Byzantine-tolerant uniform node sampling service in large-scale networks

We consider the problem of achieving uniform node sampling in large scale systems in presence of Byzantine nodes. This service offers a single simple primitive that returns, upon invocation, the identifier of a random node that belongs to the system. We first propose an omniscient strategy that processes on the fly an unbounded and arbitrarily biased input stream made of node identifiers exchanged within the system, and outputs a stream that preserves the uniformity property (same probability to appear in the sample). We show that this property holds despite any arbitrary bias introduced by the adversary. We then propose a strategy that is capable of approximating the omniscient strategy without requiring any prior knowledge on the composition of the input stream. We show through both theoretical analysis and extensive simulations that this strategy accurately approximates the omniscient one. We evaluate the resilience of the strategy by studying two representative attacks. We quantify the minimum number of identifiers that Byzantine nodes must insert in the input stream to prevent uniformity. Finally, we propose a new construction in series that allows to both increase the accuracy of a single sketch and decrease the time to converge to a uniform output stream.