In the traditional Secure Multi-party Computation (SMC), each participant can obtain the final result, but this coarse-grained access control may not be suitable for the requirements of specific users to decrypt ciphertexts, thus a new encryption scheme which has more accurate access control on the decryption authority of computation results was put forward. Combined with predicate encryption, a predicate encryption scheme with multiplicative homomorphic property for the secure multi-party computation was constructed. Compared with the existing predicate encryption, it supports the homomorphic operation, and is more accurate in access control on the decryption authority of computation results. In the current background of cloud environment, the secure multi-party computation of more fine-grained access control on computation results is realized, which is proved secure under INDistinguishable Attribute-Hiding against Chosen Plaintext Attacks (IND-AH-CPA).

Focusing on the function defect of the traditional Identity-Based Encryption (IBE) scheme that the ciphertexts can not be calculated directly, a new IBE scheme was proposed. The homomorphism transformation mechanism proposed by Gentry was used to transform the hierarchical IBE scheme proposed by Agrawal into a homomorphic hierarchical IBE scheme. Compared with the GSW (Gentry, Sahai, Waters) scheme (GENTRY C, SAHAI A, WATERS B. Homomorphic encryption from learning with errors:conceptually-simpler, asymptotically-faster, attribute-based. CRYPTO 2013:Proceedings of the 33rd Annual Cryptology Conference on Advances in Cryptology. Berlin:Springer, 2013:75-92) and CM (Clear, Mcgoldrick) scheme (CLEAR M, MCGOLDRICK C. Bootstrappable identity-based fully homomorphic encryption. CANS 2014:Proceedings of 13th International Conference on Cryptology and Network Security. Berlin:Springer, 2014:1-19), the construction method of the proposed scheme was more natural, the level of space complexity was reduced from cubic to square with higher efficiency. In the current environment of cloud computing, the proposed scheme can contribute to the transformation from theory to practice of fully homomorphic encryption scheme based on Learning With Errors (LWE) problem. The performance analysis and the verification results under the random oracle model prove the security for Indistinguishability of the Identity-Based Encryption Scheme under Chosen-Plaintext Attack (IND-ID-CPA) of the proposed scheme.