**Constructing Veriﬁable Random Functions with Large Input Spaces**

*Susan Hohenberger and Brent Waters*

**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.

**Category / Keywords: **foundations / VRF, PRF, large inputs, standard model

**Publication Info: **To appear in Eurocrypt 2010. This is the full version.

**Date: **received 24 Feb 2010, last revised 23 May 2010

**Contact author: **susan at cs jhu edu

**Available format(s): **PDF | BibTeX Citation

**Note: **An earlier draft did not properly handle input zero. This is now addressed.

**Version: **20100524:014924 (All versions of this report)

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