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. © 2010 Springer-Verlag.
CITATION STYLE
Hohenberger, S., & Waters, B. (2010). Constructing verifiable random functions with large input spaces. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6110 LNCS, pp. 656–672). https://doi.org/10.1007/978-3-642-13190-5_33
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