Simulatable VRFs with Applications to Multi-Theorem NIZK

This paper introduces simulatable verifiable random functions (sVRF). VRFs are similar to pseudorandom functions, except that they are also verifiable: corresponding to each seed SK, there is a public key PK, and for y = FPK(x), it is possible to prove that y is indeed the value of the function seeded by SK. A simulatable VRF is a VRF for which this proof can be simulated, so a simulator can pretend that the value of FPK(x) is any y. Our contributions are as follows. We introduce the notion of sVRF. We give two constructions: one from general assumptions (based on NIZK), but inefficient, just as a proof of concept; the other construction is practical and based on a special assumption about composite-order groups with bilinear maps. We then use an sVRF to get a direct transformation from a single-theorem non-interactive zero-knowledge proof system for a language L to a multi-theorem non-interactive proof system for the same language L.