Advertisement

Realistic Failures in Secure Multi-party Computation

  • Vassilis Zikas
  • Sarah Hauser
  • Ueli Maurer
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5444)

Abstract

In secure multi-party computation, the different ways in which the adversary can control the corrupted players are described by different corruption types. The three most common corruption types are active corruption (the adversary has full control over the corrupted player), passive corruption (the adversary sees what the corrupted player sees) and fail-corruption (the adversary can force the corrupted player to crash irrevocably). Because fail-corruption is inadequate for modeling recoverable failures, the so-called omission corruption was proposed and studied mainly in the context of Byzantine Agreement (BA). It allows the adversary to selectively block messages sent from and to the corrupted player, but without actually seeing the message.

In this paper we propose a modular study of omission failures in MPC, by introducing the notions of send-omission (the adversary can selectively block outgoing messages) and receive-omission (the adversary can selectively block incoming messages) corruption. We provide security definitions for protocols tolerating a threshold adversary who can actively, receive-omission, and send-omission corrupt up to t a , t ρ , and t σ players, respectively. We show that the condition 3t a  + t ρ  + t σ < n is necessary and sufficient for perfectly secure MPC tolerating such an adversary. Along the way we provide perfectly secure protocols for BA under the same bound. As an implication of our results, we show that an adversary who actively corrupts up to t a players and omission corrupts (according to the already existing notion) up to t ω players can be tolerated for perfectly secure MPC if 3t a  + 2t ω < n. This significantly improves a result by Koo in TCC 2006.

Keywords

Input Gate Byzantine Agreement Secure Multiparty Computation Protocol Reconstruct Realistic Failure 
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.

References

  1. [Bea91a]
    Beaver, D.: Foundations of secure interactive computing. In: Feigenbaum, J. (ed.) CRYPTO 1991. LNCS, vol. 576, pp. 377–391. Springer, Heidelberg (1992)Google Scholar
  2. [Bea91b]
    Beaver, D.: Secure multiparty protocols and zero-knowledge proof systems tolerating a faulty minority. Journal of Cryptology 4(2), 370–381 (1991)CrossRefzbMATHGoogle Scholar
  3. [BGP89]
    Berman, P.J., Garray, J., Perry, J.: Towards optimal distributed consensus. In: FOCS 1989, pp. 410–415 (1989)Google Scholar
  4. [BGW88]
    Ben-Or, M., Goldwasser, S., Wigderson, A.: Completeness theorems for non-cryptographic fault-tolerant distributed computation. In: STOC 1988, pp. 1–10 (1988)Google Scholar
  5. [BPW03]
    Backes, M., Pfitzmann, B., Waidner, M.: A universally composable cryptographic library (2003)Google Scholar
  6. [Can00]
    Canetti, R.: Security and composition of multiparty cryptographic protocols. Journal of Cryptology 13(1), 143–202 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  7. [CCD88]
    Chaum, D., Crépeau, C., Damgård, I.: Multiparty unconditionally secure protocols (extended abstract). In: STOC 1988, pp. 11–19 (1988)Google Scholar
  8. [DDWY93]
    Dolev, D., Dwork, C., Waarts, O., Yung, M.: Perfectly secure message transmission. Journal of the ACM 40(1), 17–47 (1993)MathSciNetCrossRefzbMATHGoogle Scholar
  9. [DM00]
    Dodis, Y., Micali, S.: Parallel reducibility for information-theoretically secure computation. In: Bellare, M. (ed.) CRYPTO 2000. LNCS, vol. 1880, pp. 74–92. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  10. [DS82]
    Dolev, D., Strong, H.R.: Polynomial algorithms for multiple processor agreement. In: STOC 1982, pp. 401–407 (1982)Google Scholar
  11. [FHM98]
    Fitzi, M., Hirt, M., Maurer, U.: Trading correctness for privacy in unconditional multi-party computation. In: Krawczyk, H. (ed.) CRYPTO 1998. LNCS, vol. 1462, pp. 121–136. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  12. [FM98]
    Fitzi, M., Maurer, U.: Efficient byzantine agreement secure against general adversaries. In: Kutten, S. (ed.) DISC 1998. LNCS, vol. 1499, pp. 134–148. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  13. [FM00]
    Fitzi, M., Maurer, U.: From partial consistency to global broadcast. In: STOC 2000, pp. 494–503 (2000)Google Scholar
  14. [GL02]
    Goldwasser, S., Lindell, Y.: Secure computation without agreement. In: Malkhi, D. (ed.) DISC 2002. LNCS, vol. 2508, pp. 17–32. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  15. [GMW87]
    Goldreich, O., Micali, S., Wigderson, A.: How to play any mental game — a completeness theorem for protocols with honest majority. In: STOC 1987, pp. 218–229 (1987)Google Scholar
  16. [GP92]
    Garay, J.A., Perry, K.J.: A continuum of failure models for distributed computing. In: Segall, A., Zaks, S. (eds.) WDAG 1992. LNCS, vol. 647, pp. 153–165. Springer, Heidelberg (1992)CrossRefGoogle Scholar
  17. [Had85]
    Hadzilacos, V.: Issues of fault tolerance in concurrent computations (databases, reliability, transactions, agreement protocols, distributed computing). PhD thesis, Cambridge, MA, USA (1985)Google Scholar
  18. [HMP00]
    Hirt, M., Maurer, U., Przydatek, B.: Efficient secure multi-party computation. In: Okamoto, T. (ed.) ASIACRYPT 2000. LNCS, vol. 1976, pp. 143–161. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  19. [IKLP06]
    Ishai, Y., Kushilevitz, E., Lindell, Y., Petrank, E.: On combining privacy with guaranteed output delivery in secure multiparty computation. In: Dwork, C. (ed.) CRYPTO 2006. LNCS, vol. 4117, pp. 483–500. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  20. [Koo06]
    Koo, C.-Y.: Secure computation with partial message loss. In: Halevi, S., Rabin, T. (eds.) TCC 2006. LNCS, vol. 3876, pp. 502–521. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  21. [LF82]
    Lamport, L., Fischer, M.J.: Byzantine generals and transaction commit protocols. Technical Report Opus 62, SRI International (Menlo Park CA), TR (1982)Google Scholar
  22. [LSP82]
    Lamport, L., Shostak, R., Pease, M.: The byzantine generals problem. ACM Transactions on Programming Languages and Systems 4(3), 382–401 (1982)CrossRefzbMATHGoogle Scholar
  23. [MP91]
    Meyer, F.J., Pradhan, D.K.: Consensus with dual failure modes. IEEE Transactions on Parallel and Distributed Systems 2(2), 214–222 (1991)CrossRefGoogle Scholar
  24. [MR91]
    Micali, S., Rogaway, P.: Secure computation. In: Feigenbaum, J. (ed.) CRYPTO 1991. LNCS, vol. 576, pp. 392–404. Springer, Heidelberg (1992)Google Scholar
  25. [PR03]
    Parvedy, P.R., Raynal, M.: Uniform agreement despite process omission failures. In: International Symposium on Parallel and Distributed Processing — IPDPS 2003, p. 212.2 (2003)Google Scholar
  26. [PT86]
    Perry, K.J., Toueg, S.: Distributed agreement in the presence of processor and communication faults. IEEE Trans. Softw. Eng. 12(3), 477–482 (1986)CrossRefzbMATHGoogle Scholar
  27. [PW01]
    Pfitzmann, B., Waidner, M.: A model for asynchronous reactive systems and its application to secure message transmission. In: IEEE Symposium on Security and Privacy, pp. 184–200 (2001)Google Scholar
  28. [Ray02]
    Raynal, M.: Consensus in synchronous systems: A concise guided tour. In: Pacific Rim International Symposium on Dependable Computing — PRDC 2002, p. 221 (2002)Google Scholar
  29. [RB89]
    Rabin, T., Ben-Or, M.: Verifiable secret sharing and multiparty protocols with honest majority. In: STOC 1989, pp. 73–85 (1989)Google Scholar
  30. [Yao82]
    Yao, A.C.: Protocols for secure computations. In: FOCS 1982, pp. 160–164 (1982)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Vassilis Zikas
    • 1
  • Sarah Hauser
    • 1
  • Ueli Maurer
    • 1
  1. 1.Department of Computer ScienceETH ZurichZurichSwitzerland

Personalised recommendations