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 -