Multi-valued byzantine broadcast: The t < n case

Abstract

Byzantine broadcast is a distributed primitive that allows a specific party to consistently distribute a message among n parties in the presence of potential misbehavior of up to t of the parties. All known protocols implementing broadcast of an l-bit message from point-to-point channels tolerating any t < n Byzantine corruptions have communication complexity at least Ω(ln2). In this paper we give cryptographically secure and information-theoretically secure protocols for t < n that communicate O(ln) bits when l is sufficiently large. This matches the optimal communication complexity bound for any protocol allowing to broadcast l-bit messages. While broadcast protocols with the optimal communication complexity exist for t < n.