On Optimal Probabilistic Asynchronous Byzantine Agreement

  • Amjed Shareef
  • C. Pandu Rangan
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4904)


An important problem in the fault tolerant distributed systems is reaching a consensus among a set of non faulty processes, even in the presence of some corrupted processes. The problem is couched in terms of generals attempting to decide on a common plan of attack. This is in fact the well known Byzantine Generals Problem. We present a consensus protocol of O(ln) communication complexity in asynchronous networks (there is no common global clock and message delivery time is indefinite) with a small error probability where n is the number of players and l is the length of message, given l is sufficiently large, such that l ≥ n 3. This improves the previous result with O(ln 2) communication complexity[5]. Further more, we have proposed a reliable broadcast protocol in asynchronous networks with the assumption that messages delivery time is finite. Both of our protocols can tolerate up to \(t < \frac{n}{3}\) corrupted players and is computationally secure.


Distributed computing byzantine agreement problem fault tolerance computationally bounded byzantine adversary 


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  1. 1.
    Ben-Or, C.M.: Another Advantage of Free Choice: Completely Asynchronous Agreement Protocols. In: PODC 1983. Proc. Second ACM Symp. Principles of Distributed Computing, pp. 27–30 (1983)Google Scholar
  2. 2.
    Berman, P., Garay, J.A.: Randomized distributed agreement revisited. In: 23th International Symposium on Fault-Tolerant Computing (FTCS-23), pp. 412–413 (1993)Google Scholar
  3. 3.
    Bracha, G.: An asynchronous [(n − 1)/3]-resilient consensus protocol. In: PODC. Proc. 3rd ACM Symposium on Principles of Distributed Computing, pp. 154–162 (1984)Google Scholar
  4. 4.
    Cachin, C., Kursawe, K., Petzold, F., Shoup, V.: Secure and efficient asynchronous broadcast protocols (extended abstract). In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 524–541. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  5. 5.
    Cachin, C., Kursawe, K., Shoup, V.: Random oracles in Constantinople: Practical asynchronous Byzantine agreement using cryptography. Journal of Cryptology 18(3), 219–246 (2005)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Carter, L., Wegman, M.N.: Universal classes of hash functions. Journal of Computing and system sciences (JCSS) 18(4), 143–154 (1979) (Preliminary version appeared in STOC 1977)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Chandra, T.D., Toueg, S.: Unreliable Failure Detectors for Reliable Distributed Systems. J. ACM 43(2), 225–267 (1996)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Desmedt, Y., Kurosawa, K.: A Generalization and a Variant of Two Threshold Cryptosystems Based on Factoring. In: ISC 2007. Proceedings of 10th International Conference, vol. 4779, pp. 351–361. Springer, Heidelberg (2007)Google Scholar
  9. 9.
    Fischer, C.M.J., Lynch, N., Paterson, M.S.: Impossibility of Distributed Consensus with One Faulty Process. J. ACM 32(2), 374–382 (1985)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Fitzi, M., Hirt, M.: Optimally efficient multi-valued byzantine agreement. In: PODC 2006. Proceedings of the 25th annual ACM symposium on Principles of distributed computing, Denver, Colorado, USA (July 23 - 26, 2006)Google Scholar
  11. 11.
    Pease, M., Shostak, R., Lamport, L.: Reaching agreement in the presence of faults. Journal of the ACM 27(2), 228–234 (1980)zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Rabin, C.M.: Randomized Byzantine Generals. In: FOCS 1983. Proc. 24th IEEE Symp. Foundations of Computer Science, pp. 403–409 (1983)Google Scholar
  13. 13.
    Ramasamy, C.H.V., Cachin, C.: Parsimonious asynchronous Byzantine-fault-tolerant atomic broadcast. In: Anderson, J.H., Prencipe, G., Wattenhofer, R. (eds.) OPODIS 2005. LNCS, vol. 3974, Springer, Heidelberg (2006)CrossRefGoogle Scholar
  14. 14.
    Shoup, V.: Practical threshold signatures. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, pp. 207–220. Springer, Heidelberg (2000)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Amjed Shareef
    • 1
  • C. Pandu Rangan
    • 1
  1. 1.Indian Institute of Technology MadrasDepartment of Computer Science and EngineeringChennaiIndia

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