Easy impossibility proofs for distributed consensus problems
Distributed Computing
Modular construction of nearly optimal Byzantine agreement protocols
Proceedings of the eighth annual ACM Symposium on Principles of distributed computing
Early stopping in Byzantine agreement
Journal of the ACM (JACM)
Coordinated traversal: (t+1)-round Byzantine agreement in polynomial time
Journal of Algorithms
Bounds on information exchange for Byzantine agreement
Journal of the ACM (JACM)
Reaching Agreement in the Presence of Faults
Journal of the ACM (JACM)
The Byzantine Generals Problem
ACM Transactions on Programming Languages and Systems (TOPLAS)
Asymptotically Optimal Distributed Consensus (Extended Abstract)
ICALP '89 Proceedings of the 16th International Colloquium on Automata, Languages and Programming
Another advantage of free choice (Extended Abstract): Completely asynchronous agreement protocols
PODC '83 Proceedings of the second annual ACM symposium on Principles of distributed computing
A Simple and Efficient Randomized Byzantine Agreement Algorithm
IEEE Transactions on Software Engineering
SFCS '83 Proceedings of the 24th Annual Symposium on Foundations of Computer Science
Towards optimal distributed consensus
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
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This paper presents a new Byzantine agreement protocol that tolerates t processor faults using 3t + 1 processors, t + o(t) rounds, O(t^2) total message bits, and O(t^@?) maximum message size, for any @? 0. The protocol is optimal or near optimal in all cost measures: the number of processors is optimal, the message bit complexity is optimal, the number of rounds exceeds the lower bound by o(t), and the maximum message size exceeds the lower bound by O(t^@?). The round complexity is uniformly better than 2.(t + 1) and thus is reasonable even for small t. This is the first Byzantine agreement protocol to have optimal message bit complexity. The new protocol is constructed by recursively applying a simple, yet general, transformation that changes the number of rounds, total message bits, and maximum message size required by a Byzantine agreement protocol, but preserves correctness, number of processor faults tolerated, and total number of processors. Each application of this new transformation reduces the number of message bits sent-at the expense of adding rounds of communication. Surprisingly, the base case of the recursive construction is the agreement protocol of Lamport, Shostak, and Pease, which has a number of message bits exponential in t.