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||American English|
|Title of host publication||33rd International Symposium on Distributed Computing, DISC 2019|
|Publisher||Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing|
|State||Published - Oct 2019|
|Event||33rd International Symposium on Distributed Computing, DISC 2019 - Budapest, Hungary|
Duration: 14 Oct 2019 → 18 Oct 2019
|Name||Leibniz International Proceedings in Informatics, LIPIcs|
|Conference||33rd International Symposium on Distributed Computing, DISC 2019|
|Period||14/10/19 → 18/10/19|
Bibliographical noteFunding Information:
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.
© Ran Cohen, Iftach Haitner, Nikolaos Makriyannis, Matan Orland, and Alex Samorodnitsky.
- Byzantine agreement
- Lower bound
- Round complexity