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This paper introduces a novel sleepy consensus protocol that accommodates fully fluctuating participation from miners while relying on minimal assumptions, specifically a public key infrastructure (PKI) and a verifiable random function (VRF). By employing a new technique called graded wakeness, the protocol enables nodes to maintain consistent opinions about the activity status of other nodes without the need for verifiable delay functions (VDFs). The protocol also incorporates an extension for uncorruption, allowing corrupt nodes to regain honest status, thus enhancing the robustness of consensus mechanisms in blockchain systems.
Achieving fully fluctuating participation in sleepy consensus without relying on heavy cryptographic primitives like VDFs could revolutionize blockchain protocols.
Bitcoin's proof-of-work (PoW)-based protocol is remarkable for how little it asks of its participants. Not only can miners take breaks from work whenever they please, but it is almost unique in offering a path of contrition: corrupt miners can reclaim honest status simply by resuming mining on the longest chain. The protocol only requires that honest miners hold the majority of computational power at any given time. Analogous proof-of-stake (PoS) protocols, usually formalized via the sleepy model of Pass and Shi (2017), have fallen short of matching this robustness. In fact, sleepy consensus protocols in the plain PKI model must heavily restrict fluctuations in adversarial participation over time. The recent work of Efron, Neu, and Pitassi (2025) enables fully fluctuating participation in the sleepy model by introducing the external adversary model. Their protocol, however, relies on verifiable delay functions (VDFs), a strong cryptographic primitive that somewhat resembles PoW, by assuming that the adversary cannot compute sequential work significantly faster than honest nodes. In this work, we design a sleepy consensus protocol for fully fluctuating participation with an external adversary under an honest majority, from minimal assumptions: a public key infrastructure (PKI) and a verifiable random function (VRF). In particular, we make no VDF or hardware assumptions. Our key technique is graded wakeness, a novel primitive that allows nodes to form consistent opinions on which other nodes are awake. We further extend our protocol to handle uncorruption, where corrupt nodes return to honesty. This extension requires only a mild additional assumption on the unpredictability of VRF outputs for liveness.
