Best-Possible Unpredictable Proof-of-Stake: An Impossibility and a Practical Design

The proof-of-stake (PoS) protocols aim to reduce the unnecessary computing power waste seen in Bitcoin. Various practical and provably secure designs have been proposed, like Ouroboros Praos (Eurocrypt 2018) and Snow White (FC 2019). However, the essential security property of unpredictability in these protocols remains insufficiently explored. This paper delves into this property in the cryptographic setting to achieve the "best possible" unpredictability for PoS protocols.We first present an impossibility result for all PoS protocols under the single-extension design framework, where each honest player extends one chain per round. The state-of-the-art permissionless PoS protocols (e.g., Praos, Snow White, and more), are all under this single-extension framework. Our impossibility result states that, if a single-extension PoS protocol achieves the best possible unpredictability, then this protocol cannot be proven secure unless more than 73% of stake is honest.To overcome this impossibility, we introduce a new design framework called multi-extension PoS, allowing each honest player to extend multiple chains using greedy strategy in a round. This strategy allows us to construct a class of PoS protocols that achieve the best possible unpredictability. Additionally, we design a new tiebreak rule for the multi-extension protocol to choose the best chain that can be extended faster, ensuring that the adversary cannot slow-down the chain growth of honest players. It is noteworthy that these protocols can be proven secure, assuming a much smaller fraction (e.g., 57%) of stake to be honest.For a comprehensive security analysis in the cryptographic setting, we develop several new techniques. Analyzing chain growth becomes highly non-trivial as players can extend multiple chains. We introduce a new analysis framework using the Markov chain to assess the chain growth of a multi-extension protocol. To prove the common prefix property, we introduce a concept called "virtual chains" and present a reduction from the regular version of the common prefix to "common prefix w.r.t. virtual chains."