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Theory of Cryptography Conference

TCC 2009: Theory of Cryptography pp 36–53Cite as

Fairness with an Honest Minority and a Rational Majority

  • Conference paper

Part of the Lecture Notes in Computer Science book series (LNSC,volume 5444)

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.

Keywords

  • game theory
  • fairness
  • secret sharing

The original version of the book was revised: The copyright line was incorrect. The Erratum to the book is available at DOI: 10.1007/978-3-642-00457-5_36

Earlier versions of this paper are [34,35].

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Author information

Authors and Affiliations

  1. Goldman, Sachs & Co., New York, NY

    Shien Jin Ong

  2. Harvard School of Engineering and Applied Sciences, Cambridge, MA

    David C. Parkes

  3. Herzliya Interdisciplinary Center, Herzliya, Israel

    Alon Rosen

  4. Harvard School of Engineering and Applied Sciences and, Center for Research on Computation and Society, Cambridge, MA

    Salil Vadhan

Authors
  1. Shien Jin Ong
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  2. David C. Parkes
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  3. Alon Rosen
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  4. Salil Vadhan
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Editor information

Editors and Affiliations

  1. Faculty of Mathematics and Computer Science, The Weizmann Institute of Science, 76100, Rehovot, Israel

    Omer Reingold

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© 2009 Springer-Verlag Berlin Heidelberg

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Ong, S.J., Parkes, D.C., Rosen, A., Vadhan, S. (2009). Fairness with an Honest Minority and a Rational Majority. In: Reingold, O. (eds) Theory of Cryptography. TCC 2009. Lecture Notes in Computer Science, vol 5444. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00457-5_3

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  • DOI: https://doi.org/10.1007/978-3-642-00457-5_3

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