Lattice Ciphertext Policy Attribute-based Encryption in the Standard Model

A lattice ciphertext policy attribute based encryption (CP-ABE) scheme is presented, in which the ciphertext policy achieved is the AND-gates on multi-valued attributes. The previous construction with AND-gates on multi-valued attributes as ciphertext policy is based on bilinear paring technology. In this paper, inspired by the recent progress of lattice identity based encryption scheme, we achieve this access structure from lattice technology. There are two constructions given, and both of them can be viewed as an extension and generalization of the lattice identity based encryption schemes proposed by Agrawal et al., respectively. In addition, our constructions are shown to be secure under the learning with errors assumption in the standard model.