Dynamic participation has recently become a crucial requirement for devising permissionless consensus protocols. This notion, originally formalized by Pass and Shi (ASIACRYPT 2017) through their "sleepy model", captures the essence of a system's ability to handle participants joining or leaving during a protocol execution. A dynamically available consensus protocol preserves safety and liveness while allowing dynamic participation. Blockchain protocols, such as Bitcoin's consensus protocol, have implicitly adopted this concept. In the context of Ethereum's consensus protocol, Gasper, Neu, Tas, and Tse (S&P 2021) presented an attack against LMD-GHOST -- the component of Gasper designed to ensure dynamic availability. Consequently, LMD-GHOST results unable to fulfill its intended function of providing dynamic availability for the protocol. Despite attempts to mitigate this issue, the modified protocol still does not achieve dynamic availability, highlighting the need for more secure dynamically available protocols. In this work, we present RLMD-GHOST, a synchronous consensus protocol that not only ensures dynamic availability but also maintains safety during bounded periods of asynchrony. This protocol is particularly appealing for practical systems where strict synchrony assumptions may not always hold, contrary to general assumptions in standard synchronous protocols. Additionally, we present the "generalized sleepy model", within which our results are proven. Building upon the original sleepy model proposed by Pass and Shi, our model extends it with more generalized and stronger constraints on the corruption and sleepiness power of the adversary. This approach allows us to explore a wide range of dynamic participation regimes, spanning from complete dynamic participation to no dynamic participation, i.e., with every participant online.

翻译：动态参与近年来已成为设计无需许可共识协议的关键需求。这一概念最初由Pass和Shi通过其"休眠模型"（ASIACRYPT 2017）予以形式化，刻画了系统在协议执行过程中处理节点加入或退出能力的本质。动态可用共识协议在允许动态参与的同时保持安全性与活性。区块链协议（例如比特币的共识协议）已隐式采纳了这一概念。在以太坊共识协议Gasper的背景下，Neu、Tas和Tse（S&P 2021）针对LMD-GHOST（Gasper中旨在保证动态可用性的组件）提出了一种攻击。因此，LMD-GHOST无法实现其原本设计目标——为协议提供动态可用性。尽管已有缓解该问题的尝试，但修改后的协议仍未达到动态可用性，凸显了对更安全动态可用协议的需求。本文提出RLMD-GHOST，一种同步共识协议，既能保证动态可用性，又能在有界异步期间维持安全性。该协议对实际系统尤为具有吸引力——与标准同步协议的一般假设不同，实际系统中严格的同步假设未必始终成立。此外，我们提出了"广义休眠模型"，并在该模型框架下证明了相关结论。该模型基于Pass和Shi提出的原始休眠模型，通过引入对敌手腐败能力和休眠能力的更广义且更强的约束条件加以扩展。这一方法使我们能够探索完整的动态参与谱系——从完全动态参与到无动态参与（即所有参与者在线）的广泛区间。