Advances in Cryptology – EUROCRYPT 2010

Volume 6110 of the series Lecture Notes in Computer Science pp 656-672

Constructing Verifiable Random Functions with Large Input Spaces

  • Susan HohenbergerAffiliated withJohns Hopkins University
  • , Brent WatersAffiliated withUniversity of Texas at Austin


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 2 n 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.