Efficient Fully Secure Predicate Encryption for Conjunctions, Disjunctions and k-CNF/DNF formulae

Predicate encryption is an important cryptographic primitive that has found wide applications as it allows for fine-grained key management. In a predicate encryption scheme for a class P of predicates, the owner of the master secret key can derive a secret key SkP for any predicate P ∈ P. Similarly, when encrypting plaintext M , the sender can specify an attribute vector ~x for the ciphertext Ct. Then, key SkP can decrypt all ciphertexts Ct with attribute vector ~x such that P (~x) = 1. In this paper, we give fully secure implementations Conjunctions, Disjunctions and k-CNF/DNF predicates that guarantee the security of the plaintext and of the attribute. Our constructions for Disjunctions and Conjunctions are linear in the number of variables. Previous fully secure constructions for Disjunction required time exponential in the number of variables while for Conjunctions the best previous construction was quadratic in the number of variables.