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Probabilistic Opaque Quorum Systems

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Book cover Distributed Computing (DISC 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4731))

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Abstract

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 > 3.15 b servers as n and b grow.

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Authors and Affiliations

  1. Carnegie Mellon University, Pittsburgh, PA, USA

    Michael G. Merideth

  2. University of North Carolina, Chapel Hill, NC, USA

    Michael K. Reiter

Authors
  1. Michael G. Merideth
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  2. Michael K. Reiter
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Editor information

Andrzej Pelc

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© 2007 Springer-Verlag Berlin Heidelberg

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Merideth, M.G., Reiter, M.K. (2007). Probabilistic Opaque Quorum Systems. In: Pelc, A. (eds) Distributed Computing. DISC 2007. Lecture Notes in Computer Science, vol 4731. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75142-7_31

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  • DOI: https://doi.org/10.1007/978-3-540-75142-7_31

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-75141-0

  • Online ISBN: 978-3-540-75142-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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