Prioritized-MVBA: A New Approach to Design an Optimal Asynchronous Byzantine Agreement Protocol

The multi-valued byzantine agreement protocol (MVBA) in the authenticated setting has been widely used as a core to design atomic broadcast and fault-tolerant state machine replication protocols in asynchronous networks. Originating from the seminal work of Cachin et al. \cite{CACHIN01}, subsequent research endeavors have sought to optimize protocol efficiency in terms of communication complexity. Notable advancements following Cachin's contributions include: i) VABA \cite{BYZ17}, requiring multiple protocol instances to achieve agreement on a party's request, and ii) Dumbo-MVBA \cite{LU20}, employing a cryptographic asynchronous dispersal and recovery methods to manage communication complexity alongside additional computational and communication rounds overheads. Our objective is to devise an MVBA protocol that achieves agreement in each instance without extra computation and communication rounds while maintaining the optimal metrics. Central to our design approach is the introduction of the committee in the classic MVBA protocol, wherein a randomly selected subset of ($f+1$, where $n=3f+1$) parties get selected and simultaneously broadcast their requests (transactions) to gather verifiable proofs. Successive distributions of these proofs afford us the necessary properties to employ the asynchronous binary Byzantine agreement (ABBA) protocol for reaching an agreement on a selected party's requests. By integrating the committee and ABBA protocols, we devise the optimal MVBA protocol, termed pMVBA (Prioritized-MVBA). This protocol exhibits resilience to tolerate up to $\lfloor \frac{n}{3}\rfloor$ Byzantine failures, with an expected runtime of $O(1)$, optimal message complexity of $O(n^2)$, and optimal communication complexity $O((l+\lambda)n^2)$ .