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Characterization of Secure Multiparty Computation Without Broadcast

  • Ran Cohen
  • Iftach Haitner
  • Eran Omri
  • Lior Rotem
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9562)

Abstract

A major challenge in the study of cryptography is characterizing the necessary and sufficient assumptions required to carry out a given cryptographic task. The focus of this work is the necessity of a broadcast channel for securely computing symmetric functionalities (where all the parties receive the same output) when one third of the parties, or more, might be corrupted. Assuming all parties are connected via a peer-to-peer network, but no broadcast channel (nor a secure setup phase) is available, we prove the following characterization:

  • A symmetric n-party functionality can be securely computed facing \(n/3\le t<n/2\) corruptions (i.e., honest majority), if and only if it is \((n-2t)\) -dominated; a functionality is k-dominated, if any k-size subset of its input variables can be set to determine its output.

  • Assuming the existence of one-way functions, a symmetric n-party functionality can be securely computed facing \(t\ge n/2\) corruptions (i.e., no honest majority), if and only if it is 1-dominated and can be securely computed with broadcast.

It follows that, in case a third of the parties might be corrupted, broadcast is necessary for securely computing non-dominated functionalities (in which “small” subsets of the inputs cannot determine the output), including, as interesting special cases, the Boolean XOR and coin-flipping functionalities.

Keywords

Broadcast Point-to-point communication Multiparty computation Coin flipping Fairness Impossibility result 

References

  1. 1.
    Beimel, A., Omri, E., Orlov, I.: Protocols for multiparty coin toss with dishonest majority. In: Rabin, T. (ed.) CRYPTO 2010. LNCS, vol. 6223, pp. 538–557. Springer, Heidelberg (2010) CrossRefGoogle Scholar
  2. 2.
    Ben-Or, M., Goldwasser, S., Wigderson, A.: Completeness theorems for non-cryptographic fault-tolerant distributed computation (extended abstract). In: Proceedings of the 29th Annual Symposium on Foundations of Computer Science (FOCS), pp. 1–10 (1988)Google Scholar
  3. 3.
    Blum, M.: Coin flipping by telephone. In: Advances in Cryptology - CRYPTO 1981, pp. 11–15 (1981)Google Scholar
  4. 4.
    Broder, A.Z., Dolev, D.: Flipping coins in many pockets (Byzantine agreement on uniformly random values). In: Proceedings of the 25th Annual Symposium on Foundations of Computer Science (FOCS), pp. 157–170 (1984)Google Scholar
  5. 5.
    Chaum, D., Crépeau, C., Damgård, I.: Multiparty unconditionally secure protocols (extended abstract). In: Proceedings of the 10th Annual ACM Symposium on Theory of Computing (STOC), pp. 11–19 (1988)Google Scholar
  6. 6.
    Chor, B., Goldwasser, S., Micali, S., Awerbuch, B.: Verifiable secret sharing and achieving simultaneity in the presence of faults (extended abstract). In: Proceedings of the 26th Annual Symposium on Foundations of Computer Science (FOCS), pp. 383–395 (1985)Google Scholar
  7. 7.
    Cleve, R.: Limits on the security of coin flips when half the processors are faulty. In: Proceedings of the 18th Annual ACM Symposium on Theory of Computing (STOC), pp. 364–369 (1986)Google Scholar
  8. 8.
    Cohen, R., Haitner, I., Omri, E., Rotem, L.: Characterization of secure multiparty computation without broadcast. Cryptology ePrint Archive, Report 2015/846 (2015). http://eprint.iacr.org/
  9. 9.
    Cohen, R., Lindell, Y.: Fairness versus guaranteed output delivery in secure multiparty computation. In: Sarkar, P., Iwata, T. (eds.) ASIACRYPT 2014, Part II. LNCS, vol. 8874, pp. 466–485. Springer, Heidelberg (2014) Google Scholar
  10. 10.
    Dolev, D., Strong, R.: Authenticated algorithms for Byzantine agreement. SIAM J. Comput. 12(4), 656–666 (1983)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Fischer, M.J., Lynch, N.A., Merritt, M.: Easy impossibility proofs for distributed consensus problems. In: Proceedings of the Fourth Annual ACM Symposium on Principles of Distributed Computing (PODC), pp. 59–70 (1985)Google Scholar
  12. 12.
    Fitzi, M., Gottesman, D., Hirt, M., Holenstein, T., Smith, A.: Detectable Byzantine agreement secure against faulty majorities. In: Proceedings of the 21st Annual ACM Symposium on Principles of Distributed Computing (PODC), pp. 118–126 (2002)Google Scholar
  13. 13.
    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
  14. 14.
    Goldreich, O.: Foundations of Cryptography Basic Applications, vol. 2. Cambridge University Press, New York (2004)CrossRefzbMATHGoogle Scholar
  15. 15.
    Goldreich, O., Micali, S., Wigderson, A.: How to play any mental game or a completeness theorem for protocols with honest majority. In: Proceedings of the 19th Annual ACM Symposium on Theory of Computing (STOC), pp. 218–229 (1987)Google Scholar
  16. 16.
    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
  17. 17.
    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) CrossRefGoogle Scholar
  18. 18.
    Haitner, I., Tsfadia, E.: An almost-optimally fair three-party coin-flipping protocol. In: Proceedings of the 46th Annual ACM Symposium on Theory of Computing (STOC), pp. 817–836 (2014)Google Scholar
  19. 19.
    Lamport, L.: The weak Byzantine generals problem. J. ACM 30(3), 668–676 (1983)MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Lamport, L., Shostak, R.E., Pease, M.C.: The Byzantine generals problem. ACM Trans. Program. Lang. Syst. 4(3), 382–401 (1982)CrossRefzbMATHGoogle Scholar
  21. 21.
    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
  22. 22.
    Pease, M.C., Shostak, R.E., Lamport, L.: Reaching agreement in the presence of faults. J. ACM 27(2), 228–234 (1980)MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Pfitzmann, B., Waidner, M.: Unconditional Byzantine agreement for any number of faulty processors. In: Proceedings of the 9th Annual Symposium on Theoretical Aspects of Computer Science (STACS), pp. 339–350 (1992)Google Scholar
  24. 24.
    Rabin, T., Ben-Or, M.: Verifiable secret sharing and multiparty protocols with honest majority (extended abstract). In: Proceedings of the 30th Annual Symposium on Foundations of Computer Science (FOCS), pp. 73–85 (1989)Google Scholar
  25. 25.
    Yao, A.C.: Protocols for secure computations. In: Proceedings of the 23th Annual Symposium on Foundations of Computer Science (FOCS), pp. 160–164 (1982)Google Scholar

Copyright information

© International Association for Cryptologic Research 2016

Authors and Affiliations

  • Ran Cohen
    • 1
  • Iftach Haitner
    • 2
  • Eran Omri
    • 3
  • Lior Rotem
    • 4
  1. 1.Department of Computer ScienceBar-Ilan UniversityRamat GanIsrael
  2. 2.School of Computer ScienceTel Aviv UniversityTel AvivIsrael
  3. 3.Department of Computer Science and MathematicsAriel UniversityArielIsrael
  4. 4.School of Computer ScienceTel Aviv UniversityTel AvivIsrael

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