## 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 n/4 corruptions 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 n/3 [resp., n/4] corruptions 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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Title of host publication | 33rd International Symposium on Distributed Computing, DISC 2019 |

Editors | Jukka Suomela |

Publisher | Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing |

ISBN (Electronic) | 9783959771269 |

DOIs | |

State | Published - Oct 2019 |

Externally published | Yes |

Event | 33rd International Symposium on Distributed Computing, DISC 2019 - Budapest, Hungary Duration: 14 Oct 2019 → 18 Oct 2019 |

### Publication series

Name | Leibniz International Proceedings in Informatics, LIPIcs |
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Volume | 146 |

ISSN (Print) | 1868-8969 |

### Conference

Conference | 33rd International Symposium on Distributed Computing, DISC 2019 |
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Country/Territory | Hungary |

City | Budapest |

Period | 14/10/19 → 18/10/19 |

### Bibliographical note

Publisher Copyright:© Ran Cohen, Iftach Haitner, Nikolaos Makriyannis, Matan Orland, and Alex Samorodnitsky.

### Funding

Funding Ran Cohen: Research supported by the Northeastern University Cybersecurity and Privacy Institute Post-doctoral fellowship, IARPA under award 2019-19020700009 (ACHILLES), NSF grant TWC-1664445, NSF grant 1422965, and by the NSF MACS project. Some of this work was done while the author was a post-doc at Tel Aviv University, supported by ERC starting grant 638121. Iftach Haitner: Member of the Check Point Institute for Information Security. Research supported by ERC starting grant 638121. Nikolaos Makriyannis: Research supported by ERC starting grant 638121 and by ERC advanced grant 742754. Matan Orland: Research supported by ERC starting grant 638121. Alex Samorodnitsky: Research partially supported by ISF grant 1724/15.

Funders | Funder number |
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ACHILLES | |

ERC advanced | |

ERC starting | |

NSF MACS | |

Northeastern University Cybersecurity and Privacy Institute | |

National Sleep Foundation | TWC-1664445 |

Horizon 2020 Framework Programme | 1422965, 638121, 742754 |

Intelligence Advanced Research Projects Activity | 2019-19020700009 |

Iowa Science Foundation | 1724/15 |

Tel Aviv University |

## Keywords

- Byzantine agreement
- Lower bound
- Round complexity