Rationality and Adversarial Behavior in Multi-party Computation

  • Anna Lysyanskaya
  • Nikos Triandopoulos
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4117)


We study multi-party computation in the model where none of n participating parties are honest: they are either rational, acting in their selfish interest to maximize their utility, or adversarial, acting arbitrarily. In this new model, which we call the mixed-behavior model, we define a class of functions that can be computed in the presence of an adversary using a trusted mediator. We then give a protocol that allows the rational parties to emulate the mediator and jointly compute the function such that (1) assuming that each rational party prefers that it learns the output while others do not, no rational party has an incentive to deviate from the protocol; and (2) the rational parties are protected from a malicious adversary controlling \(\lceil \frac{n}{2} \rceil -- 2\) of the participants: the adversary can only either cause all rational participants to abort (so no one learns the function they are trying to compute), or can only learn whatever information is implied by the output of the function.


Nash Equilibrium Secret Sharing Broadcast Channel Covert Channel Malicious Adversary 
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.
    Abraham, I., Dolev, D., Gonen, R., Halpern, J.: Distributed computing meets game theory: Robust mechanisms for rational secret sharing and multiparty computation. In: Proc. 25th ACM PODC (to appear, 2006)Google Scholar
  2. 2.
    Canetti, R., Fischlin, M.: Universally composable commitments. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 19–40. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  3. 3.
    Canetti, R., Lindell, Y., Ostrovsky, R., Sahai, A.: Universally composable two-party and multi-party secure computation. In: Proc. 34th ACM Symposium on Theory of Computing (STOC), pp. 494–503 (2002)Google Scholar
  4. 4.
    De Santis, A., Di Crescenzo, G., Ostrovsky, R., Persiano, G., Sahai, A.: Robust non-interactive zero knowledge. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 566–598. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  5. 5.
    Goldreich, O.: Foundations of Cryptography. Cambridge University Press, Cambridge (2004)MATHCrossRefGoogle Scholar
  6. 6.
    Goldreich, O., Micali, S., Wigderson, A.: How to play any mental game or a completeness theorem for protocols with honest majority. In: Proc. 19th ACM Symposium on Theory of Computing (STOC), pp. 218–229 (1987)Google Scholar
  7. 7.
    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); manuscript available at: http://eprint.iacr.org/2006/142 CrossRefGoogle Scholar
  8. 8.
    Halpern, J., Teague, V.: Rational secret sharing and multiparty computation: extended abstract. In: Proc. 36th ACM Symposium on Theory of Computing (STOC), pp. 623–632 (2004)Google Scholar
  9. 9.
    Izmalkov, S., Lepinski, M., Micali, S.: Rational secure computation and ideal mechanism design. In: Proc. 46th IEEE Symposium on Foundations of Computer Science (FOCS), pp. 585–594 (2005)Google Scholar
  10. 10.
    Lepinksi, M., Micali, S., Shelat, A.: Collusion-free protocols. In: Proc. 37th ACM Symposium on Theory of Computing, pp. 543–552 (2005)Google Scholar
  11. 11.
    Lepinski, M., Micali, S., Peikert, C., Shelat, A.: Completely fair SFE and coalition-safe cheap talk. In: Proc. 23rd ACM PODC, pp. 1–10 (2004)Google Scholar
  12. 12.
    Shamir, A.: How to share a secret. Comm. of the ACM 22(11), 612–613 (1979)MATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Shoham, Y., Tennenholtz, M.: Non-cooperative computation: Boolean functions with correctness and exclusivity. Theoretical Comp. Science 343(2), 97–113 (2005)MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Anna Lysyanskaya
    • 1
  • Nikos Triandopoulos
    • 1
  1. 1.Department of Computer ScienceBrown University 

Personalised recommendations