TY - GEN

T1 - On the round complexity of randomized byzantine agreement

AU - Cohen, Ran

AU - Haitner, Iftach

AU - Makriyannis, Nikolaos

AU - Orland, Matan

AU - Samorodnitsky, Alex

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

PY - 2019/10

Y1 - 2019/10

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.

KW - Byzantine agreement

KW - Lower bound

KW - Round complexity

UR - http://www.scopus.com/inward/record.url?scp=85074567273&partnerID=8YFLogxK

U2 - 10.4230/LIPIcs.DISC.2019.12

DO - 10.4230/LIPIcs.DISC.2019.12

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AN - SCOPUS:85074567273

T3 - Leibniz International Proceedings in Informatics, LIPIcs

BT - 33rd International Symposium on Distributed Computing, DISC 2019

A2 - Suomela, Jukka

PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing

T2 - 33rd International Symposium on Distributed Computing, DISC 2019

Y2 - 14 October 2019 through 18 October 2019

ER -