License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.DISC.2019.12
URN: urn:nbn:de:0030-drops-113199
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2019/11319/
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Cohen, Ran ; Haitner, Iftach ; Makriyannis, Nikolaos ; Orland, Matan ; Samorodnitsky, Alex

On the Round Complexity of Randomized Byzantine Agreement

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LIPIcs-DISC-2019-12.pdf (0.5 MB)

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.

BibTeX - Entry

@InProceedings{cohen_et_al:LIPIcs:2019:11319,
  author =	{Ran Cohen and Iftach Haitner and Nikolaos Makriyannis and Matan Orland and Alex Samorodnitsky},
  title =	{{On the Round Complexity of Randomized Byzantine Agreement}},
  booktitle =	{33rd International Symposium on Distributed Computing (DISC 2019)},
  pages =	{12:1--12:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-126-9},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{146},
  editor =	{Jukka Suomela},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2019/11319},
  URN =		{urn:nbn:de:0030-drops-113199},
  doi =		{10.4230/LIPIcs.DISC.2019.12},
  annote =	{Keywords: Byzantine agreement, lower bound, round complexity}
}

Keywords: Byzantine agreement, lower bound, round complexity
Collection: 33rd International Symposium on Distributed Computing (DISC 2019)
Issue Date: 2019
Date of publication: 08.10.2019

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