A Transformation Approach from Constrained Pseudo-Random Functions to Constrained Verifiable Random Functions

Constrained pseudorandom functions (CPRFs) are fundamental cryptographic primitives used in broadcast encryption and attributed-based encryption. Constrained verifiable random functions (CVRFs) extend CPRFs by incorporating verifiability. A constrained key skS, derived from the master secret key sk, restricts computation to a set Sf with correct evaluation. This allows holders of skS to compute function values only for inputs in S. Prior constructions of CVRFs rely on strong assumptions like multilinear maps or indistinguishability obfuscation, which often suffer from theoretical or practical limitations. In this work, we introduce a simple, generic approach for building CVRFs from basic cryptographic primitives. Specifically, we give a general transformation from any CPRF to a CVRF, achieving provability, uniqueness, and pseudorandomness. We demonstrate that CVRFs can be generically constructed from the following cryptographic primitives: CPRFs, perfectly binding commitment schemes, and non-interactive proof systems. Compared to previous schemes, our approach features a fixed-length public key independent of the circuit depth, improving efficiency and scalability.