Weak Verifiable Random Functions

Zvika Brakerski, Shafi Goldwasser, Guy N. Rothblum, Vinod Vaikuntanathan

Abstract: Verifiable random functions (VRFs), introduced by Micali, Rabin and Vadhan, are pseudorandom functions in which the owner of the seed produces a public-key that constitutes a commitment to all values of the function and can then produce, for any input x, a proof that the function has been evaluated correctly on x, preserving pseudorandomness for all other inputs. No public-key (even a falsely generated one) should allow for proving more than one value per input. VRFs are both a natural and a useful primitive, and previous works have suggested a variety of constructions and applications. Still, there are many open questions in the study of VRFs, especially their relation to more widely studied cryptographic primitives and constructing them from a wide variety of cryptographic assumptions. In this work we define a natural relaxation of VRFs that we call weak verifiable random functions, where pseudorandomness is required to hold only for randomly selected inputs. We conduct a study of weak VRFs, focusing on applications, constructions, and their relationship to other cryptographic primitives. We show: