Approximate byzantine consensus is a fundamental problem of distributed computing. This paper presents a novel algorithm for approximate byzantine consensus, called Relay-ABC. The algorithm allows machines to achieve approximate consensus to arbitrary exactness in the presence of byzantine failures. The algorithm relies on the usage of a relayed messaging system and signed messages with unforgeable signatures that are unique to each node. The use of signatures and relays allows the strict necessary network conditions of traditional approximate byzantine consensus algorithms to be circumvented. We also provide theoretical guarantees of validity and convergence for Relay-ABC. To do this, we utilize the idea that the iteration of states in the network can be modeled by a sequence of transition matrices. We extend previous methods, which use transition matrices to prove ABC convergence, by having each state vector model not just one iteration, but a set of $D$ iterations, where $D$ is a diameter property of the graph. This allows us to accurately model the delays of messages inherent within the relay system.

翻译：近似于zantine 的共识是分布式计算的一个基本问题。 本文为近似于zantine 的共识提供了一种叫作 Relay- ABC 的新型算法。 该算法允许机器在出现 byzantine 失败时就任意精确性达成大致一致。 该算法依赖于使用转发式信息系统,并使用每个节点独有的不可追溯性签名。 使用签名和继电器可以绕过传统的zantine 共识算法的严格必要的网络条件。 我们还为 Relay- ABC 提供了有效性和趋同性的理论保证。 为此,我们利用网络中国家的迭代可由一系列过渡矩阵建模的理念。 我们扩展了以前使用过渡矩阵来证明ABC趋同性的方法,即每个向量模型不只使用一个迭代号,而使用一套$D的迭代号,这是图的直径属性。 这使我们能够精确地模拟中继系统所固有的信息的延迟。