In this paper we present the Multidimensional Byzantine Agreement (MBA) Protocol, a leaderless Byzantine agreement protocol defined for complete and synchronous networks that allows a network of nodes to reach consensus on a vector of relevant information regarding a set of observed events. The consensus process is carried out in parallel on each component, and the output is a vector whose components are either values with wide agreement in the network (even if no individual node agrees on every value) or a special value \(\bot \) that signals irreconcilable disagreement. The MBA Protocol is probabilistic and its execution halts with probability 1, and the number of steps necessary to halt follows a Bernoulli-like distribution. The design combines a Multidimensional Graded Consensus and a Multidimensional Binary Byzantine Agreement, the generalization to the multidimensional case of two protocols presented by Micali et al. (SIAM J Comput 26(4):873–933, 1997; Byzantine agreement, made trivial, 2016). We prove the correctness and security of the protocol assuming a synchronous network where less than a third of the nodes are malicious.

在本文中，我们介绍了多维拜占庭协议 (MBA) 协议，这是一种为完整和同步网络定义的无领导者拜占庭协议协议，它允许节点网络就一组观察到的事件的相关信息向量达成共识。共识过程在每个组件上并行执行，输出是一个向量，其组件是网络中具有广泛一致性的值（即使没有单个节点对每个值都达成一致）或特殊值\(\bot \)这表明不可调和的分歧。MBA 协议是概率性的，它的执行以概率 1 停止，停止所需的步骤数遵循类伯努利分布。该设计结合了一个多维分级共识和多维二进制拜占庭协议，对 Micali 等人提出的两种协议的多维情况的推广。（SIAM J Comput 26(4):873–933, 1997；拜占庭协议，微不足道，2016）。我们假设同步网络中只有不到三分之一的节点是恶意的，我们证明了协议的正确性和安全性。