On Several Verifiable Random Functions and the q-decisional Bilinear Diffie-Hellman Inversion Assumption

Abstract

In 1999, Micali, Rabin and Vadhan introduced the notion of Verifiable Random Functions (VRF)\citeFOCS:MicRabVad99. VRFs compute for a given input x and a secret key $sk$ a unique function value $y=V_sk (x)$, and additionally a publicly verifiable proof π. Each owner of the corresponding public key $pk$ can use the proof to non-interactivly verify that the function value was computed correctly. Furthermore, the function value provides the property of pseudorandomness. Most constructions in the past are based on q-type assumptions. Since these assumptions get stronger for a larger factor q, it is desirable to show the existence of VRFs under static or general assumptions. In this work we will show for the constructions presented in \citePKC:DodYam05 \citeCCS:BonMonRag10 the equivalence of breaking the VRF and solving the underlying q-type assumption.