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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].

References

  1. Abraham, I., Dolev, D., Gonen, R., Halpern, J.Y.: Distributed computing meets game theory: robust mechanisms for rational secret sharing and multiparty computation. In: PODC 2006, pp. 53–62 (2006)

    Google Scholar 

  2. Aiyer, A.S., Alvisi, L., Clement, A., Dahlin, M., Martin, J.-P., Porth, C.: Bar fault tolerance for cooperative services. In: SOSP, pp. 45–58 (2005)

    Google Scholar 

  3. Babaioff, M., Lavi, R., Pavlov, E.: Mechanism design for single-value domains. In: Proc. Nat. Conf. on Artificial Intelligence, AAAI 2005 (2005)

    Google Scholar 

  4. Basu, K., Weibull, J.W.: Strategy subsets closed under rational behavior. Economics Letters 36, 141–146 (1991)

    MathSciNet  CrossRef  MATH  Google Scholar 

  5. Ben-Or, M., Goldwasser, S., Wigderson, A.: Completeness theorems for non-cryptographic fault-tolerant distributed computation (extended abstract). In: STOC 1988, pp. 1–10 (1988)

    Google Scholar 

  6. Blakely, G.: Safeguarding cryptographic keys. In: AFIPS, vol. 48, p. 313 (1979)

    Google Scholar 

  7. Boneh, D., Naor, M.: Timed commitments. In: Bellare, M. (ed.) CRYPTO 2000. LNCS, vol. 1880, pp. 236–254. Springer, Heidelberg (2000)

    CrossRef  Google Scholar 

  8. Chaum, D., Crépeau, C., Damgård, I.: Multiparty unconditionally secure protocols (extended abstract). In: STOC 1988, pp. 11–19 (1988)

    Google Scholar 

  9. Chor, B., Goldwasser, S., Micali, S., Awerbuch, B.: Verifiable secret sharing and achieving simultaneity in the presence of faults (extended abstract). In: FOCS, pp. 383–395. IEEE, Los Alamitos (1985)

    Google Scholar 

  10. Cleve, R.: Limits on the security of coin flips when half the processors are faulty (extended abstract). In: STOC, pp. 364–369. ACM, New York (1986)

    Google Scholar 

  11. Davis, G.B., Sandholm, T.W.: Algorithms for Rationalizability and CURB Sets. In: AAAI 2006 (2006)

    Google Scholar 

  12. Even, S., Goldreich, O., Lempel, A.: A randomized protocol for signing contracts. Commun. ACM 28(6), 637–647 (1985)

    MathSciNet  CrossRef  MATH  Google Scholar 

  13. Feigenbaum, J., Papadimitriou, C., Sami, R., Shenker, S.: A BGP-based mechanism for lowest-cost routing. In: PODC, pp. 173–182 (2002)

    Google Scholar 

  14. Feigenbaum, J., Papadimitriou, C.H., Shenker, S.: Sharing the cost of multicast transmissions. Journal of Computer and System Sciences 63, 21–41 (2001)

    MathSciNet  CrossRef  MATH  Google Scholar 

  15. Feigenbaum, J., Shenker, S.: Distributed Algorithmic Mechanism Design: Recent Results and Future Directions. In: Proc. 6th Int’l Workshop on Discrete Algorithms and Methods for Mobile Computing and Communications, pp. 1–13 (2002)

    Google Scholar 

  16. Fuchsbauer, G., Katz, J., Levieil, E., Naccache, D.: Efficient rational secret sharing in the standard communication model. Cryptology ePrint Archive, Report 2008/488 (2008), http://eprint.iacr.org/

  17. Garay, J.A., Jakobsson, M.: Timed release of standard digital signatures. In: Proc. Financial Cryptography 2002, pp. 168–182 (2002)

    Google Scholar 

  18. Goldreich, O., Micali, S., Wigderson, A.: How to play any mental game or a completeness theorem for protocols with honest majority. In: STOC, pp. 218–229. ACM, New York (1987)

    Google Scholar 

  19. Gordon, S.D., Katz, J.: Rational secret sharing, revisited. In: De Prisco, R., Yung, M. (eds.) SCN 2006. LNCS, vol. 4116, pp. 229–241. Springer, Heidelberg (2006)

    CrossRef  Google Scholar 

  20. Halpern, J.Y., Teague, V.: Rational secret sharing and multiparty computation: extended abstract. In: Babai, L. (ed.) STOC, pp. 623–632. ACM, New York (2004)

    Google Scholar 

  21. Izmalkov, S., Micali, S., Lepinski, M.: Rational secure computation and ideal mechanism design. In: FOCS, pp. 585–595. IEEE Computer Society, Los Alamitos (2005)

    Google Scholar 

  22. Kalai, E.: Large robust games. Econometrica 72(6), 1631–1665 (2004)

    MathSciNet  CrossRef  MATH  Google Scholar 

  23. Katz, J.: Bridging game theory and cryptography: Recent results and future directions. In: Canetti, R. (ed.) TCC 2008. LNCS, vol. 4948, pp. 251–272. Springer, Heidelberg (2008)

    CrossRef  Google Scholar 

  24. Kol, G., Naor, M.: Cryptography and game theory: Designing protocols for exchanging information. In: Canetti, R. (ed.) TCC 2008. LNCS, vol. 4948, pp. 320–339. Springer, Heidelberg (2008)

    CrossRef  Google Scholar 

  25. Kol, G., Naor, M.: Games for exchanging information. In: STOC, pp. 423–432. ACM, New York (2008)

    Google Scholar 

  26. Lavi, R., Nisan, N.: Online ascending auctions for gradually expiring goods. In: SODA 2005 (2005)

    Google Scholar 

  27. Lehmann, D., O’Callaghan, L.I., Shoham, Y.: Truth revelation in approximately efficient combinatorial auctions. Journal of the ACM 49(5)

    Google Scholar 

  28. Lepinski, M., Micali, S., Peikert, C., Shelat, A.: Completely fair sfe and coalition-safe cheap talk. In: PODC 2004, pp. 1–10 (2004)

    Google Scholar 

  29. Lepinski, M., Micali, S., Shelat, A.: Collusion-free protocols. In: Gabow, H.N., Fagin, R. (eds.) STOC, pp. 543–552. ACM, New York (2005)

    Google Scholar 

  30. Lysyanskaya, A., Triandopoulos, N.: Rationality and adversarial behavior in multi-party computation. In: Dwork, C. (ed.) CRYPTO 2006. LNCS, vol. 4117, pp. 180–197. Springer, Heidelberg (2006)

    CrossRef  Google Scholar 

  31. McGrew, R., Porter, R., Shoham, Y.: Towards a general theory of non-cooperative computation. In: TARK, pp. 59–71 (2003)

    Google Scholar 

  32. Nisan, N., Ronen, A.: Algorithmic mechanism design. Games and Economic Behavior 35, 166–196 (2001)

    MathSciNet  CrossRef  MATH  Google Scholar 

  33. O’Neill, A., Sangwan, A.: Honesty, rationality, and malice in secret sharing and MPC: Robust protocols for real-world populations (manuscript, 2008)

    Google Scholar 

  34. Ong, S.J., Parkes, D., Rosen, A., Vadhan, S.: Fairness with an honest minority and a rational majority (April 2007), http://eecs.harvard.edu/~salil/Fairness-abs.html

  35. Ong, S.J., Parkes, D., Rosen, A., Vadhan, S.: Fairness with an honest minority and a rational majority. Cryptology ePrint Archive, Report 2008/097 (March 2008), http://eprint.iacr.org/

  36. Parkes, D.C., Shneidman, J.: Distributed implementations of Vickrey-Clarke-Groves mechanisms. In: Proc. 3rd AAMAS, pp. 261–268 (2004)

    Google Scholar 

  37. Petcu, A., Faltings, B., Parkes, D.: M-dpop: Faithful distributed implementation of efficient social choice problems. In: AAMAS 2006, pp. 1397–1404 (May 2006)

    Google Scholar 

  38. Pinkas, B.: Fair secure two-party computation. In: Biham, E. (ed.) EUROCRYPT 2003. LNCS, vol. 2656, pp. 87–105. Springer, Heidelberg (2003)

    CrossRef  Google Scholar 

  39. Rabin, T., Ben-Or, M.: Verifiable secret sharing and multiparty protocols with honest majority (extended abstract). In: STOC, pp. 73–85. ACM, New York (1989)

    Google Scholar 

  40. Selten, R.: A reexamination of the perfectness concept for equilibrium points in extensive games. International Journal of Game Theory 4, 25–55 (1975)

    MathSciNet  CrossRef  MATH  Google Scholar 

  41. Shamir, A.: How to share a secret. Commun. ACM 22(11), 612–613 (1979)

    MathSciNet  CrossRef  MATH  Google Scholar 

  42. Shneidman, J., Parkes, D.C.: Specification faithfulness in networks with rational nodes. In: PODC 2004, St. John’s, Canada (2004)

    Google Scholar 

  43. Shoham, Y., Tennenholtz, M.: Non-cooperative computation: Boolean functions with correctness and exclusivity. Theor. Comput. Sci. 343(1-2), 97–113 (2005)

    MathSciNet  CrossRef  MATH  Google Scholar 

  44. Wegman, M.N., Carter, L.: New hash functions and their use in authentication and set equality. J. Comput. Syst. Sci. 22(3), 265–279 (1981)

    MathSciNet  CrossRef  MATH  Google Scholar 

  45. Yao, A.C.-C.: How to generate and exchange secrets (extended abstract). In: FOCS, pp. 162–167. IEEE, Los Alamitos (1986)

    Google Scholar 

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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

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-00456-8

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