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On the Round Complexity of Randomized Byzantine Agreement
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| 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., $$1/2+ o(1)$$ 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 $$1-\Theta (1)$$ 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., $$1/2 + o(1)$$ 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. |
BibTeX
@article{jofc-2022-32799,
title={On the Round Complexity of Randomized Byzantine Agreement},
journal={Journal of Cryptology},
publisher={Springer},
volume={35},
doi={10.1007/s00145-022-09421-7},
author={Ran Cohen and Iftach Haitner and Nikolaos Makriyannis and Matan Orland and Alex Samorodnitsky},
year=2022
}