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.
@article{arxiv.1907.11329,
title = {On the Round Complexity of Randomized Byzantine Agreement},
author = {Ran Cohen and Iftach Haitner and Nikolaos Makriyannis and Matan Orland and Alex Samorodnitsky},
journal= {arXiv preprint arXiv:1907.11329},
year = {2023}
}