Abstract
We present a family of verifiable random functions which are provably secure for exponentially-large input spaces under a noninteractive complexity assumption. Prior constructions required either an interactive complexity assumption or one that could tolerate a factor 2n security loss for n-bit inputs. Our construction is practical and inspired by the pseudorandom functions of Naor and Reingold and the verifiable random functions of Lysyanskaya. Set in a bilinear group, where the Decisional Diffie-Hellman problem is easy to solve, we require the l- Decisional Diffie-Hellman Exponent assumption in the standard model, without a common reference string. Our core idea is to apply a simulation technique where the large space of VRF inputs is collapsed into a small (polynomial-size) input in the view of the reduction algorithm. This view, however, is information-theoretically hidden from the attacker. Since the input space is exponentially large, we can first apply a collision-resistant hash function to handle arbitrarily-large inputs.
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Hohenberger, S., Waters, B. (2010). Constructing Verifiable Random Functions with Large Input Spaces. In: Gilbert, H. (eds) Advances in Cryptology – EUROCRYPT 2010. EUROCRYPT 2010. Lecture Notes in Computer Science, vol 6110. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13190-5_33
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