Consensus, abstracting a myriad of problems in which processes have to agree on a single value, is one of the most celebrated problems of fault-tolerant distributed computing. Consensus applications include fundamental services for the environments of the Cloud and Blockchain, and in such challenging environments, malicious behaviors are often modeled as adversarial Byzantine faults. At OPODIS 2010, Mostefaoui and Raynal (in short MR) presented a Byzantine-tolerant solution to consensus in which the decided value cannot be a value proposed only by Byzantine processes. MR has optimal resilience coping with up to t < n/3 Byzantine nodes over n processes. MR provides this multivalued consensus object (which accepts proposals taken from a finite set of values) assuming the availability of a single Binary consensus object (which accepts proposals taken from the set {0,1}). This work, which focuses on multivalued consensus, aims at the design of an even more robust solution than MR. Our proposal expands MR's fault-model with self-stabilization, a vigorous notion of fault-tolerance. In addition to tolerating Byzantine, self-stabilizing systems can automatically recover after the occurrence of arbitrary transient-faults. These faults represent any violation of the assumptions according to which the system was designed to operate (provided that the algorithm code remains intact). To the best of our knowledge, we propose the first self-stabilizing solution for intrusion-tolerant multivalued consensus for asynchronous message-passing systems prone to Byzantine failures. Our solution has a O(t) stabilization time from arbitrary transient faults.

翻译：共识抽象了众多问题，在这些问题中进程必须就单个值达成一致，是容错分布式计算中最著名的问题之一。共识应用包括云计算和区块链环境中的基本服务，而在此类具有挑战性的环境中，恶意行为通常被建模为对抗性拜占庭故障。在OPODIS 2010会议上，Mostefaoui和Raynal（简称MR）提出了一种拜占庭容错的共识解决方案，其中决定的值不能仅由拜占庭进程提出。MR具有最优的鲁棒性，能够处理n个进程中多达t < n/3个拜占庭节点。MR提供了这种多值共识对象（接受从有限值集合中提出的提案），假设存在单个二进制共识对象（接受从集合{0,1}中提出的提案）。本研究聚焦于多值共识，旨在设计一种比MR更鲁棒的解决方案。我们的方案将MR的故障模型扩展为自稳定这一强健的容错概念。除了容忍拜占庭故障外，自稳定系统还能在任意瞬态故障发生后自动恢复。这些故障代表对系统设计运行假设的任何违反（前提是算法代码保持完整）。据我们所知，我们提出了首个针对异步消息传递系统中拜占庭故障的入侵容忍多值共识的自稳定解决方案。我们的方案具有从任意瞬态故障中恢复的O(t)稳定时间。