## Abstract

We prove lower bounds on the round complexity of randomized Byzantine agreement (BA) protocols, bounding the halting probability of such protocols after one and two rounds. In particular, we prove that: 1. BA protocols resilient against n/3 [resp., n/4] corruptions terminate (under attack) at the end of the first round with probability at most o(1) [resp., 1 / 2 + o(1)]. 2. BA protocols resilient against a fraction of corruptions greater than 1/4 terminate at the end of the second round with probability at most 1 - Θ (1). 3. For a large class of protocols (including all BA protocols used in practice) and under a plausible combinatorial conjecture, BA protocols resilient against a fraction of corruptions greater than 1/3 [resp., 1/4] terminate at the end of the second round with probability at most o(1) [resp., 1 / 2 + o(1)]. The above bounds hold even when the parties use a trusted setup phase, e.g., a public-key infrastructure (PKI). The third bound essentially matches the recent protocol of Micali (ITCS’17) that tolerates up to n/3 corruptions and terminates at the end of the third round with constant probability.

Original language | English |
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Article number | 10 |

Journal | Journal of Cryptology |

Volume | 35 |

Issue number | 2 |

State | Published - Apr 2022 |

Externally published | Yes |

### Bibliographical note

Publisher Copyright:© 2022, International Association for Cryptologic Research.

### Funding

Iftach Haitner: Member of the Check Point Institute for Information Security. Research supported by Israel Science Foundation Grant 666/19. Research supported by ERC starting Grant 638121. Ran Cohen: Research supported in part by NSF Grant No. 2055568. Some of this work was done while the author was a post-doc at Tel Aviv University, supported by ERC starting Grant 638121. Nikolaos Makriyannis: This work was done while the author was a post-doc at Technion, supported by ERC advanced Grant 742754. Research supported by ERC starting Grant 638121. Alex Samorodnitsky: Research partially supported by ISF Grant 1724/15. Matan Orland: Research supported by ERC starting Grant 638121.

Funders | Funder number |
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National Science Foundation | 2055568 |

European Commission | 638121, 742754 |

Israel Science Foundation | 666/19, 1724/15 |

Tel Aviv University | |

Technion-Israel Institute of Technology |

## Keywords

- Byzantine agreement
- Lower bound
- Round complexity