A Verifiable Random Function with Short Proofs and Keys

We give a simple and efficient construction of a verifiable random function (VRF) on groups equipped with a bilinear mapping. Our construction is direct; it bypasses an expensive Goldreich-Levin transformation from a unique signature to a VRF in contrast to prior works of Micali-Rabin-Vadhan [MRV99] and Lysyanskaya [Lys02]. Our proofs of security are based on a decisional bilinear Diffie-Hellman inversion assumption (DBDHI), previously used in [BB04a] to construct an identity based encryption scheme. Our VRF’s proofs and keys have constant size in contrast to proofs and keys of VRFs in [Lys02] and [Dod03], which are linear in the size of the message. We operate over an elliptic group, which is significantly shorter than the multiplicative group Z∗n used in [MRV99], yet we achieve the same security. Furthermore, our scheme can be made distributed and proactive.