An efficient and information theoretically secure rational secret sharing scheme based on symmetric bivariate polynomials

Christophe Tartary*, Huaxiong Wang, Yun Zhang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

Abstract

The design of rational cryptographic protocols is a recently created research area at the intersection of cryptography and game theory. In this paper, we propose a new m-out-of-n rational secret sharing scheme requiring neither the involvement of the dealer (except during the initial share distribution) nor a trusted mediator. Our protocol leads to a Nash equilibrium surviving the iterated deletion of weakly dominated strategies for m ≥ 4. Our construction is information theoretically secure and it is immune against backward induction attacks. Contrary to Kol and Naor who used a specific cryptographic primitive in their TCC'08 paper (namely, meaningful/meaningless encryption), the immunity of our scheme is based on the use of bivariate polynomials and one-time pads. To the best of our knowledge, it is the first time that such polynomials have been used for rational secret sharing. Our scheme is efficient and does not require any physical assumptions such as envelopes or ballot boxes. As most of existing rational protocols, our construction requires simultaneous broadcast channels. However, our proposed scheme does not require any computational assumption and it provides information theoretical security.

Original languageEnglish
Pages (from-to)1395-1416
Number of pages22
JournalInternational Journal of Foundations of Computer Science
Volume22
Issue number6
DOIs
Publication statusPublished - Sep 2011

Keywords

  • bivariate polynomial
  • information theoretical security
  • rational cryptography
  • Secret sharing scheme

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