Verifiable Random Functions from Standard Assumptions

The question whether there exist verifiable random functions with exponential-sized input space and full adaptive security based on a non-interactive, constant-size assumption is a longstanding open problem. We construct the first verifiable random functions which achieve all these properties simultaneously. Our construction can securely be instantiated in groups with symmetric bilinear map, based on any member of the (n− 1)-linear assumption family with n ≥ 3. This includes, for example, the 2-linear assumption, which is also known as the decision linear (DLIN) assumption.