Brahms: Byzantine Resilient Random Membership Sampling

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Brahms: Byzantine Resilient Random Membership Sampling (2008)

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by Edward Bortnikov , Maxim Gurevich , Idit Keidar , Gabriel Kliot , Alexander Shraer

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47 - 2 self

BibTeX

@TECHREPORT{Bortnikov08brahms:byzantine,
    author = {Edward Bortnikov and Maxim Gurevich and Idit Keidar and Gabriel Kliot and Alexander Shraer},
    title = {Brahms: Byzantine Resilient Random Membership Sampling},
    institution = {},
    year = {2008}
}

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Abstract

We present Brahms, an algorithm for sampling random nodes in a large dynamic system prone to malicious behavior. Brahms stores small membership views at each node, and yet overcomes Byzantine attacks by a linear portion of the system. Brahms is composed of two components. The first one is a resilient gossip-based membership protocol. The second one uses a novel memory-efficient approach for uniform sampling from a possibly biased stream of ids that traverse the node. We evaluate Brahms using rigorous analysis, backed by simulations, which show that our theoretical model captures the protocol’s essentials. We study two representative attacks, and show that with high probability, an attacker cannot create a partition between correct nodes. We further prove that each node’s sample converges to a uniform one over time. To our knowledge, no such properties were proven for gossip protocols in the past.

Keyphrases

byzantine resilient random membership sampling novel memory-efficient approach rigorous analysis linear portion overcomes byzantine attack protocol essential representative attack attacker cannot gossip protocol first one theoretical model large dynamic system prone present brahms node sample converges random node malicious behavior brahms store small membership view correct node high probability uniform sampling resilient gossip-based membership protocol

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