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|Title:||Rational secret sharing||Authors:||Zhang, Yun||Keywords:||DRNTU::Science::Mathematics::Discrete mathematics::Cryptography||Issue Date:||2012||Source:||Zhang, Y. (2012). Rational secret sharing. Doctoral thesis, Nanyang Technological University, Singapore.||Abstract:||This thesis contains three main contributions as follows. First, we propose an information theoretically secure $t$-out-of-$n$ rational secret sharing scheme based on symmetric bivariate polynomials, which induces a Nash equilibrium surviving the iterated elimination of weakly dominated strategies. Second, we propose an efficient protocol for rational $t$-out-of-$n$ secret sharing based on the Chinese Remainder Theorem. Under some computational assumptions related to the discrete logarithm problem and RSA, this construction leads to a $(t-1)$-resilient computational strict Nash equilibrium that is stable with respect to trembles. Finally, we give transformations from any (classical) linear secret sharing scheme to a rational secret sharing scheme with a mediator. The rational secret sharing scheme obtained induces a Nash equilibrium surviving iterated deletion of weakly dominated strategies with resilience to any subset in the adversary structure, relies on no cryptographic assumption and provides information-theoretic security.||URI:||https://hdl.handle.net/10356/48667||DOI:||10.32657/10356/48667||Fulltext Permission:||open||Fulltext Availability:||With Fulltext|
|Appears in Collections:||SPMS Theses|
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