Paper 2011/392

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

Yun Zhang, Christophe Tartary, and Huaxiong Wang


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.

Available format(s)
Cryptographic protocols
Publication info
Published elsewhere. the original version has been published by ACISP 2011 and here we make some modifications
rational cryptographycomputational strict Nash equilibriumstability with respect to tremblesAsmuth-Bloom sharing
Contact author(s)
zhan0233 @ e ntu edu sg
2011-07-20: received
Short URL
Creative Commons Attribution


      author = {Yun Zhang and Christophe Tartary and Huaxiong Wang},
      title = {An Efficient Rational Secret Sharing Scheme Based on the Chinese Remainder Theorem (Revised Version)},
      howpublished = {Cryptology ePrint Archive, Paper 2011/392},
      year = {2011},
      note = {\url{}},
      url = {}
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