From Almost Everywhere to Everywhere: Byzantine Agreement with $\tilde{O}(n^{3/2})$ Bits

Abstract

We address the problem of designing distributed algorithms for large scale networks that are robust to Byzantine faults. We consider a message passing, full information synchronous model: the adversary is malicious, controls a constant fraction of processors, and can view all messages in a round before sending out its own messages for that round. Furthermore, each corrupt processor may send an unlimited number of messages. The only constraint on the adversary is that it must choose its corrupt processors at the start, without knowledge of the processors’ private random bits. To the authors’ best knowledge, there have been no protocols for such a model that compute Byzantine agreement without all-to-all communication, even if private channels or cryptography are assumed, unless corrupt processors’ messages are limited.

In this paper, we give a polylogarithmic time algorithm to agree on a small representative committee of processors using only $\tilde{O}(n^{3/2})$ total bits which succeeds with high probability. This representative set can then be used to efficiently solve Byzantine agreement, leader election, or other problems. This work extends the authors’ work on scalable almost everywhere agreement.