Enhancing Long-Range Security for Proof-of-Stake Consensus via Sampleable Verifiable Delay Functions

Long-range attacks constitute a fundamental weakness of Proof-of-Stake (PoS) blockchains: once signing keys are leaked or obtained, fabricating a convincing alternative chain history becomes effectively costless. To mitigate this issue, we introduce a sampleable verifiable delay function (sVDF) that embeds compact, verifiable time samples into block headers and drives a time-aware fork-choice rule that lexicographically prioritizes cumulative sVDF iterations. We formalize the threat model and protocol interfaces, prove that our sVDF satisfies correctness, uniqueness, and sequentiality under standard cryptographic assumptions, and show that the augmented protocol increases the amount of sequential work required for a successful long-range forgery. Our experimental analysis indicates that moderate hardware heterogeneity and periodically refreshed anchors suffice to keep the catch-up probability low within realistic regimes. Our design is backward compatible, incurs modest bandwidth and verification overhead, and can serve as an additive defense for existing PoS blockchains.