Research On Predicate Encryption Theory And Its Popularization

Predicate encryption is a novel research notion for public-key cryptography. It is an extension of a series of research based on identity-based encryption, attribute-based encryption and searchable encryption. It supports search queries on encrypted data, and this offers a new solution for traditional coarse-grained public-key encryption. In a general predicate encryption scheme, secret keys correspond to predicates f and ciphertexts are associated with attributes I. The secret key SKf corresponding to a predicate f can be used to decrypt a ciphertext associated with attribute I if and only if f (I)＝1.In this paper we give a symmetric-key predicate encryption scheme on bilinear pairings which supports inner product queries firstly. This scheme is based on compos-ite order bilinear groups, and proven to be selectively secure under a non-interactive assumption. Moreover, using dual pairing vector spaces, we also present a public-key predicate encryption scheme which is based on prime order bilinear groups, and prove that this scheme is simulation secure in the generic group model. Secondly, we introduce lattice and pseudo-commutativity of invertible difference encoding, and give a lattice-based predicate encryption scheme. Based on the lattice-based predi-cate encryption scheme, we construct a lattice-based hierarchical predicate encryption scheme. It is shown to be weak attribute hiding based on the difficulty of the learning with errors(LWE) problem in the standard model. Finally, we make an analysis and comparison between some predicate encryption schemes and our schemes on the bilin-ear pairing and lattice respectively. As can be seen from the results, our schemes have the shorter ciphertext and secret keys than other schemes.