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 $O((l+\lambda)n^2)$ .

翻译：认证环境下的多值拜占庭共识协议（MVBA）被广泛用作异步网络中原子广播与容错状态机复制协议的核心设计基础。自Cachin等人开创性工作\cite{CACHIN01}以来，后续研究致力于优化协议的通信效率。Cachin贡献后的重要进展包括：i）VABA\cite{BYZ17}需通过多个协议实例对参与方的请求达成共识；ii）Dumbo-MVBA\cite{LU20}采用密码学异步分发与恢复方法管理通信复杂度，同时引入额外计算与通信轮次开销。我们的目标是设计一种MVBA协议，在保持最优指标的前提下，无需额外计算与通信轮次即可在每个实例中达成共识。该设计方法的核心在于引入经典MVBA协议中的委员会机制：随机选取包含（f+1，其中n=3f+1）个参与方的子集，这些参与方同步广播其请求（交易）以收集可验证证明。通过连续分发这些证明，我们获得使用异步二进制拜占庭共识协议（ABBA）就选定参与方的请求达成共识的必要特性。通过整合委员会与ABBA协议，我们设计了最优MVBA协议——pMVBA（基于优先级的MVBA）。该协议能够容忍最多\lfloor n/3\rfloor个拜占庭故障，预期运行时间为O(1)，消息复杂度最优为O(n^2)，通信复杂度最优为O((l+\lambda)n^2)。