/T1_4 10.91 Tf
47.02 0 Td
(S)Tj
/T1_3 7.97 Tf
5.72 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
7.16 1.64 Td
[(for)-345(1)]TJ
/T1_1 10.91 Tf
25.54 0 Td
(\267)Tj
/T1_2 10.91 Tf
11.73 0 Td
(i)Tj
/T1_1 10.91 Tf
7.02 0 Td
(6)Tj
/T1_0 10.91 Tf
(=)Tj
/T1_2 10.91 Tf
11.74 0 Td
(L)Tj
/T1_1 10.91 Tf
10.68 0 Td
(\267)Tj
/T1_2 10.91 Tf
11.74 0 Td
(n)Tj
/T1_3 7.97 Tf
6.54 -1.64 Td
(c)Tj
/T1_0 10.91 Tf
7.94 1.64 Td
[(\257rst)-345(c)26(hec)28(ks)-345(if)-424(^)]TJ
/T1_2 10.91 Tf
66.6 0 Td
(\271)Tj
/T1_5 7.97 Tf
6.57 3.96 Td
(0)Tj
/T1_3 7.97 Tf
0 -7.01 TD
(i)Tj
/T1_0 10.91 Tf
6.64 3.05 Td
(=)Tj
/T1_6 10.91 Tf
11.74 0 Td
[(MA)27(C)]TJ
/T1_3 7.97 Tf
23.48 -1.78 Td
(ak)Tj
/T1_8 5.98 Tf
8.9 -1.21 Td
(i)Tj
/T1_0 10.91 Tf
3.66 2.99 Td
(\()Tj
/T1_2 10.91 Tf
(\277)Tj
/T1_5 7.97 Tf
10.25 3.96 Td
(0)Tj
/T1_9 7.97 Tf
-1.24 -6.66 Td
(C)Tj
/T1_1 10.91 Tf
4.73 2.7 Td
(jj)Tj
/T1_0 10.91 Tf
6.64 0 Td
(\271)Tj
/T1_2 10.91 Tf
-0.58 0 Td
(\277)Tj
/T1_5 7.97 Tf
6 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-1.23 -7.01 Td
(i)Tj
/T1_1 10.91 Tf
4.03 3.05 Td
(jj)Tj
/T1_2 10.91 Tf
6.06 0 Td
(y)Tj
/T1_5 7.97 Tf
5.74 3.96 Td
(0)Tj
/T1_9 7.97 Tf
-0.4 -6.66 Td
(C)Tj
/T1_1 10.91 Tf
4.74 2.7 Td
(jj)Tj
/T1_2 10.91 Tf
6.05 0 Td
(\265)Tj
/T1_5 7.97 Tf
5.43 3.96 Td
(0)Tj
/T1_9 7.97 Tf
-0.31 -6.66 Td
(C)Tj
/T1_1 10.91 Tf
4.73 2.7 Td
(jj)Tj
/T1_4 10.91 Tf
6.06 0 Td
(SID)Tj
/T1_5 7.97 Tf
17.18 3.96 Td
(0)Tj
/T1_9 7.97 Tf
0 -6.66 TD
(c)Tj
/T1_1 10.91 Tf
4.73 2.7 Td
(jj)Tj
/T1_4 10.91 Tf
6.06 0 Td
(C)Tj
/T1_1 10.91 Tf
(jj)Tj
/T1_4 10.91 Tf
11.79 0 Td
(S)Tj
/T1_3 7.97 Tf
5.72 -1.64 Td
(i)Tj
/T1_1 10.91 Tf
3.38 1.64 Td
(jj)Tj
/T1_0 10.91 Tf
6.06 0 Td
[(11\))-345(is)-346(correct.)]TJ
-402.04 -21.92 Td
[(If)-342(the)-342(equation)-342(is)-342(incorrect,)]TJ
/T1_4 10.91 Tf
134.22 0 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
7.11 1.63 Td
(rejects)Tj
/T1_4 10.91 Tf
34.42 0 Td
(C)Tj
/T1_0 10.91 Tf
[(.)-470(Otherwise,)]TJ
/T1_4 10.91 Tf
68.63 0 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
7.11 1.63 Td
(computes)Tj
/T1_2 10.91 Tf
48.63 0 Td
(t)Tj
/T1_5 7.97 Tf
3.94 3.96 Td
(0)Tj
/T1_3 7.97 Tf
0 -7.01 TD
(i)Tj
/T1_0 10.91 Tf
6.57 3.05 Td
[(=)-292(\()]TJ
/T1_2 10.91 Tf
15.91 0 Td
(y)Tj
/T1_5 7.97 Tf
5.74 3.96 Td
(0)Tj
/T1_9 7.97 Tf
-0.39 -6.65 Td
(C)Tj
/T1_0 10.91 Tf
4.73 2.69 Td
(\))Tj
/T1_10 7.97 Tf
4.24 3.96 Td
(H)Tj
/T1_11 5.98 Tf
5.98 -1.1 Td
(2)Tj
/T1_7 7.97 Tf
4.15 1.1 Td
(\()Tj
/T1_3 7.97 Tf
(K)Tj
/T1_8 5.98 Tf
10.43 -1.21 Td
(i)Tj
/T1_7 7.97 Tf
3.16 1.21 Td
(\))Tj
/T1_0 10.91 Tf
6.82 -3.96 Td
[(mo)-27(d)]TJ
/T1_2 10.91 Tf
23.93 0 Td
(p)Tj
/T1_0 10.91 Tf
9.22 0 Td
[(and)-342(uses)]TJ
/T1_2 10.91 Tf
44.54 0 Td
(t)Tj
/T1_5 7.97 Tf
3.94 3.96 Td
(0)Tj
/T1_3 7.97 Tf
T*
(i)Tj
/T1_0 10.91 Tf
-464.49 -18.86 Td
[(to)-333(decrypt)-345(^)]TJ
/T1_4 10.91 Tf
53.04 0 Td
(c)Tj
/T1_5 7.97 Tf
5.73 3.96 Td
(0)Tj
/T1_3 7.97 Tf
0 -7.02 TD
(i)Tj
/T1_0 10.91 Tf
7.01 3.06 Td
[(and)-333(obtains)-333(the)-333(new)-333(\257nal)-333(group)-333(k)27(ey)]TJ
/T1_2 10.91 Tf
175.48 0 Td
(K)Tj
/T1_5 7.97 Tf
10.04 3.96 Td
(0)Tj
/T1_0 10.91 Tf
2.79 -3.96 Td
[(,)-333(iden)27(tit)27(y)]TJ
/T1_4 10.91 Tf
46.96 0 Td
(C)Tj
/T1_0 10.91 Tf
5.72 0 Td
(,)Tj
/T1_2 10.91 Tf
6.67 0 Td
(y)Tj
/T1_3 7.97 Tf
5.34 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
7.02 1.64 Td
(and)Tj
/T1_4 10.91 Tf
21.2 0 Td
(SID)Tj
/T1_5 7.97 Tf
17.18 3.96 Td
(0)Tj
/T1_9 7.97 Tf
0 -6.66 TD
(c)Tj
/T1_0 10.91 Tf
4.73 2.7 Td
[(.)-444(If)-333(the)-333(iden)27(tit)28(y)]TJ
/T1_4 10.91 Tf
77.84 0 Td
(C)Tj
/T1_0 10.91 Tf
(,)Tj
/T1_2 10.91 Tf
12.39 0 Td
(y)Tj
/T1_3 7.97 Tf
5.35 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
-464.49 -20.28 Td
(and)Tj
/T1_4 10.91 Tf
20.48 0 Td
(SID)Tj
/T1_5 7.97 Tf
17.18 3.96 Td
(0)Tj
/T1_9 7.97 Tf
0 -6.65 TD
(c)Tj
/T1_0 10.91 Tf
7.65 2.69 Td
[(are)-266(not)-267(decrypted)-267(correctly)82(,)]TJ
/T1_4 10.91 Tf
132.79 0 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
6.29 1.63 Td
[(rejects)-279(^)]TJ
/T1_4 10.91 Tf
33.6 0 Td
(c)Tj
/T1_5 7.97 Tf
5.73 3.96 Td
(0)Tj
/T1_3 7.97 Tf
0 -7.01 TD
(i)Tj
/T1_0 10.91 Tf
3.38 3.05 Td
[(.)-422(Otherwise,)]TJ
/T1_4 10.91 Tf
61.68 0 Td
(S)Tj
/T1_3 7.97 Tf
5.72 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
6.3 1.63 Td
[(con\257rms)-266(and)-267(accepts)-268(the)-267(new)-267(\257nal)]TJ
-306.53 -21.92 Td
[(group)-371(k)27(ey)]TJ
/T1_2 10.91 Tf
51.44 0 Td
(K)Tj
/T1_5 7.97 Tf
10.05 3.96 Td
(0)Tj
/T1_0 10.91 Tf
6.84 -3.96 Td
[(if)-370(the)-371(k)26(ey)-370(con\257rmation)-371(co)-27(de)]TJ
/T1_2 10.91 Tf
139.32 0 Td
(\265)Tj
/T1_5 7.97 Tf
5.42 3.96 Td
(0)Tj
/T1_9 7.97 Tf
-0.3 -6.65 Td
(C)Tj
/T1_0 10.91 Tf
8.44 2.69 Td
(=)Tj
/T1_6 10.91 Tf
12.2 0 Td
(H)Tj
/T1_7 7.97 Tf
7.73 -1.63 Td
(1)Tj
/T1_0 10.91 Tf
4.73 1.63 Td
(\()Tj
/T1_4 10.91 Tf
(SID)Tj
/T1_5 7.97 Tf
21.41 3.96 Td
(0)Tj
/T1_9 7.97 Tf
0 -6.65 TD
(c)Tj
/T1_1 10.91 Tf
4.74 2.69 Td
(jj)Tj
/T1_6 10.91 Tf
6.05 0 Td
(UID)Tj
/T1_9 7.97 Tf
18.41 -1.63 Td
(C)Tj
/T1_1 10.91 Tf
4.73 1.63 Td
(jj)Tj
/T1_2 10.91 Tf
6.06 0 Td
(K)Tj
/T1_5 7.97 Tf
10.04 3.96 Td
(0)Tj
/T1_1 10.91 Tf
2.8 -3.96 Td
(jj)Tj
/T1_2 10.91 Tf
6.05 0 Td
(\277)Tj
/T1_5 7.97 Tf
6.01 3.96 Td
(0)Tj
/T1_9 7.97 Tf
-1.24 -6.65 Td
(C)Tj
/T1_1 10.91 Tf
4.73 2.69 Td
(jj)Tj
/T1_2 10.91 Tf
6.06 0 Td
(y)Tj
/T1_5 7.97 Tf
5.74 3.96 Td
(0)Tj
/T1_9 7.97 Tf
-0.39 -6.65 Td
(C)Tj
/T1_0 10.91 Tf
4.73 2.69 Td
[(\))-371(holds.)-557(Next,)]TJ
/T1_4 10.91 Tf
72.5 0 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
7.42 1.63 Td
(selects)Tj
/T1_2 10.91 Tf
-437.45 -21.91 Td
(\277)Tj
/T1_5 7.97 Tf
6 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-1.23 -7.02 Td
(i)Tj
/T1_1 10.91 Tf
8.93 3.06 Td
(2)Tj
/T1_2 10.91 Tf
12.17 0 Td
(Z)Tj
/T1_5 7.97 Tf
8.22 3.96 Td
(\244)Tj
/T1_3 7.97 Tf
-0.78 -6.66 Td
(q)Tj
/T1_0 10.91 Tf
10.27 2.7 Td
[(and)-436(new)-436(session)-436(iden)27(tit)27(y)]TJ
/T1_4 10.91 Tf
124.33 0 Td
(SID)Tj
/T1_5 7.97 Tf
17.18 3.96 Td
(0)Tj
/T1_3 7.97 Tf
0 -7.02 TD
(i)Tj
/T1_0 10.91 Tf
8.14 3.06 Td
[(and)-436(encrypts)]TJ
/T1_2 10.91 Tf
67.47 0 Td
(K)Tj
/T1_5 7.97 Tf
10.04 3.96 Td
(0)Tj
/T1_1 10.91 Tf
2.8 -3.96 Td
(jj)Tj
/T1_4 10.91 Tf
6.05 0 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.64 Td
(i)Tj
/T1_1 10.91 Tf
3.38 1.64 Td
(jj)Tj
/T1_4 10.91 Tf
6.06 0 Td
(SID)Tj
/T1_5 7.97 Tf
17.18 3.96 Td
(0)Tj
/T1_3 7.97 Tf
T*
(i)Tj
/T1_1 10.91 Tf
3.38 3.06 Td
(jj)Tj
/T1_2 10.91 Tf
6.06 0 Td
(\277)Tj
/T1_5 7.97 Tf
6 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-1.24 -7.02 Td
(i)Tj
/T1_0 10.91 Tf
8.79 3.06 Td
(using)Tj
/T1_2 10.91 Tf
29.66 0 Td
(K)Tj
/T1_3 7.97 Tf
9.26 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
8.14 1.64 Td
[(and)-436(obtains)-448(^)]TJ
/T1_4 10.91 Tf
61.68 0 Td
(c)Tj
/T1_5 7.97 Tf
5.73 3.96 Td
(00)Tj
/T1_3 7.97 Tf
T*
(i)Tj
/T1_0 10.91 Tf
9.99 3.06 Td
(=)Tj
/T1_1 10.91 Tf
-459.39 -21.92 Td
(E)Tj
/T1_3 7.97 Tf
5.76 -1.69 Td
(K)Tj
/T1_8 5.98 Tf
7.14 -1.21 Td
(i)Tj
/T1_0 10.91 Tf
3.65 2.9 Td
(\()Tj
/T1_2 10.91 Tf
4.25 0 Td
(K)Tj
/T1_5 7.97 Tf
10.04 3.96 Td
(0)Tj
/T1_1 10.91 Tf
2.79 -3.96 Td
(jj)Tj
/T1_4 10.91 Tf
6.06 0 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.63 Td
(i)Tj
/T1_1 10.91 Tf
3.38 1.63 Td
(jj)Tj
/T1_4 10.91 Tf
6.06 0 Td
(SID)Tj
/T1_5 7.97 Tf
17.17 3.96 Td
(0)Tj
/T1_3 7.97 Tf
0 -7.01 TD
(i)Tj
/T1_1 10.91 Tf
3.38 3.05 Td
(jj)Tj
/T1_2 10.91 Tf
6.06 0 Td
(\277)Tj
/T1_5 7.97 Tf
6 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-1.23 -7.01 Td
(i)Tj
/T1_0 10.91 Tf
4.03 3.05 Td
(\).)Tj
/T1_4 10.91 Tf
14.29 0 Td
(S)Tj
/T1_3 7.97 Tf
5.72 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
7.74 1.63 Td
[(then)-400(computes)-399(the)-400(k)27(ey)-399(con\257rmation)-400(co)-28(de)]TJ
/T1_2 10.91 Tf
204.99 0 Td
(\265)Tj
/T1_5 7.97 Tf
5.42 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.3 -7.01 Td
(i)Tj
/T1_0 10.91 Tf
7.62 3.05 Td
(=)Tj
/T1_6 10.91 Tf
12.72 0 Td
(H)Tj
/T1_7 7.97 Tf
7.72 -1.63 Td
(1)Tj
/T1_0 10.91 Tf
4.73 1.63 Td
(\()Tj
/T1_4 10.91 Tf
(SID)Tj
/T1_5 7.97 Tf
21.42 3.96 Td
(0)Tj
/T1_3 7.97 Tf
T*
(i)Tj
/T1_1 10.91 Tf
3.38 3.05 Td
(jj)Tj
/T1_4 10.91 Tf
6.06 0 Td
(UID)Tj
/T1_3 7.97 Tf
17.18 -1.63 Td
(i)Tj
/T1_1 10.91 Tf
3.38 1.63 Td
(jj)Tj
/T1_2 10.91 Tf
6.06 0 Td
(K)Tj
/T1_5 7.97 Tf
10.04 3.96 Td
(0)Tj
/T1_1 10.91 Tf
2.79 -3.96 Td
(jj)Tj
/T1_2 10.91 Tf
6.06 0 Td
(\277)Tj
/T1_5 7.97 Tf
6 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-1.23 -7.01 Td
(i)Tj
/T1_1 10.91 Tf
4.03 3.05 Td
(jj)Tj
/T1_2 10.91 Tf
6.06 0 Td
(z)Tj
/T1_3 7.97 Tf
5.07 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
3.38 1.63 Td
(\),)Tj
-460.6 -21.91 Td
(where)Tj
/T1_4 10.91 Tf
31.54 0 Td
(UID)Tj
/T1_3 7.97 Tf
17.17 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
6.41 1.64 Td
(=)Tj
/T1_4 10.91 Tf
11.52 0 Td
(S)Tj
/T1_3 7.97 Tf
5.72 -1.64 Td
(i)Tj
/T1_1 10.91 Tf
3.38 1.64 Td
(jj)Tj
/T1_4 10.91 Tf
6.06 0 Td
(U)Tj
/T1_3 7.97 Tf
5.73 -1.64 Td
(i;)Tj
/T1_7 7.97 Tf
5.23 0 Td
(1)Tj
/T1_1 10.91 Tf
4.73 1.64 Td
(jj)Tj
/T1_4 10.91 Tf
6.06 0 Td
(U)Tj
/T1_3 7.97 Tf
5.73 -1.64 Td
(i;)Tj
/T1_7 7.97 Tf
5.23 0 Td
(2)Tj
/T1_1 10.91 Tf
4.73 1.64 Td
[(jj)-166(\242)-167(\242)-167(\242)-166(jj)]TJ
/T1_4 10.91 Tf
28.48 0 Td
(U)Tj
/T1_3 7.97 Tf
5.72 -1.64 Td
(i;n)Tj
/T1_8 5.98 Tf
10.37 -1.22 Td
(i)Tj
/T1_0 10.91 Tf
3.66 2.86 Td
[(.)-444(Finally)82(,)]TJ
/T1_4 10.91 Tf
47.11 0 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
7.01 1.64 Td
(broadcast)Tj
/T1_1 10.91 Tf
49.78 0 Td
(f)Tj
/T1_4 10.91 Tf
(SID)Tj
/T1_5 7.97 Tf
22.63 3.95 Td
(0)Tj
/T1_3 7.97 Tf
T*
(i)Tj
/T1_1 10.91 Tf
3.38 3.06 Td
(jj)Tj
/T1_4 10.91 Tf
6.06 0 Td
(UID)Tj
/T1_3 7.97 Tf
17.17 -1.64 Td
(i)Tj
/T1_1 10.91 Tf
3.38 1.64 Td
(jj)Tj
/T1_4 10.91 Tf
6.06 0 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.64 Td
(i)Tj
/T1_1 10.91 Tf
3.38 1.64 Td
(jj)Tj
/T1_0 10.91 Tf
6.19 0 Td
(^)Tj
/T1_4 10.91 Tf
-0.13 0 Td
(c)Tj
/T1_5 7.97 Tf
5.72 3.95 Td
(00)Tj
/T1_3 7.97 Tf
T*
(i)Tj
/T1_1 10.91 Tf
5.09 3.06 Td
(jj)Tj
/T1_2 10.91 Tf
6.06 0 Td
(\265)Tj
/T1_5 7.97 Tf
5.42 3.95 Td
(0)Tj
/T1_3 7.97 Tf
-0.3 -7.01 Td
(i)Tj
/T1_1 10.91 Tf
3.38 3.06 Td
(g)Tj
/T1_0 10.91 Tf
9.09 0 Td
[(to)-333(subgroup)]TJ
/T1_1 10.91 Tf
60.68 0 Td
(G)Tj
/T1_3 7.97 Tf
6.49 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
3.38 1.64 Td
(.)Tj
-455.96 -21.92 Td
[(Round)-333(2)]TJ
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.44 w
q 1 0 0 1 0 -335.84 cm
0 0 m
40.75 0 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 112.7614 435.4164 Tm
(:)Tj
-40.75 -21.92 Td
(\()Tj
/T1_2 10.91 Tf
(i)Tj
/T1_0 10.91 Tf
(\))Tj
1.0003 0 0 1.0003 72 769.82 Tm
14.982 -356.23 Td
[(Eac)27(h)-251(remaining)-252(user)]TJ
/T1_4 10.91 Tf
98.488 0 Td
(V)Tj
/T1_3 7.97 Tf
5.73 -1.69 Td
(L;j)Tj
/T1_0 10.91 Tf
15.24 1.69 Td
[(for)-251(1)]TJ
/T1_1 10.91 Tf
24.28 0 Td
(\267)Tj
/T1_2 10.91 Tf
11.52 0 Td
(j)Tj
/T1_1 10.91 Tf
8.14 0 Td
(\267)Tj
/T1_2 10.91 Tf
11.51 0 Td
(n)Tj
/T1_3 7.97 Tf
6.55 -1.69 Td
(L)Tj
/T1_1 10.91 Tf
6.9 1.69 Td
(\241)Tj
/T1_2 10.91 Tf
9.13 0 Td
(`)Tj
/T1_0 10.91 Tf
7.29 0 Td
[(\257rst)-251(decrypts)]TJ
/T1_4 10.91 Tf
64.75 0 Td
(c)Tj
/T1_5 7.97 Tf
5.73 3.96 Td
(0)Tj
/T1_3 7.97 Tf
0 -7.19 TD
(L;j)Tj
/T1_0 10.91 Tf
15.23 3.23 Td
[(and)-252(c)27(hec)28(ks)-251(if)-252(the)-252(iden)27(tities)]TJ
/T1_4 10.91 Tf
126.25 0 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.69 Td
(L)Tj
/T1_0 10.91 Tf
6.25 1.69 Td
(,)Tj
/T1_4 10.91 Tf
5.96 0 Td
(V)Tj
/T1_3 7.97 Tf
5.72 -1.69 Td
(L;j)Tj
/T1_0 10.91 Tf
-455.38 -20.22 Td
(and)Tj
/T1_4 10.91 Tf
21.18 0 Td
(SID)Tj
/T1_5 7.97 Tf
17.17 3.95 Td
(0)Tj
/T1_3 7.97 Tf
T*
(L)Tj
/T1_0 10.91 Tf
9.87 3.24 Td
[(are)-330(decrypted)-331(correctly)83(.)-443(If)-331(the)-330(iden)27(tities)-330(are)-331(not)-331(correct,)]TJ
/T1_4 10.91 Tf
270.87 0 Td
(V)Tj
/T1_3 7.97 Tf
5.73 -1.69 Td
(L;j)Tj
/T1_0 10.91 Tf
16.09 1.69 Td
(rejects)Tj
/T1_4 10.91 Tf
34.3 0 Td
(S)Tj
/T1_3 7.97 Tf
5.72 -1.69 Td
(L)Tj
/T1_0 10.91 Tf
6.26 1.69 Td
[(.)-443(Otherwise,)]TJ
/T1_4 10.91 Tf
62.47 0 Td
(V)Tj
/T1_3 7.97 Tf
5.72 -1.69 Td
(L;j)Tj
/T1_0 10.91 Tf
-455.38 -20.23 Td
[(uses)-330(passw)27(ord)]TJ
/T1_6 10.91 Tf
70.18 0 Td
[(p)27(w)]TJ
/T1_3 7.97 Tf
12.94 -2.62 Td
(L;j)Tj
/T1_0 10.91 Tf
16.09 2.62 Td
[(to)-330(c)27(hec)28(k)-329(the)-331(v)55(alidit)28(y)-329(of)]TJ
/T1_2 10.91 Tf
112.83 0 Td
(v)Tj
/T1_5 7.97 Tf
5.68 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.4 -7.19 Td
(L;j)Tj
/T1_0 10.91 Tf
15.52 3.23 Td
(=)Tj
/T1_6 10.91 Tf
11.52 0 Td
(H)Tj
/T1_7 7.97 Tf
7.72 -1.64 Td
(1)Tj
/T1_0 10.91 Tf
4.73 1.64 Td
(\()Tj
/T1_6 10.91 Tf
[(p)27(w)]TJ
/T1_3 7.97 Tf
17.18 -2.62 Td
(L;j)Tj
/T1_1 10.91 Tf
12.49 2.62 Td
(jj)Tj
/T1_2 10.91 Tf
6.06 0 Td
(\277)Tj
/T1_5 7.97 Tf
6 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-1.23 -7.19 Td
(L)Tj
/T1_1 10.91 Tf
6.25 3.23 Td
(jj)Tj
/T1_2 10.91 Tf
6.06 0 Td
(\277)Tj
/T1_5 7.97 Tf
6 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-1.23 -7.19 Td
(L;j)Tj
/T1_1 10.91 Tf
12.49 3.23 Td
(jj)Tj
/T1_4 10.91 Tf
6.06 0 Td
(SID)Tj
/T1_5 7.97 Tf
17.17 3.96 Td
(0)Tj
/T1_3 7.97 Tf
T*
(L)Tj
/T1_0 10.91 Tf
6.26 3.23 Td
[(\).)-443(If)-330(it)-330(is)-330(incorrect,)]TJ
/T1_4 10.91 Tf
93.28 0 Td
(V)Tj
/T1_3 7.97 Tf
5.73 -1.69 Td
(L;j)Tj
/T1_0 10.91 Tf
-455.38 -20.23 Td
(rejects)Tj
/T1_4 10.91 Tf
33.97 0 Td
(S)Tj
/T1_3 7.97 Tf
5.72 -1.68 Td
(J)Tj
/T1_0 10.91 Tf
5.87 1.68 Td
[(.)-433(Otherwise,)]TJ
/T1_4 10.91 Tf
62.09 0 Td
(V)Tj
/T1_3 7.97 Tf
5.73 -1.68 Td
(L;j)Tj
/T1_0 10.91 Tf
15.76 1.68 Td
[(c)27(hec)28(ks)-300(if)-379(^)]TJ
/T1_2 10.91 Tf
42.97 0 Td
(\271)Tj
/T1_5 7.97 Tf
6.57 3.96 Td
(0)Tj
/T1_3 7.97 Tf
T*
(L;j)Tj
/T1_0 10.91 Tf
15.52 3.23 Td
(=)Tj
/T1_6 10.91 Tf
11.51 0 Td
[(MA)27(C)]TJ
/T1_3 7.97 Tf
23.48 -1.77 Td
(ak)Tj
/T1_8 5.98 Tf
8.91 -1.34 Td
(L;j)Tj
/T1_0 10.91 Tf
11.72 3.11 Td
(\()Tj
/T1_2 10.91 Tf
4.25 0 Td
(\277)Tj
/T1_5 7.97 Tf
6 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-1.24 -7.19 Td
(L)Tj
/T1_1 10.91 Tf
6.26 3.23 Td
(jj)Tj
/T1_2 10.91 Tf
6.06 0 Td
(\277)Tj
/T1_5 7.97 Tf
6 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-1.24 -7.19 Td
(L;j)Tj
/T1_1 10.91 Tf
12.5 3.23 Td
(jj)Tj
/T1_2 10.91 Tf
6.05 0 Td
(z)Tj
/T1_5 7.97 Tf
5.56 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.48 -7.19 Td
(L)Tj
/T1_1 10.91 Tf
6.25 3.23 Td
(jj)Tj
/T1_2 10.91 Tf
6.06 0 Td
(\265)Tj
/T1_5 7.97 Tf
5.42 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.3 -7.19 Td
(L)Tj
/T1_1 10.91 Tf
6.26 3.23 Td
(jj)Tj
/T1_4 10.91 Tf
6.05 0 Td
(SID)Tj
/T1_5 7.97 Tf
17.18 3.96 Td
(0)Tj
/T1_3 7.97 Tf
T*
(L)Tj
/T1_1 10.91 Tf
6.26 3.23 Td
(jj)Tj
/T1_4 10.91 Tf
6.06 0 Td
(S)Tj
/T1_3 7.97 Tf
5.72 -1.68 Td
(L)Tj
/T1_1 10.91 Tf
6.26 1.68 Td
(jj)Tj
/T1_4 10.91 Tf
6.06 0 Td
(V)Tj
/T1_3 7.97 Tf
5.72 -1.68 Td
(L;j)Tj
/T1_1 10.91 Tf
12.49 1.68 Td
(jj)Tj
/T1_0 10.91 Tf
6.06 0 Td
[(11\))-300(is)-300(v)54(alid.)-432(If)]TJ
-401.09 -21.91 Td
[(the)-295(equation)-296(is)-296(in)27(v)55(alid,)]TJ
/T1_4 10.91 Tf
110.9 0 Td
(V)Tj
/T1_3 7.97 Tf
5.73 -1.69 Td
(L;j)Tj
/T1_0 10.91 Tf
15.71 1.69 Td
[(rejects)-296(the)-295(malicious)-296(subgroup)-296(con)27(troller)]TJ
/T1_4 10.91 Tf
195.18 0 Td
(S)Tj
/T1_3 7.97 Tf
5.72 -1.69 Td
(L)Tj
/T1_0 10.91 Tf
6.26 1.69 Td
[(.)-431(Otherwise,)]TJ
/T1_4 10.91 Tf
62.03 0 Td
(V)Tj
/T1_3 7.97 Tf
5.73 -1.69 Td
(L;j)Tj
/T1_0 10.91 Tf
15.71 1.69 Td
(computes)Tj
/T1_2 10.91 Tf
-422.97 -21.92 Td
(t)Tj
/T1_5 7.97 Tf
3.94 3.96 Td
(0)Tj
/T1_3 7.97 Tf
T*
(L;j)Tj
/T1_0 10.91 Tf
16.66 3.23 Td
[(=)-382(\()]TJ
/T1_2 10.91 Tf
(z)Tj
/T1_5 7.97 Tf
22.45 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.48 -7.19 Td
(L)Tj
/T1_0 10.91 Tf
6.25 3.23 Td
(\))Tj
/T1_3 7.97 Tf
4.24 3.96 Td
(r)Tj
/T1_8 5.98 Tf
3.82 -1.34 Td
(L;j)Tj
/T1_0 10.91 Tf
14.76 -2.62 Td
[(mo)-27(d)]TJ
/T1_2 10.91 Tf
23.93 0 Td
(p)Tj
/T1_0 10.91 Tf
9.81 0 Td
[(and)-396(uses)]TJ
/T1_2 10.91 Tf
45.72 0 Td
(t)Tj
/T1_5 7.97 Tf
3.94 3.96 Td
(0)Tj
/T1_3 7.97 Tf
T*
(L;j)Tj
/T1_0 10.91 Tf
16.81 3.23 Td
[(to)-396(decrypt)-408(^)]TJ
/T1_4 10.91 Tf
54.42 0 Td
(c)Tj
/T1_5 7.97 Tf
5.72 3.96 Td
(0)Tj
/T1_3 7.97 Tf
T*
(L;j)Tj
/T1_0 10.91 Tf
16.81 3.23 Td
[(and)-396(obtains)-396(new)-396(subgroup)-396(k)26(ey)]TJ
/T1_2 10.91 Tf
152.33 0 Td
(K)Tj
/T1_5 7.97 Tf
10.04 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.78 -7.19 Td
(L)Tj
/T1_0 10.91 Tf
6.26 3.23 Td
[(,)-411(new)-396(\257nal)]TJ
-416.65 -21.92 Td
[(group)-437(k)27(ey)]TJ
/T1_2 10.91 Tf
52.89 0 Td
(K)Tj
/T1_5 7.97 Tf
10.05 3.96 Td
(0)Tj
/T1_0 10.91 Tf
2.79 -3.96 Td
[(,)-463(iden)27(tit)28(y)]TJ
/T1_4 10.91 Tf
49.51 0 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.68 Td
(L)Tj
/T1_0 10.91 Tf
6.25 1.68 Td
(,)Tj
/T1_2 10.91 Tf
8.08 0 Td
(z)Tj
/T1_3 7.97 Tf
5.08 -1.68 Td
(L;j)Tj
/T1_0 10.91 Tf
17.26 1.68 Td
(and)Tj
/T1_4 10.91 Tf
22.34 0 Td
(SID)Tj
/T1_5 7.97 Tf
17.17 3.96 Td
(0)Tj
/T1_3 7.97 Tf
T*
(L)Tj
/T1_0 10.91 Tf
6.26 3.23 Td
[(.)-756(If)-438(the)-437(iden)27(tit)28(y)]TJ
/T1_4 10.91 Tf
84.67 0 Td
(S)Tj
/T1_3 7.97 Tf
5.72 -1.68 Td
(L)Tj
/T1_0 10.91 Tf
6.26 1.68 Td
(,)Tj
/T1_2 10.91 Tf
8.08 0 Td
(z)Tj
/T1_3 7.97 Tf
5.07 -1.68 Td
(L;j)Tj
/T1_0 10.91 Tf
17.26 1.68 Td
(and)Tj
/T1_4 10.91 Tf
22.35 0 Td
(SID)Tj
/T1_5 7.97 Tf
17.17 3.96 Td
(0)Tj
/T1_3 7.97 Tf
T*
(L)Tj
/T1_0 10.91 Tf
11.03 3.23 Td
[(are)-437(not)-437(decrypted)]TJ
-381.02 -21.91 Td
[(correctly)83(,)-362(then)]TJ
/T1_4 10.91 Tf
72.75 0 Td
(V)Tj
/T1_3 7.97 Tf
5.72 -1.69 Td
(L;j)Tj
/T1_0 10.91 Tf
16.39 1.69 Td
[(rejects)-369(^)]TJ
/T1_4 10.91 Tf
34.58 0 Td
(c)Tj
/T1_5 7.97 Tf
5.73 3.96 Td
(0)Tj
/T1_3 7.97 Tf
T*
(L;j)Tj
/T1_0 10.91 Tf
12.49 3.23 Td
[(.)-516(Otherwise,)]TJ
/T1_4 10.91 Tf
63.61 0 Td
(V)Tj
/T1_3 7.97 Tf
5.72 -1.69 Td
(L;j)Tj
/T1_0 10.91 Tf
16.39 1.69 Td
[(con\257rms)-356(and)-358(accepts)-357(b)-28(oth)-357(subgroup)-357(k)27(ey)]TJ
/T1_2 10.91 Tf
197.51 0 Td
(K)Tj
/T1_5 7.97 Tf
10.04 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.78 -7.19 Td
(L)Tj
/T1_0 10.91 Tf
10.15 3.23 Td
(and)Tj
-450.3 -21.92 Td
[(\257nal)-333(group)-333(k)27(ey)]TJ
/T1_2 10.91 Tf
74.86 0 Td
(K)Tj
/T1_5 7.97 Tf
10.04 3.96 Td
(0)Tj
/T1_0 10.91 Tf
6.43 -3.96 Td
[(if)-333(the)-333(k)27(ey)-333(con\257rmation)-333(co)-28(de)]TJ
/T1_2 10.91 Tf
137.27 0 Td
(\265)Tj
/T1_5 7.97 Tf
5.42 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.3 -7.19 Td
(L)Tj
/T1_0 10.91 Tf
9.28 3.23 Td
(=)Tj
/T1_6 10.91 Tf
11.51 0 Td
(H)Tj
/T1_7 7.97 Tf
7.73 -1.63 Td
(1)Tj
/T1_0 10.91 Tf
4.73 1.63 Td
(\()Tj
/T1_4 10.91 Tf
(SID)Tj
/T1_5 7.97 Tf
21.42 3.96 Td
(0)Tj
/T1_3 7.97 Tf
T*
(L)Tj
/T1_1 10.91 Tf
6.25 3.23 Td
(jj)Tj
/T1_4 10.91 Tf
6.06 0 Td
(UID)Tj
/T1_5 7.97 Tf
17.18 3.96 Td
(0)Tj
/T1_3 7.97 Tf
T*
(L)Tj
/T1_1 10.91 Tf
6.25 3.23 Td
(jj)Tj
/T1_2 10.91 Tf
6.06 0 Td
(K)Tj
/T1_5 7.97 Tf
10.05 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.79 -7.19 Td
(L)Tj
/T1_1 10.91 Tf
6.26 3.23 Td
(jj)Tj
/T1_2 10.91 Tf
6.06 0 Td
(K)Tj
/T1_5 7.97 Tf
10.04 3.96 Td
(0)Tj
/T1_1 10.91 Tf
2.8 -3.96 Td
(jj)Tj
/T1_2 10.91 Tf
6.06 0 Td
(\277)Tj
/T1_5 7.97 Tf
6 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-1.24 -7.19 Td
(L)Tj
/T1_0 10.91 Tf
6.26 3.23 Td
[(\))-333(holds.)]TJ
-381.69 -21.92 Td
(\()Tj
/T1_2 10.91 Tf
(ii)Tj
/T1_0 10.91 Tf
[(\))-411(Eac)27(h)]TJ
/T1_4 10.91 Tf
48.45 0 Td
(U)Tj
/T1_3 7.97 Tf
5.73 -1.63 Td
(i;j)Tj
/T1_0 10.91 Tf
14.11 1.63 Td
[(for)-411(1)]TJ
/T1_1 10.91 Tf
27.45 0 Td
(\267)Tj
/T1_2 10.91 Tf
12.93 0 Td
(i)Tj
/T1_1 10.91 Tf
8.22 0 Td
(6)Tj
/T1_0 10.91 Tf
(=)Tj
/T1_2 10.91 Tf
12.93 0 Td
(L)Tj
/T1_1 10.91 Tf
11.88 0 Td
(\267)Tj
/T1_2 10.91 Tf
12.93 0 Td
(n)Tj
/T1_3 7.97 Tf
6.55 -1.63 Td
(c)Tj
/T1_0 10.91 Tf
8.65 1.63 Td
[(and)-411(1)]TJ
/T1_1 10.91 Tf
31.97 0 Td
(\267)Tj
/T1_2 10.91 Tf
12.94 0 Td
(j)Tj
/T1_1 10.91 Tf
9.57 0 Td
(\267)Tj
/T1_2 10.91 Tf
12.93 0 Td
(n)Tj
/T1_3 7.97 Tf
6.55 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
7.87 1.63 Td
(uses)Tj
/T1_2 10.91 Tf
24 0 Td
(K)Tj
/T1_3 7.97 Tf
9.26 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
7.87 1.63 Td
[(to)-411(decrypt)-424(^)]TJ
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/T1_3 7.97 Tf
5.29 -1.63 Td
(i;j)Tj
/T1_0 10.91 Tf
13.65 1.63 Td
[(are)-369(c)27(hec)28(k)27(ed)-368(b)26(y)]TJ
/T1_2 10.91 Tf
74.53 0 Td
(U)Tj
/T1_3 7.97 Tf
5.73 -1.63 Td
(i;j)Tj
/T1_0 10.91 Tf
13.64 1.63 Td
[(in)-370(Phase)-369(1)-370(Round)-370(2.)-553(If)-370(either)]TJ
/T1_2 10.91 Tf
147.57 0 Td
(c)Tj
/T1_3 7.97 Tf
5.72 -1.63 Td
(i;j)Tj
/T1_0 10.91 Tf
13.65 1.63 Td
(or)Tj
/T1_4 10.91 Tf
13.76 0 Td
(v)Tj
/T1_3 7.97 Tf
5.28 -1.63 Td
(i;j)Tj
/T1_0 10.91 Tf
13.65 1.63 Td
[(is)-369(not)-370(v)55(alid,)-378(then)]TJ
/T1_2 10.91 Tf
86.27 0 Td
(U)Tj
/T1_3 7.97 Tf
5.73 -1.63 Td
(i;j)Tj
/T1_0 10.91 Tf
-458.26 -20.28 Td
[(rejects)-354(the)-355(in)27(v)55(alid)]TJ
/T1_2 10.91 Tf
88.95 0 Td
(S)Tj
/T1_3 7.97 Tf
5.72 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
3.38 1.64 Td
[(.)-508(As)]TJ
/T1_1 10.91 Tf
24.93 0 Td
(A)Tj
/T1_0 10.91 Tf
12.58 0 Td
[(do)-27(es)-355(not)-354(kno)26(w)-353(the)-355(encryption)-355(k)27(ey)]TJ
/T1_4 10.91 Tf
166.59 0 Td
(ek)Tj
/T1_3 7.97 Tf
10.76 -1.64 Td
(i;j)Tj
/T1_0 10.91 Tf
13.48 1.64 Td
(of)Tj
/T1_2 10.91 Tf
12.65 0 Td
(U)Tj
/T1_3 7.97 Tf
5.73 -1.64 Td
(i;j)Tj
/T1_0 10.91 Tf
13.48 1.64 Td
[(and)-354(the)-355(symmetric-k)27(ey)]TJ
-358.25 -21.92 Td
[(encryption)-333(sc)27(heme)]TJ
/T1_6 10.91 Tf
91.58 0 Td
(SKE)Tj
/T1_0 10.91 Tf
23.79 0 Td
[(is)-333(assumed)-333(to)-333(b)-28(e)-334(secure,)-333(therefore)]TJ
/T1_1 10.91 Tf
164.53 0 Td
(A)Tj
/T1_0 10.91 Tf
12.35 0 Td
[(is)-333(not)-333(able)-334(to)-333(pro)-28(duce)-333(a)-334(v)55(alid)]TJ
/T1_2 10.91 Tf
143.69 0 Td
(c)Tj
/T1_3 7.97 Tf
5.73 -1.63 Td
(i;j)Tj
/T1_0 10.91 Tf
9.61 1.63 Td
(.)Tj
/T1_1 10.91 Tf
7.88 0 Td
(A)Tj
/T1_0 10.91 Tf
-459.16 -21.91 Td
[(also)-301(do)-27(es)-302(not)-301(kno)27(w)-300(the)-301(passw)27(ord)]TJ
/T1_6 10.91 Tf
158.12 0 Td
[(p)27(w)]TJ
/T1_3 7.97 Tf
12.94 -2.62 Td
(i;j)Tj
/T1_0 10.91 Tf
12.9 2.62 Td
(of)Tj
/T1_2 10.91 Tf
12.07 0 Td
(U)Tj
/T1_3 7.97 Tf
5.72 -1.64 Td
(i;j)Tj
/T1_0 10.91 Tf
9.62 1.64 Td
[(,)-307(therefore)]TJ
/T1_1 10.91 Tf
51.84 0 Td
(A)Tj
/T1_0 10.91 Tf
11.99 0 Td
[(is)-301(not)-301(able)-301(to)-301(pro)-28(duce)-301(a)-301(v)54(alid)]TJ
/T1_4 10.91 Tf
141.23 0 Td
(v)Tj
/T1_3 7.97 Tf
5.29 -1.64 Td
(i;j)Tj
/T1_0 10.91 Tf
9.61 1.64 Td
[(.)-433(Hence)]TJ
/T1_1 10.91 Tf
-431.33 -21.92 Td
(A)Tj
/T1_0 10.91 Tf
12.34 0 Td
[(is)-333(not)-333(able)-334(to)-333(imp)-28(ersonate)]TJ
/T1_2 10.91 Tf
128.3 0 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
7.01 1.64 Td
[(in)-333(Phase)-333(1.)]TJ
-136.45 -21.92 Td
[(Next,)-308(consider)]TJ
/T1_1 10.91 Tf
71.59 0 Td
(A)Tj
/T1_0 10.91 Tf
12.01 0 Td
[(imp)-27(ersonating)]TJ
/T1_2 10.91 Tf
70.95 0 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
6.68 1.63 Td
[(in)-302(Phase)-303(2.)-434(As)-303(the)-302(functionalit)26(y)-301(of)-303(Round)-303(1)-302(and)-303(Round)-303(2)-302(of)]TJ
-183.89 -21.91 Td
[(Phase)-247(1)-247(are)-247(same)-247(as)-248(that)-247(of)-247(Round)-247(1)-247(and)-248(Round)-247(2)-247(of)-247(Phase)-248(2)-247(resp)-28(ectiv)27(ely)-246(and)-247(the)-247(di\256erence)-248(b)-27(et)26(w)28(een)]TJ
0 -21.92 TD
[(the)-428(t)27(w)28(o)-428(phases)-428(are)-428(the)-429(comm)27(unications)-427(b)-28(et)27(w)28(een)]TJ
/T1_2 10.91 Tf
240.73 0 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
8.05 1.64 Td
(and)Tj
/T1_2 10.91 Tf
22.24 0 Td
(U)Tj
/T1_3 7.97 Tf
5.73 -1.64 Td
(i;j)Tj
/T1_0 10.91 Tf
14.29 1.64 Td
[(in)-427(Phase)-429(1)-428(and)-429(the)-428(comm)27(unication)]TJ
-296.77 -21.92 Td
[(b)-27(et)27(w)27(een)]TJ
/T1_2 10.91 Tf
42.64 0 Td
(C)Tj
/T1_0 10.91 Tf
9.89 0 Td
(and)Tj
/T1_2 10.91 Tf
21.73 0 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
7.54 1.63 Td
[(in)-382(Phase)-381(2,)-394(hence)-382(the)-382(pro)-28(of)-382(of)]TJ
/T1_1 10.91 Tf
150.4 0 Td
(A)Tj
/T1_0 10.91 Tf
12.87 0 Td
[(imp)-28(ersonating)]TJ
/T1_2 10.91 Tf
71.82 0 Td
(S)Tj
/T1_3 7.97 Tf
5.72 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
7.55 1.63 Td
[(in)-381(Phase)-382(2)-382(is)-381(similar)-382(to)-382(the)]TJ
-335.89 -21.91 Td
[(imp)-27(ersonation)-334(of)]TJ
/T1_2 10.91 Tf
83.7 0 Td
(U)Tj
/T1_3 7.97 Tf
5.73 -1.64 Td
(i;j)Tj
/T1_0 10.91 Tf
13.25 1.64 Td
[(in)-333(Phase)-333(1.)-445(Hence,)-333(w)27(e)-333(omit)-333(the)-333(pro)-28(of)-333(here.)]TJ
-85.75 -21.92 Td
[(Next)-368(consider)]TJ
/T1_1 10.91 Tf
69.92 0 Td
(A)Tj
/T1_0 10.91 Tf
12.72 0 Td
[(imp)-27(ersonating)]TJ
/T1_2 10.91 Tf
71.66 0 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
7.39 1.64 Td
[(in)-367(Phase)-368(3)-368(Round)-368(1,)-377(then)]TJ
/T1_1 10.91 Tf
128.14 0 Td
(A)Tj
/T1_0 10.91 Tf
12.72 0 Td
[(needs)-368(to)-368(compute)-368(v)55(alid)-380(^)]TJ
/T1_2 10.91 Tf
115.18 0 Td
(c)Tj
/T1_3 7.97 Tf
5.72 -1.64 Td
(i;j)Tj
/T1_0 10.91 Tf
13.28 1.64 Td
(=)Tj
/T1_1 10.91 Tf
-459.39 -21.92 Td
(E)Tj
/T1_3 7.97 Tf
5.76 -1.63 Td
(t)Tj
/T1_5 5.98 Tf
3.05 -1.22 Td
(i;j)Tj
/T1_0 10.91 Tf
9.33 2.85 Td
(\()Tj
/T1_4 10.91 Tf
4.25 0 Td
(K)Tj
/T1_3 7.97 Tf
9.26 -1.63 Td
(i)Tj
/T1_1 10.91 Tf
3.38 1.63 Td
(jj)Tj
/T1_4 10.91 Tf
6.06 0 Td
(K)Tj
/T1_1 10.91 Tf
10.04 0 Td
(jj)Tj
/T1_2 10.91 Tf
6.06 0 Td
(S)Tj
/T1_3 7.97 Tf
5.72 -1.63 Td
(i)Tj
/T1_1 10.91 Tf
3.39 1.63 Td
(jj)Tj
/T1_4 10.91 Tf
6.05 0 Td
(z)Tj
/T1_3 7.97 Tf
5.08 -1.63 Td
(i;j)Tj
/T1_1 10.91 Tf
9.61 1.63 Td
(jj)Tj
/T1_2 10.91 Tf
6.06 0 Td
(SID)Tj
/T1_3 7.97 Tf
17.18 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
3.38 1.63 Td
[(\),)-560(^)]TJ
/T1_4 10.91 Tf
12.52 0 Td
(\271)Tj
/T1_3 7.97 Tf
6.57 -1.63 Td
(i;j)Tj
/T1_0 10.91 Tf
14.8 1.63 Td
(=)Tj
/T1_6 10.91 Tf
13.67 0 Td
[(MA)28(C)]TJ
/T1_3 7.97 Tf
23.48 -1.77 Td
(ak)Tj
/T1_5 5.98 Tf
8.9 -1.22 Td
(i;j)Tj
/T1_0 10.91 Tf
9.33 2.99 Td
(\()Tj
/T1_4 10.91 Tf
(\277)Tj
/T1_3 7.97 Tf
9.01 -1.63 Td
(i)Tj
/T1_1 10.91 Tf
3.38 1.63 Td
(jj)Tj
/T1_4 10.91 Tf
6.06 0 Td
(\277)Tj
/T1_3 7.97 Tf
4.77 -1.63 Td
(i;j)Tj
/T1_1 10.91 Tf
9.61 1.63 Td
(jj)Tj
/T1_4 10.91 Tf
6.06 0 Td
(z)Tj
/T1_3 7.97 Tf
5.07 -1.63 Td
(i)Tj
/T1_1 10.91 Tf
3.38 1.63 Td
(jj)Tj
/T1_4 10.91 Tf
6.06 0 Td
(\265)Tj
/T1_3 7.97 Tf
5.12 -1.63 Td
(i)Tj
/T1_1 10.91 Tf
3.38 1.63 Td
(jj)Tj
/T1_2 10.91 Tf
6.06 0 Td
(SID)Tj
/T1_3 7.97 Tf
17.18 -1.63 Td
(i)Tj
/T1_1 10.91 Tf
3.38 1.63 Td
(jj)Tj
/T1_2 10.91 Tf
6.06 0 Td
(S)Tj
/T1_3 7.97 Tf
5.72 -1.63 Td
(i)Tj
/T1_1 10.91 Tf
3.38 1.63 Td
(jj)Tj
/T1_2 10.91 Tf
6.06 0 Td
(U)Tj
/T1_3 7.97 Tf
5.73 -1.63 Td
(i;j)Tj
/T1_1 10.91 Tf
9.61 1.63 Td
(jj)Tj
/T1_0 10.91 Tf
6.06 0 Td
[(11\))-452(and)]TJ
/T1_4 10.91 Tf
42.58 0 Td
(\265)Tj
/T1_3 7.97 Tf
5.12 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
8.56 1.63 Td
(=)Tj
/T1_6 10.91 Tf
13.67 0 Td
(H)Tj
/T1_7 7.97 Tf
7.72 -1.63 Td
(1)Tj
/T1_0 10.91 Tf
4.74 1.63 Td
(\()Tj
/T1_2 10.91 Tf
(SID)Tj
/T1_3 7.97 Tf
21.41 -1.63 Td
(i)Tj
/T1_1 10.91 Tf
3.38 1.63 Td
(jj)Tj
/T1_2 10.91 Tf
6.06 0 Td
(UID)Tj
/T1_3 7.97 Tf
17.18 -1.63 Td
(i)Tj
/T1_1 10.91 Tf
-464.49 -20.28 Td
(jj)Tj
/T1_4 10.91 Tf
6.06 0 Td
(K)Tj
/T1_3 7.97 Tf
9.26 -1.64 Td
(i)Tj
/T1_1 10.91 Tf
3.38 1.64 Td
(jj)Tj
/T1_4 10.91 Tf
6.06 0 Td
(K)Tj
/T1_1 10.91 Tf
10.04 0 Td
(jj)Tj
/T1_4 10.91 Tf
6.06 0 Td
(\277)Tj
/T1_3 7.97 Tf
4.77 -1.64 Td
(i)Tj
/T1_1 10.91 Tf
3.38 1.64 Td
(jj)Tj
/T1_4 10.91 Tf
6.06 0 Td
(z)Tj
/T1_3 7.97 Tf
5.07 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
3.38 1.64 Td
[(\).)-490(The)-348(v)54(alidit)28(y)-348(of)-361(^)]TJ
/T1_2 10.91 Tf
87.04 0 Td
(c)Tj
/T1_3 7.97 Tf
5.72 -1.64 Td
(i;j)Tj
/T1_0 10.91 Tf
13.42 1.64 Td
[(and)-427(^)]TJ
/T1_4 10.91 Tf
21.37 0 Td
(\271)Tj
/T1_3 7.97 Tf
6.57 -1.64 Td
(i;j)Tj
/T1_0 10.91 Tf
13.42 1.64 Td
[(are)-348(c)27(hec)28(k)-348(b)27(y)]TJ
/T1_2 10.91 Tf
63.24 0 Td
(U)Tj
/T1_3 7.97 Tf
5.72 -1.64 Td
(i;j)Tj
/T1_0 10.91 Tf
13.42 1.64 Td
[(in)-348(Phase)-349(3)-348(Round)-349(2.)-490(If)-348(either)-349(one)-348(of)]TJ
-293.3 -21.92 Td
(^)Tj
/T1_2 10.91 Tf
-0.14 0 Td
(c)Tj
/T1_3 7.97 Tf
5.73 -1.64 Td
(i;j)Tj
/T1_0 10.91 Tf
13.62 1.64 Td
[(or)-445(^)]TJ
/T1_4 10.91 Tf
13.72 0 Td
(\271)Tj
/T1_3 7.97 Tf
6.58 -1.64 Td
(i;j)Tj
/T1_0 10.91 Tf
13.62 1.64 Td
[(is)-366(not)-368(correct,)-375(then)]TJ
/T1_2 10.91 Tf
96.21 0 Td
(U)Tj
/T1_3 7.97 Tf
5.72 -1.64 Td
(i;j)Tj
/T1_0 10.91 Tf
13.62 1.64 Td
[(rejects)-367(in)27(v)55(alid)]TJ
/T1_2 10.91 Tf
70.21 0 Td
(S)Tj
/T1_3 7.97 Tf
5.72 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
3.38 1.64 Td
[(.)-546(As)]TJ
/T1_1 10.91 Tf
25.47 0 Td
(A)Tj
/T1_0 10.91 Tf
12.72 0 Td
[(do)-27(es)-367(not)-367(kno)26(w)-366(the)-367(authen)27(tication)-366(k)26(ey)]TJ
/T1_4 10.91 Tf
-286.32 -21.92 Td
(ak)Tj
/T1_3 7.97 Tf
11.44 -1.63 Td
(i;j)Tj
/T1_0 10.91 Tf
13.84 1.63 Td
[(and)-387(the)-388(message)-387(authen)26(tication)-386(co)-28(de)-387(sc)26(heme)]TJ
/T1_6 10.91 Tf
220.34 0 Td
[(MA)27(CS)]TJ
/T1_0 10.91 Tf
33.76 0 Td
[(is)-387(assumed)-388(to)-387(b)-28(e)-387(secure,)-402(therefore)]TJ
/T1_1 10.91 Tf
168.23 0 Td
(A)Tj
/T1_0 10.91 Tf
12.93 0 Td
(is)Tj
-460.54 -21.91 Td
[(not)-331(able)-331(to)-331(compute)-331(a)-332(v)55(alid)-409(^)]TJ
/T1_4 10.91 Tf
135.28 0 Td
(\271)Tj
/T1_3 7.97 Tf
6.57 -1.64 Td
(i;j)Tj
/T1_0 10.91 Tf
9.61 1.64 Td
[(.)-444(F)83(urthermore,)]TJ
/T1_1 10.91 Tf
74.14 0 Td
(A)Tj
/T1_0 10.91 Tf
12.32 0 Td
[(do)-27(es)-331(not)-332(kno)27(w)-330(passw)27(ord)]TJ
/T1_6 10.91 Tf
119.48 0 Td
[(p)27(w)]TJ
/T1_3 7.97 Tf
12.94 -2.62 Td
(i;j)Tj
/T1_0 10.91 Tf
13.22 2.62 Td
(of)Tj
/T1_2 10.91 Tf
12.4 0 Td
(U)Tj
/T1_3 7.97 Tf
5.73 -1.64 Td
(i;j)Tj
/T1_0 10.91 Tf
9.61 1.64 Td
[(,)-331(hence)]TJ
/T1_1 10.91 Tf
36.92 0 Td
(A)Tj
/T1_0 10.91 Tf
12.32 0 Td
(is)Tj
-460.54 -21.92 Td
[(not)-322(able)-322(to)-322(obtain)]TJ
/T1_4 10.91 Tf
89.19 0 Td
(z)Tj
/T1_3 7.97 Tf
5.07 -1.63 Td
(i;j)Tj
/T1_0 10.91 Tf
13.13 1.63 Td
(from)Tj
/T1_4 10.91 Tf
25.66 0 Td
(z)Tj
/T1_8 7.97 Tf
5.55 3.96 Td
(\244)Tj
/T1_3 7.97 Tf
-0.48 -7.01 Td
(i;j)Tj
/T1_0 10.91 Tf
13.13 3.05 Td
[(to)-322(compute)-322(v)55(alid)]TJ
/T1_4 10.91 Tf
83.55 0 Td
(t)Tj
/T1_3 7.97 Tf
3.94 -1.63 Td
(i;j)Tj
/T1_0 10.91 Tf
12.64 1.63 Td
(=)Tj
/T1_4 10.91 Tf
11.51 0 Td
(g)Tj
/T1_3 7.97 Tf
5.6 3.96 Td
(r)Tj
/T1_5 5.98 Tf
3.82 -1.22 Td
(i)Tj
/T1_3 7.97 Tf
3.16 1.22 Td
(r)Tj
/T1_5 5.98 Tf
3.82 -1.22 Td
(i;j)Tj
/T1_0 10.91 Tf
9.33 -2.74 Td
[(.)-440(Therefore,)]TJ
/T1_1 10.91 Tf
60.21 0 Td
(A)Tj
/T1_0 10.91 Tf
12.22 0 Td
[(is)-322(not)-322(able)-322(to)-323(compute)]TJ
-361.05 -21.92 Td
[(the)-333(ciphertext)-346(^)]TJ
/T1_2 10.91 Tf
70.62 0 Td
(c)Tj
/T1_3 7.97 Tf
5.72 -1.63 Td
(i;j)Tj
/T1_0 10.91 Tf
9.62 1.63 Td
[(.)-444(Hence)]TJ
/T1_1 10.91 Tf
40.29 0 Td
(A)Tj
/T1_0 10.91 Tf
12.34 0 Td
[(is)-333(not)-333(able)-334(to)-333(imp)-28(ersonate)]TJ
/T1_2 10.91 Tf
128.3 0 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
7.01 1.63 Td
[(in)-333(Phase)-333(3.)]TJ
-262.7 -21.91 Td
[(Finally)83(,)-358(consider)]TJ
/T1_1 10.91 Tf
82.24 0 Td
(A)Tj
/T1_0 10.91 Tf
12.57 0 Td
[(imp)-27(ersonating)-354(main)-354(con)27(troller)]TJ
/T1_2 10.91 Tf
148.06 0 Td
(C)Tj
/T1_0 10.91 Tf
9.58 0 Td
[(in)-353(Phase)-354(2)-354(Round)-354(1.)-506(The)-354(pro)-28(of)-354(is)-354(similar)]TJ
-269.38 -21.92 Td
[(to)-402(the)-402(imp)-28(ersonation)-402(of)-403(a)-402(subgroup)-403(con)27(troller)]TJ
/T1_2 10.91 Tf
226.36 0 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
7.77 1.63 Td
[(in)-402(Phase)-402(1)-403(Round)-402(1.)-652(Hence)-402(w)27(e)-402(omit)-402(the)-402(pro)-28(of)]TJ
-239.86 -21.91 Td
[(here.)-916(Next)-491(consider)]TJ
/T1_1 10.91 Tf
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S
Q
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BT
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1.0003 0 0 1.0003 84.4335 187.627 Tm
(1)Tj
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[(247.8)-432(nanoseconds)-433(for)-433(a)-433(160-bit)-433(HMA)27(C\(SHA-1\))-432(MA)28(C)-432(computation,)-456(250.6)-433(nanoseconds)-433(for)-433(a)-433(160-bit)-433(SHA-1)-433(Hash)]TJ
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[(computation)-348(and)-348(12.63)-348(nanoseconds)-349(p)-28(er)-348(b)27(yte)-347(for)-348(the)-349(AES/CBC)-348(\(128-bit)-348(k)27(ey\))-347(encryption)-348(algorithm.)-474(In)-348(comparison,)]TJ
0 -10.96 TD
[(RSA)-259(1024-bit)-260(signature)-260(generation)-260(tak)28(es)-259(3.02)-260(milliseconds)-260(p)-29(er)-260(op)-28(eration)-260(and)-260(RSA)-260(1024-bit)-260(signature)-260(v)28(eri\257cation)-259(tak)28(es)]TJ
T*
[(0.13)-289(milliseconds)-290(p)-28(er)-290(op)-29(eration)-289(using)-290(17)-290(as)-290(the)-289(public)-290(exp)-28(onen)27(t)-289(on)-289(the)-290(same)-290(system.)-439(Hence)-290(the)-289(MA)27(C)-288(algorithm,)-301(hash)]TJ
0 -10.95 TD
[(function)-342(and)-343(symmetric)-342(k)27(ey)-341(encryption)-343(sc)28(heme)-342(are)-343(e\261cien)28(t.)]TJ
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(262)Tj
ET
q
1 0 0 1 -62.5 824 cm
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1.0003 0 0 1.0003 72 758.8569 Tm
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[(are)-445(indep)-28(enden)27(t)-444(to)-445(eac)27(h)]TJ
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[(J)24(;k)]TJ
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[(can)-409(obtain)]TJ
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[(J)35(;j)]TJ
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13.54 -2.62 Td
(from)Tj
/T1_1 10.91 Tf
-445.73 -21.91 Td
(z)Tj
/T1_2 7.97 Tf
5.07 -1.69 Td
(J)Tj
/T1_0 10.91 Tf
9.99 1.69 Td
(and)Tj
/T1_1 10.91 Tf
21.69 0 Td
(z)Tj
/T1_2 7.97 Tf
5.08 -1.69 Td
[(J)24(;j)]TJ
/T1_0 10.91 Tf
15.28 1.69 Td
[(resp)-27(ectiv)27(ely)-377(as)-378(this)-378(is)-377(the)]TJ
/T1_11 10.91 Tf
126.3 0 Td
(CDH)Tj
/T1_0 10.91 Tf
26.69 0 Td
[(problem)-377(and)-378(is)-377(assumed)-378(to)-378(b)-28(e)-377(di\261cult.)-578(F)82(urthermore,)]TJ
/T1_7 10.91 Tf
-210.1 -21.92 Td
(U)Tj
/T1_2 7.97 Tf
5.73 -1.78 Td
[(J)24(;k)]TJ
/T1_0 10.91 Tf
15.93 1.78 Td
[(is)-370(not)-370(able)-370(to)-370(obtain)]TJ
/T1_1 10.91 Tf
102.64 0 Td
(z)Tj
/T1_2 7.97 Tf
5.08 -1.69 Td
[(J)24(;j)]TJ
/T1_0 10.91 Tf
15.2 1.69 Td
(from)Tj
/T1_1 10.91 Tf
26.18 0 Td
(z)Tj
/T1_6 7.97 Tf
5.55 3.96 Td
(\244)Tj
/T1_2 7.97 Tf
-0.48 -7.19 Td
[(J)24(;j)]TJ
/T1_0 10.91 Tf
14.86 3.23 Td
(=)Tj
/T1_1 10.91 Tf
12.18 0 Td
(z)Tj
/T1_2 7.97 Tf
5.07 -1.69 Td
[(J)23(;j)]TJ
/T1_5 10.91 Tf
13.86 1.69 Td
(\242)Tj
/T1_1 10.91 Tf
5.72 0 Td
(h)Tj
/T1_12 7.97 Tf
6.28 4.38 Td
(H)Tj
/T1_10 5.98 Tf
5.98 -1.1 Td
(1)Tj
/T1_8 7.97 Tf
4.15 1.1 Td
(\()Tj
/T1_13 7.97 Tf
(SID)Tj
/T1_4 5.98 Tf
15.99 -1.34 Td
(J)Tj
/T1_6 7.97 Tf
5.13 1.34 Td
(jj)Tj
/T1_13 7.97 Tf
4.71 0 Td
(U)Tj
/T1_4 5.98 Tf
4.23 -1.34 Td
[(J)35(;j)]TJ
/T1_6 7.97 Tf
10.03 1.34 Td
(jj)Tj
/T1_13 7.97 Tf
4.71 0 Td
(S)Tj
/T1_4 5.98 Tf
4.23 -1.34 Td
(J)Tj
/T1_6 7.97 Tf
5.14 1.34 Td
(jj)Tj
/T1_12 7.97 Tf
[(p)29(w)]TJ
/T1_4 5.98 Tf
14.74 -2.05 Td
[(J)35(;j)]TJ
/T1_6 7.97 Tf
10.03 2.05 Td
(jj)Tj
/T1_2 7.97 Tf
(\277)Tj
/T1_4 5.98 Tf
8.46 -1.34 Td
(J)Tj
/T1_6 7.97 Tf
5.14 1.34 Td
(jj)Tj
/T1_2 7.97 Tf
(\277)Tj
/T1_4 5.98 Tf
8.46 -1.34 Td
[(J)35(;j)]TJ
/T1_8 7.97 Tf
10.03 1.34 Td
(\))Tj
/T1_0 10.91 Tf
7.83 -4.38 Td
(as)Tj
/T1_7 10.91 Tf
13.79 0 Td
(U)Tj
/T1_2 7.97 Tf
5.72 -1.78 Td
[(J)23(;k)]TJ
/T1_0 10.91 Tf
15.94 1.78 Td
[(do)-27(es)-370(not)-370(kno)26(w)]TJ
-398.24 -21.92 Td
[(the)-327(passw)27(ord)]TJ
/T1_11 10.91 Tf
65.75 0 Td
[(p)27(w)]TJ
/T1_2 7.97 Tf
12.94 -2.62 Td
[(J)24(;j)]TJ
/T1_0 10.91 Tf
14.73 2.62 Td
[(of)-327(user)]TJ
/T1_7 10.91 Tf
35.4 0 Td
(U)Tj
/T1_2 7.97 Tf
5.72 -1.69 Td
[(J)23(;j)]TJ
/T1_0 10.91 Tf
14.73 1.69 Td
[(for)-327(1)]TJ
/T1_5 10.91 Tf
25.11 0 Td
(\267)Tj
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11.51 0 Td
(j)Tj
/T1_5 10.91 Tf
8.15 0 Td
(\267)Tj
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11.51 0 Td
(n)Tj
/T1_2 7.97 Tf
6.55 -1.69 Td
(J)Tj
/T1_0 10.91 Tf
5.87 1.69 Td
[(.)-442(Hence,)-328(new)-327(user)]TJ
/T1_7 10.91 Tf
88.64 0 Td
(U)Tj
/T1_2 7.97 Tf
5.72 -1.77 Td
[(J)24(;k)]TJ
/T1_0 10.91 Tf
15.47 1.77 Td
[(is)-326(not)-327(able)-327(to)-328(obtain)-327(previous)]TJ
-327.8 -21.91 Td
[(subgroup)-333(k)27(ey)]TJ
/T1_1 10.91 Tf
67.04 0 Td
(K)Tj
/T1_2 7.97 Tf
9.26 -1.69 Td
(J)Tj
/T1_0 10.91 Tf
5.88 1.69 Td
(.)Tj
-65.25 -21.92 Td
[(Next,)-298(consider)-289(the)-289(new)-289(user)]TJ
/T1_7 10.91 Tf
134.19 0 Td
(U)Tj
/T1_2 7.97 Tf
5.73 -1.78 Td
[(J)24(;k)]TJ
/T1_0 10.91 Tf
15.05 1.78 Td
[(tries)-288(to)-289(obtain)-289(previous)-289(\257nal)-289(group)-289(k)26(ey)]TJ
/T1_1 10.91 Tf
186.47 0 Td
(K)Tj
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13.07 0 Td
(=)Tj
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11.52 0 Td
(g)Tj
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5.59 3.96 Td
(r)Tj
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3.82 -1 Td
(C)Tj
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3.67 1 Td
(r)Tj
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3.82 -1 Td
(C)Tj
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3.68 1 Td
(+)Tj
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6.58 5.97 Td
(P)Tj
/T1_4 5.98 Tf
8.94 -2.23 Td
(n)Tj
4.6 -1 Td
(c)Tj
-4.6 -5.39 Td
(i)Tj
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2.66 0 Td
(=1)Tj
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11.15 2.65 Td
(r)Tj
/T1_13 5.98 Tf
3.82 -1 Td
(C)Tj
/T1_12 7.97 Tf
3.67 1 Td
(H)Tj
/T1_10 5.98 Tf
5.98 -1.11 Td
(2)Tj
/T1_8 7.97 Tf
4.15 1.11 Td
(\()Tj
/T1_2 7.97 Tf
(K)Tj
/T1_4 5.98 Tf
10.43 -1.22 Td
(i)Tj
/T1_8 7.97 Tf
3.16 1.22 Td
(\))Tj
/T1_0 10.91 Tf
-464.08 -25.88 Td
[(from)-357(the)-358(new)-358(group)-358(k)27(ey)]TJ
/T1_1 10.91 Tf
118.94 0 Td
(K)Tj
/T1_6 7.97 Tf
10.05 3.96 Td
(0)Tj
/T1_0 10.91 Tf
6.27 -3.96 Td
(=)Tj
/T1_1 10.91 Tf
11.96 0 Td
(g)Tj
/T1_2 7.97 Tf
5.59 5.18 Td
(r)Tj
/T1_3 5.98 Tf
4.06 2.81 Td
(0)Tj
/T1_13 5.98 Tf
-0.24 -5.09 Td
(C)Tj
/T1_2 7.97 Tf
3.67 2.28 Td
(r)Tj
/T1_3 5.98 Tf
4.06 2.81 Td
(0)Tj
/T1_13 5.98 Tf
-0.24 -5.09 Td
(C)Tj
/T1_8 7.97 Tf
3.68 2.28 Td
(+)Tj
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(r)Tj
/T1_3 5.98 Tf
10.64 2.81 Td
(0)Tj
/T1_13 5.98 Tf
-0.24 -5.09 Td
(C)Tj
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3.67 2.28 Td
(H)Tj
/T1_10 5.98 Tf
5.98 -1.11 Td
(2)Tj
/T1_8 7.97 Tf
4.15 1.11 Td
(\()Tj
/T1_2 7.97 Tf
(K)Tj
/T1_3 5.98 Tf
10.99 2.81 Td
(0)Tj
/T1_4 5.98 Tf
-0.56 -5.52 Td
(J)Tj
/T1_8 7.97 Tf
5.14 2.71 Td
(\)+)Tj
/T1_9 7.97 Tf
9.87 5.97 Td
(P)Tj
/T1_4 5.98 Tf
8.94 -2.23 Td
(n)Tj
4.6 -1 Td
(c)Tj
-4.6 -5.58 Td
(i)Tj
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2.66 0 Td
(=1)Tj
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9.24 0 Td
(;i)Tj
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4.94 0 Td
(6)Tj
/T1_10 5.98 Tf
(=)Tj
/T1_4 5.98 Tf
5.58 0 Td
(J)Tj
/T1_2 7.97 Tf
6.55 2.84 Td
(r)Tj
/T1_3 5.98 Tf
4.06 2.81 Td
(0)Tj
/T1_13 5.98 Tf
-0.24 -5.09 Td
(C)Tj
/T1_12 7.97 Tf
3.67 2.28 Td
(H)Tj
/T1_10 5.98 Tf
5.98 -1.11 Td
(2)Tj
/T1_8 7.97 Tf
4.15 1.11 Td
(\()Tj
/T1_2 7.97 Tf
(K)Tj
/T1_4 5.98 Tf
10.43 -1.22 Td
(i)Tj
/T1_8 7.97 Tf
3.16 1.22 Td
(\))Tj
/T1_0 10.91 Tf
3.79 -5.18 Td
[(.)-518(As)]TJ
/T1_1 10.91 Tf
25.07 0 Td
(r)Tj
/T1_6 7.97 Tf
5.22 3.96 Td
(0)Tj
/T1_13 7.97 Tf
-0.3 -6.65 Td
(C)Tj
/T1_0 10.91 Tf
8.63 2.69 Td
(and)Tj
/T1_1 10.91 Tf
21.48 0 Td
(r)Tj
/T1_13 7.97 Tf
4.92 -1.63 Td
(C)Tj
/T1_0 10.91 Tf
8.63 1.63 Td
[(are)-358(random)-358(and)-358(inde-)]TJ
-364 -21.91 Td
[(p)-27(enden)27(t)-379(to)-379(eac)26(h)-378(other,)-391(therefore,)]TJ
/T1_1 10.91 Tf
162.81 0 Td
(g)Tj
/T1_2 7.97 Tf
5.6 3.95 Td
(r)Tj
/T1_3 5.98 Tf
4.05 2.82 Td
(0)Tj
/T1_13 5.98 Tf
-0.23 -5.09 Td
(C)Tj
/T1_2 7.97 Tf
3.67 2.27 Td
(r)Tj
/T1_3 5.98 Tf
4.06 2.82 Td
(0)Tj
/T1_13 5.98 Tf
-0.24 -5.09 Td
(C)Tj
/T1_0 10.91 Tf
8.31 -1.68 Td
(and)Tj
/T1_1 10.91 Tf
21.71 0 Td
(g)Tj
/T1_2 7.97 Tf
5.59 3.95 Td
(r)Tj
/T1_13 5.98 Tf
3.82 -0.99 Td
(C)Tj
/T1_2 7.97 Tf
3.68 0.99 Td
(r)Tj
/T1_13 5.98 Tf
3.82 -0.99 Td
(C)Tj
/T1_0 10.91 Tf
8.31 -2.96 Td
[(are)-379(indep)-27(enden)26(t)-378(to)-380(eac)27(h)-378(other)-380(and)]TJ
/T1_1 10.91 Tf
170.61 0 Td
(g)Tj
/T1_2 7.97 Tf
5.59 3.95 Td
(r)Tj
/T1_3 5.98 Tf
4.05 2.82 Td
(0)Tj
/T1_13 5.98 Tf
-0.23 -5.09 Td
(C)Tj
/T1_12 7.97 Tf
3.67 2.27 Td
(H)Tj
/T1_10 5.98 Tf
5.98 -1.1 Td
(2)Tj
/T1_8 7.97 Tf
4.15 1.1 Td
(\()Tj
/T1_2 7.97 Tf
(K)Tj
/T1_4 5.98 Tf
10.43 -1.21 Td
(i)Tj
/T1_8 7.97 Tf
3.16 1.21 Td
(\))Tj
/T1_0 10.91 Tf
7.93 -3.95 Td
(and)Tj
/T1_1 10.91 Tf
-450.3 -21.92 Td
(g)Tj
/T1_2 7.97 Tf
5.59 3.96 Td
(r)Tj
/T1_13 5.98 Tf
3.82 -1 Td
(C)Tj
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3.68 1 Td
(H)Tj
/T1_10 5.98 Tf
5.97 -1.11 Td
(2)Tj
/T1_8 7.97 Tf
4.15 1.11 Td
(\()Tj
/T1_2 7.97 Tf
(K)Tj
/T1_4 5.98 Tf
10.43 -1.22 Td
(i)Tj
/T1_8 7.97 Tf
3.16 1.22 Td
(\))Tj
/T1_0 10.91 Tf
8.58 -3.96 Td
[(for)-438(1)]TJ
/T1_5 10.91 Tf
28.24 0 Td
(\267)Tj
/T1_1 10.91 Tf
13.43 0 Td
(i)Tj
/T1_5 10.91 Tf
8.71 0 Td
(6)Tj
/T1_0 10.91 Tf
(=)Tj
/T1_1 10.91 Tf
13.43 0 Td
(J)Tj
/T1_5 10.91 Tf
12.04 0 Td
(\267)Tj
/T1_1 10.91 Tf
13.43 0 Td
(n)Tj
/T1_2 7.97 Tf
6.55 -1.64 Td
(c)Tj
/T1_0 10.91 Tf
8.95 1.64 Td
[(are)-438(indep)-28(enden)27(t)-438(to)-439(eac)27(h)-438(other.)-761(F)82(urthermore,)-464(as)]TJ
/T1_1 10.91 Tf
240.94 0 Td
(K)Tj
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10.05 3.96 Td
(0)Tj
/T1_2 7.97 Tf
-0.78 -7.19 Td
(J)Tj
/T1_0 10.91 Tf
10.65 3.23 Td
(and)Tj
/T1_1 10.91 Tf
22.36 0 Td
(K)Tj
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9.26 -1.69 Td
(J)Tj
/T1_0 10.91 Tf
10.66 1.69 Td
(are)Tj
-453.3 -21.92 Td
[(random)-435(and)-436(indep)-27(enden)26(t)-434(to)-436(eac)27(h)-434(other,)-462(therefore)]TJ
/T1_11 10.91 Tf
246.32 0 Td
(H)Tj
/T1_8 7.97 Tf
7.72 -1.63 Td
(2)Tj
/T1_0 10.91 Tf
4.74 1.63 Td
(\()Tj
/T1_1 10.91 Tf
(K)Tj
/T1_6 7.97 Tf
14.28 3.96 Td
(0)Tj
/T1_2 7.97 Tf
-0.78 -7.19 Td
(J)Tj
/T1_0 10.91 Tf
5.87 3.23 Td
[(\))-435(and)]TJ
/T1_11 10.91 Tf
31.31 0 Td
(H)Tj
/T1_8 7.97 Tf
7.73 -1.63 Td
(2)Tj
/T1_0 10.91 Tf
4.73 1.63 Td
(\()Tj
/T1_1 10.91 Tf
(K)Tj
/T1_2 7.97 Tf
13.5 -1.68 Td
(J)Tj
/T1_0 10.91 Tf
5.87 1.68 Td
[(\))-435(are)-436(indep)-28(enden)27(t)-435(to)-435(eac)27(h)]TJ
-341.29 -21.91 Td
[(other)-293(as)-293(the)-294(output)-293(of)-293(the)-294(hash)-293(function)]TJ
/T1_11 10.91 Tf
192.37 0 Td
(H)Tj
/T1_8 7.97 Tf
7.73 -1.64 Td
(2)Tj
/T1_0 10.91 Tf
7.93 1.64 Td
[(is)-293(indep)-27(enden)26(t.)-430(Hence,)]TJ
/T1_1 10.91 Tf
111.52 0 Td
(g)Tj
/T1_2 7.97 Tf
5.59 3.95 Td
(r)Tj
/T1_3 5.98 Tf
4.06 2.82 Td
(0)Tj
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-0.24 -5.09 Td
(C)Tj
/T1_12 7.97 Tf
3.68 2.27 Td
(H)Tj
/T1_10 5.98 Tf
5.97 -1.1 Td
(2)Tj
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4.15 1.1 Td
(\()Tj
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3.3 0 Td
(K)Tj
/T1_3 5.98 Tf
7.7 2.82 Td
(0)Tj
/T1_4 5.98 Tf
-0.57 -5.52 Td
(J)Tj
/T1_8 7.97 Tf
5.14 2.7 Td
(\))Tj
/T1_0 10.91 Tf
6.99 -3.95 Td
(and)Tj
/T1_1 10.91 Tf
20.77 0 Td
(g)Tj
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5.59 3.95 Td
(r)Tj
/T1_13 5.98 Tf
3.83 -0.99 Td
(C)Tj
/T1_12 7.97 Tf
3.67 0.99 Td
(H)Tj
/T1_10 5.98 Tf
5.97 -1.1 Td
(2)Tj
/T1_8 7.97 Tf
4.15 1.1 Td
(\()Tj
/T1_2 7.97 Tf
3.3 0 Td
(K)Tj
/T1_4 5.98 Tf
7.14 -1.33 Td
(J)Tj
/T1_8 7.97 Tf
5.13 1.33 Td
(\))Tj
/T1_0 10.91 Tf
6.99 -3.95 Td
[(are)-293(also)]TJ
-431.86 -21.92 Td
[(indep)-27(enden)27(t)-279(to)-279(eac)27(h)-278(other.)-426(Hence,)]TJ
/T1_1 10.91 Tf
165.42 0 Td
(K)Tj
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10.04 3.96 Td
(0)Tj
/T1_0 10.91 Tf
5.84 -3.96 Td
(and)Tj
/T1_1 10.91 Tf
20.62 0 Td
(K)Tj
/T1_0 10.91 Tf
13.08 0 Td
[(are)-279(indep)-28(enden)27(t)-278(to)-279(eac)27(h)-278(other.)-427(If)]TJ
/T1_7 10.91 Tf
158.38 0 Td
(U)Tj
/T1_2 7.97 Tf
5.73 -1.78 Td
[(J)24(;k)]TJ
/T1_0 10.91 Tf
14.94 1.78 Td
[(can)-279(obtain)]TJ
/T1_1 10.91 Tf
52.74 0 Td
(g)Tj
/T1_2 7.97 Tf
5.6 3.96 Td
(r)Tj
/T1_13 5.98 Tf
3.82 -1 Td
(C)Tj
/T1_2 7.97 Tf
3.67 1 Td
(r)Tj
/T1_13 5.98 Tf
3.82 -1 Td
(C)Tj
/T1_0 10.91 Tf
-463.7 -24.88 Td
(from)Tj
/T1_1 10.91 Tf
25.2 0 Td
(y)Tj
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5.35 -1.63 Td
(C)Tj
/T1_0 10.91 Tf
7.76 1.63 Td
(=)Tj
/T1_1 10.91 Tf
11.51 0 Td
(g)Tj
/T1_2 7.97 Tf
5.6 3.96 Td
(r)Tj
/T1_13 5.98 Tf
3.82 -0.99 Td
(C)Tj
/T1_0 10.91 Tf
7.22 -2.97 Td
(and)Tj
/T1_1 10.91 Tf
20.63 0 Td
(g)Tj
/T1_2 7.97 Tf
5.59 3.96 Td
(r)Tj
/T1_13 5.98 Tf
3.82 -0.99 Td
(C)Tj
/T1_12 7.97 Tf
3.68 0.99 Td
(H)Tj
/T1_10 5.98 Tf
5.97 -1.1 Td
(2)Tj
/T1_8 7.97 Tf
4.15 1.1 Td
(\()Tj
/T1_2 7.97 Tf
3.3 0 Td
(K)Tj
/T1_4 5.98 Tf
7.13 -1.21 Td
(i)Tj
/T1_8 7.97 Tf
3.17 1.21 Td
(\))Tj
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6.84 -3.96 Td
(from)Tj
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25.21 0 Td
(y)Tj
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5.34 -1.63 Td
(C)Tj
/T1_0 10.91 Tf
7.76 1.63 Td
(=)Tj
/T1_1 10.91 Tf
11.51 0 Td
(g)Tj
/T1_2 7.97 Tf
5.6 3.96 Td
(r)Tj
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/T1_5 7.97 Tf
10.04 3.96 Td
(0)Tj
/T1_0 10.91 Tf
5.81 -3.96 Td
[(from)-276(the)-277(public)-277(information)-276(sen)27(t)]TJ
-314.81 -21.92 Td
[(in)-325(the)-325(Join)-325(Proto)-28(col.)-442(F)83(or)-325(case)-325(\(a\),)-327(w)27(e)-324(\257rst)-325(consider)]TJ
/T1_3 10.91 Tf
247.15 0 Td
(A)Tj
/T1_0 10.91 Tf
12.26 0 Td
[(imp)-27(ersonating)]TJ
/T1_1 10.91 Tf
71.19 0 Td
(S)Tj
/T1_2 7.97 Tf
5.73 -1.69 Td
(J)Tj
/T1_0 10.91 Tf
9.42 1.69 Td
[(in)-324(the)-326(Join)-325(Proto)-27(col.)-442(The)]TJ
-345.75 -21.91 Td
[(pro)-27(of)-244(that)]TJ
/T1_3 10.91 Tf
50.17 0 Td
(A)Tj
/T1_0 10.91 Tf
11.36 0 Td
[(is)-243(not)-243(able)-244(to)-243(imp)-28(ersonate)]TJ
/T1_1 10.91 Tf
123.39 0 Td
(S)Tj
/T1_2 7.97 Tf
5.73 -1.69 Td
(J)Tj
/T1_0 10.91 Tf
8.52 1.69 Td
[(in)-243(Phase)-243(1)-243(and)-244(Phase)-243(2)-243(of)-244(the)-243(Join)-243(Proto)-28(col)-243(is)-243(the)-244(same)-243(as)]TJ
-199.17 -21.92 Td
[(the)-226(pro)-27(of)-227(that)]TJ
/T1_3 10.91 Tf
67.41 0 Td
(A)Tj
/T1_0 10.91 Tf
11.18 0 Td
[(is)-225(not)-226(able)-227(to)-226(imp)-28(ersonate)]TJ
/T1_1 10.91 Tf
122.45 0 Td
(S)Tj
/T1_2 7.97 Tf
5.73 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
5.84 1.64 Td
[(in)-226(Phase)-226(1)-226(and)-226(Phase)-226(2)-226(of)-227(the)-226(IKA)-226(proto)-28(col)-226(as)-226(sho)27(wn)-225(in)]TJ
-212.61 -21.92 Td
[(Theorem)-247(43.)-416(Hence)-248(w)27(e)-246(omit)-248(the)-248(pro)-27(of)-248(here.)-416(Next,)-265(consider)]TJ
/T1_3 10.91 Tf
278.25 0 Td
(A)Tj
/T1_0 10.91 Tf
11.41 0 Td
[(imp)-27(ersonating)]TJ
/T1_1 10.91 Tf
70.35 0 Td
(S)Tj
/T1_2 7.97 Tf
5.72 -1.69 Td
(J)Tj
/T1_0 10.91 Tf
8.57 1.69 Td
[(in)-247(Phase)-248(3)-248(Round)-247(1,)]TJ
-374.3 -21.91 Td
(then)Tj
/T1_3 10.91 Tf
23.69 0 Td
(A)Tj
/T1_0 10.91 Tf
11.2 0 Td
[(needs)-228(to)-228(compute)-228(v)55(alid)-240(^)]TJ
/T1_1 10.91 Tf
109.07 0 Td
(c)Tj
/T1_5 7.97 Tf
5.73 3.95 Td
(0)Tj
/T1_2 7.97 Tf
0 -7.27 TD
[(J)24(;k)]TJ
/T1_0 10.91 Tf
14.93 3.32 Td
(=)Tj
/T1_3 10.91 Tf
11.51 0 Td
(E)Tj
/T1_2 7.97 Tf
5.76 -2.31 Td
(t)Tj
/T1_6 5.98 Tf
3.06 2.74 Td
(0)Tj
/T1_7 5.98 Tf
0 -5.58 TD
[(J)35(;k)]TJ
/T1_0 10.91 Tf
11.2 5.15 Td
(\()Tj
/T1_4 10.91 Tf
(K)Tj
/T1_5 7.97 Tf
14.28 3.95 Td
(0)Tj
/T1_2 7.97 Tf
-0.78 -7.19 Td
(J)Tj
/T1_3 10.91 Tf
5.87 3.24 Td
(jj)Tj
/T1_4 10.91 Tf
6.06 0 Td
(K)Tj
/T1_5 7.97 Tf
10.05 3.95 Td
(0)Tj
/T1_3 10.91 Tf
2.79 -3.95 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(S)Tj
/T1_2 7.97 Tf
5.72 -1.69 Td
(J)Tj
/T1_3 10.91 Tf
5.87 1.69 Td
(jj)Tj
/T1_4 10.91 Tf
6.06 0 Td
(z)Tj
/T1_5 7.97 Tf
5.56 3.95 Td
(0)Tj
/T1_2 7.97 Tf
-0.48 -7.27 Td
[(J)24(;k)]TJ
/T1_3 10.91 Tf
11.9 3.32 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(SID)Tj
/T1_5 7.97 Tf
17.17 3.95 Td
(0)Tj
/T1_2 7.97 Tf
0 -7.19 TD
(J)Tj
/T1_0 10.91 Tf
5.87 3.24 Td
[(\),)-262(^)]TJ
/T1_1 10.91 Tf
9.99 0 Td
(c)Tj
/T1_5 7.97 Tf
5.73 3.95 Td
(00)Tj
/T1_2 7.97 Tf
T*
(J)Tj
/T1_0 10.91 Tf
8.9 3.24 Td
(=)Tj
/T1_3 10.91 Tf
11.51 0 Td
(E)Tj
/T1_2 7.97 Tf
5.76 -1.69 Td
(K)Tj
/T1_7 5.98 Tf
7.14 -1.34 Td
(J)Tj
/T1_0 10.91 Tf
5.63 3.03 Td
(\()Tj
/T1_4 10.91 Tf
(K)Tj
/T1_5 7.97 Tf
14.28 3.95 Td
(0)Tj
/T1_2 7.97 Tf
-0.78 -7.19 Td
(J)Tj
/T1_3 10.91 Tf
5.87 3.24 Td
(jj)Tj
/T1_4 10.91 Tf
6.06 0 Td
(K)Tj
/T1_5 7.97 Tf
10.05 3.95 Td
(0)Tj
/T1_3 10.91 Tf
2.79 -3.95 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(S)Tj
/T1_2 7.97 Tf
5.72 -1.69 Td
(J)Tj
/T1_3 10.91 Tf
5.88 1.69 Td
(jj)Tj
/T1_1 10.91 Tf
6.05 0 Td
(SID)Tj
/T1_5 7.97 Tf
17.18 3.95 Td
(0)Tj
/T1_2 7.97 Tf
T*
(J)Tj
/T1_3 10.91 Tf
5.87 3.24 Td
(jj)Tj
/T1_4 10.91 Tf
6.06 0 Td
(\277)Tj
/T1_5 7.97 Tf
6 3.95 Td
(0)Tj
/T1_2 7.97 Tf
-1.23 -7.19 Td
(J)Tj
/T1_0 10.91 Tf
5.87 3.24 Td
(\),)Tj
-459.74 -21.92 Td
(^)Tj
/T1_4 10.91 Tf
-0.86 0 Td
(\271)Tj
/T1_5 7.97 Tf
6.57 3.96 Td
(0)Tj
/T1_2 7.97 Tf
0 -7.28 TD
[(J)23(;k)]TJ
/T1_0 10.91 Tf
15.51 3.32 Td
(=)Tj
/T1_8 10.91 Tf
12.09 0 Td
[(MA)27(C)]TJ
/T1_2 7.97 Tf
23.48 -1.78 Td
(ak)Tj
/T1_7 5.98 Tf
8.9 -1.4 Td
[(J)34(;k)]TJ
/T1_0 10.91 Tf
11.21 3.18 Td
(\()Tj
/T1_4 10.91 Tf
(\277)Tj
/T1_5 7.97 Tf
10.24 3.96 Td
(0)Tj
/T1_2 7.97 Tf
-1.24 -7.19 Td
(J)Tj
/T1_3 10.91 Tf
5.87 3.23 Td
(jj)Tj
/T1_4 10.91 Tf
6.06 0 Td
(\277)Tj
/T1_5 7.97 Tf
6.01 3.96 Td
(0)Tj
/T1_2 7.97 Tf
-1.24 -7.28 Td
[(J)23(;k)]TJ
/T1_3 10.91 Tf
11.9 3.32 Td
(jj)Tj
/T1_4 10.91 Tf
6.06 0 Td
(z)Tj
/T1_5 7.97 Tf
5.55 3.96 Td
(0)Tj
/T1_2 7.97 Tf
-0.48 -7.19 Td
(J)Tj
/T1_3 10.91 Tf
5.88 3.23 Td
(jj)Tj
/T1_4 10.91 Tf
6.05 0 Td
(\265)Tj
/T1_5 7.97 Tf
5.43 3.96 Td
(0)Tj
/T1_2 7.97 Tf
-0.31 -7.19 Td
(J)Tj
/T1_3 10.91 Tf
5.87 3.23 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(SID)Tj
/T1_5 7.97 Tf
17.18 3.96 Td
(0)Tj
/T1_2 7.97 Tf
0 -7.19 TD
(J)Tj
/T1_3 10.91 Tf
5.87 3.23 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(S)Tj
/T1_2 7.97 Tf
5.73 -1.69 Td
(J)Tj
/T1_3 10.91 Tf
5.87 1.69 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(U)Tj
/T1_2 7.97 Tf
5.72 -1.78 Td
[(J)23(;k)]TJ
/T1_3 10.91 Tf
11.9 1.78 Td
(jj)Tj
/T1_0 10.91 Tf
6.06 0 Td
[(11\))-365(and)]TJ
/T1_4 10.91 Tf
40.68 0 Td
(\265)Tj
/T1_5 7.97 Tf
5.43 3.96 Td
(0)Tj
/T1_2 7.97 Tf
-0.31 -7.19 Td
(J)Tj
/T1_0 10.91 Tf
9.48 3.23 Td
(=)Tj
/T1_8 10.91 Tf
12.09 0 Td
(H)Tj
/T1_9 7.97 Tf
7.73 -1.64 Td
(1)Tj
/T1_0 10.91 Tf
4.73 1.64 Td
(\()Tj
/T1_1 10.91 Tf
(SID)Tj
/T1_5 7.97 Tf
21.42 3.96 Td
(0)Tj
/T1_2 7.97 Tf
T*
(J)Tj
/T1_3 10.91 Tf
5.87 3.23 Td
(jj)Tj
/T1_1 10.91 Tf
6.06 0 Td
(UID)Tj
/T1_5 7.97 Tf
17.17 3.96 Td
(0)Tj
/T1_2 7.97 Tf
T*
(J)Tj
/T1_3 10.91 Tf
5.87 3.23 Td
(jj)Tj
/T1_4 10.91 Tf
6.06 0 Td
(K)Tj
/T1_5 7.97 Tf
10.04 3.96 Td
(0)Tj
/T1_2 7.97 Tf
-0.78 -7.19 Td
(J)Tj
/T1_3 10.91 Tf
5.88 3.23 Td
(jj)Tj
/T1_4 10.91 Tf
6.05 0 Td
(K)Tj
/T1_5 7.97 Tf
10.05 3.96 Td
(0)Tj
/T1_3 10.91 Tf
2.79 -3.96 Td
(jj)Tj
/T1_4 10.91 Tf
6.06 0 Td
(\277)Tj
/T1_5 7.97 Tf
6 3.96 Td
(0)Tj
/T1_2 7.97 Tf
-1.23 -7.19 Td
(J)Tj
/T1_3 10.91 Tf
5.87 3.23 Td
(jj)Tj
/T1_4 10.91 Tf
6.06 0 Td
(z)Tj
/T1_5 7.97 Tf
5.55 3.96 Td
(0)Tj
/T1_2 7.97 Tf
-0.48 -7.19 Td
(J)Tj
/T1_0 10.91 Tf
5.87 3.23 Td
[(\).)-539(The)]TJ
-435.93 -21.92 Td
[(v)55(alidit)28(y)-335(of)-349(^)]TJ
/T1_1 10.91 Tf
51.57 0 Td
(c)Tj
/T1_5 7.97 Tf
5.72 3.96 Td
(0)Tj
/T1_2 7.97 Tf
0 -7.28 TD
[(J)23(;k)]TJ
/T1_0 10.91 Tf
15.57 3.32 Td
[(and)-415(^)]TJ
/T1_4 10.91 Tf
21.24 0 Td
(\271)Tj
/T1_5 7.97 Tf
6.57 3.96 Td
(0)Tj
/T1_2 7.97 Tf
T*
[(J)23(;k)]TJ
/T1_0 10.91 Tf
15.57 3.32 Td
[(are)-336(c)27(hec)27(k)28(ed)-335(b)27(y)]TJ
/T1_1 10.91 Tf
73.44 0 Td
(U)Tj
/T1_2 7.97 Tf
5.73 -1.77 Td
[(J)24(;k)]TJ
/T1_0 10.91 Tf
15.57 1.77 Td
[(in)-336(Phase)-336(3)-336(Round)-337(2)-336(and)-336(the)-337(v)55(alidit)28(y)-336(of)-349(^)]TJ
/T1_1 10.91 Tf
189.7 0 Td
(c)Tj
/T1_5 7.97 Tf
5.72 3.96 Td
(00)Tj
/T1_2 7.97 Tf
0 -7.19 TD
(J)Tj
/T1_0 10.91 Tf
9.54 3.23 Td
[(is)-336(c)27(hec)28(k)-336(b)27(y)]TJ
/T1_1 10.91 Tf
-415.94 -21.91 Td
(U)Tj
/T1_2 7.97 Tf
5.73 -1.69 Td
[(J)24(;j)]TJ
/T1_0 10.91 Tf
14.88 1.69 Td
[(in)-340(Phase)-341(3)-341(Round)-341(2.)-467(If)-341(either)-341(one)-341(of)-354(^)]TJ
/T1_1 10.91 Tf
177.32 0 Td
(c)Tj
/T1_5 7.97 Tf
5.72 3.95 Td
(0)Tj
/T1_2 7.97 Tf
0 -7.27 TD
[(J)23(;k)]TJ
/T1_0 10.91 Tf
15.62 3.32 Td
[(or)-420(^)]TJ
/T1_4 10.91 Tf
13.45 0 Td
(\271)Tj
/T1_5 7.97 Tf
6.57 3.95 Td
(0)Tj
/T1_2 7.97 Tf
T*
[(J)24(;k)]TJ
/T1_0 10.91 Tf
15.62 3.32 Td
[(is)-340(not)-341(correct,)-343(then)]TJ
/T1_1 10.91 Tf
94.99 0 Td
(U)Tj
/T1_2 7.97 Tf
5.73 -1.78 Td
[(J)24(;k)]TJ
/T1_0 10.91 Tf
15.62 1.78 Td
[(rejects)-340(in)27(v)55(alid)]TJ
/T1_1 10.91 Tf
69.63 0 Td
(S)Tj
/T1_2 7.97 Tf
5.72 -1.69 Td
(J)Tj
/T1_0 10.91 Tf
5.87 1.69 Td
[(.)-467(If)]TJ
-452.33 -21.92 Td
(^)Tj
/T1_1 10.91 Tf
-0.14 0 Td
(c)Tj
/T1_5 7.97 Tf
5.73 3.96 Td
(00)Tj
/T1_2 7.97 Tf
0 -7.19 TD
(J)Tj
/T1_0 10.91 Tf
9.05 3.23 Td
[(is)-291(not)-291(correct,)-300(then)]TJ
/T1_1 10.91 Tf
92.9 0 Td
(U)Tj
/T1_2 7.97 Tf
5.73 -1.69 Td
[(J)24(;j)]TJ
/T1_0 10.91 Tf
14.34 1.69 Td
[(rejects)-291(in)27(v)55(alid)]TJ
/T1_1 10.91 Tf
68.55 0 Td
(S)Tj
/T1_2 7.97 Tf
5.73 -1.69 Td
(J)Tj
/T1_0 10.91 Tf
5.87 1.69 Td
[(.)-430(As)]TJ
/T1_3 10.91 Tf
23.38 0 Td
(A)Tj
/T1_0 10.91 Tf
11.89 0 Td
[(do)-27(es)-292(not)-291(kno)26(w)-290(the)-292(authen)27(tication)-290(k)27(ey)]TJ
/T1_4 10.91 Tf
180.61 0 Td
(ak)Tj
/T1_2 7.97 Tf
11.44 -1.78 Td
[(J)24(;k)]TJ
/T1_0 10.91 Tf
15.08 1.78 Td
(and)Tj
-450.3 -21.92 Td
[(the)-328(message)-329(authen)27(tication)-327(co)-28(de)-329(sc)27(heme)]TJ
/T1_8 10.91 Tf
195.32 0 Td
[(MA)27(CS)]TJ
/T1_0 10.91 Tf
33.12 0 Td
[(is)-328(assumed)-328(to)-329(b)-28(e)-328(secure,)-330(therefore)]TJ
/T1_3 10.91 Tf
164.22 0 Td
(A)Tj
/T1_0 10.91 Tf
12.3 0 Td
[(is)-328(not)-328(able)-329(to)]TJ
-404.96 -21.91 Td
[(compute)-361(a)-362(v)54(alid)-440(^)]TJ
/T1_4 10.91 Tf
80.61 0 Td
(\271)Tj
/T1_5 7.97 Tf
6.57 3.95 Td
(0)Tj
/T1_2 7.97 Tf
0 -7.27 TD
[(J)23(;k)]TJ
/T1_0 10.91 Tf
11.9 3.32 Td
[(.)-530(F)82(urthermore,)]TJ
/T1_3 10.91 Tf
75.49 0 Td
(A)Tj
/T1_0 10.91 Tf
12.65 0 Td
[(do)-28(es)-362(not)-361(kno)26(w)-361(passw)27(ord)]TJ
/T1_8 10.91 Tf
120.82 0 Td
[(p)27(w)]TJ
/T1_2 7.97 Tf
12.94 -2.62 Td
[(J)24(;k)]TJ
/T1_0 10.91 Tf
15.85 2.62 Td
(of)Tj
/T1_1 10.91 Tf
12.73 0 Td
(U)Tj
/T1_2 7.97 Tf
5.73 -1.78 Td
[(J)24(;k)]TJ
/T1_0 10.91 Tf
11.9 1.78 Td
[(,)-368(hence)]TJ
/T1_3 10.91 Tf
37.66 0 Td
(A)Tj
/T1_0 10.91 Tf
12.65 0 Td
[(is)-362(not)-362(able)]TJ
-417.5 -21.92 Td
[(to)-331(obtain)]TJ
/T1_4 10.91 Tf
47.22 0 Td
(z)Tj
/T1_5 7.97 Tf
5.55 3.96 Td
(0)Tj
/T1_2 7.97 Tf
-0.48 -7.28 Td
[(J)24(;k)]TJ
/T1_0 10.91 Tf
15.52 3.32 Td
[(from)-331(\()]TJ
/T1_4 10.91 Tf
30 0 Td
(z)Tj
/T1_5 7.97 Tf
5.55 3.96 Td
(\244)Tj
/T1_2 7.97 Tf
-0.48 -7.28 Td
[(J)24(;k)]TJ
/T1_0 10.91 Tf
11.9 3.32 Td
(\))Tj
/T1_5 7.97 Tf
4.24 3.96 Td
(0)Tj
/T1_0 10.91 Tf
6.41 -3.96 Td
[(to)-331(compute)-332(v)55(alid)]TJ
/T1_4 10.91 Tf
83.86 0 Td
(t)Tj
/T1_5 7.97 Tf
3.94 3.96 Td
(0)Tj
/T1_2 7.97 Tf
0 -7.28 TD
[(J)24(;k)]TJ
/T1_0 10.91 Tf
14.93 3.32 Td
(=)Tj
/T1_4 10.91 Tf
11.51 0 Td
(g)Tj
/T1_2 7.97 Tf
5.59 5.11 Td
(r)Tj
/T1_6 5.98 Tf
4.06 2.81 Td
(0)Tj
/T1_7 5.98 Tf
-0.24 -5.52 Td
(J)Tj
/T1_2 7.97 Tf
5.14 2.71 Td
(r)Tj
/T1_6 5.98 Tf
4.05 2.81 Td
(0)Tj
/T1_7 5.98 Tf
-0.23 -5.58 Td
[(J)35(;k)]TJ
/T1_0 10.91 Tf
11.2 -2.34 Td
[(.)-443(Therefore,)]TJ
/T1_3 10.91 Tf
60.32 0 Td
(A)Tj
/T1_0 10.91 Tf
12.33 0 Td
[(is)-331(not)-331(able)-332(to)-331(compute)-331(the)]TJ
-341.89 -21.92 Td
[(v)55(alid)-346(ciphertext)-360(^)]TJ
/T1_1 10.91 Tf
78.5 0 Td
(c)Tj
/T1_5 7.97 Tf
5.72 3.96 Td
(0)Tj
/T1_2 7.97 Tf
T*
[(J)23(;k)]TJ
/T1_0 10.91 Tf
15.7 3.32 Td
[(as)-347(the)-347(symmetric)-348(k)27(ey)-346(encryption)-348(sc)27(heme)]TJ
/T1_8 10.91 Tf
197.47 0 Td
(SKE)Tj
/T1_0 10.91 Tf
23.94 0 Td
[(is)-347(secure.)-487(As)]TJ
/T1_3 10.91 Tf
64.9 0 Td
(A)Tj
/T1_0 10.91 Tf
12.5 0 Td
[(do)-28(es)-347(not)-347(kno)26(w)]TJ
-398.73 -21.91 Td
[(the)-370(existing)-371(subgroup)-370(k)26(ey)]TJ
/T1_4 10.91 Tf
127.81 0 Td
(K)Tj
/T1_2 7.97 Tf
9.26 -1.69 Td
(J)Tj
/T1_0 10.91 Tf
9.91 1.69 Td
[(and)-370(the)-371(symmetric)-371(k)27(ey)-369(encryption)-371(sc)27(heme)]TJ
/T1_8 10.91 Tf
206.81 0 Td
(SKE)Tj
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/T1_1 10.91 Tf
4.73 2.7 Td
(jj)Tj
/T1_0 10.91 Tf
6.64 0 Td
(\271)Tj
/T1_4 10.91 Tf
-0.58 0 Td
(\277)Tj
/T1_5 7.97 Tf
6 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-1.23 -7.19 Td
(J)Tj
/T1_1 10.91 Tf
5.87 3.23 Td
(jj)Tj
/T1_2 10.91 Tf
6.06 0 Td
(SID)Tj
/T1_5 7.97 Tf
17.17 3.96 Td
(0)Tj
/T1_6 7.97 Tf
T*
(c)Tj
/T1_0 10.91 Tf
4.74 2.7 Td
(\),)Tj
/T1_2 10.91 Tf
12.34 0 Td
(c)Tj
/T1_5 7.97 Tf
5.72 3.96 Td
(0)Tj
/T1_3 7.97 Tf
0 -7.02 TD
(i)Tj
/T1_0 10.91 Tf
8.32 3.06 Td
(=)Tj
/T1_1 10.91 Tf
13.43 0 Td
(E)Tj
/T1_3 7.97 Tf
5.75 -1.78 Td
(ek)Tj
/T1_7 5.98 Tf
8.34 -1.21 Td
(i)Tj
/T1_0 10.91 Tf
3.66 2.99 Td
(\()Tj
/T1_4 10.91 Tf
(\277)Tj
/T1_5 7.97 Tf
10.24 3.96 Td
(0)Tj
/T1_6 7.97 Tf
-1.23 -6.66 Td
(C)Tj
/T1_1 10.91 Tf
4.73 2.7 Td
(jj)Tj
/T1_0 10.91 Tf
6.63 0 Td
(\271)Tj
/T1_4 10.91 Tf
-0.57 0 Td
(\277)Tj
/T1_5 7.97 Tf
6 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-1.24 -7.02 Td
(i)Tj
/T1_1 10.91 Tf
4.03 3.06 Td
(jj)Tj
/T1_2 10.91 Tf
6.06 0 Td
(C)Tj
/T1_1 10.91 Tf
(jj)Tj
/T1_2 10.91 Tf
11.79 0 Td
(S)Tj
/T1_3 7.97 Tf
5.72 -1.64 Td
(i)Tj
/T1_1 10.91 Tf
3.38 1.64 Td
(jj)Tj
/T1_2 10.91 Tf
6.06 0 Td
(SID)Tj
/T1_5 7.97 Tf
17.18 3.96 Td
(0)Tj
/T1_6 7.97 Tf
0 -6.66 TD
(c)Tj
/T1_0 10.91 Tf
4.73 2.7 Td
(\))Tj
-463.63 -21.92 Td
(and)Tj
/T1_4 10.91 Tf
20.8 0 Td
(v)Tj
/T1_5 7.97 Tf
5.67 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.39 -7.01 Td
(i)Tj
/T1_0 10.91 Tf
6.41 3.05 Td
(=)Tj
/T1_8 10.91 Tf
11.51 0 Td
(H)Tj
/T1_9 7.97 Tf
7.73 -1.63 Td
(1)Tj
/T1_0 10.91 Tf
4.73 1.63 Td
(\()Tj
/T1_8 10.91 Tf
[(p)27(w)]TJ
/T1_3 7.97 Tf
17.18 -2.62 Td
(i)Tj
/T1_1 10.91 Tf
3.38 2.62 Td
(jj)Tj
/T1_4 10.91 Tf
6.06 0 Td
(\277)Tj
/T1_5 7.97 Tf
6 3.96 Td
(0)Tj
/T1_6 7.97 Tf
-1.24 -6.65 Td
(C)Tj
/T1_1 10.91 Tf
4.74 2.69 Td
(jj)Tj
/T1_0 10.91 Tf
6.63 0 Td
(\271)Tj
/T1_4 10.91 Tf
-0.58 0 Td
(\277)Tj
/T1_5 7.97 Tf
6.01 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-1.24 -7.01 Td
(i)Tj
/T1_1 10.91 Tf
4.03 3.05 Td
(jj)Tj
/T1_2 10.91 Tf
6.06 0 Td
(SID)Tj
/T1_5 7.97 Tf
17.18 3.96 Td
(0)Tj
/T1_6 7.97 Tf
0 -6.65 TD
(c)Tj
/T1_0 10.91 Tf
4.73 2.69 Td
[(\))-295(for)-296(1)]TJ
/T1_1 10.91 Tf
32.23 0 Td
(\267)Tj
/T1_4 10.91 Tf
11.51 0 Td
(i)Tj
/T1_1 10.91 Tf
6.79 0 Td
(6)Tj
/T1_0 10.91 Tf
(=)Tj
/T1_4 10.91 Tf
11.51 0 Td
(J)Tj
/T1_1 10.91 Tf
10.13 0 Td
(\267)Tj
/T1_4 10.91 Tf
11.51 0 Td
(n)Tj
/T1_3 7.97 Tf
6.54 -1.63 Td
(c)Tj
/T1_0 10.91 Tf
4.17 1.63 Td
[(.)-431(The)-296(v)55(alidit)27(y)-294(of)]TJ
/T1_2 10.91 Tf
80.43 0 Td
(c)Tj
/T1_5 7.97 Tf
5.72 3.96 Td
(0)Tj
/T1_3 7.97 Tf
0 -7.19 TD
(J)Tj
/T1_0 10.91 Tf
9.1 3.23 Td
(and)Tj
/T1_4 10.91 Tf
20.8 0 Td
(v)Tj
/T1_5 7.97 Tf
5.67 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.39 -7.19 Td
(J)Tj
/T1_0 10.91 Tf
9.1 3.23 Td
(\()Tj
/T1_2 10.91 Tf
(c)Tj
/T1_5 7.97 Tf
9.96 3.96 Td
(0)Tj
/T1_3 7.97 Tf
0 -7.01 TD
(i)Tj
/T1_0 10.91 Tf
6.61 3.05 Td
(and)Tj
/T1_4 10.91 Tf
20.8 0 Td
(v)Tj
/T1_5 7.97 Tf
5.67 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.39 -7.01 Td
(i)Tj
/T1_0 10.91 Tf
3.38 3.05 Td
[(\))-296(are)-295(c)26(hec)28(k)28(ed)]TJ
-406.25 -21.91 Td
[(b)27(y)]TJ
/T1_2 10.91 Tf
15.6 0 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.69 Td
(J)Tj
/T1_0 10.91 Tf
9.96 1.69 Td
(\()Tj
/T1_2 10.91 Tf
(S)Tj
/T1_3 7.97 Tf
9.97 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
3.38 1.64 Td
[(\))-374(in)-375(Phase)-375(2)-376(Round)-375(2.)-569(If)-375(either)]TJ
/T1_2 10.91 Tf
156.42 0 Td
(c)Tj
/T1_5 7.97 Tf
5.72 3.95 Td
(0)Tj
/T1_3 7.97 Tf
0 -7.19 TD
(J)Tj
/T1_0 10.91 Tf
9.96 3.24 Td
(or)Tj
/T1_4 10.91 Tf
13.82 0 Td
(v)Tj
/T1_5 7.97 Tf
5.68 3.95 Td
(0)Tj
/T1_3 7.97 Tf
-0.39 -7.19 Td
(J)Tj
/T1_0 10.91 Tf
9.96 3.24 Td
(\()Tj
/T1_2 10.91 Tf
(c)Tj
/T1_5 7.97 Tf
9.97 3.95 Td
(0)Tj
/T1_3 7.97 Tf
-0.01 -7.01 Td
(i)Tj
/T1_0 10.91 Tf
7.48 3.06 Td
(or)Tj
/T1_4 10.91 Tf
13.81 0 Td
(v)Tj
/T1_5 7.97 Tf
5.68 3.95 Td
(0)Tj
/T1_3 7.97 Tf
-0.39 -7.01 Td
(i)Tj
/T1_0 10.91 Tf
3.38 3.06 Td
[(\))-374(is)-375(not)-376(v)55(alid,)-385(then)]TJ
/T1_2 10.91 Tf
94.85 0 Td
(S)Tj
/T1_3 7.97 Tf
5.72 -1.69 Td
(J)Tj
/T1_0 10.91 Tf
9.97 1.69 Td
(\()Tj
/T1_2 10.91 Tf
(S)Tj
/T1_3 7.97 Tf
9.96 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
3.38 1.64 Td
[(\))-375(rejects)-375(the)]TJ
-409.61 -21.92 Td
[(in)27(v)56(alid)]TJ
/T1_2 10.91 Tf
35.56 0 Td
(C)Tj
/T1_0 10.91 Tf
[(.)-559(As)]TJ
/T1_1 10.91 Tf
31.4 0 Td
(A)Tj
/T1_0 10.91 Tf
12.76 0 Td
[(do)-27(es)-372(not)-372(kno)27(w)-371(the)-372(encryption)-371(k)26(ey)]TJ
/T1_4 10.91 Tf
167.71 0 Td
(ek)Tj
/T1_3 7.97 Tf
10.76 -1.69 Td
(J)Tj
/T1_0 10.91 Tf
9.93 1.69 Td
(and)Tj
/T1_4 10.91 Tf
21.62 0 Td
(ek)Tj
/T1_3 7.97 Tf
10.76 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
7.43 1.64 Td
(of)Tj
/T1_2 10.91 Tf
12.84 0 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.69 Td
(J)Tj
/T1_0 10.91 Tf
9.92 1.69 Td
(and)Tj
/T1_2 10.91 Tf
21.63 0 Td
(S)Tj
/T1_3 7.97 Tf
5.72 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
7.44 1.64 Td
[(resp)-27(ectiv)27(ely)-371(and)-372(the)]TJ
-371.21 -21.92 Td
[(symmetric-k)27(ey)-321(encryption)-322(sc)26(heme)]TJ
/T1_8 10.91 Tf
164.02 0 Td
(SKE)Tj
/T1_0 10.91 Tf
23.66 0 Td
[(is)-322(assumed)-322(to)-323(b)-28(e)-322(secure,)-324(therefore)]TJ
/T1_1 10.91 Tf
163.84 0 Td
(A)Tj
/T1_0 10.91 Tf
12.22 0 Td
[(is)-322(not)-322(able)-323(to)-322(pro)-28(duce)]TJ
-363.74 -21.91 Td
[(v)55(alid)]TJ
/T1_2 10.91 Tf
25.42 0 Td
(c)Tj
/T1_5 7.97 Tf
5.72 3.95 Td
(0)Tj
/T1_3 7.97 Tf
T*
(J)Tj
/T1_0 10.91 Tf
8.57 3.24 Td
(and)Tj
/T1_2 10.91 Tf
20.27 0 Td
(c)Tj
/T1_5 7.97 Tf
5.72 3.95 Td
(0)Tj
/T1_3 7.97 Tf
0 -7.01 TD
(i)Tj
/T1_0 10.91 Tf
3.38 3.06 Td
(.)Tj
/T1_1 10.91 Tf
7.57 0 Td
(A)Tj
/T1_0 10.91 Tf
11.4 0 Td
[(also)-247(do)-28(es)-247(not)-247(kno)27(w)-247(passw)27(ord)]TJ
/T1_8 10.91 Tf
136.75 0 Td
[(p)27(w)]TJ
/T1_3 7.97 Tf
12.94 -2.62 Td
(J)Tj
/T1_0 10.91 Tf
8.57 2.62 Td
(and)Tj
/T1_8 10.91 Tf
20.26 0 Td
[(p)27(w)]TJ
/T1_3 7.97 Tf
12.94 -2.62 Td
(i)Tj
/T1_0 10.91 Tf
6.08 2.62 Td
(of)Tj
/T1_2 10.91 Tf
11.48 0 Td
(S)Tj
/T1_3 7.97 Tf
5.72 -1.69 Td
(J)Tj
/T1_0 10.91 Tf
8.57 1.69 Td
(and)Tj
/T1_2 10.91 Tf
20.27 0 Td
(S)Tj
/T1_3 7.97 Tf
5.72 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
6.08 1.64 Td
[(resp)-27(ectiv)26(ely)84(,)-264(therefore)]TJ
/T1_1 10.91 Tf
105.71 0 Td
(A)Tj
/T1_0 10.91 Tf
11.4 0 Td
(is)Tj
-460.54 -21.92 Td
[(not)-259(able)-259(to)-259(pro)-28(duce)-259(v)54(alid)]TJ
/T1_4 10.91 Tf
119.59 0 Td
(v)Tj
/T1_5 7.97 Tf
5.68 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.39 -7.19 Td
(J)Tj
/T1_0 10.91 Tf
8.69 3.23 Td
(and)Tj
/T1_4 10.91 Tf
20.4 0 Td
(v)Tj
/T1_5 7.97 Tf
5.68 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.39 -7.02 Td
(i)Tj
/T1_0 10.91 Tf
3.38 3.06 Td
[(.)-419(Hence)]TJ
/T1_1 10.91 Tf
39.21 0 Td
(A)Tj
/T1_0 10.91 Tf
11.54 0 Td
[(is)-259(not)-259(able)-259(to)-259(imp)-28(ersonate)]TJ
/T1_2 10.91 Tf
124.25 0 Td
(C)Tj
/T1_0 10.91 Tf
8.56 0 Td
[(in)-258(Phase)-260(2)-259(Round)-259(1.)-420(Next)]TJ
-346.2 -21.92 Td
(consider)Tj
/T1_1 10.91 Tf
42.69 0 Td
(A)Tj
/T1_0 10.91 Tf
12.52 0 Td
[(imp)-27(ersonating)-350(main)-350(con)26(troller)]TJ
/T1_2 10.91 Tf
147.93 0 Td
(C)Tj
/T1_0 10.91 Tf
9.54 0 Td
[(in)-350(Phase)-350(2)-350(Round)-350(3.)-494(Then)]TJ
/T1_1 10.91 Tf
132.09 0 Td
(A)Tj
/T1_0 10.91 Tf
12.52 0 Td
[(needs)-350(to)-350(compute)-350(v)55(alid)]TJ
-357.15 -21.91 Td
(^)Tj
/T1_2 10.91 Tf
-0.14 0 Td
(c)Tj
/T1_5 7.97 Tf
5.73 3.95 Td
(0)Tj
/T1_3 7.97 Tf
0 -7.19 TD
(J)Tj
/T1_0 10.91 Tf
10.83 3.24 Td
(=)Tj
/T1_1 10.91 Tf
13.45 0 Td
(E)Tj
/T1_3 7.97 Tf
5.75 -2.31 Td
(t)Tj
/T1_10 5.98 Tf
3.06 2.74 Td
(0)Tj
/T1_7 5.98 Tf
0 -5.51 TD
(J)Tj
/T1_0 10.91 Tf
5.63 5.08 Td
(\()Tj
/T1_4 10.91 Tf
(K)Tj
/T1_5 7.97 Tf
14.29 3.95 Td
(0)Tj
/T1_1 10.91 Tf
2.79 -3.95 Td
(jj)Tj
/T1_2 10.91 Tf
6.06 0 Td
(C)Tj
/T1_1 10.91 Tf
(jj)Tj
/T1_4 10.91 Tf
11.78 0 Td
(y)Tj
/T1_5 7.97 Tf
5.74 3.95 Td
(0)Tj
/T1_3 7.97 Tf
-0.39 -7.19 Td
(J)Tj
/T1_1 10.91 Tf
5.87 3.24 Td
(jj)Tj
/T1_2 10.91 Tf
6.06 0 Td
(SID)Tj
/T1_5 7.97 Tf
17.18 3.95 Td
(0)Tj
/T1_6 7.97 Tf
0 -6.65 TD
(c)Tj
/T1_0 10.91 Tf
4.73 2.7 Td
[(\),)-545(^)]TJ
/T1_4 10.91 Tf
12.36 0 Td
(\271)Tj
/T1_5 7.97 Tf
6.57 3.95 Td
(0)Tj
/T1_3 7.97 Tf
0 -7.19 TD
(J)Tj
/T1_0 10.91 Tf
10.83 3.24 Td
(=)Tj
/T1_8 10.91 Tf
13.45 0 Td
[(MA)28(C)]TJ
/T1_3 7.97 Tf
23.48 -1.78 Td
(ak)Tj
/T1_7 5.98 Tf
8.9 -1.34 Td
(J)Tj
/T1_0 10.91 Tf
5.63 3.12 Td
(\()Tj
/T1_4 10.91 Tf
4.25 0 Td
(\277)Tj
/T1_5 7.97 Tf
6 3.95 Td
(0)Tj
/T1_6 7.97 Tf
-1.24 -6.65 Td
(C)Tj
/T1_1 10.91 Tf
4.73 2.7 Td
(jj)Tj
/T1_0 10.91 Tf
6.64 0 Td
(\271)Tj
/T1_4 10.91 Tf
-0.58 0 Td
(\277)Tj
/T1_5 7.97 Tf
6.01 3.95 Td
(0)Tj
/T1_3 7.97 Tf
-1.24 -7.19 Td
(J)Tj
/T1_1 10.91 Tf
5.87 3.24 Td
(jj)Tj
/T1_4 10.91 Tf
6.06 0 Td
(y)Tj
/T1_5 7.97 Tf
5.74 3.95 Td
(0)Tj
/T1_6 7.97 Tf
-0.39 -6.65 Td
(C)Tj
/T1_1 10.91 Tf
4.73 2.7 Td
(jj)Tj
/T1_4 10.91 Tf
6.06 0 Td
(\265)Tj
/T1_5 7.97 Tf
5.42 3.95 Td
(0)Tj
/T1_6 7.97 Tf
-0.3 -6.65 Td
(C)Tj
/T1_1 10.91 Tf
4.73 2.7 Td
(jj)Tj
/T1_2 10.91 Tf
6.06 0 Td
(SID)Tj
/T1_5 7.97 Tf
17.17 3.95 Td
(0)Tj
/T1_6 7.97 Tf
0 -6.65 TD
(c)Tj
/T1_1 10.91 Tf
4.74 2.7 Td
(jj)Tj
/T1_2 10.91 Tf
6.05 0 Td
(C)Tj
/T1_1 10.91 Tf
(jj)Tj
/T1_2 10.91 Tf
11.79 0 Td
(S)Tj
/T1_3 7.97 Tf
5.72 -1.69 Td
(J)Tj
/T1_1 10.91 Tf
5.88 1.69 Td
(jj)Tj
/T1_0 10.91 Tf
6.05 0 Td
[(11\),)-479(^)]TJ
/T1_2 10.91 Tf
23.27 0 Td
(c)Tj
/T1_5 7.97 Tf
5.72 3.95 Td
(0)Tj
/T1_3 7.97 Tf
0 -7.01 TD
(i)Tj
/T1_0 10.91 Tf
8.35 3.06 Td
(=)Tj
/T1_1 10.91 Tf
13.44 0 Td
(E)Tj
/T1_3 7.97 Tf
5.76 -2.31 Td
(t)Tj
/T1_10 5.98 Tf
3.05 2.74 Td
(0)Tj
/T1_7 5.98 Tf
0 -5.39 TD
(i)Tj
/T1_0 10.91 Tf
3.66 4.96 Td
(\()Tj
/T1_4 10.91 Tf
4.25 0 Td
(K)Tj
/T1_5 7.97 Tf
10.04 3.95 Td
(0)Tj
/T1_1 10.91 Tf
2.79 -3.95 Td
(jj)Tj
/T1_2 10.91 Tf
6.06 0 Td
(C)Tj
/T1_1 10.91 Tf
(jj)Tj
/T1_4 10.91 Tf
11.79 0 Td
(y)Tj
/T1_3 7.97 Tf
5.34 -1.64 Td
(i)Tj
/T1_1 10.91 Tf
3.38 1.64 Td
(jj)Tj
/T1_2 10.91 Tf
6.06 0 Td
(SID)Tj
/T1_5 7.97 Tf
17.18 3.95 Td
(0)Tj
/T1_6 7.97 Tf
0 -6.65 TD
(c)Tj
/T1_0 10.91 Tf
4.73 2.7 Td
(\),)Tj
-459.74 -21.92 Td
(^)Tj
/T1_4 10.91 Tf
-0.86 0 Td
(\271)Tj
/T1_5 7.97 Tf
6.57 3.96 Td
(0)Tj
/T1_3 7.97 Tf
0 -7.01 TD
(i)Tj
/T1_0 10.91 Tf
6.79 3.05 Td
(=)Tj
/T1_8 10.91 Tf
11.89 0 Td
[(MA)27(C)]TJ
/T1_3 7.97 Tf
23.48 -1.78 Td
(ak)Tj
/T1_7 5.98 Tf
8.91 -1.21 Td
(i)Tj
/T1_0 10.91 Tf
3.65 2.99 Td
(\()Tj
/T1_4 10.91 Tf
4.25 0 Td
(\277)Tj
/T1_5 7.97 Tf
6 3.96 Td
(0)Tj
/T1_6 7.97 Tf
-1.24 -6.66 Td
(C)Tj
/T1_1 10.91 Tf
4.73 2.7 Td
(jj)Tj
/T1_0 10.91 Tf
6.64 0 Td
(\271)Tj
/T1_4 10.91 Tf
-0.58 0 Td
(\277)Tj
/T1_5 7.97 Tf
6.01 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-1.24 -7.01 Td
(i)Tj
/T1_1 10.91 Tf
4.03 3.05 Td
(jj)Tj
/T1_4 10.91 Tf
6.06 0 Td
(y)Tj
/T1_5 7.97 Tf
5.74 3.96 Td
(0)Tj
/T1_6 7.97 Tf
-0.39 -6.66 Td
(C)Tj
/T1_1 10.91 Tf
4.73 2.7 Td
(jj)Tj
/T1_4 10.91 Tf
6.06 0 Td
(\265)Tj
/T1_5 7.97 Tf
5.42 3.96 Td
(0)Tj
/T1_6 7.97 Tf
-0.3 -6.66 Td
(C)Tj
/T1_1 10.91 Tf
4.73 2.7 Td
(jj)Tj
/T1_2 10.91 Tf
6.06 0 Td
(SID)Tj
/T1_5 7.97 Tf
17.17 3.96 Td
(0)Tj
/T1_6 7.97 Tf
0 -6.66 TD
(c)Tj
/T1_1 10.91 Tf
4.73 2.7 Td
(jj)Tj
/T1_2 10.91 Tf
6.06 0 Td
(C)Tj
/T1_1 10.91 Tf
(jj)Tj
/T1_2 10.91 Tf
11.79 0 Td
(S)Tj
/T1_3 7.97 Tf
5.72 -1.64 Td
(i)Tj
/T1_1 10.91 Tf
3.38 1.64 Td
(jj)Tj
/T1_0 10.91 Tf
6.06 0 Td
[(11\))-354(for)-354(1)]TJ
/T1_1 10.91 Tf
44.79 0 Td
(\267)Tj
/T1_4 10.91 Tf
11.9 0 Td
(i)Tj
/T1_1 10.91 Tf
7.16 0 Td
(6)Tj
/T1_0 10.91 Tf
(=)Tj
/T1_4 10.91 Tf
11.89 0 Td
(J)Tj
/T1_1 10.91 Tf
10.51 0 Td
(\267)Tj
/T1_4 10.91 Tf
11.89 0 Td
(n)Tj
/T1_3 7.97 Tf
6.55 -1.64 Td
(c)Tj
/T1_0 10.91 Tf
8.02 1.64 Td
(and)Tj
/T1_4 10.91 Tf
21.44 0 Td
(\265)Tj
/T1_5 7.97 Tf
5.42 3.96 Td
(0)Tj
/T1_6 7.97 Tf
-0.3 -6.66 Td
(C)Tj
/T1_0 10.91 Tf
8.14 2.7 Td
(=)Tj
/T1_8 10.91 Tf
11.89 0 Td
(H)Tj
/T1_9 7.97 Tf
7.73 -1.64 Td
(1)Tj
/T1_0 10.91 Tf
4.73 1.64 Td
(\()Tj
/T1_2 10.91 Tf
(SID)Tj
/T1_5 7.97 Tf
21.41 3.96 Td
(0)Tj
/T1_6 7.97 Tf
T*
(c)Tj
/T1_1 10.91 Tf
4.74 2.7 Td
(jj)Tj
/T1_8 10.91 Tf
6.05 0 Td
(UID)Tj
/T1_6 7.97 Tf
18.41 -1.64 Td
(C)Tj
/T1_1 10.91 Tf
4.73 1.64 Td
(jj)Tj
/T1_4 10.91 Tf
6.06 0 Td
(K)Tj
/T1_5 7.97 Tf
10.04 3.96 Td
(0)Tj
/T1_1 10.91 Tf
2.8 -3.96 Td
(jj)Tj
/T1_4 10.91 Tf
6.05 0 Td
(\277)Tj
/T1_5 7.97 Tf
6.01 3.96 Td
(0)Tj
/T1_6 7.97 Tf
-1.24 -6.66 Td
(C)Tj
/T1_1 10.91 Tf
4.73 2.7 Td
(jj)Tj
/T1_4 10.91 Tf
6.06 0 Td
(y)Tj
/T1_5 7.97 Tf
5.74 3.96 Td
(0)Tj
/T1_6 7.97 Tf
-0.39 -6.66 Td
(C)Tj
/T1_0 10.91 Tf
4.73 2.7 Td
(\).)Tj
-460.6 -21.92 Td
[(The)-344(v)55(alidit)28(y)-344(of)-356(^)]TJ
/T1_2 10.91 Tf
74.28 0 Td
(c)Tj
/T1_5 7.97 Tf
5.72 3.96 Td
(0)Tj
/T1_3 7.97 Tf
0 -7.19 TD
(J)Tj
/T1_0 10.91 Tf
9.63 3.23 Td
[(and)-422(^)]TJ
/T1_4 10.91 Tf
21.32 0 Td
(\271)Tj
/T1_5 7.97 Tf
6.57 3.96 Td
(0)Tj
/T1_3 7.97 Tf
T*
(J)Tj
/T1_0 10.91 Tf
9.63 3.23 Td
[(\()-12(^)]TJ
/T1_2 10.91 Tf
4.24 0 Td
(c)Tj
/T1_5 7.97 Tf
5.72 3.96 Td
(0)Tj
/T1_3 7.97 Tf
0 -7.01 TD
(i)Tj
/T1_0 10.91 Tf
7.14 3.05 Td
[(and)-423(^)]TJ
/T1_4 10.91 Tf
21.32 0 Td
(\271)Tj
/T1_5 7.97 Tf
6.57 3.96 Td
(0)Tj
/T1_3 7.97 Tf
T*
(i)Tj
/T1_0 10.91 Tf
3.39 3.05 Td
[(\))-343(are)-344(c)26(hec)28(k)28(ed)-343(b)26(y)]TJ
/T1_2 10.91 Tf
81.69 0 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.68 Td
(J)Tj
/T1_0 10.91 Tf
9.62 1.68 Td
(\()Tj
/T1_2 10.91 Tf
(S)Tj
/T1_3 7.97 Tf
9.97 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
3.38 1.63 Td
[(\))-344(in)-344(Phase)-344(3)-344(Round)-344(1.)-477(If)-345(either)-344(one)-344(of)]TJ
-285.78 -21.91 Td
(^)Tj
/T1_2 10.91 Tf
-0.14 0 Td
(c)Tj
/T1_5 7.97 Tf
5.73 3.95 Td
(0)Tj
/T1_3 7.97 Tf
0 -7.18 TD
(J)Tj
/T1_0 10.91 Tf
9.21 3.23 Td
[(or)-384(^)]TJ
/T1_4 10.91 Tf
13.06 0 Td
(\271)Tj
/T1_5 7.97 Tf
6.57 3.95 Td
(0)Tj
/T1_3 7.97 Tf
T*
(J)Tj
/T1_0 10.91 Tf
9.21 3.23 Td
[(\()-12(^)]TJ
/T1_2 10.91 Tf
4.24 0 Td
(c)Tj
/T1_5 7.97 Tf
5.73 3.95 Td
(0)Tj
/T1_3 7.97 Tf
0 -7.01 TD
(i)Tj
/T1_0 10.91 Tf
6.72 3.06 Td
[(or)-384(^)]TJ
/T1_4 10.91 Tf
13.06 0 Td
(\271)Tj
/T1_5 7.97 Tf
6.57 3.95 Td
(0)Tj
/T1_3 7.97 Tf
T*
(i)Tj
/T1_0 10.91 Tf
3.38 3.06 Td
[(\))-306(is)-306(not)-306(correct,)-311(then)]TJ
/T1_2 10.91 Tf
101.09 0 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.69 Td
(J)Tj
/T1_0 10.91 Tf
9.21 1.69 Td
(\()Tj
/T1_2 10.91 Tf
(S)Tj
/T1_3 7.97 Tf
9.97 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
3.38 1.64 Td
[(\))-305(rejects)-306(in)26(v)56(alid)]TJ
/T1_2 10.91 Tf
76.45 0 Td
(C)Tj
/T1_0 10.91 Tf
5.72 0 Td
[(.)-435(As)]TJ
/T1_1 10.91 Tf
23.6 0 Td
(A)Tj
/T1_0 10.91 Tf
12.05 0 Td
[(do)-27(es)-306(not)-306(kno)26(w)-305(passw)27(ord)]TJ
/T1_8 10.91 Tf
118.38 0 Td
[(p)27(w)]TJ
/T1_3 7.97 Tf
12.94 -2.62 Td
(J)Tj
/T1_0 10.91 Tf
-462 -19.3 Td
(and)Tj
/T1_8 10.91 Tf
21.42 0 Td
[(p)27(w)]TJ
/T1_3 7.97 Tf
12.94 -2.62 Td
(i)Tj
/T1_0 10.91 Tf
7.23 2.62 Td
(of)Tj
/T1_2 10.91 Tf
12.64 0 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.69 Td
(J)Tj
/T1_0 10.91 Tf
9.72 1.69 Td
(and)Tj
/T1_2 10.91 Tf
21.42 0 Td
(S)Tj
/T1_3 7.97 Tf
5.73 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
7.23 1.64 Td
[(for)-353(1)]TJ
/T1_1 10.91 Tf
25.76 0 Td
(\267)Tj
/T1_4 10.91 Tf
11.87 0 Td
(i)Tj
/T1_1 10.91 Tf
7.15 0 Td
(6)Tj
/T1_0 10.91 Tf
(=)Tj
/T1_4 10.91 Tf
11.88 0 Td
(J)Tj
/T1_1 10.91 Tf
10.49 0 Td
(\267)Tj
/T1_4 10.91 Tf
11.87 0 Td
(n)Tj
/T1_3 7.97 Tf
6.55 -1.64 Td
(c)Tj
/T1_0 10.91 Tf
8.01 1.64 Td
[(resp)-28(ectiv)27(ely)83(,)-357(hence)]TJ
/T1_1 10.91 Tf
92.38 0 Td
(A)Tj
/T1_0 10.91 Tf
12.56 0 Td
[(is)-353(not)-353(able)-353(to)-354(obtain)]TJ
/T1_4 10.91 Tf
101.73 0 Td
(y)Tj
/T1_5 7.97 Tf
5.74 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.4 -7.19 Td
(J)Tj
/T1_0 10.91 Tf
9.73 3.23 Td
[(from)-353(\()]TJ
/T1_4 10.91 Tf
30.24 0 Td
(y)Tj
/T1_5 7.97 Tf
5.74 3.96 Td
(\244)Tj
/T1_3 7.97 Tf
-0.4 -7.19 Td
(J)Tj
/T1_0 10.91 Tf
5.88 3.23 Td
(\))Tj
/T1_5 7.97 Tf
4.24 3.96 Td
(0)Tj
/T1_0 10.91 Tf
-465.08 -25.88 Td
(and)Tj
/T1_4 10.91 Tf
21.08 0 Td
(y)Tj
/T1_3 7.97 Tf
5.34 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
6.89 1.63 Td
(from)Tj
/T1_4 10.91 Tf
25.65 0 Td
(y)Tj
/T1_5 7.97 Tf
5.74 3.96 Td
(\244)Tj
/T1_3 7.97 Tf
-0.39 -7.01 Td
(i)Tj
/T1_0 10.91 Tf
8.63 3.05 Td
[(to)-321(compute)-322(v)55(alid)]TJ
/T1_4 10.91 Tf
83.53 0 Td
(t)Tj
/T1_5 7.97 Tf
3.94 3.96 Td
(0)Tj
/T1_3 7.97 Tf
0 -7.19 TD
(J)Tj
/T1_0 10.91 Tf
8.9 3.23 Td
(=)Tj
/T1_4 10.91 Tf
11.51 0 Td
(g)Tj
/T1_3 7.97 Tf
5.59 3.96 Td
(r)Tj
/T1_10 5.98 Tf
4.06 2.81 Td
(0)Tj
/T1_6 5.98 Tf
-0.23 -5.08 Td
(C)Tj
/T1_11 7.97 Tf
3.67 2.27 Td
(H)Tj
/T1_12 5.98 Tf
5.97 -1.1 Td
(2)Tj
/T1_9 7.97 Tf
4.15 1.1 Td
(\()Tj
/T1_3 7.97 Tf
3.3 0 Td
(K)Tj
/T1_10 5.98 Tf
7.7 2.81 Td
(0)Tj
/T1_7 5.98 Tf
-0.56 -5.51 Td
(J)Tj
/T1_9 7.97 Tf
5.13 2.7 Td
(\))Tj
/T1_0 10.91 Tf
7.3 -3.96 Td
(and)Tj
/T1_4 10.91 Tf
21.08 0 Td
(t)Tj
/T1_5 7.97 Tf
3.94 3.96 Td
(0)Tj
/T1_3 7.97 Tf
0 -7.01 TD
(i)Tj
/T1_0 10.91 Tf
6.4 3.05 Td
(=)Tj
/T1_4 10.91 Tf
11.52 0 Td
(g)Tj
/T1_3 7.97 Tf
5.59 3.96 Td
(r)Tj
/T1_10 5.98 Tf
4.06 2.81 Td
(0)Tj
/T1_6 5.98 Tf
-0.24 -5.08 Td
(C)Tj
/T1_11 7.97 Tf
3.67 2.27 Td
(H)Tj
/T1_12 5.98 Tf
5.98 -1.1 Td
(2)Tj
/T1_9 7.97 Tf
4.15 1.1 Td
(\()Tj
/T1_3 7.97 Tf
(K)Tj
/T1_7 5.98 Tf
10.43 -1.21 Td
(i)Tj
/T1_9 7.97 Tf
3.16 1.21 Td
(\))Tj
/T1_0 10.91 Tf
7.3 -3.96 Td
[(resp)-27(ectiv)27(ely)83(.)-440(Therefore,)]TJ
/T1_1 10.91 Tf
115.12 0 Td
(A)Tj
/T1_0 10.91 Tf
12.22 0 Td
[(is)-321(not)]TJ
-441.28 -21.91 Td
[(able)-297(to)-298(compute)-298(the)-298(v)55(alid)-297(ciphertext)-310(^)]TJ
/T1_2 10.91 Tf
175.23 0 Td
(c)Tj
/T1_5 7.97 Tf
5.73 3.96 Td
(0)Tj
/T1_3 7.97 Tf
0 -7.19 TD
(J)Tj
/T1_0 10.91 Tf
9.11 3.23 Td
[(and)-310(^)]TJ
/T1_2 10.91 Tf
20.82 0 Td
(c)Tj
/T1_5 7.97 Tf
5.73 3.96 Td
(0)Tj
/T1_3 7.97 Tf
0 -7.02 TD
(i)Tj
/T1_0 10.91 Tf
6.63 3.06 Td
[(for)-297(1)]TJ
/T1_1 10.91 Tf
24.78 0 Td
(\267)Tj
/T1_4 10.91 Tf
11.52 0 Td
(i)Tj
/T1_1 10.91 Tf
6.78 0 Td
(6)Tj
/T1_0 10.91 Tf
(=)Tj
/T1_4 10.91 Tf
11.51 0 Td
(J)Tj
/T1_1 10.91 Tf
10.13 0 Td
(\267)Tj
/T1_4 10.91 Tf
11.51 0 Td
(n)Tj
/T1_3 7.97 Tf
6.55 -1.64 Td
(c)Tj
/T1_0 10.91 Tf
7.41 1.64 Td
[(as)-297(the)-298(symmetric-k)27(ey)-297(encryption)]TJ
-313.44 -21.92 Td
[(sc)27(heme)]TJ
/T1_8 10.91 Tf
37.76 0 Td
(SKE)Tj
/T1_0 10.91 Tf
24.22 0 Td
[(is)-373(assumed)-373(to)-374(b)-28(e)-373(secure.)-565(F)83(urthermore,)]TJ
/T1_1 10.91 Tf
189.83 0 Td
(A)Tj
/T1_0 10.91 Tf
12.78 0 Td
[(do)-27(es)-374(not)-373(kno)27(w)-373(the)-373(authen)27(tication)-373(k)27(ey)]TJ
/T1_4 10.91 Tf
185.97 0 Td
(ak)Tj
/T1_3 7.97 Tf
11.44 -1.69 Td
(J)Tj
/T1_0 10.91 Tf
-462 -20.23 Td
(and)Tj
/T1_4 10.91 Tf
21.54 0 Td
(ak)Tj
/T1_3 7.97 Tf
11.44 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
7.35 1.63 Td
[(for)-364(1)]TJ
/T1_1 10.91 Tf
26.07 0 Td
(\267)Tj
/T1_4 10.91 Tf
12.07 0 Td
(i)Tj
/T1_1 10.91 Tf
7.34 0 Td
(6)Tj
/T1_0 10.91 Tf
(=)Tj
/T1_4 10.91 Tf
12.07 0 Td
(J)Tj
/T1_1 10.91 Tf
10.69 0 Td
(\267)Tj
/T1_4 10.91 Tf
12.06 0 Td
(n)Tj
/T1_3 7.97 Tf
6.55 -1.63 Td
(c)Tj
/T1_0 10.91 Tf
8.13 1.63 Td
[(and)-364(the)-364(message)-364(authen)27(tication)-363(co)-28(de)-364(sc)27(heme)]TJ
/T1_8 10.91 Tf
218.8 0 Td
[(MA)27(CS)]TJ
/T1_0 10.91 Tf
33.51 0 Td
[(is)-363(assumed)-364(to)-364(b)-28(e)]TJ
-387.62 -21.91 Td
[(secure,)-349(therefore)]TJ
/T1_1 10.91 Tf
81.95 0 Td
(A)Tj
/T1_0 10.91 Tf
12.49 0 Td
[(is)-345(not)-346(able)-346(to)-346(compute)-346(a)-346(v)55(alid)-424(^)]TJ
/T1_4 10.91 Tf
147.35 0 Td
(\271)Tj
/T1_5 7.97 Tf
6.57 3.96 Td
(0)Tj
/T1_3 7.97 Tf
0 -7.19 TD
(J)Tj
/T1_0 10.91 Tf
9.64 3.23 Td
[(and)-425(^)]TJ
/T1_4 10.91 Tf
21.35 0 Td
(\271)Tj
/T1_5 7.97 Tf
6.57 3.96 Td
(0)Tj
/T1_3 7.97 Tf
0 -7.02 TD
(i)Tj
/T1_0 10.91 Tf
7.15 3.06 Td
[(resp)-27(ectiv)26(ely)84(.)-482(Hence,)]TJ
/T1_1 10.91 Tf
98.83 0 Td
(A)Tj
/T1_0 10.91 Tf
12.48 0 Td
[(is)-346(not)-346(able)-346(to)]TJ
-404.38 -21.92 Td
[(imp)-27(ersonate)]TJ
/T1_2 10.91 Tf
61.21 0 Td
(C)Tj
/T1_0 10.91 Tf
8.98 0 Td
[(in)-298(Phase)-299(2)-298(Round)-299(3.)-433(Therefore,)]TJ
/T1_1 10.91 Tf
152.68 0 Td
(A)Tj
/T1_0 10.91 Tf
11.96 0 Td
[(is)-298(not)-299(able)-299(to)-298(imp)-28(ersonate)]TJ
/T1_2 10.91 Tf
126.41 0 Td
(C)Tj
/T1_0 10.91 Tf
8.98 0 Td
[(in)-298(the)-298(Join)-299(Proto)-28(col.)]TJ
-353.29 -21.91 Td
[(W)83(e)-440(consider)-442(case)-441(\(b\))-441(as)-441(follo)27(ws:)-660(as)-441(the)-441(adv)27(ersary)]TJ
/T1_1 10.91 Tf
249.42 0 Td
(A)Tj
/T1_0 10.91 Tf
13.52 0 Td
[(is)-441(not)-441(a)-441(joining)-442(user,)-468(therefore,)]TJ
/T1_1 10.91 Tf
158.12 0 Td
(A)Tj
/T1_0 10.91 Tf
13.52 0 Td
(can)Tj
-451.51 -21.92 Td
[(only)-375(obtain)-376(the)-376(public)-376(exc)27(hange)-375(information)-376(sen)27(t)-375(in)-376(the)-376(Join)-376(Proto)-28(col.)-572(First,)-386(w)27(e)-375(consider)-376(if)]TJ
/T1_1 10.91 Tf
447.73 0 Td
(A)Tj
/T1_0 10.91 Tf
12.81 0 Td
(is)Tj
-460.54 -21.92 Td
[(able)-398(to)-398(obtain)-399(the)-398(new)-398(subgroup)-399(k)27(ey)]TJ
/T1_4 10.91 Tf
183.49 0 Td
(K)Tj
/T1_5 7.97 Tf
10.04 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-0.78 -7.19 Td
(J)Tj
/T1_0 10.91 Tf
10.22 3.23 Td
[(from)-398(the)-398(public)-399(information)-398(sen)27(t.)-639(But)-398(b)27(y)-398(ignoring)-398(the)]TJ
-202.97 -21.91 Td
[(authen)27(tication)-381(information)-382(\()]TJ
/T1_4 10.91 Tf
136.81 0 Td
(\271)Tj
/T1_5 7.97 Tf
6.58 3.95 Td
(0)Tj
/T1_3 7.97 Tf
0 -7.27 TD
[(J)24(;k)]TJ
/T1_0 10.91 Tf
11.9 3.32 Td
[(,)-473(\271)]TJ
/T1_4 10.91 Tf
7.33 0 Td
(\271)Tj
/T1_5 7.97 Tf
6.57 3.95 Td
(0)Tj
/T1_3 7.97 Tf
T*
[(J)24(;k)]TJ
/T1_0 10.91 Tf
11.9 3.32 Td
[(,)-473(^)]TJ
/T1_4 10.91 Tf
7.33 0 Td
(\271)Tj
/T1_5 7.97 Tf
6.57 3.95 Td
(0)Tj
/T1_3 7.97 Tf
T*
[(J)24(;k)]TJ
/T1_0 10.91 Tf
16.07 3.32 Td
(and)Tj
/T1_4 10.91 Tf
21.74 0 Td
(\265)Tj
/T1_5 7.97 Tf
5.42 3.95 Td
(0)Tj
/T1_3 7.97 Tf
-0.3 -7.19 Td
(J)Tj
/T1_0 10.91 Tf
5.87 3.24 Td
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(L)Tj
/T1_3 10.91 Tf
9.89 3.23 Td
[(from)-333(the)-334(Lea)27(v)28(e)-332(Proto)-28(col.)]TJ
-268.32 -21.92 Td
[(Next)-420(w)27(e)-420(consider)-420(the)-420(lea)26(ving)-419(user)]TJ
/T1_4 10.91 Tf
169.77 0 Td
(U)Tj
/T1_2 7.97 Tf
5.73 -1.77 Td
(L;l)Tj
/T1_5 5.98 Tf
10.64 -1.41 Td
(k)Tj
/T1_3 10.91 Tf
9.65 3.18 Td
(\(1)Tj
/T1_6 10.91 Tf
14.31 0 Td
(\267)Tj
/T1_0 10.91 Tf
13.09 0 Td
(k)Tj
/T1_6 10.91 Tf
10.63 0 Td
(\267)Tj
/T1_0 10.91 Tf
13.1 0 Td
(`)Tj
/T1_3 10.91 Tf
4.54 0 Td
[(\))-420(tries)-420(to)-421(obtain)-420(the)-420(new)-421(\257nal)-420(group)-420(k)26(ey)]TJ
/T1_0 10.91 Tf
-268.39 -21.91 Td
(K)Tj
/T1_1 7.97 Tf
10.04 3.95 Td
(0)Tj
/T1_3 10.91 Tf
5.85 -3.95 Td
(=)Tj
/T1_0 10.91 Tf
11.53 0 Td
(g)Tj
/T1_2 7.97 Tf
5.59 5.17 Td
(r)Tj
/T1_7 5.98 Tf
4.06 2.81 Td
(0)Tj
/T1_8 5.98 Tf
-0.24 -5.08 Td
(C)Tj
/T1_2 7.97 Tf
3.67 2.27 Td
(r)Tj
/T1_7 5.98 Tf
4.06 2.81 Td
(0)Tj
/T1_8 5.98 Tf
-0.24 -5.08 Td
(C)Tj
/T1_9 7.97 Tf
3.68 2.27 Td
(+)Tj
/T1_2 7.97 Tf
(r)Tj
/T1_7 5.98 Tf
10.64 2.81 Td
(0)Tj
/T1_8 5.98 Tf
-0.24 -5.08 Td
(C)Tj
/T1_10 7.97 Tf
3.67 2.27 Td
(H)Tj
/T1_11 5.98 Tf
5.98 -1.11 Td
(2)Tj
/T1_9 7.97 Tf
4.15 1.11 Td
(\()Tj
/T1_2 7.97 Tf
(K)Tj
/T1_7 5.98 Tf
10.99 2.81 Td
(0)Tj
/T1_5 5.98 Tf
-0.56 -5.51 Td
(L)Tj
/T1_9 7.97 Tf
5.56 2.7 Td
(\)+)Tj
/T1_12 7.97 Tf
9.87 5.98 Td
(P)Tj
/T1_5 5.98 Tf
8.94 -2.24 Td
(n)Tj
4.6 -0.99 Td
(c)Tj
-4.6 -5.59 Td
(i)Tj
/T1_11 5.98 Tf
2.66 0 Td
(=1)Tj
/T1_5 5.98 Tf
9.24 0 Td
(;i)Tj
/T1_7 5.98 Tf
4.93 0 Td
(6)Tj
/T1_11 5.98 Tf
(=)Tj
/T1_5 5.98 Tf
(L)Tj
/T1_2 7.97 Tf
12.56 2.84 Td
(r)Tj
/T1_7 5.98 Tf
4.06 2.81 Td
(0)Tj
/T1_8 5.98 Tf
-0.24 -5.08 Td
(C)Tj
/T1_10 7.97 Tf
3.67 2.27 Td
(H)Tj
/T1_11 5.98 Tf
5.98 -1.11 Td
(2)Tj
/T1_9 7.97 Tf
4.15 1.11 Td
(\()Tj
/T1_2 7.97 Tf
(K)Tj
/T1_5 5.98 Tf
10.43 -1.21 Td
(i)Tj
/T1_9 7.97 Tf
3.16 1.21 Td
(\))Tj
/T1_3 10.91 Tf
7.44 -5.17 Td
[(from)-334(the)-334(previous)-335(\257nal)-334(group)-334(k)26(ey)]TJ
/T1_0 10.91 Tf
162.9 0 Td
(K)Tj
/T1_3 10.91 Tf
13.09 0 Td
(=)Tj
/T1_0 10.91 Tf
11.53 0 Td
(g)Tj
/T1_2 7.97 Tf
5.6 3.95 Td
(r)Tj
/T1_8 5.98 Tf
3.82 -0.99 Td
(C)Tj
/T1_2 7.97 Tf
3.67 0.99 Td
(r)Tj
/T1_8 5.98 Tf
3.82 -0.99 Td
(C)Tj
/T1_9 7.97 Tf
3.67 0.99 Td
(+)Tj
/T1_12 7.97 Tf
6.59 5.98 Td
(P)Tj
/T1_5 5.98 Tf
8.93 -2.24 Td
(n)Tj
4.6 -0.99 Td
(c)Tj
-4.6 -5.4 Td
(i)Tj
/T1_11 5.98 Tf
(=1)Tj
/T1_2 7.97 Tf
13.82 2.65 Td
(r)Tj
/T1_8 5.98 Tf
3.82 -0.99 Td
(C)Tj
/T1_10 7.97 Tf
3.67 0.99 Td
(H)Tj
/T1_11 5.98 Tf
5.98 -1.1 Td
(2)Tj
/T1_9 7.97 Tf
4.15 1.1 Td
(\()Tj
/T1_2 7.97 Tf
(K)Tj
/T1_5 5.98 Tf
10.43 -1.21 Td
(i)Tj
/T1_9 7.97 Tf
3.16 1.21 Td
(\))Tj
/T1_3 10.91 Tf
3.79 -3.95 Td
[(.)-447(As)]TJ
/T1_0 10.91 Tf
-447.48 -21.92 Td
(r)Tj
/T1_1 7.97 Tf
5.22 3.96 Td
(0)Tj
/T1_8 7.97 Tf
-0.3 -6.66 Td
(C)Tj
/T1_3 10.91 Tf
9.24 2.7 Td
(and)Tj
/T1_0 10.91 Tf
22.09 0 Td
(r)Tj
/T1_8 7.97 Tf
4.92 -1.64 Td
(C)Tj
/T1_3 10.91 Tf
9.24 1.64 Td
[(are)-414(random)-414(and)-413(indep)-28(enden)27(t)-413(to)-414(eac)27(h)-413(other,)-434(therefore,)]TJ
/T1_0 10.91 Tf
266.94 0 Td
(g)Tj
/T1_2 7.97 Tf
5.6 3.96 Td
(r)Tj
/T1_7 5.98 Tf
4.05 2.81 Td
(0)Tj
/T1_8 5.98 Tf
-0.23 -5.09 Td
(C)Tj
/T1_2 7.97 Tf
3.67 2.28 Td
(r)Tj
/T1_7 5.98 Tf
4.06 2.81 Td
(0)Tj
/T1_8 5.98 Tf
-0.24 -5.09 Td
(C)Tj
/T1_3 10.91 Tf
8.68 -1.68 Td
(and)Tj
/T1_0 10.91 Tf
22.09 0 Td
(g)Tj
/T1_2 7.97 Tf
5.59 3.96 Td
(r)Tj
/T1_8 5.98 Tf
3.82 -1 Td
(C)Tj
/T1_2 7.97 Tf
3.68 1 Td
(r)Tj
/T1_8 5.98 Tf
3.82 -1 Td
(C)Tj
/T1_3 10.91 Tf
8.68 -2.96 Td
[(are)-413(indep)-28(enden)27(t)]TJ
-390.62 -21.92 Td
[(to)-467(eac)27(h)-466(other)-467(and)]TJ
/T1_0 10.91 Tf
93.42 0 Td
(g)Tj
/T1_2 7.97 Tf
5.59 3.96 Td
(r)Tj
/T1_7 5.98 Tf
4.06 2.81 Td
(0)Tj
/T1_8 5.98 Tf
-0.24 -5.08 Td
(C)Tj
/T1_10 7.97 Tf
3.67 2.27 Td
(H)Tj
/T1_11 5.98 Tf
5.98 -1.11 Td
(2)Tj
/T1_9 7.97 Tf
4.15 1.11 Td
(\()Tj
/T1_2 7.97 Tf
(K)Tj
/T1_5 5.98 Tf
10.43 -1.21 Td
(i)Tj
/T1_9 7.97 Tf
3.16 1.21 Td
(\))Tj
/T1_3 10.91 Tf
8.89 -3.96 Td
(and)Tj
/T1_0 10.91 Tf
22.66 0 Td
(g)Tj
/T1_2 7.97 Tf
5.59 3.96 Td
(r)Tj
/T1_8 5.98 Tf
3.82 -1 Td
(C)Tj
/T1_10 7.97 Tf
3.68 1 Td
(H)Tj
/T1_11 5.98 Tf
5.97 -1.11 Td
(2)Tj
/T1_9 7.97 Tf
4.15 1.11 Td
(\()Tj
/T1_2 7.97 Tf
(K)Tj
/T1_5 5.98 Tf
10.43 -1.21 Td
(i)Tj
/T1_9 7.97 Tf
3.17 1.21 Td
(\))Tj
/T1_3 10.91 Tf
8.88 -3.96 Td
[(for)-467(1)]TJ
/T1_6 10.91 Tf
29.06 0 Td
(\267)Tj
/T1_0 10.91 Tf
13.95 0 Td
(i)Tj
/T1_6 10.91 Tf
9.21 0 Td
(6)Tj
/T1_3 10.91 Tf
(=)Tj
/T1_0 10.91 Tf
13.95 0 Td
(L)Tj
/T1_6 10.91 Tf
12.88 0 Td
(\267)Tj
/T1_0 10.91 Tf
13.94 0 Td
(n)Tj
/T1_2 7.97 Tf
6.55 -1.63 Td
(c)Tj
/T1_3 10.91 Tf
9.26 1.63 Td
[(are)-466(indep)-28(enden)27(t)-466(to)-468(eac)27(h)-466(other.)]TJ
-316.26 -21.91 Td
[(F)83(urthermore,)-448(as)]TJ
/T1_0 10.91 Tf
81.94 0 Td
(K)Tj
/T1_1 7.97 Tf
10.04 3.95 Td
(0)Tj
/T1_2 7.97 Tf
-0.78 -7.19 Td
(L)Tj
/T1_3 10.91 Tf
10.9 3.24 Td
(and)Tj
/T1_0 10.91 Tf
22.21 0 Td
(K)Tj
/T1_2 7.97 Tf
9.26 -1.69 Td
(L)Tj
/T1_3 10.91 Tf
10.9 1.69 Td
[(are)-425(random)-425(and)-426(indep)-27(enden)26(t)-424(to)-426(eac)27(h)-424(other,)-449(therefore)]TJ
/T1_13 10.91 Tf
264.73 0 Td
(H)Tj
/T1_9 7.97 Tf
7.73 -1.64 Td
(2)Tj
/T1_3 10.91 Tf
4.73 1.64 Td
(\()Tj
/T1_0 10.91 Tf
(K)Tj
/T1_1 7.97 Tf
14.28 3.95 Td
(0)Tj
/T1_2 7.97 Tf
-0.78 -7.19 Td
(L)Tj
/T1_3 10.91 Tf
6.26 3.24 Td
[(\))-425(and)]TJ
/T1_13 10.91 Tf
-441.42 -21.92 Td
(H)Tj
/T1_9 7.97 Tf
7.73 -1.64 Td
(2)Tj
/T1_3 10.91 Tf
4.73 1.64 Td
(\()Tj
/T1_0 10.91 Tf
(K)Tj
/T1_2 7.97 Tf
13.5 -1.69 Td
(L)Tj
/T1_3 10.91 Tf
6.26 1.69 Td
[(\))-267(are)-269(indep)-28(enden)27(t)-267(to)-269(eac)27(h)-267(other)-269(as)-268(the)-268(output)-269(of)-268(the)-268(hash)-269(function)]TJ
/T1_13 10.91 Tf
312.39 0 Td
(H)Tj
/T1_9 7.97 Tf
7.73 -1.64 Td
(2)Tj
/T1_3 10.91 Tf
7.66 1.64 Td
[(is)-268(indep)-27(enden)26(t.)-421(Hence,)]TJ
/T1_0 10.91 Tf
-360 -21.92 Td
(g)Tj
/T1_2 7.97 Tf
5.59 3.96 Td
(r)Tj
/T1_7 5.98 Tf
4.06 2.81 Td
(0)Tj
/T1_8 5.98 Tf
-0.24 -5.08 Td
(C)Tj
/T1_10 7.97 Tf
3.68 2.27 Td
(H)Tj
/T1_11 5.98 Tf
5.97 -1.11 Td
(2)Tj
/T1_9 7.97 Tf
4.15 1.11 Td
(\()Tj
/T1_2 7.97 Tf
(K)Tj
/T1_7 5.98 Tf
11 2.81 Td
(0)Tj
/T1_5 5.98 Tf
-0.57 -5.51 Td
(L)Tj
/T1_9 7.97 Tf
5.56 2.7 Td
(\))Tj
/T1_3 10.91 Tf
6.31 -3.96 Td
(and)Tj
/T1_0 10.91 Tf
20.09 0 Td
(g)Tj
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5.59 3.96 Td
(r)Tj
/T1_8 5.98 Tf
3.82 -0.99 Td
(C)Tj
/T1_10 7.97 Tf
3.68 0.99 Td
(H)Tj
/T1_11 5.98 Tf
5.97 -1.11 Td
(2)Tj
/T1_9 7.97 Tf
4.15 1.11 Td
(\()Tj
/T1_2 7.97 Tf
3.3 0 Td
(K)Tj
/T1_5 5.98 Tf
7.14 -1.34 Td
(L)Tj
/T1_9 7.97 Tf
5.55 1.34 Td
(\))Tj
/T1_3 10.91 Tf
6.31 -3.96 Td
[(are)-231(also)-231(indep)-28(enden)27(t)-230(to)-231(eac)27(h)-230(other.)-411(Hence)]TJ
/T1_0 10.91 Tf
197.85 0 Td
(K)Tj
/T1_1 7.97 Tf
10.05 3.96 Td
(0)Tj
/T1_3 10.91 Tf
5.31 -3.96 Td
(and)Tj
/T1_0 10.91 Tf
20.09 0 Td
(K)Tj
/T1_3 10.91 Tf
12.56 0 Td
[(are)-231(indep)-28(enden)27(t)-230(to)-231(eac)27(h)]TJ
-356.97 -21.91 Td
[(other)-348(and)-349(lea)27(ving)-348(user)]TJ
/T1_4 10.91 Tf
110.46 0 Td
(U)Tj
/T1_2 7.97 Tf
5.73 -1.78 Td
(L;l)Tj
/T1_5 5.98 Tf
10.64 -1.4 Td
(k)Tj
/T1_3 10.91 Tf
8.87 3.18 Td
[(is)-348(not)-349(able)-349(to)-349(obtain)]TJ
/T1_0 10.91 Tf
101.48 0 Td
(K)Tj
/T1_1 7.97 Tf
10.05 3.95 Td
(0)Tj
/T1_3 10.91 Tf
6.59 -3.95 Td
(from)Tj
/T1_0 10.91 Tf
25.95 0 Td
(K)Tj
/T1_3 10.91 Tf
10.05 0 Td
[(.)-490(Therefore,)]TJ
/T1_4 10.91 Tf
61.06 0 Td
(U)Tj
/T1_2 7.97 Tf
5.73 -1.78 Td
(L;l)Tj
/T1_5 5.98 Tf
10.63 -1.4 Td
(k)Tj
/T1_3 10.91 Tf
8.88 3.18 Td
[(only)-348(has)-349(the)-349(public)]TJ
-376.12 -21.92 Td
[(information)-239(sen)27(t)-239(in)-239(the)-239(Lea)26(v)28(e)-238(Proto)-28(col.)-413(But)-240(b)27(y)-238(ignoring)-240(the)-239(authen)27(tication)-239(information)-239(\()]TJ
/T1_0 10.91 Tf
414.67 0 Td
(\271)Tj
/T1_1 7.97 Tf
6.57 3.96 Td
(0)Tj
/T1_2 7.97 Tf
0 -7.19 TD
(L)Tj
/T1_3 10.91 Tf
6.26 3.23 Td
[(,)-336(\271)]TJ
/T1_0 10.91 Tf
5.84 0 Td
(\271)Tj
/T1_1 7.97 Tf
6.57 3.96 Td
(0)Tj
/T1_2 7.97 Tf
T*
(L)Tj
/T1_3 10.91 Tf
6.26 3.23 Td
[(,)-337(^)]TJ
/T1_0 10.91 Tf
5.84 0 Td
(\271)Tj
/T1_1 7.97 Tf
6.58 3.96 Td
(0)Tj
/T1_2 7.97 Tf
T*
(L)Tj
/T1_3 10.91 Tf
6.25 3.23 Td
(,)Tj
-463.98 -21.92 Td
(^)Tj
/T1_0 10.91 Tf
-0.86 0 Td
(\271)Tj
/T1_1 7.97 Tf
6.57 3.96 Td
(0)Tj
/T1_2 7.97 Tf
0 -7.01 TD
(i)Tj
/T1_3 10.91 Tf
6.55 3.05 Td
(and)Tj
/T1_0 10.91 Tf
20.74 0 Td
(\265)Tj
/T1_1 7.97 Tf
5.42 3.96 Td
(0)Tj
/T1_8 7.97 Tf
-0.3 -6.65 Td
(C)Tj
/T1_3 10.91 Tf
4.73 2.69 Td
[(\))-290(sen)27(t,)-298(the)-290(prop)-28(osed)-291(Lea)27(v)28(e)-289(proto)-28(col)-291(to)-290(form)-291(the)-290(new)-290(\257nal)-291(group)-290(k)27(ey)]TJ
/T1_0 10.91 Tf
321.58 0 Td
(K)Tj
/T1_1 7.97 Tf
10.05 3.96 Td
(0)Tj
/T1_3 10.91 Tf
5.96 -3.96 Td
[(is)-290(just)-290(the)-291(EST)83(AR)]TJ
-381.3 -21.91 Td
[(proto)-27(col,)-368(where)-361(Phase)-362(2)-361(Round)-361(2)-361(\()]TJ
/T1_4 10.91 Tf
168.64 0 Td
(S)Tj
/T1_2 7.97 Tf
5.72 -1.69 Td
(L)Tj
/T1_3 10.91 Tf
10.2 1.69 Td
[(sends)-360(new)-361(\()]TJ
/T1_0 10.91 Tf
56.46 0 Td
(y)Tj
/T1_1 7.97 Tf
5.74 3.96 Td
(\244)Tj
/T1_2 7.97 Tf
-0.39 -7.19 Td
(L)Tj
/T1_3 10.91 Tf
6.26 3.23 Td
(\))Tj
/T1_1 7.97 Tf
4.24 3.96 Td
(0)Tj
/T1_3 10.91 Tf
6.73 -3.96 Td
(while)Tj
/T1_4 10.91 Tf
28.78 0 Td
(S)Tj
/T1_2 7.97 Tf
5.73 -1.64 Td
(i)Tj
/T1_3 10.91 Tf
7.32 1.64 Td
[(for)-360(1)]TJ
/T1_6 10.91 Tf
25.98 0 Td
(\267)Tj
/T1_0 10.91 Tf
12.02 0 Td
(i)Tj
/T1_6 10.91 Tf
7.29 0 Td
(6)Tj
/T1_3 10.91 Tf
(=)Tj
/T1_0 10.91 Tf
12.01 0 Td
(L)Tj
/T1_6 10.91 Tf
10.96 0 Td
(\267)Tj
/T1_0 10.91 Tf
12.02 0 Td
(n)Tj
/T1_2 7.97 Tf
6.54 -1.64 Td
(c)Tj
/T1_3 10.91 Tf
8.11 1.64 Td
(uses)Tj
/T1_0 10.91 Tf
23.44 0 Td
(y)Tj
/T1_1 7.97 Tf
5.74 3.96 Td
(\244)Tj
/T1_2 7.97 Tf
-0.39 -7.02 Td
(i)Tj
/T1_3 10.91 Tf
9.06 3.06 Td
(that)Tj
/T1_4 10.91 Tf
23.94 0 Td
(C)Tj
/T1_3 10.91 Tf
-462.15 -21.92 Td
[(kno)27(ws)-314(from)-315(previous)-315(GKA\),)-316(Phase)-315(2)-315(Round)-315(3)-316(and)-315(Phase)-315(3)-315(Round)-316(1)-315(is)-315(just)-315(Round)-315(1,)-319(Round)-316(2)-315(and)]TJ
0 -21.92 TD
[(Computation)-273(of)-273(Key)-273(of)-273(the)-273(EST)82(AR)-272(proto)-28(col.)-424(By)-273(Theorem)-273(41,)-286(it)-273(is)-273(sho)27(wn)-272(that)-273(the)-273(EST)82(AR)-272(proto)-28(col)]TJ
0 -21.91 TD
[(is)-332(secure.)-444(Hence,)-332(lea)27(ving)-332(user)]TJ
/T1_4 10.91 Tf
143.49 0 Td
(U)Tj
/T1_2 7.97 Tf
5.72 -1.78 Td
(L;l)Tj
/T1_5 5.98 Tf
10.64 -1.4 Td
(k)Tj
/T1_3 10.91 Tf
8.69 3.18 Td
(\(1)Tj
/T1_6 10.91 Tf
12.72 0 Td
(\267)Tj
/T1_0 10.91 Tf
11.52 0 Td
(k)Tj
/T1_6 10.91 Tf
9.05 0 Td
(\267)Tj
/T1_0 10.91 Tf
11.51 0 Td
(`)Tj
/T1_3 10.91 Tf
4.54 0 Td
[(\))-332(is)-332(not)-332(able)-333(to)-332(obtain)-332(the)-332(new)-332(\257nal)-333(group)-332(k)27(ey)]TJ
/T1_0 10.91 Tf
224.44 0 Td
(K)Tj
/T1_1 7.97 Tf
10.04 3.96 Td
(0)Tj
/T1_3 10.91 Tf
6.42 -3.96 Td
(in)Tj
-458.78 -21.92 Td
[(this)-361(case.)-530(The)-362(new)-361(\257nal)-362(group)-362(k)27(ey)]TJ
/T1_0 10.91 Tf
171.07 0 Td
(K)Tj
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(n)Tj
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6.54 -1.64 Td
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30.21 0 Td
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11.84 0 Td
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12.46 0 Td
[(tries)-343(to)]TJ
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[(obtain)-372(the)-373(new)-373(subgroup)-373(k)27(ey)]TJ
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(L)Tj
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10.32 3.23 Td
[(and)-373(new)-373(\257nal)-373(group)-372(k)26(ey)]TJ
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120.64 0 Td
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10.05 3.96 Td
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6.86 -3.96 Td
[(from)-372(the)-373(public)-373(information)-373(in)-373(the)]TJ
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[(Lea)27(v)28(e)-332(Proto)-28(col.)]TJ
16.93 -21.92 Td
[(F)83(or)-367(case)-368(\(a\),)-377(w)27(e)-367(\257rst)-368(consider)]TJ
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12.72 0 Td
[(tries)-367(to)-368(imp)-28(ersonate)-368(subgroup)-368(con)27(troller)]TJ
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[(.)-548(As)]TJ
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[(do)-27(es)-368(not)]TJ
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[(send)-414(an)27(y)-413(information)-414(in)-414(Phase)-415(1,)-434(hence)-414(w)27(e)-414(\257rst)-414(consider)]TJ
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[(in)-414(Phase)-414(2.)]TJ
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78.35 0 Td
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13.61 0 Td
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11.16 1.69 Td
[(in)-449(Phase)-449(2)-449(of)-449(the)-450(Lea)27(v)28(e)-448(Proto)-28(col)-449(is)-450(the)-449(same)]TJ
-243.46 -21.92 Td
[(as)-438(the)-438(pro)-28(of)-438(that)]TJ
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88.89 0 Td
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13.49 0 Td
[(is)-438(not)-438(able)-438(to)-439(imp)-28(ersonate)]TJ
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134.02 0 Td
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(i)Tj
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8.16 1.63 Td
[(in)-438(Phase)-438(2)-438(of)-439(the)-438(IKA)-438(proto)-28(col)-438(as)-439(sho)27(wn)-437(in)]TJ
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[(Theorem)-316(43.)-438(Hence)-316(w)26(e)-315(omit)-316(the)-316(pro)-28(of)-316(here.)-438(Next,)-320(consider)]TJ
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284.57 0 Td
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12.15 0 Td
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9.71 1.69 Td
[(in)-315(Phase)-316(3)-316(Round)]TJ
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[(1.)-470(Then)]TJ
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42.19 0 Td
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12.44 0 Td
[(selects)-341(random)]TJ
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74.26 0 Td
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(\244)Tj
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(q)Tj
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5.51 2.7 Td
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6.78 0 Td
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(0)Tj
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15.68 3.23 Td
(2)Tj
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(\244)Tj
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(q)Tj
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9.25 2.7 Td
[(for)-341(1)]TJ
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25.43 0 Td
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11.67 0 Td
(j)Tj
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(n)Tj
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8.74 1.69 Td
(\241)Tj
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10.97 0 Td
(`)Tj
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8.28 0 Td
[(and)-341(session)-342(iden)26(tit)28(y)]TJ
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97.71 0 Td
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17.18 3.96 Td
(0)Tj
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0 -7.19 TD
(L)Tj
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6.25 3.23 Td
[(.)-471(Next,)]TJ
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-433.65 -21.92 Td
(A)Tj
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13.15 0 Td
[(needs)-406(to)-408(compute)-407(v)55(alid)]TJ
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116.88 0 Td
(c)Tj
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5.73 3.96 Td
(0)Tj
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T*
(L;j)Tj
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16.86 3.23 Td
(=)Tj
/T1_1 10.91 Tf
12.85 0 Td
(E)Tj
/T1_3 7.97 Tf
5.76 -1.77 Td
(ek)Tj
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8.33 -1.34 Td
(L;j)Tj
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11.73 3.11 Td
(\()Tj
/T1_2 10.91 Tf
(\277)Tj
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10.24 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-1.23 -7.19 Td
(L)Tj
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6.25 3.23 Td
(jj)Tj
/T1_2 10.91 Tf
6.06 0 Td
(\277)Tj
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6 3.96 Td
(0)Tj
/T1_3 7.97 Tf
-1.23 -7.19 Td
(L;j)Tj
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12.49 3.23 Td
(jj)Tj
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6.06 0 Td
(S)Tj
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5.72 -1.68 Td
(L)Tj
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6.26 1.68 Td
(jj)Tj
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6.06 0 Td
(V)Tj
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5.72 -1.68 Td
(L;j)Tj
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12.49 1.68 Td
(jj)Tj
/T1_4 10.91 Tf
6.06 0 Td
(SID)Tj
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17.18 3.96 Td
(0)Tj
/T1_3 7.97 Tf
T*
(L)Tj
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6.26 3.23 Td
(\),)Tj
/T1_2 10.91 Tf
11.91 0 Td
(v)Tj
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5.67 3.96 Td
(0)Tj
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-0.39 -7.19 Td
(L;j)Tj
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16.86 3.23 Td
(=)Tj
/T1_9 10.91 Tf
12.86 0 Td
(H)Tj
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7.72 -1.63 Td
(1)Tj
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4.73 1.63 Td
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[(p)27(w)]TJ
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17.18 -2.62 Td
(L;j)Tj
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12.49 2.62 Td
(jj)Tj
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6.06 0 Td
(\277)Tj
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(0)Tj
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-1.23 -7.19 Td
(L)Tj
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6.25 3.23 Td
(jj)Tj
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6.06 0 Td
(\277)Tj
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6 3.96 Td
(0)Tj
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-1.23 -7.19 Td
(L;j)Tj
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12.49 3.23 Td
(jj)Tj
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6.06 0 Td
(SID)Tj
/T1_6 7.97 Tf
17.17 3.96 Td
(0)Tj
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T*
(L)Tj
/T1_0 10.91 Tf
6.26 3.23 Td
(\),)Tj
-460.46 -21.91 Td
(^)Tj
/T1_4 10.91 Tf
-0.14 0 Td
(c)Tj
/T1_6 7.97 Tf
5.73 3.95 Td
(0)Tj
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T*
(L;j)Tj
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15.8 3.24 Td
(=)Tj
/T1_1 10.91 Tf
11.8 0 Td
(E)Tj
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5.76 -2.31 Td
(t)Tj
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3.06 2.74 Td
(0)Tj
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0 -5.51 TD
(L;j)Tj
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11.72 5.08 Td
(\()Tj
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(K)Tj
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14.29 3.95 Td
(0)Tj
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-0.78 -7.19 Td
(L)Tj
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6.25 3.24 Td
(jj)Tj
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6.06 0 Td
(K)Tj
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10.04 3.95 Td
(0)Tj
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2.8 -3.95 Td
(jj)Tj
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6.06 0 Td
(S)Tj
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5.72 -1.69 Td
(L)Tj
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6.26 1.69 Td
(jj)Tj
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6.06 0 Td
(z)Tj
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5.07 -1.69 Td
(L;j)Tj
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12.49 1.69 Td
(jj)Tj
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6.06 0 Td
(SID)Tj
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17.18 3.95 Td
(0)Tj
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0 -7.19 TD
(L)Tj
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6.25 3.24 Td
[(\),)-432(^)]TJ
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11.12 0 Td
(\271)Tj
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6.57 3.95 Td
(0)Tj
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T*
(L;j)Tj
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15.81 3.24 Td
(=)Tj
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11.8 0 Td
[(MA)27(C)]TJ
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23.48 -1.78 Td
(ak)Tj
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8.91 -1.34 Td
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11.72 3.12 Td
(\()Tj
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(\277)Tj
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10.25 3.95 Td
(0)Tj
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-1.24 -7.19 Td
(L)Tj
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6.26 3.24 Td
(jj)Tj
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6.06 0 Td
(\277)Tj
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6 3.95 Td
(0)Tj
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-1.24 -7.19 Td
(L;j)Tj
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12.49 3.24 Td
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6.06 0 Td
(z)Tj
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5.55 3.95 Td
(0)Tj
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-0.48 -7.19 Td
(L)Tj
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6.26 3.24 Td
(jj)Tj
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6.06 0 Td
(\265)Tj
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5.42 3.95 Td
(0)Tj
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-0.3 -7.19 Td
(L)Tj
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6.25 3.24 Td
(jj)Tj
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6.06 0 Td
(SID)Tj
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17.18 3.95 Td
(0)Tj
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T*
(L)Tj
/T1_1 10.91 Tf
6.26 3.24 Td
(jj)Tj
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6.05 0 Td
(S)Tj
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5.73 -1.69 Td
(L)Tj
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6.26 1.69 Td
(jj)Tj
/T1_4 10.91 Tf
6.05 0 Td
(V)Tj
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5.73 -1.69 Td
(L;j)Tj
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12.49 1.69 Td
(jj)Tj
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6.06 0 Td
[(11\))-349(and)]TJ
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40.33 0 Td
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5.43 3.95 Td
(0)Tj
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(L)Tj
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9.58 3.24 Td
(=)Tj
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-459.39 -21.92 Td
(H)Tj
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7.73 -1.64 Td
(1)Tj
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4.73 1.64 Td
(\()Tj
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(SID)Tj
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21.41 3.96 Td
(0)Tj
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T*
(L)Tj
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6.26 3.23 Td
(jj)Tj
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6.06 0 Td
(UID)Tj
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17.18 3.96 Td
(0)Tj
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T*
(L)Tj
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6.25 3.23 Td
(jj)Tj
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6.06 0 Td
(K)Tj
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10.04 3.96 Td
(0)Tj
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-0.78 -7.19 Td
(L)Tj
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6.26 3.23 Td
(jj)Tj
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6.06 0 Td
(K)Tj
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10.04 3.96 Td
(0)Tj
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2.79 -3.96 Td
(jj)Tj
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6.06 0 Td
(\277)Tj
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6 3.96 Td
(0)Tj
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(L)Tj
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6.26 3.23 Td
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6.05 0 Td
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5.56 3.96 Td
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(L)Tj
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6.25 3.23 Td
[(\).)-692(The)-415(v)54(alidit)28(y)-415(of)]TJ
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91.44 0 Td
(c)Tj
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5.72 3.96 Td
(0)Tj
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T*
(L;j)Tj
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12.49 3.23 Td
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7.79 0 Td
(v)Tj
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5.68 3.96 Td
(0)Tj
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(L;j)Tj
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12.49 3.23 Td
[(,)-448(^)]TJ
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7.79 0 Td
(c)Tj
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5.72 3.96 Td
(0)Tj
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T*
(L;j)Tj
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17.03 3.23 Td
[(and)-494(^)]TJ
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22.1 0 Td
(\271)Tj
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6.58 3.96 Td
(0)Tj
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T*
(L;j)Tj
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17.02 3.23 Td
[(are)-415(c)26(hec)28(k)28(ed)-415(b)27(y)]TJ
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76.04 0 Td
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5.73 -1.69 Td
(L;j)Tj
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17.02 1.69 Td
(for)Tj
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9.6 0 Td
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12.63 0 Td
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9.26 0 Td
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12.63 0 Td
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6.55 -1.68 Td
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9.12 1.68 Td
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11.35 0 Td
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8.85 0 Td
[(in)-395(Phase)-394(3)-395(Round)-395(2.)-629(If)-395(either)-394(one)-395(of)]TJ
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183.78 0 Td
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-404.56 -21.91 Td
[(imp)-27(ersonate)]TJ
/T1_6 10.91 Tf
61.59 0 Td
(S)Tj
/T1_4 7.97 Tf
5.72 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
7.02 1.64 Td
[(in)-333(the)-333(Lea)27(v)27(e)-332(Proto)-28(col.)]TJ
-57.4 -21.92 Td
[(Next,)-463(w)27(e)-437(consider)]TJ
/T1_1 10.91 Tf
91.94 0 Td
(A)Tj
/T1_0 10.91 Tf
13.48 0 Td
[(tries)-437(to)-437(imp)-28(ersonate)]TJ
/T1_6 10.91 Tf
102.65 0 Td
(C)Tj
/T1_0 10.91 Tf
5.72 0 Td
[(.)-757(Then)-437(in)-437(Phase)-438(2)-437(Round)-438(1,)]TJ
/T1_1 10.91 Tf
147.8 0 Td
(A)Tj
/T1_0 10.91 Tf
13.48 0 Td
[(selects)-437(randoms)]TJ
/T1_2 10.91 Tf
-392 -21.92 Td
(\277)Tj
/T1_3 7.97 Tf
6 3.96 Td
(0)Tj
/T1_10 7.97 Tf
-1.23 -6.65 Td
(C)Tj
/T1_1 10.91 Tf
8.17 2.69 Td
(2)Tj
/T1_2 10.91 Tf
10.71 0 Td
(Z)Tj
/T1_3 7.97 Tf
8.23 3.96 Td
(\244)Tj
/T1_4 7.97 Tf
-0.78 -6.65 Td
(q)Tj
/T1_0 10.91 Tf
5.51 2.69 Td
[(,)-414(\271)]TJ
/T1_2 10.91 Tf
6.97 0 Td
(\277)Tj
/T1_3 7.97 Tf
6 3.96 Td
(0)Tj
/T1_4 7.97 Tf
-1.23 -7.19 Td
(L)Tj
/T1_1 10.91 Tf
9.69 3.23 Td
(2)Tj
/T1_2 10.91 Tf
10.71 0 Td
(Z)Tj
/T1_3 7.97 Tf
8.23 3.96 Td
(\244)Tj
/T1_4 7.97 Tf
-0.78 -6.65 Td
(q)Tj
/T1_0 10.91 Tf
5.51 2.69 Td
[(,)-414(\271)]TJ
/T1_2 10.91 Tf
6.97 0 Td
(\277)Tj
/T1_3 7.97 Tf
6.01 3.96 Td
(0)Tj
/T1_4 7.97 Tf
-1.24 -7.01 Td
(i)Tj
/T1_1 10.91 Tf
7.47 3.05 Td
(2)Tj
/T1_2 10.91 Tf
10.71 0 Td
(Z)Tj
/T1_3 7.97 Tf
8.23 3.96 Td
(\244)Tj
/T1_4 7.97 Tf
-0.78 -6.65 Td
(q)Tj
/T1_0 10.91 Tf
9.39 2.69 Td
[(for)-355(1)]TJ
/T1_1 10.91 Tf
25.83 0 Td
(\267)Tj
/T1_2 10.91 Tf
11.92 0 Td
(i)Tj
/T1_1 10.91 Tf
7.2 0 Td
(6)Tj
/T1_0 10.91 Tf
(=)Tj
/T1_2 10.91 Tf
11.93 0 Td
(L)Tj
/T1_1 10.91 Tf
10.86 0 Td
(\267)Tj
/T1_2 10.91 Tf
11.92 0 Td
(n)Tj
/T1_4 7.97 Tf
6.55 -1.63 Td
(c)Tj
/T1_0 10.91 Tf
8.04 1.63 Td
[(and)-356(session)-356(iden)27(tit)28(y)]TJ
/T1_6 10.91 Tf
98.17 0 Td
(SID)Tj
/T1_3 7.97 Tf
17.18 3.96 Td
(0)Tj
/T1_10 7.97 Tf
0 -6.65 TD
(c)Tj
/T1_0 10.91 Tf
4.73 2.69 Td
[(.)-512(Next,)]TJ
/T1_1 10.91 Tf
38.61 0 Td
(A)Tj
/T1_0 10.91 Tf
12.59 0 Td
[(has)-356(to)-356(compute)]TJ
-394 -21.91 Td
[(the)-421(v)55(alid)]TJ
/T1_6 10.91 Tf
47.06 0 Td
(c)Tj
/T1_3 7.97 Tf
5.72 3.95 Td
(0)Tj
/T1_4 7.97 Tf
0 -7.18 TD
(L)Tj
/T1_0 10.91 Tf
10.89 3.23 Td
(=)Tj
/T1_1 10.91 Tf
13.11 0 Td
(E)Tj
/T1_4 7.97 Tf
5.75 -1.78 Td
(ek)Tj
/T1_8 5.98 Tf
8.34 -1.34 Td
(L)Tj
/T1_0 10.91 Tf
6.05 3.12 Td
(\()Tj
/T1_2 10.91 Tf
(\277)Tj
/T1_3 7.97 Tf
10.25 3.95 Td
(0)Tj
/T1_10 7.97 Tf
-1.24 -6.65 Td
(C)Tj
/T1_1 10.91 Tf
4.73 2.7 Td
(jj)Tj
/T1_0 10.91 Tf
6.64 0 Td
(\271)Tj
/T1_2 10.91 Tf
-0.58 0 Td
(\277)Tj
/T1_3 7.97 Tf
6 3.95 Td
(0)Tj
/T1_4 7.97 Tf
-1.23 -7.18 Td
(L)Tj
/T1_1 10.91 Tf
6.25 3.23 Td
(jj)Tj
/T1_6 10.91 Tf
6.06 0 Td
(C)Tj
/T1_1 10.91 Tf
(jj)Tj
/T1_6 10.91 Tf
11.79 0 Td
(S)Tj
/T1_4 7.97 Tf
5.72 -1.69 Td
(L)Tj
/T1_1 10.91 Tf
6.26 1.69 Td
(jj)Tj
/T1_6 10.91 Tf
6.06 0 Td
(SID)Tj
/T1_3 7.97 Tf
17.18 3.95 Td
(0)Tj
/T1_10 7.97 Tf
-0.01 -6.65 Td
(c)Tj
/T1_0 10.91 Tf
4.74 2.7 Td
(\),)Tj
/T1_2 10.91 Tf
12.1 0 Td
(v)Tj
/T1_3 7.97 Tf
5.68 3.95 Td
(0)Tj
/T1_4 7.97 Tf
-0.39 -7.18 Td
(L)Tj
/T1_0 10.91 Tf
10.88 3.23 Td
(=)Tj
/T1_5 10.91 Tf
13.11 0 Td
(H)Tj
/T1_9 7.97 Tf
7.73 -1.64 Td
(1)Tj
/T1_0 10.91 Tf
4.73 1.64 Td
(\()Tj
/T1_5 10.91 Tf
[(p)27(w)]TJ
/T1_4 7.97 Tf
17.18 -2.62 Td
(L)Tj
/T1_1 10.91 Tf
6.25 2.62 Td
(jj)Tj
/T1_2 10.91 Tf
6.06 0 Td
(\277)Tj
/T1_3 7.97 Tf
6 3.95 Td
(0)Tj
/T1_10 7.97 Tf
-1.23 -6.65 Td
(C)Tj
/T1_1 10.91 Tf
4.73 2.7 Td
(jj)Tj
/T1_0 10.91 Tf
6.63 0 Td
(\271)Tj
/T1_2 10.91 Tf
-0.57 0 Td
(\277)Tj
/T1_3 7.97 Tf
6 3.95 Td
(0)Tj
/T1_4 7.97 Tf
-1.24 -7.18 Td
(L)Tj
/T1_1 10.91 Tf
6.26 3.23 Td
(jj)Tj
/T1_6 10.91 Tf
6.06 0 Td
(SID)Tj
/T1_3 7.97 Tf
17.18 3.95 Td
(0)Tj
/T1_10 7.97 Tf
0 -6.65 TD
(c)Tj
/T1_0 10.91 Tf
4.73 2.7 Td
(\),)Tj
/T1_6 10.91 Tf
12.1 0 Td
(c)Tj
/T1_3 7.97 Tf
5.73 3.95 Td
(0)Tj
/T1_4 7.97 Tf
0 -7.01 TD
(i)Tj
/T1_0 10.91 Tf
8.01 3.06 Td
(=)Tj
/T1_1 10.91 Tf
13.11 0 Td
(E)Tj
/T1_4 7.97 Tf
5.75 -1.78 Td
(ek)Tj
/T1_8 5.98 Tf
8.34 -1.21 Td
(i)Tj
/T1_0 10.91 Tf
3.66 2.99 Td
(\()Tj
/T1_2 10.91 Tf
(\277)Tj
/T1_3 7.97 Tf
10.24 3.95 Td
(0)Tj
/T1_10 7.97 Tf
-1.23 -6.65 Td
(C)Tj
/T1_1 10.91 Tf
4.73 2.7 Td
(jj)Tj
/T1_0 10.91 Tf
6.63 0 Td
(\271)Tj
/T1_2 10.91 Tf
-0.57 0 Td
(\277)Tj
/T1_3 7.97 Tf
6 3.95 Td
(0)Tj
/T1_4 7.97 Tf
-1.24 -7.01 Td
(i)Tj
/T1_1 10.91 Tf
4.03 3.06 Td
(jj)Tj
/T1_6 10.91 Tf
6.06 0 Td
(C)Tj
/T1_1 10.91 Tf
(jj)Tj
/T1_6 10.91 Tf
11.79 0 Td
(S)Tj
/T1_4 7.97 Tf
5.72 -1.64 Td
(i)Tj
/T1_1 10.91 Tf
3.38 1.64 Td
(jj)Tj
/T1_6 10.91 Tf
6.06 0 Td
(SID)Tj
/T1_3 7.97 Tf
17.18 3.95 Td
(0)Tj
/T1_10 7.97 Tf
0 -6.65 TD
(c)Tj
/T1_0 10.91 Tf
4.73 2.7 Td
(\))Tj
-463.63 -21.92 Td
(and)Tj
/T1_2 10.91 Tf
20.71 0 Td
(v)Tj
/T1_3 7.97 Tf
5.68 3.96 Td
(0)Tj
/T1_4 7.97 Tf
-0.39 -7.01 Td
(i)Tj
/T1_0 10.91 Tf
6.41 3.05 Td
(=)Tj
/T1_5 10.91 Tf
11.51 0 Td
(H)Tj
/T1_9 7.97 Tf
7.73 -1.64 Td
(1)Tj
/T1_0 10.91 Tf
4.73 1.64 Td
(\()Tj
/T1_5 10.91 Tf
[(p)27(w)]TJ
/T1_4 7.97 Tf
17.18 -2.62 Td
(i)Tj
/T1_1 10.91 Tf
3.38 2.62 Td
(jj)Tj
/T1_2 10.91 Tf
6.05 0 Td
(\277)Tj
/T1_3 7.97 Tf
6.01 3.96 Td
(0)Tj
/T1_10 7.97 Tf
-1.24 -6.66 Td
(C)Tj
/T1_1 10.91 Tf
4.73 2.7 Td
(jj)Tj
/T1_0 10.91 Tf
6.64 0 Td
(\271)Tj
/T1_2 10.91 Tf
-0.58 0 Td
(\277)Tj
/T1_3 7.97 Tf
6 3.96 Td
(0)Tj
/T1_4 7.97 Tf
-1.23 -7.01 Td
(i)Tj
/T1_1 10.91 Tf
4.03 3.05 Td
(jj)Tj
/T1_6 10.91 Tf
6.06 0 Td
(SID)Tj
/T1_3 7.97 Tf
17.17 3.96 Td
(0)Tj
/T1_10 7.97 Tf
0 -6.66 TD
(c)Tj
/T1_0 10.91 Tf
4.74 2.7 Td
[(\))-287(for)-289(1)]TJ
/T1_1 10.91 Tf
32.06 0 Td
(\267)Tj
/T1_2 10.91 Tf
11.51 0 Td
(i)Tj
/T1_1 10.91 Tf
6.79 0 Td
(6)Tj
/T1_0 10.91 Tf
(=)Tj
/T1_2 10.91 Tf
11.51 0 Td
(L)Tj
/T1_1 10.91 Tf
10.45 0 Td
(\267)Tj
/T1_2 10.91 Tf
11.52 0 Td
(n)Tj
/T1_4 7.97 Tf
6.54 -1.64 Td
(c)Tj
/T1_0 10.91 Tf
4.17 1.64 Td
[(.)-429(The)-288(v)55(alidit)27(y)-287(of)]TJ
/T1_6 10.91 Tf
80.15 0 Td
(c)Tj
/T1_3 7.97 Tf
5.73 3.96 Td
(0)Tj
/T1_4 7.97 Tf
0 -7.19 TD
(L)Tj
/T1_0 10.91 Tf
9.4 3.23 Td
(and)Tj
/T1_2 10.91 Tf
20.71 0 Td
(v)Tj
/T1_3 7.97 Tf
5.68 3.96 Td
(0)Tj
/T1_4 7.97 Tf
-0.39 -7.19 Td
(L)Tj
/T1_0 10.91 Tf
9.4 3.23 Td
(\()Tj
/T1_6 10.91 Tf
(c)Tj
/T1_3 7.97 Tf
9.96 3.96 Td
(0)Tj
/T1_4 7.97 Tf
0 -7.01 TD
(i)Tj
/T1_0 10.91 Tf
6.53 3.05 Td
(and)Tj
/T1_2 10.91 Tf
20.71 0 Td
(v)Tj
/T1_3 7.97 Tf
5.68 3.96 Td
(0)Tj
/T1_4 7.97 Tf
-0.39 -7.01 Td
(i)Tj
/T1_0 10.91 Tf
3.38 3.05 Td
[(\))-287(are)-289(c)27(hec)28(k)28(ed)]TJ
-406.42 -21.92 Td
[(b)27(y)]TJ
/T1_6 10.91 Tf
14.06 0 Td
(S)Tj
/T1_4 7.97 Tf
5.72 -1.68 Td
(L)Tj
/T1_0 10.91 Tf
8.81 1.68 Td
(\()Tj
/T1_6 10.91 Tf
(S)Tj
/T1_4 7.97 Tf
9.96 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
3.38 1.63 Td
[(\))-233(in)-234(Phase)-233(2)-234(Round)-233(2.)-412(If)-233(either)]TJ
/T1_6 10.91 Tf
143.89 0 Td
(c)Tj
/T1_3 7.97 Tf
5.72 3.96 Td
(0)Tj
/T1_4 7.97 Tf
0 -7.19 TD
(L)Tj
/T1_0 10.91 Tf
8.81 3.23 Td
(or)Tj
/T1_2 10.91 Tf
12.27 0 Td
(v)Tj
/T1_3 7.97 Tf
5.67 3.96 Td
(0)Tj
/T1_4 7.97 Tf
-0.39 -7.19 Td
(L)Tj
/T1_0 10.91 Tf
8.81 3.23 Td
(\()Tj
/T1_6 10.91 Tf
(c)Tj
/T1_3 7.97 Tf
9.96 3.96 Td
(0)Tj
/T1_4 7.97 Tf
0 -7.01 TD
(i)Tj
/T1_0 10.91 Tf
5.93 3.05 Td
(or)Tj
/T1_2 10.91 Tf
12.27 0 Td
(v)Tj
/T1_3 7.97 Tf
5.68 3.96 Td
(0)Tj
/T1_4 7.97 Tf
-0.39 -7.01 Td
(i)Tj
/T1_0 10.91 Tf
3.38 3.05 Td
[(\))-233(is)-233(not)-234(v)55(alid,)-253(then)]TJ
/T1_6 10.91 Tf
87.23 0 Td
(S)Tj
/T1_4 7.97 Tf
5.73 -1.68 Td
(L)Tj
/T1_0 10.91 Tf
8.8 1.68 Td
(\()Tj
/T1_6 10.91 Tf
(S)Tj
/T1_4 7.97 Tf
9.97 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
3.38 1.63 Td
[(\))-233(rejects)-233(the)-234(in)27(v)56(alid)]TJ
/T1_6 10.91 Tf
-378.65 -21.91 Td
(C)Tj
/T1_0 10.91 Tf
[(.)-429(As)]TJ
/T1_1 10.91 Tf
29.09 0 Td
(A)Tj
/T1_0 10.91 Tf
11.88 0 Td
[(do)-27(es)-290(not)-291(kno)27(w)-289(the)-291(encryption)-290(k)27(ey)]TJ
/T1_2 10.91 Tf
162.38 0 Td
(ek)Tj
/T1_4 7.97 Tf
10.76 -1.69 Td
(L)Tj
/T1_0 10.91 Tf
9.42 1.69 Td
(and)Tj
/T1_2 10.91 Tf
20.74 0 Td
(ek)Tj
/T1_4 7.97 Tf
10.75 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
6.55 1.64 Td
(of)Tj
/T1_6 10.91 Tf
11.95 0 Td
(S)Tj
/T1_4 7.97 Tf
5.73 -1.69 Td
(L)Tj
/T1_0 10.91 Tf
9.42 1.69 Td
(and)Tj
/T1_6 10.91 Tf
20.74 0 Td
(S)Tj
/T1_4 7.97 Tf
5.72 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
6.55 1.64 Td
[(for)-290(1)]TJ
/T1_1 10.91 Tf
24.71 0 Td
(\267)Tj
/T1_2 10.91 Tf
11.51 0 Td
(i)Tj
/T1_1 10.91 Tf
6.78 0 Td
(6)Tj
/T1_0 10.91 Tf
(=)Tj
/T1_2 10.91 Tf
11.52 0 Td
(L)Tj
/T1_1 10.91 Tf
10.45 0 Td
(\267)Tj
/T1_2 10.91 Tf
11.51 0 Td
(n)Tj
/T1_4 7.97 Tf
6.55 -1.64 Td
(c)Tj
/T1_0 10.91 Tf
7.33 1.64 Td
[(resp)-27(ectiv)27(ely)]TJ
-412.04 -21.92 Td
[(and)-332(the)-332(symmetric-k)27(ey)-331(encryption)-332(sc)27(heme)]TJ
/T1_5 10.91 Tf
204.3 0 Td
(SKE)Tj
/T1_0 10.91 Tf
23.76 0 Td
[(is)-332(assumed)-332(to)-332(b)-28(e)-332(secure,)-332(therefore)]TJ
/T1_1 10.91 Tf
164.45 0 Td
(A)Tj
/T1_0 10.91 Tf
12.33 0 Td
[(is)-332(not)-332(able)-332(to)]TJ
-404.84 -21.92 Td
[(pro)-27(duce)-349(v)54(alid)]TJ
/T1_6 10.91 Tf
68.23 0 Td
(c)Tj
/T1_3 7.97 Tf
5.72 3.96 Td
(0)Tj
/T1_4 7.97 Tf
0 -7.19 TD
(L)Tj
/T1_0 10.91 Tf
10.06 3.23 Td
(and)Tj
/T1_6 10.91 Tf
21.38 0 Td
(c)Tj
/T1_3 7.97 Tf
5.72 3.96 Td
(0)Tj
/T1_4 7.97 Tf
0 -7.01 TD
(i)Tj
/T1_0 10.91 Tf
7.19 3.05 Td
[(for)-348(1)]TJ
/T1_1 10.91 Tf
25.62 0 Td
(\267)Tj
/T1_2 10.91 Tf
11.8 0 Td
(i)Tj
/T1_1 10.91 Tf
7.06 0 Td
(6)Tj
/T1_0 10.91 Tf
(=)Tj
/T1_2 10.91 Tf
11.8 0 Td
(L)Tj
/T1_1 10.91 Tf
10.73 0 Td
(\267)Tj
/T1_2 10.91 Tf
11.79 0 Td
(n)Tj
/T1_4 7.97 Tf
6.55 -1.63 Td
(c)Tj
/T1_0 10.91 Tf
7.97 1.63 Td
[(resp)-27(ectiv)27(ely)83(.)]TJ
/T1_1 10.91 Tf
63.31 0 Td
(A)Tj
/T1_0 10.91 Tf
12.51 0 Td
[(also)-348(do)-28(es)-349(not)-349(kno)27(w)-348(the)-348(passw)26(ord)]TJ
/T1_5 10.91 Tf
161.24 0 Td
[(p)27(w)]TJ
/T1_4 7.97 Tf
12.94 -2.61 Td
(L)Tj
/T1_0 10.91 Tf
-461.62 -19.3 Td
(and)Tj
/T1_5 10.91 Tf
20.44 0 Td
[(p)27(w)]TJ
/T1_4 7.97 Tf
12.94 -2.62 Td
(i)Tj
/T1_0 10.91 Tf
6.24 2.62 Td
(of)Tj
/T1_6 10.91 Tf
11.66 0 Td
(S)Tj
/T1_4 7.97 Tf
5.72 -1.69 Td
(L)Tj
/T1_0 10.91 Tf
9.13 1.69 Td
(and)Tj
/T1_6 10.91 Tf
20.44 0 Td
(S)Tj
/T1_4 7.97 Tf
5.72 -1.64 Td
(i)Tj
/T1_0 10.91 Tf
6.25 1.64 Td
[(for)-263(1)]TJ
/T1_1 10.91 Tf
24.41 0 Td
(\267)Tj
/T1_2 10.91 Tf
11.51 0 Td
(i)Tj
/T1_1 10.91 Tf
6.79 0 Td
(6)Tj
/T1_0 10.91 Tf
(=)Tj
/T1_2 10.91 Tf
11.51 0 Td
(L)Tj
/T1_1 10.91 Tf
10.45 0 Td
(\267)Tj
/T1_2 10.91 Tf
11.51 0 Td
(n)Tj
/T1_4 7.97 Tf
6.55 -1.64 Td
(c)Tj
/T1_0 10.91 Tf
7.03 1.64 Td
[(resp)-27(ectiv)26(ely)84(,)-276(therefore)]TJ
/T1_1 10.91 Tf
106.02 0 Td
(A)Tj
/T1_0 10.91 Tf
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(r)Tj
/T1_4 5.98 Tf
4.06 2.81 Td
(0)Tj
/T1_5 5.98 Tf
-0.24 -5.08 Td
(C)Tj
/T1_6 7.97 Tf
3.67 2.27 Td
(H)Tj
/T1_7 5.98 Tf
5.98 -1.1 Td
(2)Tj
/T1_8 7.97 Tf
4.15 1.1 Td
(\()Tj
/T1_2 7.97 Tf
(K)Tj
/T1_4 5.98 Tf
10.99 2.81 Td
(0)Tj
/T1_9 5.98 Tf
-0.56 -5.51 Td
(L)Tj
/T1_8 7.97 Tf
5.56 2.7 Td
(\))Tj
/T1_0 10.91 Tf
7.23 -3.96 Td
(and)Tj
/T1_1 10.91 Tf
21.02 0 Td
(t)Tj
/T1_3 7.97 Tf
3.94 3.96 Td
(0)Tj
/T1_2 7.97 Tf
0 -7.01 TD
(i)Tj
/T1_0 10.91 Tf
6.41 3.05 Td
(=)Tj
/T1_1 10.91 Tf
11.51 0 Td
(g)Tj
/T1_2 7.97 Tf
5.59 3.96 Td
(r)Tj
/T1_4 5.98 Tf
4.06 2.81 Td
(0)Tj
/T1_5 5.98 Tf
-0.24 -5.08 Td
(C)Tj
/T1_6 7.97 Tf
3.68 2.27 Td
(H)Tj
/T1_7 5.98 Tf
5.97 -1.1 Td
(2)Tj
/T1_8 7.97 Tf
4.15 1.1 Td
(\()Tj
/T1_2 7.97 Tf
(K)Tj
/T1_9 5.98 Tf
10.43 -1.21 Td
(i)Tj
/T1_8 7.97 Tf
3.16 1.21 Td
(\))Tj
/T1_0 10.91 Tf
7.24 -3.96 Td
[(resp)-27(ectiv)26(ely)84(.)-438(Therefore,)]TJ
/T1_10 10.91 Tf
115.06 0 Td
(A)Tj
/T1_0 10.91 Tf
12.15 0 Td
[(is)-315(not)]TJ
-441.34 -21.91 Td
[(able)-293(to)-293(compute)-293(the)-293(v)55(alid)-293(ciphertext)-305(^)]TJ
/T1_11 10.91 Tf
174.93 0 Td
(c)Tj
/T1_3 7.97 Tf
5.72 3.96 Td
(0)Tj
/T1_2 7.97 Tf
0 -7.19 TD
(L)Tj
/T1_0 10.91 Tf
9.45 3.23 Td
[(and)-305(^)]TJ
/T1_11 10.91 Tf
20.77 0 Td
(c)Tj
/T1_3 7.97 Tf
5.73 3.96 Td
(0)Tj
/T1_2 7.97 Tf
0 -7.02 TD
(i)Tj
/T1_0 10.91 Tf
6.57 3.06 Td
[(for)-293(1)]TJ
/T1_10 10.91 Tf
24.74 0 Td
(\267)Tj
/T1_1 10.91 Tf
11.51 0 Td
(i)Tj
/T1_10 10.91 Tf
6.79 0 Td
(6)Tj
/T1_0 10.91 Tf
(=)Tj
/T1_1 10.91 Tf
11.51 0 Td
(L)Tj
/T1_10 10.91 Tf
10.45 0 Td
(\267)Tj
/T1_1 10.91 Tf
11.51 0 Td
(n)Tj
/T1_2 7.97 Tf
6.55 -1.64 Td
(c)Tj
/T1_0 10.91 Tf
7.36 1.64 Td
[(as)-293(the)-293(symmetric-k)27(ey)-292(encryption)]TJ
-313.59 -21.92 Td
[(sc)27(heme)]TJ
/T1_12 10.91 Tf
37.74 0 Td
(SKE)Tj
/T1_0 10.91 Tf
24.19 0 Td
[(is)-371(assumed)-372(to)-371(b)-28(e)-371(secure.)-559(F)82(urthermore,)]TJ
/T1_10 10.91 Tf
189.65 0 Td
(A)Tj
/T1_0 10.91 Tf
12.76 0 Td
[(do)-27(es)-372(not)-371(kno)27(w)-371(the)-371(authen)27(tication)-371(k)27(ey)]TJ
/T1_1 10.91 Tf
185.83 0 Td
(ak)Tj
/T1_2 7.97 Tf
11.45 -1.69 Td
(L)Tj
/T1_0 10.91 Tf
-461.62 -20.23 Td
(and)Tj
/T1_1 10.91 Tf
21.3 0 Td
(ak)Tj
/T1_2 7.97 Tf
11.44 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
7.12 1.63 Td
(of)Tj
/T1_11 10.91 Tf
12.51 0 Td
(S)Tj
/T1_2 7.97 Tf
5.73 -1.68 Td
(L)Tj
/T1_0 10.91 Tf
9.99 1.68 Td
(and)Tj
/T1_11 10.91 Tf
21.3 0 Td
(S)Tj
/T1_2 7.97 Tf
5.72 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
7.12 1.63 Td
[(for)-341(1)]TJ
/T1_10 10.91 Tf
25.43 0 Td
(\267)Tj
/T1_1 10.91 Tf
11.67 0 Td
(i)Tj
/T1_10 10.91 Tf
6.94 0 Td
(6)Tj
/T1_0 10.91 Tf
(=)Tj
/T1_1 10.91 Tf
11.68 0 Td
(L)Tj
/T1_10 10.91 Tf
10.61 0 Td
(\267)Tj
/T1_1 10.91 Tf
11.67 0 Td
(n)Tj
/T1_2 7.97 Tf
6.55 -1.63 Td
(c)Tj
/T1_0 10.91 Tf
7.89 1.63 Td
[(resp)-28(ectiv)27(ely)-341(and)-342(the)-342(message)-342(authen)26(tication)-341(co)-27(de)-343(sc)27(heme)]TJ
/T1_12 10.91 Tf
-194.67 -21.91 Td
[(MA)27(CS)]TJ
/T1_0 10.91 Tf
33.29 0 Td
[(is)-344(assumed)-345(to)-345(b)-27(e)-345(secure,)-347(therefore)]TJ
/T1_10 10.91 Tf
165.3 0 Td
(A)Tj
/T1_0 10.91 Tf
12.47 0 Td
[(is)-344(not)-344(able)-345(to)-344(compute)-345(a)-344(v)54(alid)-422(^)]TJ
/T1_1 10.91 Tf
147.23 0 Td
(\271)Tj
/T1_3 7.97 Tf
6.58 3.96 Td
(0)Tj
/T1_2 7.97 Tf
0 -7.19 TD
(L)Tj
/T1_0 10.91 Tf
10.01 3.23 Td
[(and)-423(^)]TJ
/T1_1 10.91 Tf
21.33 0 Td
(\271)Tj
/T1_3 7.97 Tf
6.57 3.96 Td
(0)Tj
/T1_2 7.97 Tf
0 -7.02 TD
(i)Tj
/T1_0 10.91 Tf
7.14 3.06 Td
[(resp)-27(ectiv)27(ely)83(.)]TJ
-409.92 -21.92 Td
(Hence,)Tj
/T1_10 10.91 Tf
35.03 0 Td
(A)Tj
/T1_0 10.91 Tf
11.83 0 Td
[(is)-286(not)-286(able)-287(to)-286(imp)-28(ersonate)]TJ
/T1_11 10.91 Tf
125.74 0 Td
(C)Tj
/T1_0 10.91 Tf
8.84 0 Td
[(in)-286(Phase)-286(2)-287(Round)-286(3.)-429(Therefore,)]TJ
/T1_10 10.91 Tf
151.99 0 Td
(A)Tj
/T1_0 10.91 Tf
11.83 0 Td
[(is)-286(not)-286(able)-286(to)-287(imp)-27(ersonate)]TJ
/T1_11 10.91 Tf
-345.26 -21.91 Td
(C)Tj
/T1_0 10.91 Tf
9.36 0 Td
[(in)-333(the)-333(Lea)27(v)27(e)-332(Proto)-28(col.)]TJ
7.57 -21.92 Td
[(Next)-310(w)27(e)-309(consider)-310(case)-310(\(b\))-310(as)-310(follo)27(ws:)-432(as)-310(the)-310(adv)27(ersary)]TJ
/T1_10 10.91 Tf
259.18 0 Td
(A)Tj
/T1_0 10.91 Tf
12.09 0 Td
[(is)-309(not)-310(a)-310(lea)26(ving)-309(user)]TJ
/T1_11 10.91 Tf
98.25 0 Td
(U)Tj
/T1_2 7.97 Tf
5.72 -1.78 Td
(L;l)Tj
/T1_9 5.98 Tf
10.64 -1.4 Td
(k)Tj
/T1_0 10.91 Tf
8.45 3.18 Td
(\(1)Tj
/T1_10 10.91 Tf
12.72 0 Td
(\267)Tj
/T1_1 10.91 Tf
11.51 0 Td
(k)Tj
/T1_10 10.91 Tf
9.05 0 Td
(\267)Tj
/T1_1 10.91 Tf
11.52 0 Td
(`)Tj
/T1_0 10.91 Tf
4.54 0 Td
(\),)Tj
-460.6 -21.92 Td
(therefore,)Tj
/T1_10 10.91 Tf
50.52 0 Td
(A)Tj
/T1_0 10.91 Tf
13.7 0 Td
[(can)-456(only)-458(obtain)-457(the)-457(public)-457(exc)27(hange)-457(information)-457(in)-457(the)-457(Lea)27(v)27(e)-456(Proto)-28(col.)-816(First)-457(w)27(e)]TJ
-64.22 -21.91 Td
[(consider)-354(if)]TJ
/T1_10 10.91 Tf
52.96 0 Td
(A)Tj
/T1_0 10.91 Tf
12.58 0 Td
[(can)-354(obtain)-354(the)-354(new)-355(subgroup)-354(k)26(ey)]TJ
/T1_1 10.91 Tf
163.55 0 Td
(K)Tj
/T1_3 7.97 Tf
10.04 3.95 Td
(0)Tj
/T1_2 7.97 Tf
-0.78 -7.19 Td
(L)Tj
/T1_0 10.91 Tf
10.12 3.24 Td
[(from)-354(the)-354(public)-355(information)-354(sen)27(t)-354(in)-354(the)-355(Lea)27(v)28(e)]TJ
-248.47 -21.92 Td
[(Proto)-27(col.)-525(But)-360(b)27(y)-359(ignoring)-360(the)-360(authen)27(tication)-359(information)-360(\()-79(^)]TJ
/T1_1 10.91 Tf
284.75 0 Td
(\271)Tj
/T1_3 7.97 Tf
6.57 3.96 Td
(0)Tj
/T1_2 7.97 Tf
0 -7.19 TD
(L;j)Tj
/T1_0 10.91 Tf
16.42 3.23 Td
(and)Tj
/T1_1 10.91 Tf
21.49 0 Td
(\265)Tj
/T1_3 7.97 Tf
5.43 3.96 Td
(0)Tj
/T1_2 7.97 Tf
-0.31 -7.19 Td
(L)Tj
/T1_0 10.91 Tf
6.26 3.23 Td
[(\))-359(sen)26(t,)-365(the)-360(prop)-28(osed)-360(Lea)27(v)27(e)]TJ
-340.61 -21.92 Td
[(proto)-27(col)-225(to)-225(form)-224(the)-225(new)-225(subgroup)-225(k)27(ey)]TJ
/T1_1 10.91 Tf
181.81 0 Td
(K)Tj
/T1_3 7.97 Tf
10.04 3.96 Td
(0)Tj
/T1_2 7.97 Tf
-0.78 -7.19 Td
(L)Tj
/T1_0 10.91 Tf
8.71 3.23 Td
[(is)-224(just)-225(the)-224(EST)82(AR)-224(proto)-27(col)-225(executed)-225(b)27(y)]TJ
/T1_11 10.91 Tf
186.35 0 Td
(S)Tj
/T1_2 7.97 Tf
5.72 -1.69 Td
(L)Tj
/T1_0 10.91 Tf
8.71 1.69 Td
[(and)-224(remaining)]TJ
-400.56 -21.91 Td
(users)Tj
/T1_11 10.91 Tf
27.53 0 Td
(V)Tj
/T1_2 7.97 Tf
5.73 -1.69 Td
(L;j)Tj
/T1_0 10.91 Tf
16.24 1.69 Td
[(for)-343(1)]TJ
/T1_10 10.91 Tf
25.48 0 Td
(\267)Tj
/T1_1 10.91 Tf
11.7 0 Td
(j)Tj
/T1_10 10.91 Tf
8.33 0 Td
(\267)Tj
/T1_1 10.91 Tf
11.7 0 Td
(n)Tj
/T1_2 7.97 Tf
6.55 -1.69 Td
(L)Tj
/T1_10 10.91 Tf
8.76 1.69 Td
(\241)Tj
/T1_1 10.91 Tf
10.98 0 Td
(`)Tj
/T1_0 10.91 Tf
4.54 0 Td
[(,)-346(where)-344(Phase)-344(1)-343(Round)-344(1)-344(together)-344(with)-344(Phase)-343(3)-344(Round)-344(1,)-346(and)-344(Phase)]TJ
-137.54 -21.92 Td
[(3)-326(Round)-326(2)-326(is)-326(just)-326(Round)-326(2)-326(and)-327(Computation)-326(of)-326(Key)-326(of)-326(the)-326(EST)82(AR)-325(proto)-28(col)-326(resp)-28(ectiv)27(ely)-325(\(w)27(e)-326(omit)]TJ
0 -21.92 TD
[(Round)-357(1)-358(of)-357(the)-358(EST)83(AR)-357(proto)-28(col)-357(as)]TJ
/T1_11 10.91 Tf
173.86 0 Td
(V)Tj
/T1_2 7.97 Tf
5.73 -1.68 Td
(L;j)Tj
/T1_0 10.91 Tf
16.39 1.68 Td
[(for)-357(1)]TJ
/T1_10 10.91 Tf
25.87 0 Td
(\267)Tj
/T1_1 10.91 Tf
11.96 0 Td
(j)Tj
/T1_10 10.91 Tf
8.58 0 Td
(\267)Tj
/T1_1 10.91 Tf
11.95 0 Td
(n)Tj
/T1_2 7.97 Tf
6.55 -1.68 Td
(L)Tj
/T1_10 10.91 Tf
8.85 1.68 Td
(\241)Tj
/T1_1 10.91 Tf
11.09 0 Td
(`)Tj
/T1_0 10.91 Tf
8.44 0 Td
(uses)Tj
/T1_1 10.91 Tf
23.41 0 Td
(z)Tj
/T1_3 7.97 Tf
5.55 3.96 Td
(\244)Tj
/T1_2 7.97 Tf
-0.48 -7.19 Td
(L;j)Tj
/T1_0 10.91 Tf
16.39 3.23 Td
(that)Tj
/T1_11 10.91 Tf
23.89 0 Td
(S)Tj
/T1_2 7.97 Tf
5.73 -1.68 Td
(L)Tj
/T1_0 10.91 Tf
10.15 1.68 Td
[(already)-357(kno)26(ws)-356(from)]TJ
-373.91 -21.91 Td
[(previous)-355(GKA\).)-355(By)-355(Theorem)-355(41,)-361(it)-355(is)-355(sho)27(wn)-354(that)-355(the)-356(EST)83(AR)-354(proto)-28(col)-355(is)-355(secure.)-510(Hence,)]TJ
/T1_10 10.91 Tf
428.33 0 Td
(A)Tj
/T1_0 10.91 Tf
12.58 0 Td
[(is)-355(not)]TJ
-440.91 -21.92 Td
[(able)-333(to)-333(obtain)-333(the)-334(new)-333(subgroup)-333(k)26(ey)]TJ
/T1_1 10.91 Tf
178.53 0 Td
(K)Tj
/T1_3 7.97 Tf
10.04 3.96 Td
(0)Tj
/T1_2 7.97 Tf
-0.78 -7.19 Td
(L)Tj
/T1_0 10.91 Tf
9.89 3.23 Td
[(from)-333(the)-333(Lea)27(v)27(e)-332(Proto)-28(col.)]TJ
-180.75 -21.92 Td
[(Next,)-314(w)27(e)-308(consider)-309(if)]TJ
/T1_10 10.91 Tf
97.24 0 Td
(A)Tj
/T1_0 10.91 Tf
12.08 0 Td
[(is)-308(able)-309(to)-309(obtain)-309(the)-309(new)-309(group)-309(k)27(ey)]TJ
/T1_1 10.91 Tf
170.94 0 Td
(K)Tj
/T1_3 7.97 Tf
10.05 3.96 Td
(0)Tj
/T1_0 10.91 Tf
6.16 -3.96 Td
[(from)-309(the)-308(public)-309(information)-309(sen)26(t)]TJ
-313.4 -21.91 Td
[(in)-416(the)-417(Lea)27(v)28(e)-416(Proto)-28(col.)-694(But)-416(b)26(y)-415(ignoring)-417(the)-416(authen)26(tication)-415(information)-417(\()]TJ
/T1_1 10.91 Tf
355.29 0 Td
(\271)Tj
/T1_3 7.97 Tf
6.57 3.96 Td
(0)Tj
/T1_2 7.97 Tf
0 -7.19 TD
(L)Tj
/T1_0 10.91 Tf
6.26 3.23 Td
[(,)-516(\271)]TJ
/T1_1 10.91 Tf
7.8 0 Td
(\271)Tj
/T1_3 7.97 Tf
6.57 3.96 Td
(0)Tj
/T1_2 7.97 Tf
T*
(L)Tj
/T1_0 10.91 Tf
6.25 3.23 Td
[(,)-516(^)]TJ
/T1_1 10.91 Tf
7.8 0 Td
(\271)Tj
/T1_3 7.97 Tf
6.57 3.96 Td
(0)Tj
/T1_2 7.97 Tf
T*
(L)Tj
/T1_0 10.91 Tf
6.26 3.23 Td
[(,)-516(^)]TJ
/T1_1 10.91 Tf
7.8 0 Td
(\271)Tj
/T1_3 7.97 Tf
6.57 3.96 Td
(0)Tj
/T1_2 7.97 Tf
0 -7.02 TD
(i)Tj
/T1_0 10.91 Tf
7.92 3.06 Td
(and)Tj
/T1_1 10.91 Tf
22.12 0 Td
(\265)Tj
/T1_3 7.97 Tf
5.42 3.96 Td
(0)Tj
/T1_5 7.97 Tf
-0.3 -6.66 Td
(C)Tj
/T1_0 10.91 Tf
4.73 2.7 Td
(\))Tj
-463.63 -21.92 Td
[(sen)27(t,)-323(the)-322(prop)-28(osed)-322(Lea)27(v)27(e)-321(proto)-27(col)-323(to)-322(form)-322(the)-322(new)-322(\257nal)-322(group)-322(k)26(ey)]TJ
/T1_1 10.91 Tf
318.26 0 Td
(K)Tj
/T1_3 7.97 Tf
10.04 3.96 Td
(0)Tj
/T1_0 10.91 Tf
6.31 -3.96 Td
[(is)-322(just)-322(the)-322(EST)83(AR)-322(proto)-27(col,)]TJ
-334.61 -21.92 Td
[(where)-310(Phase)-310(2)-310(Round)-311(2)-310(\()]TJ
/T1_11 10.91 Tf
119.71 0 Td
(S)Tj
/T1_2 7.97 Tf
5.72 -1.68 Td
(L)Tj
/T1_0 10.91 Tf
9.64 1.68 Td
[(sends)-310(new)-310(\()]TJ
/T1_1 10.91 Tf
55.36 0 Td
(y)Tj
/T1_3 7.97 Tf
5.74 3.96 Td
(\244)Tj
/T1_2 7.97 Tf
-0.39 -7.19 Td
(L)Tj
/T1_0 10.91 Tf
6.26 3.23 Td
(\))Tj
/T1_3 7.97 Tf
4.24 3.96 Td
(0)Tj
/T1_0 10.91 Tf
6.18 -3.96 Td
(while)Tj
/T1_11 10.91 Tf
28.22 0 Td
(S)Tj
/T1_2 7.97 Tf
5.73 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
6.76 1.63 Td
[(for)-310(1)]TJ
/T1_10 10.91 Tf
24.92 0 Td
(\267)Tj
/T1_1 10.91 Tf
11.52 0 Td
(i)Tj
/T1_10 10.91 Tf
6.78 0 Td
(6)Tj
/T1_0 10.91 Tf
(=)Tj
/T1_1 10.91 Tf
11.52 0 Td
(L)Tj
/T1_10 10.91 Tf
10.45 0 Td
(\267)Tj
/T1_1 10.91 Tf
11.51 0 Td
(n)Tj
/T1_2 7.97 Tf
6.55 -1.63 Td
(c)Tj
/T1_0 10.91 Tf
7.54 1.63 Td
(uses)Tj
/T1_1 10.91 Tf
22.9 0 Td
(y)Tj
/T1_3 7.97 Tf
5.74 3.96 Td
(\244)Tj
/T1_2 7.97 Tf
-0.4 -7.01 Td
(i)Tj
/T1_0 10.91 Tf
8.51 3.05 Td
(that)Tj
/T1_11 10.91 Tf
23.38 0 Td
(C)Tj
/T1_0 10.91 Tf
9.11 0 Td
[(kno)27(ws)-309(from)]TJ
-413.2 -21.91 Td
[(previous)-272(GKA\),)-273(Phase)-272(2)-273(Round)-272(3)-273(and)-272(Phase)-273(3)-272(Round)-273(1)-273(is)-272(just)-273(Round)-272(1,)-285(Round)-272(2)-273(and)-273(Computation)]TJ
0 -21.92 TD
[(of)-380(Key)-381(of)-380(the)-381(EST)83(AR)-380(proto)-28(col.)-586(By)-380(Theorem)-381(41,)-392(it)-380(is)-381(sho)27(wn)-380(that)-380(the)-381(EST)83(AR)-380(proto)-28(col)-380(is)-381(secure.)]TJ
0 -21.91 TD
(Hence,)Tj
/T1_10 10.91 Tf
35.98 0 Td
(A)Tj
/T1_0 10.91 Tf
12.77 0 Td
[(is)-372(not)-373(able)-373(to)-372(obtain)-373(the)-373(new)-372(\257nal)-373(group)-372(k)26(ey)]TJ
/T1_1 10.91 Tf
220.99 0 Td
(K)Tj
/T1_3 7.97 Tf
10.04 3.95 Td
(0)Tj
/T1_0 10.91 Tf
6.86 -3.95 Td
[(in)-372(this)-373(case.)-562(The)-373(new)-372(\257nal)-373(group)-372(k)26(ey)]TJ
/T1_1 10.91 Tf
-286.64 -21.92 Td
(K)Tj
/T1_3 7.97 Tf
10.04 3.96 Td
(0)Tj
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7.23 -3.96 Td
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q 1 0 0 1 80.83 -66.07 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 80.83 -66.07 cm
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0 13.55 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 167.0866 707.8026 Tm
(Ab)Tj
1.0003 0 0 1.0003 72 769.82 Tm
109.603 -62 Td
[(dalla)-333(et)-334(al's)-333([ABCP06])-333(User)]TJ
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 258.05 -66.07 cm
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0 13.55 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 358.1101 707.8026 Tm
(3)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 319.46 -66.07 cm
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S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 405.2533 707.8026 Tm
(4)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 352.32 -66.07 cm
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S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 432.3609 707.8026 Tm
(4\()Tj
/T1_1 10.91 Tf
(n)Tj
/T1_2 10.91 Tf
18.67 0 Td
(\241)Tj
/T1_0 10.91 Tf
10.9 0 Td
(1\))Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 407.47 -66.07 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
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q 1 0 0 1 409.46 -66.07 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 80.83 -66.27 cm
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328.63 0 l
S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 58.41 -79.61 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 60.4 -79.61 cm
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0 13.54 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 140.6692 694.2488 Tm
(I)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 80.83 -79.61 cm
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S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 164.4359 694.2488 Tm
(EKE-D)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 139.29 -79.61 cm
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S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 232.4249 694.2488 Tm
(Con)Tj
1.0003 0 0 1.0003 72 769.82 Tm
179.483 -75.55 Td
[(troller)-332(no)-28(de)]TJ
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 256.06 -79.61 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 258.05 -79.61 cm
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S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 354.8392 694.2488 Tm
(2)Tj
/T1_1 10.91 Tf
(n)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 319.46 -79.61 cm
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S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 405.2533 694.2488 Tm
(2)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 352.32 -79.61 cm
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S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 445.9947 694.2488 Tm
(2)Tj
/T1_1 10.91 Tf
(n)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 407.47 -79.61 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 409.46 -79.61 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
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q 1 0 0 1 139.29 -79.81 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
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q 1 0 0 1 58.41 -93.16 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
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q 1 0 0 1 60.4 -93.16 cm
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S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 138.3986 680.7051 Tm
(K)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 80.83 -93.16 cm
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S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 158.8343 680.7051 Tm
([BLLH06])Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 139.29 -93.16 cm
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S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 243.588 680.7051 Tm
(User)Tj
1.0003 0 0 1.0003 72 769.82 Tm
196.786 -89.09 Td
[(no)-28(des)]TJ
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 256.06 -93.16 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 258.05 -93.16 cm
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0 13.55 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 358.1101 680.7051 Tm
(2)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 319.46 -93.16 cm
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S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 405.2533 680.7051 Tm
(2)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 352.32 -93.16 cm
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0 13.55 l
S
Q
Q
BT
/T1_1 10.91 Tf
1.0003 0 0 1.0003 439.3328 680.7051 Tm
(n)Tj
/T1_0 10.91 Tf
8.97 0 Td
(+)Tj
1.0003 0 0 1.0003 72 769.82 Tm
387.11 -89.09 Td
(1)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 407.47 -93.16 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 409.46 -93.16 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 80.83 -93.36 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
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q 1 0 0 1 58.41 -106.7 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 60.4 -106.7 cm
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S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 138.5486 667.1513 Tm
(A)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 80.83 -106.7 cm
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S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 160.0046 667.1513 Tm
(Prop)Tj
1.0003 0 0 1.0003 72 769.82 Tm
111.491 -102.64 Td
(osed)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 139.29 -106.7 cm
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S
Q
Q
BT
/T1_3 10.91 Tf
1.0003 0 0 1.0003 266.8645 667.1513 Tm
(C)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 256.06 -106.7 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 258.05 -106.7 cm
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0 13.54 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 343.356 667.1513 Tm
(2)Tj
/T1_1 10.91 Tf
(n)Tj
/T1_4 7.97 Tf
12 -1.64 Td
(c)Tj
/T1_0 10.91 Tf
6.59 1.64 Td
(+)Tj
1.0003 0 0 1.0003 72 769.82 Tm
300.78 -102.64 Td
(2)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 319.46 -106.7 cm
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S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 405.2533 667.1513 Tm
(2)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 352.32 -106.7 cm
0 0 m
0 13.54 l
S
Q
Q
BT
/T1_1 10.91 Tf
1.0003 0 0 1.0003 446.6449 667.1513 Tm
(n)Tj
/T1_4 7.97 Tf
6.54 -1.64 Td
(c)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 407.47 -106.7 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 409.46 -106.7 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 139.29 -106.9 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 60.4 -120.25 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 80.83 -120.25 cm
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0 13.55 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 171.7879 653.5975 Tm
(IKA)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 139.29 -120.25 cm
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0 13.55 l
S
Q
Q
BT
/T1_3 10.91 Tf
1.0003 0 0 1.0003 265.1741 653.5975 Tm
(S)Tj
/T1_4 7.97 Tf
5.73 -1.63 Td
(i)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 256.06 -120.25 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 258.05 -120.25 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 343.7561 653.5975 Tm
(2)Tj
/T1_1 10.91 Tf
(n)Tj
/T1_4 7.97 Tf
11.99 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
5.81 1.63 Td
(+)Tj
1.0003 0 0 1.0003 72 769.82 Tm
300.39 -116.19 Td
(5)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 319.46 -120.25 cm
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0 13.55 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 405.2533 653.5975 Tm
(3)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 352.32 -120.25 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_1 10.91 Tf
1.0003 0 0 1.0003 437.6424 653.5975 Tm
(n)Tj
/T1_4 7.97 Tf
6.55 -1.63 Td
(i)Tj
/T1_0 10.91 Tf
5.8 1.63 Td
(+)Tj
1.0003 0 0 1.0003 72 769.82 Tm
388.8 -116.19 Td
(2)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 407.47 -120.25 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 409.46 -120.25 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 60.4 -133.79 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 80.83 -133.79 cm
0 0 m
0 13.54 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 161.8451 640.0537 Tm
(Proto)Tj
1.0003 0 0 1.0003 72 769.82 Tm
116.975 -129.73 Td
(col)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 139.29 -133.79 cm
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S
Q
Q
BT
/T1_3 10.91 Tf
1.0003 0 0 1.0003 262.0532 640.0537 Tm
(U)Tj
/T1_4 7.97 Tf
5.73 -1.64 Td
(i;j)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 256.06 -133.79 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 258.05 -133.79 cm
0 0 m
0 13.54 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 358.1101 640.0537 Tm
(3)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 319.46 -133.79 cm
0 0 m
0 13.54 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 405.2533 640.0537 Tm
(1)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 352.32 -133.79 cm
0 0 m
0 13.54 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 449.2756 640.0537 Tm
(2)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 407.47 -133.79 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 409.46 -133.79 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 58.41 -133.99 cm
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351.05 0 l
S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 58.41 -135.99 cm
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351.05 0 l
S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
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q 1 0 0 1 60.4 -149.73 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 80.83 -149.73 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 164.4359 624.1092 Tm
(EKE-D)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 139.29 -149.73 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 232.4249 624.1092 Tm
(Con)Tj
1.0003 0 0 1.0003 72 769.82 Tm
179.483 -145.67 Td
[(troller)-332(no)-28(de)]TJ
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 256.06 -149.73 cm
0 0 m
0 13.55 l
S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 258.05 -149.73 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_1 10.91 Tf
1.0003 0 0 1.0003 343.376 624.1092 Tm
(n)Tj
/T1_0 10.91 Tf
8.97 0 Td
(+)Tj
1.0003 0 0 1.0003 72 769.82 Tm
291.18 -145.67 Td
(2)Tj
/T1_1 10.91 Tf
(m)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 319.46 -149.73 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 405.2533 624.1092 Tm
(2)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 352.32 -149.73 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_1 10.91 Tf
1.0003 0 0 1.0003 434.5415 624.1092 Tm
(n)Tj
/T1_0 10.91 Tf
8.97 0 Td
(+)Tj
1.0003 0 0 1.0003 72 769.82 Tm
382.32 -145.67 Td
(2)Tj
/T1_1 10.91 Tf
(m)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 407.47 -149.73 cm
0 0 m
0 13.55 l
S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 409.46 -149.73 cm
0 0 m
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 139.29 -149.93 cm
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270.17 0 l
S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 58.41 -163.28 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 60.4 -163.28 cm
0 0 m
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 80.83 -163.28 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 158.8343 610.5654 Tm
([BLLH06])Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 139.29 -163.28 cm
0 0 m
0 13.55 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 223.1823 610.5654 Tm
(Existing)Tj
1.0003 0 0 1.0003 72 769.82 Tm
194.082 -159.21 Td
[(user)-333(no)-28(des)]TJ
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
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Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
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Q
Q
BT
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1.0003 0 0 1.0003 358.1101 610.5654 Tm
(0)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
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Q
Q
BT
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1.0003 0 0 1.0003 405.2533 610.5654 Tm
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ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
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Q
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BT
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(+)Tj
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ET
q
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Q
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q
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Q
Q
BT
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ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
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q
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Q
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BT
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ET
q
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Q
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q
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Q
Q
BT
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ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
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Q
Q
BT
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ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
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S
Q
Q
BT
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(n)Tj
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ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
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q
1.0002747 0 0 1.0002747 72 769.8200073 cm
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q
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Q
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q
1.0002747 0 0 1.0002747 72 769.8200073 cm
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Q
Q
BT
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ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
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Q
Q
BT
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ET
q
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Q
Q
BT
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ET
q
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Q
Q
q
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Q
Q
BT
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ET
q
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Q
Q
BT
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ET
q
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Q
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BT
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ET
q
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Q
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Q
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Q
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BT
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ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
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Q
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BT
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ET
q
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Q
Q
BT
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ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
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Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
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S
Q
Q
BT
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ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
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S
Q
Q
BT
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ET
q
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S
Q
Q
BT
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ET
q
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Q
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Q
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q
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Q
Q
BT
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ET
q
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Q
Q
BT
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ET
q
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Q
Q
BT
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ET
q
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Q
Q
q
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S
Q
Q
BT
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ET
q
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S
Q
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BT
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ET
q
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Q
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BT
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ET
q
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Q
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S
Q
Q
BT
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ET
q
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Q
Q
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S
Q
Q
BT
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ET
q
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S
Q
Q
BT
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ET
q
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Q
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BT
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ET
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Q
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BT
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(J)Tj
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9.759 1.69 Td
[(2)-278(G)]TJ
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ET
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Q
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Q
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BT
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ET
q
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Q
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BT
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ET
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Q
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BT
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S
Q
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BT
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1.0003 0 0 1.0003 239.1868 515.7189 Tm
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(i;j)Tj
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16.69 0 Td
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6.79 0 Td
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(=)Tj
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ET
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Q
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q
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S
Q
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BT
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ET
q
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S
Q
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BT
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ET
q
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S
Q
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BT
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ET
q
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Q
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q
1.0002747 0 0 1.0002747 72 769.8200073 cm
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q 1 0 0 1 409.46 -258.09 cm
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Q
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q
1.0002747 0 0 1.0002747 72 769.8200073 cm
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Q
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q
1.0002747 0 0 1.0002747 72 769.8200073 cm
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Q
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q
1.0002747 0 0 1.0002747 72 769.8200073 cm
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Q
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q
1.0002747 0 0 1.0002747 72 769.8200073 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
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q 1 0 0 1 80.83 -274.03 cm
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S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 164.4359 499.7744 Tm
(EKE-D)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 139.29 -274.03 cm
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S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 232.4249 499.7744 Tm
(Con)Tj
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179.483 -269.97 Td
[(troller)-332(no)-28(de)]TJ
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 256.06 -274.03 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 258.05 -274.03 cm
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0 13.55 l
S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 341.6555 499.7744 Tm
(2\()Tj
/T1_1 10.91 Tf
9.69 0 Td
(n)Tj
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8.97 0 Td
(\241)Tj
/T1_1 10.91 Tf
10.91 0 Td
(`)Tj
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4.54 0 Td
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ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 319.46 -274.03 cm
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S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 405.2533 499.7744 Tm
(2)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 352.32 -274.03 cm
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S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 432.821 499.7744 Tm
(2\()Tj
/T1_1 10.91 Tf
9.69 0 Td
(n)Tj
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8.97 0 Td
(\241)Tj
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10.91 0 Td
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4.54 0 Td
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ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 407.47 -274.03 cm
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Q
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q
1.0002747 0 0 1.0002747 72 769.8200073 cm
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q
1.0002747 0 0 1.0002747 72 769.8200073 cm
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q
1.0002747 0 0 1.0002747 72 769.8200073 cm
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Q
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q
1.0002747 0 0 1.0002747 72 769.8200073 cm
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S
Q
Q
BT
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1.0003 0 0 1.0003 139.2288 486.2306 Tm
(L)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 80.83 -287.57 cm
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S
Q
Q
BT
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1.0003 0 0 1.0003 158.8343 486.2306 Tm
([BLLH06])Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
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S
Q
Q
BT
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1.0003 0 0 1.0003 217.3007 486.2306 Tm
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199.963 -283.51 Td
[(user)-334(no)-27(des)]TJ
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
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Q
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q
1.0002747 0 0 1.0002747 72 769.8200073 cm
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S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 358.1101 486.2306 Tm
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ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 319.46 -287.57 cm
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S
Q
Q
BT
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1.0003 0 0 1.0003 405.2533 486.2306 Tm
(2)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 352.32 -287.57 cm
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S
Q
Q
BT
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1.0003 0 0 1.0003 430.3903 486.2306 Tm
(n)Tj
/T1_2 10.91 Tf
8.97 0 Td
(\241)Tj
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10.91 0 Td
(`)Tj
/T1_0 10.91 Tf
6.97 0 Td
(+)Tj
1.0003 0 0 1.0003 72 769.82 Tm
396.039 -283.51 Td
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ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 407.47 -287.57 cm
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Q
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q
1.0002747 0 0 1.0002747 72 769.8200073 cm
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Q
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q
1.0002747 0 0 1.0002747 72 769.8200073 cm
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Q
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q
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Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
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S
Q
Q
BT
/T1_0 10.91 Tf
1.0003 0 0 1.0003 138.9287 472.6768 Tm
(E)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 80.83 -301.12 cm
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S
Q
Q
BT
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1.0003 0 0 1.0003 160.0046 472.6768 Tm
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(osed)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
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S
Q
Q
BT
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1.0003 0 0 1.0003 266.8645 472.6768 Tm
(C)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 256.06 -301.12 cm
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S
Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
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S
Q
Q
BT
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1.0003 0 0 1.0003 346.0867 472.6768 Tm
(n)Tj
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6.55 -1.63 Td
(c)Tj
/T1_0 10.91 Tf
6.58 1.63 Td
(+)Tj
1.0003 0 0 1.0003 72 769.82 Tm
298.05 -297.06 Td
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ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
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S
Q
Q
BT
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(2)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
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q 1 0 0 1 352.32 -301.12 cm
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S
Q
Q
BT
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1.0003 0 0 1.0003 449.2756 472.6768 Tm
(1)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
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S
Q
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q
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Q
Q
q
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Q
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Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
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S
Q
Q
BT
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(A)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
0.4 w
q 1 0 0 1 80.83 -314.67 cm
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S
Q
Q
BT
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1.0003 0 0 1.0003 168.527 459.133 Tm
(Lea)Tj
1.0003 0 0 1.0003 72 769.82 Tm
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[(v)28(e)]TJ
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
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S
Q
Q
BT
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(L)Tj
ET
q
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0.4 w
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Q
Q
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
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q 1 0 0 1 258.05 -314.67 cm
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S
Q
Q
BT
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1.0003 0 0 1.0003 336.1039 459.133 Tm
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6.54 -1.69 Td
(L)Tj
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8.68 1.69 Td
(\241)Tj
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10.91 0 Td
(`)Tj
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6.97 0 Td
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(5)Tj
ET
q
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q 1 0 0 1 319.46 -314.67 cm
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S
Q
Q
BT
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(2)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
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q 1 0 0 1 352.32 -314.67 cm
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S
Q
Q
BT
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ET
q
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Q
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Q
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Q
Q
q
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S
Q
Q
BT
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(V)Tj
ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
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S
Q
Q
BT
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ET
q
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S
Q
Q
BT
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5.73 -1.63 Td
(i)Tj
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6.4 1.63 Td
(6)Tj
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(=)Tj
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11.52 0 Td
(S)Tj
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ET
q
1.0002747 0 0 1.0002747 72 769.8200073 cm
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Q
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q
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S
Q
Q
BT
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ET
q
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S
Q
Q
BT
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ET
q
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S
Q
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BT
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ET
q
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Q
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BT
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ET
q
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Q
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S
Q
Q
BT
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1.0003 0 0 1.0003 260.6228 432.0354 Tm
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ET
q
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Q
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S
Q
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BT
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ET
q
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S
Q
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BT
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ET
q
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Q
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BT
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ET
q
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Q
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q
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Q
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q
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S
Q
Q
BT
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1.0003 0 0 1.0003 239.0268 418.4817 Tm
(U)Tj
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5.72 -1.63 Td
(i;j)Tj
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13.26 1.63 Td
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16.69 0 Td
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6.78 0 Td
(6)Tj
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(=)Tj
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ET
q
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Q
Q
q
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S
Q
Q
BT
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ET
q
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S
Q
Q
BT
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ET
q
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S
Q
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BT
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ET
q
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Q
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q
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T*
[(ID-based)-316(authen)27(ticated)-315(dynamic)-317(GKA)-316(proto)-28(cols,)-319(namely)-317(Join,)-320(Lea)27(v)28(e,)-319(Merge)-316(and)-316(P)26(arti-)]TJ
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[(tion)-352(Proto)-28(cols.)-502(W)82(e)-351(also)-353(pro)27(vided)-352(an)-352(energy)-353(analysis)-352(b)-28(esides)-353(complexit)27(y)-351(analysis)-353(of)-353(our)]TJ
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[(prop)-27(osed)-406(proto)-28(cols)-405(that)-406(sho)26(ws)-404(that)-406(our)-406(prop)-28(osed)-405(proto)-28(cols)-406(are)-406(more)-406(e\261cien)27(t)-405(and)-405(the)]TJ
T*
[(energy)-333(consumed)-333(b)27(y)-333(no)-27(des)-334(running)-333(our)-333(prop)-28(osed)-333(proto)-28(cols)-334(are)-333(signi\257can)27(tly)-332(lo)26(w)28(er.)]TJ
174.5 -39.37 Td
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T*
[(b)-27(oth)-410(our)-410(prop)-28(osed)-410(GKA)-410(proto)-27(cols)-410(in)-410(Chapter)-410(9)-410(and)-410(10)-410(are)-410(more)-410(energy-e\261cien)27(t)-409(and)]TJ
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T*
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T*
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T*
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[(e\261cien)27(t)-368(and)-370(suitable)-369(than)-370(curren)27(t)-369(GKA)-369(proto)-28(cols)-369(and)-370(therefore)-370(more)-369(suitable)-370(for)-369(het-)]TJ
T*
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T*
[(proto)-27(cols,)-409(namely)-394(Join)-393(and)-394(Lea)27(v)27(e)-392(Proto)-28(col,)-409(that)-394(also)-393(pro)26(vides)-392(protection)-394(against)-394(DoS)]TJ
T*
[(attac)27(ks.)-414(W)82(e)-245(sho)26(w)28(ed)-245(with)-247(the)-246(complexit)26(y)-245(and)-247(energy)-246(analysis)-247(that)-247(our)-246(prop)-28(osed)-246(proto)-28(cols)]TJ
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[(are)-300(more)-301(energy-e\261cien)27(t)-300(and)-301(scalable)-300(for)-301(use)-301(in)-301(heterogeneous)-300(wireless)-301(net)27(w)27(orks)-299(despite)]TJ
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[(pro)27(viding)-332(the)-333(imp)-28(ortan)27(t)-333(feature)-333(of)-333(protection)-334(against)-333(DoS)-333(attac)27(ks.)]TJ
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[(t)27(w)28(o)-305(authen)27(ticated)-306(dynamic)-306(P)27(assw)28(ord-based)-306(GKA)-306(proto)-28(cols,)-311(namely)-306(the)-307(Join)-306(and)-306(Lea)27(v)27(e)]TJ
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[(Proto)-27(col,)-475(that)-447(are)-447(energy-e\261cien)27(t,)-474(scalable)-447(and)-447(also)-447(pro)27(vides)-446(protection)-447(against)-447(DoS)]TJ
T*
[(attac)27(ks)-332(in)-333(wireless)-334(net)27(w)28(orks.)]TJ
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T*
[(despite)-333(pro)27(viding)-332(the)-334(imp)-27(ortan)26(t)-332(feature)-333(of)-334(protection)-333(against)-333(DoS)-334(attac)27(ks.)]TJ
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[(passw)27(ord-based)-455(GKA)-457(proto)-28(cols)-456(in)-457(wireless)-457(net)27(w)28(orks.)-814(W)83(e)-456(prop)-28(osed)-457(an)-456(authen)27(ticated)]TJ
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T*
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T*
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[(of)-403(DoS)-403(attac)27(ks)-402(is)-403(hard)-403(to)-403(prev)27(en)28(t)-402(but)-403(w)26(e)-402(manage)-403(to)-403(design)-403(sev)27(eral)-402(GKA)-403(proto)-28(cols)-403(that)-403(pro)27(vide)]TJ
T*
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[(in)-412(this)-412(thesis)-412(will)-412(pro)27(vide)-411(a)-412(b)-28(etter)-412(understanding)-412(of)-412(constructing)-412(energy-e\261cien)26(t,)-430(authen)26(ticated,)]TJ
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T*
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[(situation)-339(and)-340(compare)-340(the)-340(accuracy)-340(of)-340(the)-340(theoretical)-340(results)-340(with)-340(the)-340(actual)-340(energy)-340(costs)-340(on)-340(user)]TJ
T*
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T*
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