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.
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