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Polynomial algorithms for multiple processor agreement

Published: 05 May 1982 Publication History

Abstract

Reaching agreement in a distributed system while handling malfunctioning behavior is a central issue for reliable computer systems. All previous algorithms for reaching the agreement required an exponential number of messages to be sent, with or without authentication. We give polynomial algorithms for reaching (Byzantine) agreement, both with and without the use of authentication protocols. We also prove that no matter what kind of information is exchanged, there is no way to reach agreement with fewer than t+1 rounds of exchange, where t is the upper bound on the number of faults.

References

[1]
W. Diffie and M. Hellman, "New direction in cryptography," IEEE Trans. on Inform. IT-22,6(1976), 644-654.
[2]
D. Dolev, "The Byzantine Generals Strike Again," Journal of Algorithms, vol. 3, no. 1, 1982.
[3]
D. Dolev, "Unanimity in an Unknown and Unreliable Environment," 22nd Annual Symposium on Foundations of Computer Science, pp. 159-168, 1981.
[4]
D. Dolev and H. R. Strong, "Authenticated Algorithms for Byzantine Agreement," submitted for publication; see also "Polynomial algorithms for multiple processor agreement," IBM Research Report RJ3342 {1981).
[5]
R. A. DeMillo, N. A. Lynch, and M. Merritt, "Cryptographic Protocols," in these proceedings.
[6]
L. Lamport, "Using Time Instead of Timeout for Fault-Tolerant Distributed Systems," Technical Report, Computer Science Laboratory, SRI International, 1981.
[7]
L. Lamport, R. Shostak, and M. Pease, "The Byzantine Generals Problem," ACM Trans. on Programming Languages and Systems, to appear.
[8]
N. Lynch, and M. Fischer, "A Lower Bound for the Time to Assure Interactive Consistency," submitted for publication.
[9]
M. Pease, R. Shostak, and L. Lamport, "Reaching Agreement in the Presence of Faults," JACM, vol. 27, no. 2, pp. 228-234, 1980.
[10]
R. L. Rivest, A. Shamir, and L. Adleman, "A method for obtaining digital signatures and public-key cryptosystems," Comm. ACM 21 (1978), 120-126.

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cover image ACM Conferences
STOC '82: Proceedings of the fourteenth annual ACM symposium on Theory of computing
May 1982
408 pages
ISBN:0897910702
DOI:10.1145/800070
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Association for Computing Machinery

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Published: 05 May 1982

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