We propose a new distributed-computing model, inspired by permissionless distributed systems such as Bitcoin and Ethereum, that allows studying permissionless consensus in a mathematically regular setting. Like in the sleepy model of Pass and Shi, we consider a synchronous, round-by-round message-passing system in which the set of online processors changes each round. Unlike the sleepy model, the set of processors may be infinite. Moreover, processors never fail; instead, an adversary can temporarily or permanently impersonate some processors. Finally, processors have access to a strong form of message-authentication that authenticates not only the sender of a message but also the round in which the message was sent. Assuming that, each round, the adversary impersonates less than 1/2 of the online processors, we present two consensus algorithms. The first ensures deterministic safety and constant latency in expectation, assuming a probabilistic leader-election oracle. The second ensures deterministic safety and deterministic liveness assuming irrevocable impersonation and eventually-stabilizing participation. The model is unrealistic in full generality. However, if we assume finitely many processes and that the set of faulty processes remains constant, the model coincides with a practically-motivated model: the static version of the sleepy model.

翻译：我们提出了一种新的分布式计算模型，受比特币和以太坊等无许可分布式系统的启发，该模型允许在数学规范的环境中研究无许可共识。与Pass和Shi的休眠模型类似，我们考虑一个同步的、逐轮消息传递系统，其中在线处理器的集合每轮都会变化。与休眠模型不同的是，处理器集合可能无限大。此外，处理器不会发生故障；相反，攻击者可以暂时或永久地冒充某些处理器。最后，处理器可以使用一种强形式的消息认证，该认证不仅验证消息的发送者，还验证消息发送的轮次。假设每轮中攻击者冒充的在线处理器数量少于1/2，我们提出了两种共识算法。第一种算法在假设存在概率性领导者选举预言机的情况下，保证了确定性安全性和期望常数延迟。第二种算法在假设不可撤销的冒充行为和最终稳定的参与度的情况下，保证了确定性安全性和确定性活跃性。该模型在完全一般化的情况下是不现实的。然而，如果我们假设有限数量的进程并且故障进程集合保持不变，该模型与一个具有实际动机的模型——即休眠模型的静态版本——是一致的。