Distributed Pseudorandom Functions for General Access Structures in NP

Distributed pseudorandom functions (DPRFs) originally introduced by Naor, Pinkas and Reingold (EUROCRYPT ’99) are pseudorandom functions (PRFs), whose computation is distributed to multiple servers. Although by distributing the function computation, we avoid single points of failures, this distribution usually implies the need for multiple interactions with the parties (servers) involved in the computation of the function. In this paper, we take distributed pseudorandom functions (DPRFs) even further, by pursuing a very natural direction. We ask if it is possible to construct distributed PRFs for a general class of access mechanism going beyond the threshold access structure and the access structure that can be described by a polynomial-size monotone span programs. More precisely, our contributions are two-fold and can be summarised as follows: (i) we introduce the notion of single round distributed PRFs for a general class of access structure (monotone functions in NP), (ii) we provide a provably secure general construction of distributed PRFs for every mNP access structure from puncturable PRFs based on indistinguishable obfuscation.