On Black-Box Reductions between Predicate Encryption Schemes

We prove that there is no black-box construction of a threshold predicate encryption system from identity-based encryption. Our result signifies nontrivial progress in a line of research suggested by Boneh, Sahai and Waters (TCC ’11), where they proposed a study of the relative power of predicate encryption for different functionalities. We rely on and extend the techniques of Boneh et al. (FOCS ’08), where they give a black-box separation of identity-based encryption from trapdoor permutations. In contrast to previous results where only trapdoor permutations were used, our starting point is a more powerful primitive, namely identitybased encryption, which allows planting exponentially many trapdoors in the public-key by only planting a single master public-key of an identitybased encryption system. This makes the combinatorial aspect of our black-box separation result much more challenging. Our work gives the first impossibility result on black-box constructions of any cryptographic primitive from identity-based encryption. We also study the more general question of constructing predicate encryption for a complexity class F, given predicate encryption for a (potentially less powerful) complexity class G. Toward that end, we rule out certain natural black-box constructions of predicate encryption for NC from predicate encryption for AC assuming a widely believed conjecture in communication complexity.