Paper 2011/392

An Efficient Rational Secret Sharing Scheme Based on the Chinese Remainder Theorem (Revised Version)

Yun Zhang, Christophe Tartary, and Huaxiong Wang

Abstract

The design of rational cryptographic protocols is a recently created research area at the intersection of cryptography and game theory. At TCC'10, Fuchsbauer \emph{et al.} introduced two equilibrium notions (computational version of strict Nash equilibrium and stability with respect to trembles) offering a computational relaxation of traditional game theory equilibria. Using trapdoor permutations, they constructed a rational $t$-out-of $n$ sharing technique satisfying these new security models. Their construction only requires standard communication networks but the share bitsize is $2 n |s| + O(k)$ for security against a single deviation and raises to $(n-t+1)\cdot (2n|s|+O(k))$ to achieve $(t-1)$-resilience where $k$ is a security parameter. In this paper, we propose a new protocol for rational $t$-out-of $n$ secret sharing scheme based on the Chinese reminder 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 with share bitsize $O(k)$. Our protocol does not rely on simultaneous channel. Instead, it only requires synchronous broadcast channel and synchronous pairwise private channels.