Protocols for Multiparty Coin Toss with Dishonest Majority

  • Amos Beimel
  • Eran Omri
  • Ilan Orlov
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6223)


Coin-tossing protocols are protocols that generate a random bit with uniform distribution. These protocols are used as a building block in many cryptographic protocols. Cleve [STOC 1986] has shown that if at least half of the parties can be malicious, then, in any Open image in new window -round coin-tossing protocol, the malicious parties can cause a bias of Open image in new window to the bit that the honest parties output. However, for more than two decades the best known protocols had bias Open image in new window , where Open image in new window is the number of corrupted parties. Recently, in a surprising result, Moran, Naor, and Segev [TCC 2009] have shown that there is an Open image in new window -round two-party coin-tossing protocol with the optimal bias of Open image in new window . We extend Moran et al. results to the multiparty model when less than 2/3 of the parties are malicious. The bias of our protocol is proportional to Open image in new window and depends on the gap between the number of malicious parties and the number of honest parties in the protocol. Specifically, for a constant number of parties or when the number of malicious parties is somewhat larger than half, we present an Open image in new window -round Open image in new window -party coin-tossing protocol with optimal bias of Open image in new window .


Secret Sharing Premature Termination Active Party Honest Party Secure Multiparty Computation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Aumann, Y., Lindell, Y.: Security against covert adversaries: Efficient protocols for realistic adversaries. In: Vadhan, S.P. (ed.) TCC 2007. LNCS, vol. 4392, pp. 137–156. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  2. 2.
    Averbuch, B., Blum, M., Chor, B., Goldwasser, S., Micali, S.: How to implement Bracha’s O(logn) Byzantine agreement algorithm (1985) (unpublished manuscript)Google Scholar
  3. 3.
    Blum, M.: Coin flipping by telephone a protocol for solving impossible problems. SIGACT News 15(1), 23–27 (1983)CrossRefGoogle Scholar
  4. 4.
    Blum, M., Micali, S.: How to generate cryptographically strong sequences of pseudo-random bits. SIAM J. on Computing 13, 850–864 (1984)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Canetti, R.: Security and composition of multiparty cryptographic protocols. J. of Cryptology 13(1), 143–202 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Cleve, R.: Limits on the security of coin flips when half the processors are faulty. In: Proc. of the 18th STOC, pp. 364–369 (1986)Google Scholar
  7. 7.
    Cleve, R., Impagliazzo, R.: Martingales, collective coin flipping and discrete control processes (1993) (manuscript)Google Scholar
  8. 8.
    Goldreich, O.: Foundations of Cryptography, Voume II Basic Applications. Cambridge University Press, Cambridge (2004)Google Scholar
  9. 9.
    Gordon, D., Katz, J.: Partial fairness in secure two-party computation. Cryptology ePrint Archive, Report 2008/206 (2008),
  10. 10.
    Katz, J.: On achieving the “best of both worlds” in secure multiparty computation. In: Proc. of the 39th STOC, pp. 11–20. ACM Press, New York (2007)Google Scholar
  11. 11.
    Lindell, Y.: Parallel coin-tossing and constant-round secure two-party computation. J. of Cryptology 16(3), 143–184 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Moran, T., Naor, M., Segev, G.: An optimally fair coin toss. In: Reingold, O. (ed.) TCC 2009. LNCS, vol. 5444, pp. 1–18. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  13. 13.
    Pass, R.: Bounded-concurrent secure multi-party computation with a dishonest majority. In: Proc. of the 36th STOC, pp. 232–241 (2004)Google Scholar
  14. 14.
    Rabin, T., Ben-Or, M.: Verifiable secret sharing and multiparty protocols with honest majority. In: Proc. of the 21st STOC, pp. 73–85 (1989)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Amos Beimel
    • 1
  • Eran Omri
    • 2
  • Ilan Orlov
    • 1
  1. 1.Dept. of Computer ScienceBen Gurion UniversityBe’er ShevaIsrael
  2. 2.Dept. of Computer ScienceBar Ilan UniversityRamat GanIsrael

Personalised recommendations