Constrained pseudorandom functions from functional encryption

Abstract

This paper demonstrates how to design constrained pseudorandom functions (CPRF) and their various extensions from any public key functional encryption (FE) with standard polynomial security against arbitrary collusions. More precisely, we start by presenting a CPRF construction that supports constraint predicates realizable by arbitrary polynomial-size circuits, based on polynomially-hard public key FE and one way functions. Next, we augment our CPRF construction with the verifiability feature, relying only on a minimal additional assumption, namely, the existence of standard public key encryption (PKE). Finally, we show how to achieve privacy for the issued keys in the context of programable pseudorandom functions (PPRF), which is an enhanced variant of CPRF supporting puncturing constraints, employing polynomially-hard FE and one way functions. All prior works addressing the above problems either work for very restricted settings or rely on highly powerful yet little-understood cryptographic objects such as multilinear maps or indistinguishability obfuscation (IO). Although, there are known transformations from FE to IO, the reductions suffer from an exponential security loss and hence cannot be directly employed to replace IO with FE in cryptographic constructions at the expense of only a polynomial loss. Thus, our results open up a new pathway towards realizing numerous variants of CPRF, which are interesting cryptographic primitives in their own right and, moreover, have already been shown instrumental in a staggering range of applications, both in classical as well as in cutting edge cryptography, based on progressively weaker and well-studied cryptographic building blocks. Our work can also be interpreted as yet another stepping stone towards establishing FE as a substitute for IO in cryptographic applications. In order to achieve our results we build upon the prefix puncturing technique developed by Garg et al. [CRYPTO 2016, EUROCRYPT 2017] [42,43].