Abstract: The fully homomorphic encryption schemes based on learning with errors problem own a great potential value in the cloud computing security. However, the existing schemes share a common flaw of large sized public keys, which may cause inefficiency of such schemes in the key and identity management. An identity-based fully homomorphic encryption scheme was presented. The scheme compromises the merits of both identity-based and fully homomorphic encryption schemes, and it overcomes the above mentioned flaw. The security of the proposed scheme reduces to the hardness of learning with errors problem and the one-wayness of trapdoor function in the random oracle model.