### Abstract

This paper studies the problem of Byzantine consensus in a synchronous message-passing system of n processes. The first deterministic algorithm, and also the simplest in its principles, was the Exponential Information Gathering protocol (EIG) proposed by Pease, Shostak and Lamport in [19]. The algorithm requires processes to send exponentially long messages. Many follow-up works reduced the cost of the algorithm. However, they had to either lower the maximum number of faulty processes t from the optimal range t < n/3 to some smaller range of t [4, 11, 18], or increase the maximum worst-case number of rounds needed for termination (the lower bound being t + 1) [3, 9, 20]. Garay and Moses were the first and only who solved the problem by using a polynomial number of communication bits, for the whole optimal range t < n/3 of the number of Byzantine processes and within the optimal number (t+1) of communication rounds. Their solution, though very complex and sophisticated, requires processes to send O(n^{9}) bits in total. In this work, we present much simpler solution that also holds for the whole optimal range t < n/3 and the optimal number t + 1 of communication rounds, and at the same time lowers the number of exchanged communication bits to O(n^{3} log n). For achieving such an improvement, processes no more exchange relayed proposed values, but information on suspicions "who suspects who", the size of which is quadratic in n in the worst case.

Original language | English (US) |
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Title of host publication | PODC 2013 - Proceedings of the 2013 ACM Symposium on Principles of Distributed Computing |

Pages | 84-91 |

Number of pages | 8 |

DOIs | |

State | Published - Sep 11 2013 |

Externally published | Yes |

Event | 2013 ACM Symposium on Principles of Distributed Computing, PODC 2013 - Montreal, QC, Canada Duration: Jul 22 2013 → Jul 24 2013 |

### Publication series

Name | Proceedings of the Annual ACM Symposium on Principles of Distributed Computing |
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### Conference

Conference | 2013 ACM Symposium on Principles of Distributed Computing, PODC 2013 |
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Country | Canada |

City | Montreal, QC |

Period | 7/22/13 → 7/24/13 |

### Keywords

- Agreement problem
- Byzantine process
- Consensus
- EIG
- Message-passing model
- Round-based protocol
- Synchronous distributed system

### ASJC Scopus subject areas

- Software
- Hardware and Architecture
- Computer Networks and Communications

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## Cite this

*PODC 2013 - Proceedings of the 2013 ACM Symposium on Principles of Distributed Computing*(pp. 84-91). (Proceedings of the Annual ACM Symposium on Principles of Distributed Computing). https://doi.org/10.1145/2484239.2484271