On the round complexity of randomized byzantine agreement

Ran Cohen; Iftach Haitner; Nikolaos Makriyannis; Matan Orland; Alex Samorodnitsky

doi:10.4230/LIPIcs.DISC.2019.12

On the round complexity of randomized byzantine agreement

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

The Rachel and Selim Benin School of Engineering and Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

9 Scopus citations

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 − 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
Editors	Jukka Suomela
Publisher	Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)	9783959771269
DOIs	https://doi.org/10.4230/LIPIcs.DISC.2019.12
State	Published - Oct 2019
Event	33rd International Symposium on Distributed Computing, DISC 2019 - Budapest, Hungary Duration: 14 Oct 2019 → 18 Oct 2019

Publication series

Name	Leibniz International Proceedings in Informatics, LIPIcs
Volume	146
ISSN (Print)	1868-8969

Conference

Conference	33rd International Symposium on Distributed Computing, DISC 2019
Country/Territory	Hungary
City	Budapest
Period	14/10/19 → 18/10/19

Bibliographical note

Funding 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.

Publisher Copyright:
© Ran Cohen, Iftach Haitner, Nikolaos Makriyannis, Matan Orland, and Alex Samorodnitsky.

Keywords

Byzantine agreement
Lower bound
Round complexity

Access to Document

10.4230/LIPIcs.DISC.2019.12

Cite this

Cohen, R., Haitner, I., Makriyannis, N., Orland, M., & Samorodnitsky, A. (2019). On the round complexity of randomized byzantine agreement. In J. Suomela (Ed.), 33rd International Symposium on Distributed Computing, DISC 2019 Article 12 (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 146). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.DISC.2019.12

@inproceedings{ac2fd8a4a9ad412aae8ae555da36cd05,

title = "On the round complexity of randomized byzantine agreement",

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 − 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{\textquoteright}17) that tolerates up to n/3 corruptions and terminates at the end of the third round with constant probability.",

keywords = "Byzantine agreement, Lower bound, Round complexity",

author = "Ran Cohen and Iftach Haitner and Nikolaos Makriyannis and Matan Orland and Alex Samorodnitsky",

note = "Funding 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. Publisher Copyright: {\textcopyright} Ran Cohen, Iftach Haitner, Nikolaos Makriyannis, Matan Orland, and Alex Samorodnitsky.; 33rd International Symposium on Distributed Computing, DISC 2019 ; Conference date: 14-10-2019 Through 18-10-2019",

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Cohen, R, Haitner, I, Makriyannis, N, Orland, M & Samorodnitsky, A 2019, On the round complexity of randomized byzantine agreement. in J Suomela (ed.), 33rd International Symposium on Distributed Computing, DISC 2019., 12, Leibniz International Proceedings in Informatics, LIPIcs, vol. 146, Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 33rd International Symposium on Distributed Computing, DISC 2019, Budapest, Hungary, 14/10/19. https://doi.org/10.4230/LIPIcs.DISC.2019.12

On the round complexity of randomized byzantine agreement. / Cohen, Ran; Haitner, Iftach; Makriyannis, Nikolaos et al.
33rd International Symposium on Distributed Computing, DISC 2019. ed. / Jukka Suomela. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 2019. 12 (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 146).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AU - Orland, Matan

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N1 - Funding 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. Publisher Copyright: © Ran Cohen, Iftach Haitner, Nikolaos Makriyannis, Matan Orland, and Alex Samorodnitsky.

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N2 - 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.

AB - 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.

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KW - Lower bound

KW - Round complexity

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Cohen R, Haitner I, Makriyannis N, Orland M, Samorodnitsky A. On the round complexity of randomized byzantine agreement. In Suomela J, editor, 33rd International Symposium on Distributed Computing, DISC 2019. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. 2019. 12. (Leibniz International Proceedings in Informatics, LIPIcs). doi: 10.4230/LIPIcs.DISC.2019.12

On the round complexity of randomized byzantine agreement

Abstract

Publication series

Conference

Bibliographical note

Keywords

Access to Document

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