On Several Verifiable Random Functions and the q-decisional Bilinear Diffie-Hellman Inversion Assumption
The 5th ACM ASIA Public-Key Cryptography Workshop (APKC 2018)
In 1999, Micali, Rabin and Vadhan introduced the notion of Verifiable Random Functions (VRF).VRFs compute for a given input x and a secret key sk a unique function value y = Vsk (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 large 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  the equivalence of breaking the VRF and solving the underlying q-type assumption.