This paper studies the design of Byzantine consensus algorithms in an \textit{asynchronous }single-hop network equipped with the "abstract MAC layer" [DISC09], which captures core properties of modern wireless MAC protocols. Newport [PODC14], Newport and Robinson [DISC18], and Tseng and Zhang [PODC22] study crash-tolerant consensus in the model. In our setting, a Byzantine faulty node may behave arbitrarily, but it cannot break the guarantees provided by the underlying abstract MAC layer. To our knowledge, we are the first to study Byzantine faults in this model. We harness the power of the abstract MAC layer to develop a Byzantine approximate consensus algorithm and a Byzantine randomized binary consensus algorithm. Both of our algorithms require \textit{only} the knowledge of the upper bound on the number of faulty nodes $f$, and do \textit{not} require the knowledge of the number of nodes $n$. This demonstrates the "power" of the abstract MAC layer, as consensus algorithms in traditional message-passing models require the knowledge of \textit{both} $n$ and $f$. Additionally, we show that it is necessary to know $f$ in order to reach consensus. Hence, from this perspective, our algorithms require the minimal knowledge. The lack of knowledge of $n$ brings the challenge of identifying a quorum explicitly, which is a common technique in traditional message-passing algorithms. A key technical novelty of our algorithms is to identify "implicit quorums" which have the necessary information for reaching consensus. The quorums are implicit because nodes do not know the identity of the quorums -- such notion is only used in the analysis.

翻译：本文研究在配备“抽象MAC层”[DISC09]的异步单跳网络中设计拜占庭共识算法，该抽象层捕获了现代无线MAC协议的核心特性。Newport[PODC14]、Newport和Robinson[DISC18]以及Tseng和Zhang[PODC22]在该模型中研究了崩溃容错共识。在我们的设定中，拜占庭故障节点可能任意行为，但无法破坏底层抽象MAC层提供的保证。据我们所知，我们是首个在此模型中研究拜占庭故障的工作。我们利用抽象MAC层的能力开发了一种拜占庭近似共识算法和一种拜占庭随机化二元共识算法。我们的两个算法仅需知道故障节点数量的上界$f$，而无需知道节点总数$n$。这体现了抽象MAC层的“能力”，因为传统消息传递模型中的共识算法需要同时知道$n$和$f$。此外，我们证明要达成共识必须知道$f$。因此从该角度看，我们的算法所需知识最少。缺乏对$n$的了解带来了显式识别法定数量的挑战，而这是传统消息传递算法中的常用技术。我们算法的关键技术创新在于识别出具有达成共识所需信息的“隐式法定数量”。这些法定数量是隐式的，因为节点不知道法定数量的身份——这一概念仅在分析中使用。