On the message complexity of binary byzantine agreement under crash failures
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The binary Byzantine Agreement problem requiresn−1 receivers to agree on the binary value broadcast by a sender even when some of thesen processes may be faulty. We investigate the message complexity of protocols that solve this problem in the case of crash failures. In particular, we derive matching upper and lower bounds on the total, worst and average case number of meassages needed in the failure-free executions of such protocols.
More specifically, we prove that any protocol that tolerates up tot faulty processes requires a total of at leastn+t−1 messages in its failure-free executions —and, therefore, at least [(n+t−1)/2] messages in the worst case and min (P0,P1)·(n+t−1) meassages in the average case, wherePv is the probability that the value of the bit that the sender wants to broadcast isv. We also give protocols that solve the problem using only the minimum number of meassages for these three complexity measures. These protocols can be implemented by using 1-bit messages. Since a lower bound on the number of messages is also a lower bound on the number of meassage bits, this means that the above tight bounds on the number of messages are also tight bounds on the number of meassage bits.
Key wordsFault-tolerance Agreement Distributed system
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- 1.Amdur ES: On the message complexity of byzantine agreement. M.S. Thesis, Department of Computer Science, University of Toronto 1988Google Scholar
- 2.Berman P, Garray J, Perry K: Recursive phase king protocols for distributed consensus. Technical Report CS-89-24, Computer Science Department, Pennsylvania State University 1989Google Scholar
- 3.Bracha G: Technical memorandum, Department of Computer Science, Cornell University 1984 (unpublished mansucript)Google Scholar
- 4.Coan B, Welch J: A byzantine agreement protocol with optimal message bit complexity. Proceedings of the 27th Annual Allerton Conference on Communication. Control and Computing pp 1062–1071, 1989Google Scholar
- 5.Cook SA, Dwork C, Reischuk R: Upper and lower bounds for parallel RAMs without simultaneous writes. SIAM J Comput 15(1):87–97 (1986).Google Scholar
- 6.Dolev D, Reischuk R: Bounds on information exchange for byzantine agreement. Research Report RJ 3587, IBM San Jose Research Laboratory 1982Google Scholar
- 7.Dolev D, Strong HR: Authenticated algorithms for byzantine agreement. SIAM J Comput 12(4):656–666 (1983)Google Scholar
- 8.Dwork C, Moses Y: Knowledge and common knowledge in a byzantine environment I: crash failures. In Proceedings of the Conference on Theoretical Aspects of Reasoning About Knowledge pp 149–169, 1986Google Scholar
- 9.Feldman P, Micali S: Byzantine agreement in constant expected time (and trusting no one). Proceedings of the 26th Annual IEEE Symposium on Foundations of Computer Science pp 267–276, 1985Google Scholar
- 10.Feldman P, Micali S: An optimal algorithm for synchronous byzantine agreement. Technical Report MIT/LCSTM-425. Laboratory for Computer Science, Massachusetts Institute of Technology 1990Google Scholar
- 11.Fischer MJ: The consensus problem in unreliable distributed systems. Research Report RR-273. Department of Computer Science, Yale University 1983Google Scholar
- 12.Fischer MJ, Lynch NA: A lower bound for the time to assure interactive consistency. Inf Process Lett 14(4):183–186 (1982)Google Scholar
- 13.Gray JN: The cost of messages. In Proceedings of the 7th ACM Symposium on Principles of Distributed Computing pp 1–7, 1988Google Scholar
- 14.Hadzilacos V: Issues of fault tolerance in concurrent computations. Ph.D. dissertation, Harvard University 1984Google Scholar
- 15.Hadzilacos V, Halpern JY: Message-optimal protocols for byzantine agreement. (forthcoming 1990)Google Scholar
- 16.Lynch NA: A hundred impossibility proofs for distributed computing. In Proceedings of the 8th ACM Symposium on Principles of Distributed Computing pp 1–27, 1989Google Scholar
- 17.Pease M, Shostak R, Lamport L: Reaching agreement in the presence of faults. J ACM 27(2):228–234 (1980)Google Scholar
- 18.Weber SM: Bounds on the message complexity of byzantine agreement. M.S. Thesis, Department of Computer Science, University of Toronto 1989Google Scholar