TY - GEN
T1 - Fast agreement in networks with byzantine nodes
AU - Chlebus, Bogdan S.
AU - Kowalski, Dariusz R.
AU - Olkowski, Jan
N1 - Funding Information:
by the Polish National Science Center (NCN) grant
Funding Information:
Dariusz R. Kowalski: Supported by the Polish National Science Center (NCN) grant UMO-2017/25/B/ST6/02553.
Publisher Copyright:
© Bogdan S. Chlebus, Dariusz R. Kowalski, and Jan Olkowski; licensed under Creative Commons License CC-BY 34th International Symposium on Distributed Computing (DISC 2020).
PY - 2020/10/1
Y1 - 2020/10/1
N2 - We study Consensus in synchronous networks with arbitrary connected topologies. Nodes may be faulty, in the sense of either Byzantine or proneness to crashing. Let t denote a known upper bound on the number of faulty nodes, and Ds denote a maximum diameter of a network obtained by removing up to s nodes, assuming the network is (s + 1)-connected. We give an algorithm for Consensus running in time t + D2t with nodes subject to Byzantine faults. We show that, for any algorithm solving Consensus for Byzantine nodes, there is a network G and an execution of the algorithm on this network that takes Ω(t + D2t) rounds. We give an algorithm solving Consensus in t + Dt communication rounds with Byzantine nodes using authenticated messages of polynomial size. We show that for any numbers t and d > 4, there exists a network G and an algorithm solving Consensus with Byzantine nodes using authenticated messages in fewer than t + 3 rounds on G, but all algorithms solving Consensus without message authentication require at least t + d rounds on G. This separates Consensus with Byzantine nodes from Consensus with Byzantine nodes using message authentication, with respect to asymptotic time performance in networks of arbitrary connected topologies, which is unlike complete networks. Let f denote the number of failures actually occurring in an execution and unknown to the nodes. We develop an algorithm solving Consensus against crash failures and running in time O(f + Df ), assuming only that nodes know their names and can differentiate among ports; this algorithm is also communication-efficient, by using messages of size O(m log n), where n is the number of nodes and m is the number of edges. We give a lower bound t + Dt − 2 on the running time of any deterministic solution to Consensus in (t + 1)-connected networks, if t nodes may crash.
AB - We study Consensus in synchronous networks with arbitrary connected topologies. Nodes may be faulty, in the sense of either Byzantine or proneness to crashing. Let t denote a known upper bound on the number of faulty nodes, and Ds denote a maximum diameter of a network obtained by removing up to s nodes, assuming the network is (s + 1)-connected. We give an algorithm for Consensus running in time t + D2t with nodes subject to Byzantine faults. We show that, for any algorithm solving Consensus for Byzantine nodes, there is a network G and an execution of the algorithm on this network that takes Ω(t + D2t) rounds. We give an algorithm solving Consensus in t + Dt communication rounds with Byzantine nodes using authenticated messages of polynomial size. We show that for any numbers t and d > 4, there exists a network G and an algorithm solving Consensus with Byzantine nodes using authenticated messages in fewer than t + 3 rounds on G, but all algorithms solving Consensus without message authentication require at least t + d rounds on G. This separates Consensus with Byzantine nodes from Consensus with Byzantine nodes using message authentication, with respect to asymptotic time performance in networks of arbitrary connected topologies, which is unlike complete networks. Let f denote the number of failures actually occurring in an execution and unknown to the nodes. We develop an algorithm solving Consensus against crash failures and running in time O(f + Df ), assuming only that nodes know their names and can differentiate among ports; this algorithm is also communication-efficient, by using messages of size O(m log n), where n is the number of nodes and m is the number of edges. We give a lower bound t + Dt − 2 on the running time of any deterministic solution to Consensus in (t + 1)-connected networks, if t nodes may crash.
KW - Byzantine fault
KW - Consensus
KW - Distributed algorithm
KW - Lower bound
KW - Message authentication
KW - Network
KW - Node crash
UR - http://www.scopus.com/inward/record.url?scp=85101847458&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85101847458&partnerID=8YFLogxK
U2 - 10.4230/LIPIcs.DISC.2020.30
DO - 10.4230/LIPIcs.DISC.2020.30
M3 - Conference contribution
AN - SCOPUS:85101847458
T3 - Leibniz International Proceedings in Informatics, LIPIcs
BT - 34th International Symposium on Distributed Computing, DISC 2020
A2 - Attiya, Hagit
PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
T2 - 34th International Symposium on Distributed Computing, DISC 2020
Y2 - 12 October 2020 through 16 October 2020
ER -