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: Constructions. We present constructions of weak VRFs based on a variety of assumptions, including general assumptions such as (enhanced) trapdoor permutations, as well as constructions based on specific number-theoretic assumptions such as the Diffie-Hellman assumption in bilinear groups. Separations. Verifiable random functions (both weak and standard) cannot be constructed from one-way permutations in a black-box manner. This constitutes the first result separating (standard) VRFs from any cryptographic primitive. Applications. Weak VRFs capture the essence of constructing non-interactive zero-knowledge proofs for all NP languages. © 2009 Springer Berlin Heidelberg.
CITATION STYLE
Brakerski, Z., Goldwasser, S., Rothblum, G. N., & Vaikuntanathan, V. (2009). Weak verifiable random functions. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 5444 LNCS, pp. 558–576). https://doi.org/10.1007/978-3-642-00457-5_33
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