Please use this identifier to cite or link to this item: https://hdl.handle.net/10356/86844
Title: On The Secrecy Gain Of Extremal Even l-modular Lattices
Authors: Oggier, Frédérique
Belfiore, Jean-Claude
Keywords: Lattices
Secrecy Gain
Issue Date: 2018
Source: Oggier, F., & Belfiore, J.-C. (2018). On The Secrecy Gain Of Extremal Even l-modular Lattices. Experimental Mathematics, in press.
Series/Report no.: Experimental Mathematics
Abstract: The secrecy gain is a lattice invariant that appears in the context of wiretap lattice coding. It has been studied for unimodular lattices, for 2 −, 3 −, and 5 −modular lattices. This paper studies the secrecy gain for extremal even l-modular lattices, for l ∈ {2, 3, 5, 6, 7, 11, 14, 15, 23}. We compute the highest secrecy gains as a function of the lattice dimension and the lattice level l. We show in particular that l = 2, 3, 6, 7, 11 are best for the respective ranges of dimensions {80, 76, 72}, {68, 64, 60, 56, 52, 48}, {44, 40, 36}, {34, 32, 30, 28, 26, 24, 22}, {18, 16, 14, 12, 10, 8}. This suggests that within a range of dimensions where different levels exist, the highest value of l tends to give the best secrecy gain. A lower bound computation on the maximal secrecy gain further shows that extremal lattices provide secrecy gains which are very close to this lower bound, thus confirming the good behavior of this class of lattices with respect to the secrecy gain.
URI: https://hdl.handle.net/10356/86844
http://hdl.handle.net/10220/44358
ISSN: 1058-6458
DOI: 10.1080/10586458.2017.1423249
Rights: © 2018 Taylor & Francis. This is the author created version of a work that has been peer reviewed and accepted for publication by Experimental Mathematics, Taylor & Francis. It incorporates referee’s comments but changes resulting from the publishing process, such as copyediting, structural formatting, may not be reflected in this document. The published version is available at: [http://dx.doi.org/10.1080/10586458.2017.1423249].
Fulltext Permission: open
Fulltext Availability: With Fulltext
Appears in Collections:SPMS Journal Articles

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