International Association for Cryptologic Research

International Association
for Cryptologic Research


Paper: Constructing Verifiable Random Functions with Large Input Spaces

Susan Hohenberger
Brent Waters
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Abstract: We present a family of verifiable random functions which are provably secure for exponentially-large input spaces under a non-interactive 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 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.
  title={Constructing Verifiable Random Functions with Large Input Spaces},
  booktitle={IACR Eprint archive},
  keywords={foundations / VRF, PRF, large inputs, standard model},
  note={To appear in Eurocrypt 2010.   This is the full version. 14753 received 24 Feb 2010, last revised 23 May 2010},
  author={Susan Hohenberger and Brent Waters},