A new solution for the byzantine generals problem
Information and Control
Distributed agreement in the presence of processor and communication faults
IEEE Transactions on Software Engineering
A communication-efficient canonical form for fault-tolerant distributed protocols
PODC '86 Proceedings of the fifth annual ACM symposium on Principles of distributed computing
Early stopping in Byzantine agreement
Journal of the ACM (JACM)
Knowledge and common knowledge in a byzantine environment: crash failures
Information and Computation
Modular construction of a Byzantine agreement protocol with optimal message bit complexity
Information and Computation
Bounds on information exchange for Byzantine agreement
Journal of the ACM (JACM)
Impossibility of distributed consensus with one faulty process
Journal of the ACM (JACM)
A simple proof of the uniform consensus synchronous lower bound
Information Processing Letters
Optimal Early Stopping in Distributed Consensus (Extended Abstract)
WDAG '92 Proceedings of the 6th International Workshop on Distributed Algorithms
Resolving message complexity of Byzantine Agreement and beyond
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Uniform consensus is harder than consensus
Journal of Algorithms
Optimal early stopping uniform consensus in synchronous systems with process omission failures
Proceedings of the sixteenth annual ACM symposium on Parallelism in algorithms and architectures
Optimally efficient multi-valued byzantine agreement
Proceedings of the twenty-fifth annual ACM symposium on Principles of distributed computing
Robust gossiping with an application to consensus
Journal of Computer and System Sciences
Lower Bounds for Achieving Synchronous Consensus with Orderly Crash Failure
ICDCSW '07 Proceedings of the 27th International Conference on Distributed Computing Systems Workshops
'Eventual' is earlier than 'immediate'
SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
Continuous Consensus with Failures and Recoveries
DISC '08 Proceedings of the 22nd international symposium on Distributed Computing
Scalable byzantine computation
ACM SIGACT News
Breaking the O(n2) bit barrier: Scalable byzantine agreement with an adaptive adversary
Journal of the ACM (JACM)
Error-free multi-valued broadcast and byzantine agreement with optimal communication complexity
OPODIS'11 Proceedings of the 15th international conference on Principles of Distributed Systems
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In consensus, the n nodes of a distributed system seek to take a consistent decision on some output, despite up to t of them crashing or even failing maliciously, i.e., behaving "Byzantine''. It is known that it is impossible to guarantee that synchronous, deterministic algorithms consistently decide on an output in fewer than f+1 rounds in executions in which the actual number of faults is f ≤ t. This even holds if faults are crash-only, and in this case the bound can be matched precisely. However, the question of whether this can be done efficiently, i.e., with little communication, so far has not been addressed. In this work, we show that algorithms tolerating Byzantine faults and deciding within f+2 rounds must send Ω(nt+t2f) messages; as a byproduct, our analysis shows that decision within f +1 rounds is impossible in this setting (unless f=t). Moreover, we prove that any crash-resilient algorithm deciding in f+1 rounds has worst-case message complexity Ω(n2f). Interestingly, this changes drastically if we restrict the fault model further. If crashes are orderly, i.e., in each round, each node picks an order in which its messages are sent, and crashing nodes successfully transmit a prefix of their sequence, deciding in f+1 rounds can be guaranteed with O(nt) messages.