Near-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 ${\cal O}(|m|+n\kappa)$ bits per node, where $|m|$ represents the length of the application message and $\kappa=\Omega(\log n)$ is a security parameter. This communication complexity is optimal up to the parameter $\kappa$. This significantly improves upon the state-of-the-art MBRB solution (Albouy, Frey, Raynal, and Ta\"iani, TCS 2023), which incurs communication of ${\cal O}(n|m|+n^2\kappa)$ 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 application message $m$. Instead, nodes forward authenticated fragments of the encoding of $m$ using an erasure-correcting code. Under the cryptographic assumptions of threshold signatures and vector commitments, and assuming $n > 3t+2d$, where the adversary drops at most $d$ messages per broadcast, our algorithm allows at least $\ell = n - t - (1 + \epsilon)d$ (for any arbitrarily low $\epsilon> 0$) correct nodes to reconstruct $m$, despite missing fragments caused by the malicious nodes and the message adversary.