Byzantine Consensus in Abstract MAC Layer

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.