Full secure identity-based encryption scheme with short public key size over lattices in the standard model

An efficient identity-based encryption (IBE) scheme over lattice is proposed in this paper. Under the hardness of the learning with errors (LWE) problem, the proposed scheme is semantic secure against adaptive chosen identity and chosen plaintext attack in the standard model. To improve the efficiency of the lattice-based IBE scheme, unlike the identity string is encoded into a matrix by a group of public matrices in several known constructions, the identity string of l bits is encoded into a vector with the help of l + 1 vectors in this paper. With the help of this idea, we achieve the private key extraction of IBE scheme at the same lattice. Then, the public key of the proposed scheme only consists of one n x m matrix and l + 1 vectors, compared with that the public keys of the known lattice-based IBE schemes all consist as a group of n x m matrices. Hence, the public key size of this scheme is shorter than that of the known constructions.