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On blackbox reductions between predicate encryption schemes
 of Lecture Notes in Computer Science
, 2012
"... We prove that there is no blackbox construction of a threshold predicate encryption system from identitybased 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 en ..."
Abstract

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We prove that there is no blackbox construction of a threshold predicate encryption system from identitybased 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 blackbox separation of identitybased 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 publickey by only planting a single master publickey of an identitybased encryption system. This makes the combinatorial aspect of our blackbox separation result much more challenging. Our work gives the first impossibility result on blackbox constructions of any cryptographic primitive from identitybased 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 blackbox constructions of predicate encryption for NC 1 from predicate encryption for AC 0 assuming a widely believed conjecture in communication complexity.