Fairness with an Honest Minority and a Rational Majority

  • Authors:
  • Shien Jin Ong;David C. Parkes;Alon Rosen;Salil Vadhan

  • Affiliations:
  • Goldman, Sachs & Co., New York, NY,;Harvard School of Engineering and Applied Sciences, Cambridge,;Herzliya Interdisciplinary Center, Herzliya, Israel;Harvard School of Engineering and Applied Sciences and, Center for Research on Computation and Society, Cambridge,

  • Venue:
  • TCC '09 Proceedings of the 6th Theory of Cryptography Conference on Theory of Cryptography
  • Year:
  • 2009

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Abstract

We provide a simple protocol for secret reconstruction in any threshold secret sharing scheme, and prove that it is fair when executed with many rational parties together with a small minority of honest parties. That is, all parties will learn the secret with high probability when the honest parties follow the protocol and the rational parties act in their own self-interest (as captured by a set-Nash analogue of trembling hand perfect equilibrium). The protocol only requires a standard (synchronous) broadcast channel, tolerates both early stopping and incorrectly computed messages, and only requires 2 rounds of communication. Previous protocols for this problem in the cryptographic or economic models have either required an honest majority, used strong communication channels that enable simultaneous exchange of information, or settled for approximate notions of security/equilibria. They all also required a nonconstant number of rounds of communication.