Towards Optimal Communication Byzantine Reliable Broadcast under a Message Adversary

We address the problem of Reliable Broadcast in asynchronous message-passing systems with n nodes, of which up to t are malicious (faulty), in addition to a message adversary that can drop some of the messages sent by correct (non-faulty) nodes. We present a Message-Adversary-Tolerant Byzantine Reliable Broadcast (MBRB) algorithm that communicates an almost optimal amount of O(|m|+n^2κ) bits per node, where |m| represents the length of the application message and κ=Ω(log n) is a security parameter. This improves upon the state-of-the-art MBRB solution (Albouy, Frey, Raynal, and Taïani, SSS 2021), which incurs communication of O(n|m|+n^2κ ) bits per node. Our solution sends at most 4n^2 messages overall, which is asymptotically optimal. Reduced communication is achieved by employing coding techniques that replace the need for all nodes to (re-)broadcast the entire message m. Instead, nodes forward authenticated fragments of the encoding of m using an erasure-correcting code. Under the cryptographic assumptions of PKI and collision-resistant hash, and assuming n > 3t + 2d, where the adversary drops at most d messages per broadcast, our algorithm allows most of the correct nodes to reconstruct m, despite missing fragments caused by the malicious nodes and the message adversary.