## Abstract

The problem of efficiently performing Byzantine agreement in t + 1 rounds in the face of arbitrarily malicious failures is a longstanding open problem in fault-tolerant distributed computing. The original paper by Pease, Shostak, and Lamport (J. Assoc. Comput. Mach.27, No.2 (1980), 228-234) presented a (t + 1)-round protocol for the problem that uses exponential-size communication, and many papers in the last decade have labored to improve on that. Whereas efficient (t + 1)-round protocols have been developed for weaker failure models, (t + 1)-round protocols in the Byzantine model have been known only for n = Ω(t^{2}), where n is the number of processors and t is the number of failures tolerated by the protocol. This paper presents a communication-efficient polynomial-time (t + 1)-round Byzantine agreement protocol for n > 8t. The protocol is an "early stopping" protocol, halting in min[t + 1, f + 2] rounds in the worst case, where f is the number of processors that actually fail during the run. This is provably optimal. The protocol is based on a careful combination of early stopping, fault masking, and a new technique called coordinated traversal. The combination of the three provides a powerful method of restricting the damage that a faulty processor, however malicious, can do. One of the byproducts of this protocol is a polynomial-time (t + 1)-round protocol for the Byzantine firing squad problem.

Original language | English |
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Pages (from-to) | 110-156 |

Number of pages | 47 |

Journal | Journal of Algorithms |

Volume | 17 |

Issue number | 1 |

DOIs | |

State | Published - Jul 1994 |

Externally published | Yes |

## ASJC Scopus subject areas

- Control and Optimization
- Computational Mathematics
- Computational Theory and Mathematics