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On Expected Constant-Round Protocols for Byzantine Agreement

  • Jonathan Katz
  • Chiu-Yuen Koo
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4117)

Abstract

In a seminal paper, Feldman and Micali (STOC ’88) show an n-party Byzantine agreement protocol tolerating t < n/3 malicious parties that runs in expected constant rounds. Here, we show an expected constant-round protocol for authenticated Byzantine agreement assuming honest majority (i.e., t < n/2), and relying only on the existence of a secure signature scheme and a public-key infrastructure (PKI). Combined with existing results, this gives the first expected constant-round protocol for secure computation with honest majority in a point-to-point network assuming only one-way functions and a PKI. Our key technical tool — a new primitive we introduce called moderated VSS — also yields a simpler proof of the Feldman-Micali result.

We also show a simple technique for sequential composition of protocols without simultaneous termination (something that is inherent for Byzantine agreement protocols using o(n) rounds) for the case of t<n/2.

Keywords

Broadcast Channel Broadcast Protocol Honest Party Byzantine Agreement Honest Parti 
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. 1.
    Beaver, D., Haber, S.: Cryptographic protocols provably secure against dynamic adversaries. In: Rueppel, R.A. (ed.) EUROCRYPT 1992. LNCS, vol. 658, pp. 307–323. Springer, Heidelberg (1993)CrossRefGoogle Scholar
  2. 2.
    Beaver, D., Micali, S., Rogaway, P.: The round complexity of secure protocols. In: 22nd Annual ACM Symposium on Theory of Computing (STOC) (1990)Google Scholar
  3. 3.
    Ben-Or, M.: Another advantage of free choice: Completely asynchronous agreement protocols. In: 2nd Annual ACM Symposium on Principles of Distributed Computing (PODC) (1983)Google Scholar
  4. 4.
    Ben-Or, M., El-Yaniv, R.: Resilient-optimal interactive consistency in constant time. Distributed Computing 16(4), 249–262 (2003)CrossRefGoogle Scholar
  5. 5.
    Blakley, G.R.: Safeguarding cryptographic keys. In: National Computer Conference, vol. 48, pp. 313–317. AFIPS Press (1979)Google Scholar
  6. 6.
    Bracha, G.: An O(logn) expected rounds randomized Byzantine generals protocol. J. ACM 34(4), 910–920 (1987)MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Cachin, C., Kursawe, K., Shoup, V.: Random oracles in Constantinople: Practical asynchronous Byzantine agreement using cryptography (extended abstract). In: 19th Annual ACM Symposium on Principles of Distributed Computing (PODC) (2000)Google Scholar
  8. 8.
    Canetti, R.: Universally composable security: A new paradigm for cryptographic protocols. In: 42nd Annual IEEE Symposium on Foundations of Computer Science (FOCS) (2001)Google Scholar
  9. 9.
    Canetti, R., Feige, U., Goldreich, O., Naor, M.: Adaptively secure multi-party computation. In: 28th Annual ACM Symposium on Theory of Computing (STOC) (1996)Google Scholar
  10. 10.
    Chor, B., Coan, B.: A simple and efficient randomized Byzantine agreement algorithm. IEEE Trans. Software Engineering 11(6), 531–539 (1985)CrossRefMathSciNetGoogle Scholar
  11. 11.
    Chor, B., Goldwasser, S., Micali, S., Awerbuch, B.: Verifiable secret sharing and achieving simultaneity in the presence of faults. In: 26th Annual IEEE Symposium on the Foundations of Computer Science (FOCS) (1985)Google Scholar
  12. 12.
    Damgård, I.B., Ishai, Y.: Constant-round multiparty computation using a black-box pseudorandom generator. In: Shoup, V. (ed.) CRYPTO 2005. LNCS, vol. 3621, pp. 378–394. Springer, Heidelberg (2005)Google Scholar
  13. 13.
    Dolev, D., Strong, H.R.: Authenticated algorithms for Byzantine agreement. SIAM J. Computing 12(4), 656–666 (1983)MATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Dwork, C., Shmoys, D., Stockmeyer, L.: Flipping persuasively in constant time. SIAM J. Computing 19(3), 472–499 (1990)MATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Feldman, P.: Optimal Algorithms for Byzantine Agreement. PhD thesis, Massachusetts Institute of Technology (1988)Google Scholar
  16. 16.
    Feldman, P., Micali, S.: Byzantine agreement in constant expected time and trusting no one. In: 26th Annual IEEE Symposium on the Foundations of Computer Science (FOCS) (1985)Google Scholar
  17. 17.
    Feldman, P., Micali, S.: An optimal probabilistic protocol for synchronous Byzantine agreement. SIAM J. Computing 26(4), 873–933 (1997)MATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    Fischer, M.J., Lynch, N.A.: A lower bound for the time to assure interactive consistency. Information Processing Letters 14(4), 183–186 (1982)MATHCrossRefMathSciNetGoogle Scholar
  19. 19.
    Fitzi, M., Garay, J.A., Gollakota, S., Pandu Rangan, C., Srinathan, K.: Round-optimal and efficient verifiable secret sharing. In: Halevi, S., Rabin, T. (eds.) TCC 2006. LNCS, vol. 3876, pp. 329–342. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  20. 20.
    Fitzi, M., Garay, J.A.: Efficient player-optimal protocols for strong and differential consensus. In: 22nd Annual ACM Symposium on Principles of Distributed Computing (PODC) (2003)Google Scholar
  21. 21.
    Garay, J.A., Moses, Y.: Fully polynomial Byzantine agreement for n > 3t processors in t + 1 rounds. SIAM J. Comput. 27(1), 247–290 (1998)MATHCrossRefMathSciNetGoogle Scholar
  22. 22.
    Gennaro, R., Ishai, Y., Kushilevitz, E., Rabin, T.: The round complexity of verifiable secret sharing and secure multicast. In: 33rd Annual ACM Symposium on Theory of Computing (STOC) (2001)Google Scholar
  23. 23.
    Goldwasser, S., Lindell, Y.: Secure computation without agreement. J. Cryptology 18(3), 247–287 (2005)MATHCrossRefMathSciNetGoogle Scholar
  24. 24.
    Katz, J., Koo, C.-Y.: On expected constant-round protocols for Byzantine agreement (2006), Available at: http://eprint.iacr.org/065
  25. 25.
    Kushilevitz, E., Lindell, Y., Rabin, T.: Information-theoretically secure protocols and security under composition. In: STOC (to appear, 2006)Google Scholar
  26. 26.
    Lamport, L., Shostak, R., Pease, M.: The Byzantine generals problem. ACM Trans. Program. Lang. Syst. 4(3), 382–401 (1982)MATHCrossRefGoogle Scholar
  27. 27.
    Lindell, Y., Lysyanskaya, A., Rabin, T.: On the composition of authenticated Byzantine agreement. In: 34th Annual ACM Symposium on Theory of Computing (STOC) (2002)Google Scholar
  28. 28.
    Lindell, Y., Lysyanskaya, A., Rabin, T.: Sequential composition of protocols without simultaneous termination. In: 21st Annual ACM Symposium on Principles of Distributed Computing (PODC) (2002)Google Scholar
  29. 29.
    Nielsen, J.B.: A threshold pseudorandom function construction and its applications. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol. 2442, p. 401. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  30. 30.
    Pease, M., Shostak, R., Lamport, L.: Reaching agreement in the presence of faults. J. ACM 27(2), 228–234 (1980)MATHCrossRefMathSciNetGoogle Scholar
  31. 31.
    Pfitzmann, B., Waidner, M.: Information-theoretic pseudosignatures and Byzantine agreement for t ≥ n/3. Technical Report RZ 2882 (#90830), IBM Research (1996)Google Scholar
  32. 32.
    Rabin, M.: Randomized Byzantine generals. In: 24th Annual IEEE Symposium on Foundations of Computer Science (FOCS) (1983)Google Scholar
  33. 33.
    Shamir, A.: How to share a secret. Comm. ACM 22(11), 612–613 (1979)MATHCrossRefMathSciNetGoogle Scholar
  34. 34.
    Toueg, S.: Randomized Byzantine agreements. In: 3rd Annual ACM Symposium on Principles of Distributed Computing (PODC) (1984)Google Scholar
  35. 35.
    Turpin, R., Coan, A.B.: Extending binary Byzantine agreement to multivalued Byzantine agreement. Information Processing Letters 18(2), 73–76 (1984)CrossRefGoogle Scholar
  36. 36.
    M. Waidner. Byzantinische Verteilung ohne Kryptographische Annahmen trotz Beliebig Vieler Fehler (in German). PhD thesis, University of Karlsruhe (1991)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Jonathan Katz
    • 1
  • Chiu-Yuen Koo
    • 1
  1. 1.Dept. of Computer ScienceUniversity of MarylandCollege ParkUSA

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