IRWIN AND JOAN JACOBS CENTER FOR COMMUNICATION AND INFORMATION TECHNOLOGIES Brahms: Byzantine Resilient Random Membership Sampling

We present Brahms, an algorithm for sampling random nodes in a large dynamic systemprone to Byzantine failures. Brahms stores small membership views at each node, and yetovercomes Byzantine failures of a linear portion of the system. Brahms is composed of twocomponents. The first one is a Byzantine-resistant gossip-based membership protocol. Thesecond one uses a novel memory-efficient approach for uniform sampling from a possibly bi-ased stream of ids that traverse the node. We evaluate Brahms using rigorous analysis, backedby extensive simulations, which show that our theoretical model captures the protocol’s essen-tials. We show that, with high probability, an attacker cannot create a partition between correctnodes. We further prove that each node’s sample converges to a uniform one over time. To ourknowledge, no such properties were proven for gossip-based membership in the past.