Generic Construction of (hierarchical) Functional Pseudorandom Functions.

Functional Pseudorandom (F-PRF) is a cryptography primitive which extends the standard Pseudorandom Function (PRF) to be functional, where for any function f, a functional key can be generated to compute the PRF F on x in the range of f. F-PRF can be used in MPC or to provide the authorization-like serves, but the known constructions of F- PRF are only for some special function classes or the prefix-fixing functions, how to construct it for any function is still an open problem. We have moved a little bit in this direction. Concretely, we build the first construction of F-PRF for any function based on Indistinguishability Obfuscation and Puncturable PRF, and prove its selective security. Then we have defined a new security of F-PRF called semi-adaptive security, and prove that the above construction is semi-adaptively secure if the underlying Puncturable PRF is adaptively secure. Finally, we extend the construction to be hierarchical – a party owning a functional key can generate sub-functional keys within its ability.