Trading Robustness for Correctness and Privacy in Certain Multiparty Computations, beyond an Honest Majority

  • Anne Broadbent
  • Stacey Jeffery
  • Samuel Ranellucci
  • Alain Tapp
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7412)


We improve on the classical results in information-theoreti- cally secure multiparty computation among a set of n participants, by considering the special case of the computation of the addition function over binary inputs in the secure channels model with a simultaneous broadcast channel. This simple function is a useful building block for other applications. The classical results in multiparty computation show that in this model, every function can be computed with information-theoretic security if and only if less than n/2 participants are corrupt. In this article we show that, under certain conditions, this bound can be overcome.

More precisely, let t (p), t (r) and t (c) be the privacy, robustness and correctness thresholds; that is, the minimum number of participants that must be actively corrupted in order for privacy, robustness or correctness, respectively, to be compromised. We show a series of novel tradeoffs applicable to the multiparty computation of f(x 1, …,x n ) = x 1 + … + x n for x i  ∈ {0,1}, culminating in the most general tradeoff: t (p) + t (r) = n + 1 and t (c) + t (r) = n + 1. These tradeoffs are applicable as long as t (r) < n/2, which implies that, at the cost of reducing robustness, privacy and correctness are achievable despite a dishonest majority (as an example, setting the robustness threshold to n/3 yields privacy and correctness thresholds of 2n/3 + 1).

We give applications to information-theoretically secure voting and anonymous message transmission, yielding protocols with the same tradeoffs.


multiparty computation secret sharing information- theoretic security simultaneous broadcast addition voting anonymous communication 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Yao, A.C.: Protocols for secure computations. In: Proceedings of the 23rd Annual Symposium on the Foundations of Computer Science (FOCS 1982), pp. 160–164. IEEE (1982)Google Scholar
  2. 2.
    Chaum, D., Crépeau, C., Damgård, I.: Multiparty unconditionally secure protocols. In: Simon, J. (ed.) Proceedings of the 20th annual ACM Symposium on Theory of Computing (STOC 1988), pp. 11–19. ACM (1988)Google Scholar
  3. 3.
    Ben-Or, M., Goldwasser, S., Wigderson, A.: Completeness theorems for non-cryptographic fault-tolerant distributed computation. In: Simon, J. (ed.) Proceedings of the 20th Annual ACM Symposium on Theory of Computing (STOC 1988), pp. 1–10. ACM (1988)Google Scholar
  4. 4.
    Rabin, T., Ben-Or, M.: Verifiable secret sharing and multiparty protocols with honest majority. In: Johnson, D.S. (ed.) Proceedings of the 21st Annual ACM Symposium on Theory of Computing (STOC 1989), pp. 73–85. ACM (1989)Google Scholar
  5. 5.
    Broadbent, A., Tapp, A.: Information-Theoretic Security Without an Honest Majority. In: Kurosawa, K. (ed.) ASIACRYPT 2007. LNCS, vol. 4833, pp. 410–426. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  6. 6.
    Broadbent, A., Tapp, A.: Information-theoretically secure voting without an honest majority. In: Proceedings of the IAVoSS Workshop On Trustworthy Elections, WOTE 2008 (2008), Cryptology ePrint Archive: Report 2008/266Google Scholar
  7. 7.
    Fitzi, M., Hirt, M., Holenstein, T., Wullschleger, J.: Two-Threshold Broadcast and Detectable Multi-party Computation. In: Biham, E. (ed.) EUROCRYPT 2003. LNCS, vol. 2656, pp. 51–67. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  8. 8.
    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)Google Scholar
  9. 9.
    Lucas, C., Raub, D., Maurer, U.: Hybrid-secure MPC: Trading information-theoretic robustness for computational privacy. In: Proceedings of the 29th Annual ACM SIGACT-SIGOPS Symposium on Principles of Distributed Computing (PODC 2010), pp. 219–228. ACM (2010)Google Scholar
  10. 10.
    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
  11. 11.
    Fitzi, M., Gottesman, D., Hirt, M., Holenstein, T., Smith, A.: Detectable Byzantine agreement secure against faulty majorities. In: Proceedings of the 21st Annual Symposium on Principles of Distributed Computing (PODC 2002), pp. 118–126. ACM (2002)Google Scholar
  12. 12.
    Shamir, A.: How to share a secret. Communications of the ACM 22, 612–613 (1979)MathSciNetzbMATHCrossRefGoogle Scholar
  13. 13.
    Cramer, R., Damgård, I., Maurer, U.: General Secure Multi-party Computation from any Linear Secret-Sharing Scheme. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, pp. 316–334. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  14. 14.
    Cramer, R., Damgård, I., Dziembowski, S., Hirt, M., Rabin, T.: Efficient Multiparty Computations Secure against an Adaptive Adversary. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 311–326. Springer, Heidelberg (1999)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Anne Broadbent
    • 1
    • 2
  • Stacey Jeffery
    • 1
    • 2
  • Samuel Ranellucci
    • 3
  • Alain Tapp
    • 3
  1. 1.Institute for Quantum ComputingUniversity of WaterlooCanada
  2. 2.School of Computer ScienceUniversity of WaterlooCanada
  3. 3.DIROUniversité de MontréalCanada

Personalised recommendations