Learning with error based searchable encryption scheme

A learning with error problem based encryption scheme that allows secure searching over the cipher text is proposed. Both the generation of cipher text and the trapdoor of the query are based on the problem of learning with errors. By performing an operation over the trapdoor and the cipher text, it is able to tell if the cipher text is the encryption of a plaintext. The secure searchable encryption scheme is both cipher text and trapdoor indistinguishable. The probabilities of missing and failing match occurrence in searching are both exponentially small.