The single-policy attribute-based fully homomorphic encryption scheme cannot perform homomorphic operation and access control of ciphertexts under different attribute vectors corresponding to different policy functions, and new participant ciphertexts cannot dynamically join into the homomorphic operation. In order to solve the above problems, an efficient multi-hop multi-policy attribute-based fully homomorphic encryption scheme based on Learning with Error (LWE) problem was proposed. Firstly, the single-policy attribute-based fully homomorphic encryption scheme was appropriately modified. Secondly, the scheme was mapped to multi-user scenarios. Finally, a multi-hop multi-policy fully homomorphic transformation mechanism was used to realize the homomorphic operation after adding new participant ciphertexts. The proposed scheme is proved to be INDistinguishability under Chosen Plaintext Attack (IND-CPA) secure under the chosen attribute, and has advantages of attribute-based encryption and multi-hop multi-key fully homomorphic encryption. Compared with multi-policy attribute-based fully homomorphic encryption scheme constructed by using target policy function set, the ciphertext/plaintext ratio of the proposed scheme is significantly reduced without changing the size of the individual participant's secret key.

The generation of massive data brings a huge storage and computational burden to users, and the emergence of cloud servers solves this problem well. However, data outsourcing brings convenience to users while it also causes some security problems. In order to solve the security problem of data in the outsourcing process, a simpler and more efficient cloud outsourcing data security auditing protocol throughout whole lifecycle was designed and implemented, which was combined with classical distributed string equality checking protocol and Rank-based Merkel Hash Tree (RMHT) algorithm. The protocol not only can protect the integrity of outsourced storage data, allowing users periodically audit its integrity, but also can guarantee the secure transfer of cloud data. Besides, the copy of transfer data can avoid being reserved by malicious cloud servers, protecting users' privacy well. The analyses of security and efficiency show that the proposed protocol is sufficiently secure and comparatively efficient, the security of outsourcing data throughout its whole lifecycle will be protected well.

Focusing on the issue that the traditional Identity-Based Fully Homomorphic Encryption scheme (IBFHE) cannot perform homomorphic operations on ciphertexts under different IDentities (ID), a hierarchical identity-based multi-identity fully homomorphic encryption scheme based on Learning With Error (LWE) problem was proposed. In the proposed scheme, the transformation mechanism of identity-based multi-identity homomorphic encryption scheme ([CM15] scheme) proposed by Clear et al. (CLEAR M, McGOLDRICK C. Multi-identity and multi-key leveled FHE from learning with errors. Proceedings of the 2015 Annual Cryptology Conference, LNCS 9216. Berlin:Springer, 2015:630-656) in 2015 was combined with Identity-Based Encryption (IBE) scheme proposed by Cash et al. (CASH D, HOFHEINZ D, KILTZ E, et al. Bonsai trees, or how to delegate a lattice basis. Proceedings of the 2010 Annual International Conference on the Theory and Applications of Cryptographic Techniques, LNCS 6110. Berlin:Springer, 2010:523-552) in 2010 ([CHKP10] scheme), guranteeing IND-ID-CPA (INDistinguishability of IDentity-based encryption under Chosen-Plaintext Attack) security in the random oracle model and realizing ciphertext homomorphic operation under different identities, so the application of this scheme was more promising. Compared with[CM15] scheme, the proposed scheme has advantages in terms of public key scale, private key scale, ciphertext size, and hierarchical properties, and has a wide application prospect.