Constrained Pseudorandom Functions for Unconstrained Inputs

A constrained pseudo random function (PRF) behaves like a standard PRF, but with the added feature that the (master) secret key holder, having secret key K, can produce a constrained key, K{f}, that allows for the evaluation of the PRF on all inputs satisfied by the constraint f . Most existing constrained PRF constructions can handle only bounded length inputs. In a recent work, Abusalah et al. [AFP14] constructed a constrained PRF scheme where constraints can be represented as Turing machines with unbounded inputs. Their proof of security, however, requires risky “knowledge type” assumptions such as (public coins) differing inputs obfuscation for circuits and SNARKs. In this work, we construct a constrained PRF scheme for Turing machines with unbounded inputs under weaker assumptions, namely, the existence of indistinguishability obfuscation for circuits (and DDH). ∗This work was done while the author was visiting the Simons Institute for the Theory of Computing, supported by the Simons Foundation and by the DIMACS/Simons Collaboration in Cryptography through NSF grant #CNS-1523467. †Supported by NSF CNS-0952692, CNS-1228599 and CNS-1414082. DARPA through the U.S. Office of Naval Research under Contract N00014-11-1-0382, Google Faculty Research award, the Alfred P. Sloan Fellowship, Microsoft Faculty Fellowship, and Packard Foundation Fellowship.