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 $O(|m|+n^2\kappa)$ bits per node, where $|m|$ represents the length of the application message and $\kappa=\Omega(\log n)$ is a security parameter. This improves upon the state-of-the-art MBRB solution (Albouy, Frey, Raynal, and Ta\"iani, SSS 2021), which incurs communication of $O(n|m|+n^2\kappa )$ 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 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.

翻译：我们研究了异步消息传递系统中存在 $n$ 个节点时的可靠广播问题，其中多达 $t$ 个节点是恶意的（故障节点），此外还存在一个消息敌手，可能丢弃由正确（非故障）节点发送的部分消息。我们提出了一种容忍消息敌手的拜占庭可靠广播（MBRB）算法，每个节点通信量达到近乎最优的 $O(|m|+n^2\kappa)$ 比特，其中 $|m|$ 表示应用消息的长度，$\kappa=\Omega(\log n)$ 是安全参数。这改进了现有最先进的MBRB方案（Albouy, Frey, Raynal 和 Ta\"iani, SSS 2021），该方案每个节点通信量为 $O(n|m|+n^2\kappa)$ 比特。我们的方案总计发送不超过 $4n^2$ 条消息，这在渐近意义下是最优的。通信量的减少得益于采用编码技术，取代了所有节点需（重新）广播整个消息 $m$ 的需求。相反，节点使用纠删码转发 $m$ 编码后的经过认证的片段。在PKI和抗碰撞哈希的密码学假设下，并假设 $n > 3t + 2d$（其中敌手每次广播最多丢弃 $d$ 条消息），我们的算法允许大多数正确节点重构 $m$，尽管恶意节点和消息敌手可能导致部分碎片缺失。