Epidemic algorithms for replicated database maintenance
PODC '87 Proceedings of the sixth annual ACM Symposium on Principles of distributed computing
Linearizability: a correctness condition for concurrent objects
ACM Transactions on Programming Languages and Systems (TOPLAS)
Implementing fault-tolerant services using the state machine approach: a tutorial
ACM Computing Surveys (CSUR)
Random oracles are practical: a paradigm for designing efficient protocols
CCS '93 Proceedings of the 1st ACM conference on Computer and communications security
The Byzantine Generals Problem
ACM Transactions on Programming Languages and Systems (TOPLAS)
Information and Computation
Practical byzantine fault tolerance and proactive recovery
ACM Transactions on Computer Systems (TOCS)
On the Security of Joint Signature and Encryption
EUROCRYPT '02 Proceedings of the International Conference on the Theory and Applications of Cryptographic Techniques: Advances in Cryptology
Proofs of Work and Bread Pudding Protocols
CMS '99 Proceedings of the IFIP TC6/TC11 Joint Working Conference on Secure Information Networks: Communications and Multimedia Security
Diffusion without false rumors: on propagating updates in a Byzantine environment
Theoretical Computer Science
Concentration for Independent Permutations
Combinatorics, Probability and Computing
Distributed Computing
Access cost for asynchronous Byzantine quorum systems
Distributed Computing
Fault-scalable Byzantine fault-tolerant services
Proceedings of the twentieth ACM symposium on Operating systems principles
Optimal Resilience for Erasure-Coded Byzantine Distributed Storage
DSN '06 Proceedings of the International Conference on Dependable Systems and Networks
Tolerating Byzantine Faulty Clients in a Quorum System
ICDCS '06 Proceedings of the 26th IEEE International Conference on Distributed Computing Systems
IEEE Transactions on Dependable and Secure Computing
Distributed Computing - Special issue: PODC 04
Byzantine and multi-writer k-quorums
DISC'06 Proceedings of the 20th international conference on Distributed Computing
On the availability of non-strict quorum systems
DISC'05 Proceedings of the 19th international conference on Distributed Computing
Bosco: One-Step Byzantine Asynchronous Consensus
DISC '08 Proceedings of the 22nd international symposium on Distributed Computing
Write Markers for Probabilistic Quorum Systems
OPODIS '08 Proceedings of the 12th International Conference on Principles of Distributed Systems
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Byzantine-fault-tolerant service protocols like Q/U and FaB Paxos that optimistically order requests can provide increased efficiency and fault scalability. However, these protocols require n ≥ 5b+1 servers (where b is the maximum number of faults tolerated), owing to their use of opaque Byzantine quorum systems; this is 2b more servers than required by some non-optimistic protocols. In this paper, we present a family of probabilistic opaque Byzantine quorum systems that require substantially fewer servers. Our analysis is novel in that it assumes Byzantine clients, anticipating that a faulty client may seek quorums that maximize the probability of error. Using this as motivation, we present an optional, novel protocol that allows probabilistic quorum systems to tolerate Byzantine clients. The protocol requires only one additional round of interaction between the client and the servers, and this round may be amortized over multiple operations. We consider actual error probabilities introduced by the probabilistic approach for concrete configurations of opaque quorum systems, and prove that the probability of error vanishes with as few as n 3.15b servers as n and b grow.