Partial Fairness in Secure Two-Party Computation

  • S. Dov Gordon
  • Jonathan Katz
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6110)

Abstract

A seminal result of Cleve (STOC ’86) is that complete fairness is impossible to achieve in two-party computation. In light of this, various techniques for obtaining partial fairness have been suggested in the literature. We propose a definition of partial fairness within the standard real-/ideal-world paradigm that addresses deficiencies of prior definitions. We also show broad feasibility results with respect to our definition: partial fairness is possible for any (randomized) functionality f:X ×YZ1 ×Z2 at least one of whose domains or ranges is polynomial in size. Our protocols are always private, and when one of the domains has polynomial size our protocols also simultaneously achieve the usual notion of security with abort. In contrast to some prior work, we rely on standard assumptions only.

We also show that, as far as general feasibility is concerned, our results are optimal (with respect to our definition).

References

  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.
    Beaver, D.: Foundations of secure interactive computing. In: Feigenbaum, J. (ed.) CRYPTO 1991. LNCS, vol. 576, pp. 377–391. Springer, Heidelberg (1992)Google Scholar
  3. 3.
    Beaver, D., Goldwasser, S.: Multiparty computation with faulty majority. In: 30th Annual Symposium on Foundations of Computer Science (FOCS), pp. 468–473. IEEE, Los Alamitos (1989)CrossRefGoogle Scholar
  4. 4.
    Ben-Or, M., Goldreich, O., Micali, S., Rivest, R.: A fair protocol for signing contracts. IEEE Trans. Information Theory 36(1), 40–46 (1990)CrossRefGoogle Scholar
  5. 5.
    Blum, M.: How to exchange (secret) keys. ACM Transactions on Computer Systems 1, 175–193 (1984)CrossRefGoogle Scholar
  6. 6.
    Boneh, D., Naor, M.: Timed commitments. In: Bellare, M. (ed.) CRYPTO 2000. LNCS, vol. 1880, pp. 236–254. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  7. 7.
    Cachin, C., Camenisch, J.: Optimistic fair secure computation. In: Bellare, M. (ed.) CRYPTO 2000. LNCS, vol. 1880, pp. 93–111. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  8. 8.
    Canetti, R.: Security and composition of multiparty cryptographic protocols. Journal of Cryptology 13(1), 143–202 (2000)MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Canetti, R.: Universally composable security: A new paradigm for cryptographic protocols. In: 42nd Annual Symposium on Foundations of Computer Science (FOCS), pp. 136–145. IEEE, Los Alamitos (2001)Google Scholar
  10. 10.
    Cleve, R.: Limits on the security of coin flips when half the processors are faulty. In: 18th Annual ACM Symposium on Theory of Computing (STOC), pp. 364–369. ACM Press, New York (1986)Google Scholar
  11. 11.
    Cleve, R.: Controlled gradual disclosure schemes for random bits and their applications. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 573–588. Springer, Heidelberg (1990)Google Scholar
  12. 12.
    Damgård, I.: Practical and provably secure release of a secret and exchange of signatures. Journal of Cryptology 8(4), 201–222 (1995)MATHCrossRefGoogle Scholar
  13. 13.
    Dwork, C., Naor, M., Sahai, A.: Concurrent zero-knowledge. Journal of the ACM 51(6), 851–898 (2004)MATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Even, S., Goldreich, O., Lempel, A.: A randomized protocol for signing contracts. Comm. ACM 28(6), 637–647 (1985)CrossRefMathSciNetGoogle Scholar
  15. 15.
    Franklin, M.: Complexity and Security of Distributed Protocols. PhD thesis, Columbia University (1993)Google Scholar
  16. 16.
    Galil, Z., Haber, S., Yung, M.: Cryptographic computation: Secure faut-tolerant protocols and the public-key model. In: Pomerance, C. (ed.) CRYPTO 1987. LNCS, vol. 293, pp. 135–155. Springer, Heidelberg (1988)Google Scholar
  17. 17.
    Garay, J.A., MacKenzie, P.D., Prabhakaran, M., Yang, K.: Resource fairness and composability of cryptographic protocols. In: Halevi, S., Rabin, T. (eds.) TCC 2006. LNCS, vol. 3876, pp. 404–428. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  18. 18.
    Goldreich, O.: Foundations of Cryptography. Basic Applications, vol. 2. Cambridge University Press, Cambridge (2004)Google Scholar
  19. 19.
    Goldreich, O., Lindell, Y.: Session-key generation using human passwords only. Journal of Cryptology 19(3), 241–340 (2006)MATHCrossRefMathSciNetGoogle Scholar
  20. 20.
    Goldwasser, S., Levin, L.A.: Fair computation of general functions in presence of immoral majority. In: Menezes, A., Vanstone, S.A. (eds.) CRYPTO 1990. LNCS, vol. 537, pp. 77–93. Springer, Heidelberg (1991)Google Scholar
  21. 21.
    Gordon, S.D., Katz, J.: Complete fairness in multi-party computation without an honest majority. In: Reingold, O. (ed.) TCC 2009. LNCS, vol. 5444, pp. 19–35. Springer, Heidelberg (2009)Google Scholar
  22. 22.
    Gordon, S.D., Hazay, C., Katz, J., Lindell, Y.: Complete fairness in secure two-party computation. In: 40th Annual ACM Symposium on Theory of Computing (STOC), pp. 413–422. ACM Press, New York (2008)Google Scholar
  23. 23.
    Katz, J.: On achieving the “best of both worlds” in secure multiparty computation. In: 39th Annual ACM Symposium on Theory of Computing (STOC), pp. 11–20. ACM Press, New York (2007)Google Scholar
  24. 24.
    Lepinski, M., Micali, S., Peikert, C., Shelat, A.: Completely fair SFE and coalition-safe cheap talk. In: 23rd ACM Symposium Annual on Principles of Distributed Computing, pp. 1–10. ACM Press, New York (2004)Google Scholar
  25. 25.
    Luby, M., Micali, S., Rackoff, C.: How to simultaneously exchange a secret bit by flipping a symmetrically-biased coin. In: 24th Annual Symposium on Foundations of Computer Science (FOCS), pp. 23–30. IEEE, Los Alamitos (1983)Google Scholar
  26. 26.
    Micali, S., Rogaway, P.: Secure computation. In: Feigenbaum, J. (ed.) CRYPTO 1991. LNCS, vol. 576, pp. 392–404. Springer, Heidelberg (1992)Google Scholar
  27. 27.
    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)Google Scholar
  28. 28.
    Pinkas, B.: Fair secure two-party computation. In: Biham, E. (ed.) EUROCRYPT 2003. LNCS, vol. 2656, pp. 87–105. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  29. 29.
    Yao, A.C.-C.: How to generate and exchange secrets. In: 27th Annual Symposium on Foundations of Computer Science (FOCS), pp. 162–167. IEEE, Los Alamitos (1986)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • S. Dov Gordon
    • 1
  • Jonathan Katz
    • 1
  1. 1.Department of Computer ScienceUniversity of Maryland 

Personalised recommendations