Please use this identifier to cite or link to this item: https://hdl.handle.net/10356/48667
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: http://hdl.handle.net/10356/48667
Fulltext Permission: open
Fulltext Availability: With Fulltext
Appears in Collections:SPMS Theses

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