Mathematical systems theory

, Volume 26, Issue 1, pp 131–154 | Cite as

Modular construction of an efficient 1-bit Byzantine agreement protocol

  • Brian A. Coan
  • Jennifer L. Welch
Article

Abstract

This paper presents a new Byzantine agreement protocol that toleratest processor faults usingO(t·logt) processors,t + 1 rounds,O(t 2 +o·t) total message bits (whereo is the number of processors that must decide), and messages of maximum size 1 bit. It is the first Byzantine agreement protocol that is simultaneously optimal in rounds, message bits, and message size. The new Byzantine agreement protocol is actually a protocol for the (slightly) more general Byzantine relay problem—a problem which we formulate in this paper. The Byzantine relay protocol is the result of a general recursive construction. Each step of the construction combines two smaller (in terms of number of faults tolerated) Byzantine relay protocols into one larger Byzantine relay protocol. The base case is a collection of very simple Byzantine relay protocols, each tolerant of a small constant number of processor faults. A key new feature of the protocol construction technique presented in this paper is that it does not add unproductive overhead rounds: given two constituent protocols that are optimal in the number of rounds, the composite protocol that is constructed is also optimal in the number of rounds.

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References

  1. Bar-Noy, A., and Dolov, D. (1991), Consensus algorithms with one-bit messages,Distrib. Comput.4, 105–110.MathSciNetMATHCrossRefGoogle Scholar
  2. Herman, P., Garay, J. A., and Perry, K. J. (1989), Recursive Phase King Protocols for Distributed Consensus, Technical Report CS-89-24, Department of Computer Science, Pennsylvania State University.Google Scholar
  3. Coan, B. A. (1988), Efficient agreement using fault diagnosis, inProceedings of the 26th Allerton Conference on Communication, Control, and Computing, pp. 663–672.Google Scholar
  4. Coan, B. A., and Welch, J. L. (1992), Modular construction of a Byzantine agreement protocol with optimal message bit complexity,Inform, and Comput.97, 61–85.MathSciNetMATHCrossRefGoogle Scholar
  5. Dolev, D. (1982), The Byzantine generals strike again,J. Algorithms 3, 14–30.MathSciNetMATHCrossRefGoogle Scholar
  6. Dolev, D., and Reischuk, R. (1985), Bounds on information exchange for Byzantine agreement,J. Assoc. Comput. Mach. 32, 191–204.MathSciNetMATHCrossRefGoogle Scholar
  7. Fischer, M. J., and Lynch, N. A. (1982), A lower bound for the time to assure interactive consistency,Inform, Process. Lett. 14, 183–186.MathSciNetMATHCrossRefGoogle Scholar
  8. Fischer, M. J., Lynch, N. A., and Merritt, M. (1986), Easy impossibility proofs for distributed consensus problems,Distrib. Comput. 1, 26–39.MATHCrossRefGoogle Scholar
  9. Hadzilacos, V., and Halpern, J. Y. (1993), Message-optimal protocols for Byzantine Agreement,Math. Systems Theory, this issue, pp. 41–102.Google Scholar
  10. Lamport, L., Shostak, R. E., and Pease, M. (1982), The Byzantine generals problem,ACM Trans. Program. Lang. Systems 4, 382–401.MATHCrossRefGoogle Scholar
  11. Pease, M., Shostak, R. E., and Lamport, L. (1980), Reaching agreement in the presence of faults,J Assoc. Comput. Mach. 27, 228–234.MathSciNetMATHCrossRefGoogle Scholar
  12. Perry, K. (1985), Early Stopping Protocols for Fault-Tolerant Distributed Agreement, Ph.D. Thesis, Department of Computer Science, Cornell University. (Also available as technical report TR-85-662.)Google Scholar
  13. Turpin, R., and Coan, B. A. (1984), Extending binary Byzantine agreement to multivalued Byzantine agreement,Inform. Process. Lett. 18, 73–76.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag New York Inc. 1993

Authors and Affiliations

  • Brian A. Coan
    • 1
  • Jennifer L. Welch
    • 2
  1. 1.BellcoreMorristownUSA
  2. 2.Texas A&M UniversityCollege StationUSA

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