Rational secret sharing

• Main Author: Zhang, Yun
• Other Authors: Wang Huaxiong
• Format: Theses and Dissertations
• Language: English
• Published: 2012
• Subjects: DRNTU::Science::Mathematics::Discrete mathematics::Cryptography
• Online Access: https://hdl.handle.net/10356/48667
• Institution: Nanyang Technological University

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.