An efficient rational secret sharing scheme based on the Chinese remainder theorem

Yun Zhang*, Christophe Tartary, Huaxiong Wang

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapter

3 Citations (Scopus)

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 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)•(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.

Original languageEnglish
Title of host publicationInformation Security and Privacy
Subtitle of host publication16th Australasian Conference, ACISP 2011, Melbourne, Australia, July 11-13, 2011. Proceedings
EditorsUdaya Parampalli, Philip Hawkes
Place of PublicationHeidelberg
PublisherSpringer, Springer Nature
Pages259-275
Number of pages17
ISBN (Electronic)9783642224973
ISBN (Print)9783642224966
DOIs
Publication statusPublished - 2011
Event16th Australasian Conference on Information Security and Privacy, ACISP 2011 - Melbourne, VIC, Australia
Duration: 11 Jul 201113 Jul 2011

Publication series

NameLecture Notes in Computer Science
PublisherSpringer Berlin Heidelberg
Volume6812
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other16th Australasian Conference on Information Security and Privacy, ACISP 2011
CountryAustralia
CityMelbourne, VIC
Period11/07/1113/07/11

Keywords

  • Asmuth-Bloom sharing scheme
  • computational strict Nash equilibrium
  • rational cryptography
  • stability with respect to trembles

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