Distributed control systems require high reliability and availability guarantees despite often being deployed at the edge of network infrastructure. Edge computing resources are less secure and less reliable than centralized resources in data centers. Replication and consensus protocols improve robustness to network faults and crashed or corrupted nodes, but these volatile environments can cause non-faulty nodes to temporarily diverge, increasing the time needed for replicas to converge on a consensus value, and give Byzantine attackers too much influence over the convergence process. This paper proposes proximal Byzantine consensus, a new approximate consensus protocol where clients use statistical models of streaming computations to decide a consensus value. In addition, it provides an interval around the decision value and the probability that the true (non-faulty, noise-free) value falls within this interval. Proximal consensus (PC) tolerates unreliable network conditions, Byzantine behavior, and other sources of noise that cause honest replica states to diverge. We evaluate our approach for scalar values, and compare PC simulations against a vector consensus (VC) protocol simulation. Our simulations demonstrate that consensus values selected by PC have lower error and are more robust against Byzantine attacks. We formally characterize the security guarantees against Byzantine attacks and demonstrate attacker influence is bound with high probability. Additionally, an informal complexity analysis suggests PC scales better to higher dimensions than convex hull-based protocols such as VC.

翻译：分布式控制系统通常部署在网络基础设施的边缘，尽管需要高可靠性和高可用性保障。边缘计算资源相比数据中心内的集中式资源，安全性和可靠性较低。复制与共识协议能够提升对网络故障、崩溃或受损节点的鲁棒性，但这些易变环境可能导致非故障节点暂时偏离，延长副本达成共识值所需的时间，并使拜占庭攻击者对共识过程施加过多影响。本文提出近端拜占庭共识，一种新的近似共识协议，其中客户端使用流计算的统计模型来判定共识值。此外，该协议提供了围绕决策值的区间，以及真实（非故障、无噪声）值落在此区间内的概率。近端共识能够容忍不可靠的网络条件、拜占庭行为及其他导致诚实副本状态偏离的噪声源。我们针对标量值评估了该方法，并将近端共识模拟与向量共识协议模拟进行了对比。模拟结果表明，近端共识选取的共识值误差更低，且对拜占庭攻击的鲁棒性更强。我们正式刻画了针对拜占庭攻击的安全保障，并证明攻击者影响力以高概率被约束。此外，非形式化的复杂度分析表明，相比基于凸包的协议（如向量共识），近端共识在更高维度上具有更好的可扩展性。