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On the Round Complexity of Randomized Byzantine Agreement

Authors Ran Cohen, Iftach Haitner, Nikolaos Makriyannis, Matan Orland, Alex Samorodnitsky

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ACM Subject Classification
  • Theory of computation → Cryptographic protocols
Keywords
  • Byzantine agreement
  • lower bound
  • round complexity

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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)]. 
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.

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Ran Cohen, Iftach Haitner, Nikolaos Makriyannis, Matan Orland, and Alex Samorodnitsky. On the Round Complexity of Randomized Byzantine Agreement. In 33rd International Symposium on Distributed Computing (DISC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 146, pp. 12:1-12:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019) https://doi.org/10.4230/LIPIcs.DISC.2019.12

Author Details

Ran Cohen
  • Boston University, MA, USA
  • Northeastern University, Boston, MA, USA
Iftach Haitner
  • School of Computer Science, Tel Aviv University, Israel
Nikolaos Makriyannis
  • Department of Computer Science, Technion, Haifa, Israel
Matan Orland
  • School of Computer Science, Tel Aviv University, Israel
Alex Samorodnitsky
  • School of Engineering and Computer Science, The Hebrew University of Jerusalem, Israel

Funding

  • Cohen, Ran: 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.
  • Haitner, Iftach: Member of the Check Point Institute for Information Security. Research supported by ERC starting grant 638121.
  • Makriyannis, Nikolaos: Research supported by ERC starting grant 638121 and by ERC advanced grant 742754.
  • Orland, Matan: Research supported by ERC starting grant 638121.
  • Samorodnitsky, Alex: Research partially supported by ISF grant 1724/15.

Acknowledgements

We would like to thank Rotem Oshman, Juan Garay, Ehud Friedgut, and Elchanan Mossel for very helpful discussions.

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