Paper 2019/868
On the Round Complexity of Randomized Byzantine Agreement
Ran Cohen, Iftach Haitner, Nikolaos Makriyannis, Matan Orland, and Alex Samorodnitsky
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 $1\Theta(1)$. (3) For a large class of protocols (including all BA protocols used in practice) and under a plausible combinatorial conjecture, BA protocols resilient against 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 publickey 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.
Metadata
 Available format(s)
 Category
 Cryptographic protocols
 Publication info
 Published elsewhere. Major revision. DISC 2019
 Keywords
 Byzantine agreementlower boundround complexity
 Contact author(s)

cohenran @ idc ac il
iftachh @ cs tau ac il
n makriyannis @ gmail com
matanorland @ mail tau ac il
salex @ cs huji ac il  History
 20220212: last of 3 revisions
 20190730: received
 See all versions
 Short URL
 https://ia.cr/2019/868
 License

CC BY
BibTeX
@misc{cryptoeprint:2019/868, author = {Ran Cohen and Iftach Haitner and Nikolaos Makriyannis and Matan Orland and Alex Samorodnitsky}, title = {On the Round Complexity of Randomized Byzantine Agreement}, howpublished = {Cryptology ePrint Archive, Paper 2019/868}, year = {2019}, note = {\url{https://eprint.iacr.org/2019/868}}, url = {https://eprint.iacr.org/2019/868} }