eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2019-10-08
12:1
12:17
10.4230/LIPIcs.DISC.2019.12
article
On the Round Complexity of Randomized Byzantine Agreement
Cohen, Ran
1
2
Haitner, Iftach
3
Makriyannis, Nikolaos
4
Orland, Matan
3
Samorodnitsky, Alex
5
Boston University, MA, USA
Northeastern University, Boston, MA, USA
School of Computer Science, Tel Aviv University, Israel
Department of Computer Science, Technion, Haifa, Israel
School of Engineering and Computer Science, The Hebrew University of Jerusalem, Israel
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-Theta(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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol146-disc2019/LIPIcs.DISC.2019.12/LIPIcs.DISC.2019.12.pdf
Byzantine agreement
lower bound
round complexity