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Efficient Unbiasable Verifiable Random Functions via (Non-)Black-Box Reductions

ePrint Report: Efficient Unbiasable Verifiable Random Functions via (Non-)Black-Box Reductions Nicholas Brandt We present conceptually simple and practically efficient constructions of a verifiable random function (VRF) that fulfills strong notions of unbiasability recently introduced by Giunta and Stewart (Eurocrypt 2024). Unbiasability is a crucial property for many applications of VRFs such as leader election in proof-of-stake blockchains. The only previous constructions provide heuristic security in the random oracle model or rely on the decisional Diffie–Hellman assumption with preprocessing which incurs significant overhead. In contrast, our compiler turns any VRF into an unbiasable VRF in the standard model (without any setup) using only symmetric-key primitives; and thus only with negligible computational overhead. Underlying our approach, we provide a generic black-box reduction for unbiasability of VRFs that incurs subexponential loss. Additionally, under a mild (verifiable) requirement on the underlying VRF we also show a novel non-black-box reduction that incurs only polynomial loss. This non-black-box technique allows us to replace the folklore "VUF-then-Hash" heuristic with a provably secure "Hash-then-VRF" construction at virtually no cost. In particular, if the underlying VRF hashes its input, our transformation requires only a single evaluation of a hardcore function, e.g. parity of the input (plus a PRF evaluation for full security).

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