Dynamic participation has recently become a key requirement to devise permissionless consensus protocols, as it adds a degree of robustness to events that include portions of participants going offline, preserving safety and liveness of such dynamically available protocols. This notion, formalized by Pass and Shi (ASIACRYPT 2017) with the sleepy model, has been implicitly adopted to model several blockchain protocols such as, for example, the Ethereum's consensus protocol, Gasper. Neu, Tas, and Tse (S&P 2021) show that LMD-GHOST, the dynamic availability component of Gasper, is actually not secure even in a context of full-participation, i.e., with all the validators online. Mitigations have shortly after been developed to cope with its problems, but the resulting protocol still falls short of achieving dynamic availability, motivating the research of more secure dynamically available protocols. In this work we present RLMD-GHOST, a synchronous dynamically available protocol that does not lose safety during bounded periods of asynchrony. This protocol results appealing especially for practical systems, where strict synchrony assumptions might not always hold, contrary to what is generally assumed with standard synchronous protocols. Moreover, we introduce the \emph{generalized sleepy model}, in which our results will be proved. This model takes up from the original sleepy model presented by Pass and Shi and extends it with more generalized and stronger constraints in the corruption and sleepiness power of the adversary. This allows us to explore a broad space of dynamic participation regimes which falls between complete dynamic participation and no dynamic participation, i.e., with every participant online, offering a foundation for the analysis of dynamic available protocols.

翻译：动态参与最近成为设计无需许可共识协议的关键要求，因为它增强了对部分参与者离线事件的鲁棒性，从而保障此类动态可用协议的安全性和活跃性。这一由Pass和Shi（ASIACRYPT 2017）在“睡眠模型”中形式化的概念，已被隐式应用于模拟多种区块链协议，例如以太坊的共识协议Gasper。Neu、Tas和Tse（S&P 2021）指出，Gasper的动态可用性组件LMD-GHOST即使在完全参与（即所有验证者在线）的情况下实际上也不安全。随后虽迅速提出缓解其问题的方案，但改进后的协议仍未能实现动态可用性，从而推动了对更安全的动态可用协议的研究。本文提出RLMD-GHOST，一种同步动态可用协议，在有限异步期间内不会丧失安全性。该协议对实际系统尤其具有吸引力，因为严格同步假设在实际中并不总能成立，这与标准同步协议的一般假设形成对比。此外，我们引入了“广义睡眠模型”，并在此模型下证明我们的结论。该模型继承了Pass和Shi提出的原始睡眠模型，并通过在对手的腐败能力和睡眠能力上施加更广义且更强的约束来扩展它。这使得我们能够探索介于完全动态参与与无动态参与（即所有参与者在线）之间的广泛动态参与机制空间，为动态可用协议的分析提供基础。