Aiming at the problem that the fully homomorphic encryption scheme based on single identity cannot satisfy the homomorphic operation of ciphertext under different identities, as well as the inefficiency of trapdoor function and the complexity of sampling algorithm, an improved lattice MIBFHE scheme was proposed. Firstly, we combined MP12 trapdoor function with dual LWE algorithm to construct a new IBE scheme under the standard model, and prove that the scheme is IND-sID-CPA security under the selective identity. Secondly, we used the eigenvector method to eliminate the evaluation key, and transform the above efficient IBE scheme into a single identity IBFHE scheme to satisfy the homomorphic operation. Finally, we improved the ciphertext extension method of CM15 and constructed a new Link-mask system that supports the transformation of IBFHE scheme under the standard model, and then, converted the above IBFHE scheme into MIBFHE scheme based on this system. The comparative analysis results showed that the efficiency of this scheme is improved compared with similar schemes in the trapdoor generation and preimage sampling, and the dimension of lattice and ciphertext size are significantly shortened.

Privacy security is a key issue for cloud storage. To solve this problem, the paper 1 proposes a privacy-preserving cloud storage framework, which includes the design of data organization structure, the generation and management of keys, the treatment of change of users' access right and dynamic operations of data, and the interaction between participants. We design an interactive protocol and an extirpation-based key derivation algorithm, which are combined with lazy revocation, multi-tree structure and symmetric encryption to form a privacy-preserving, efficient framework for cloud storage. A system is realized which is based on the framework. The paper analyzes the effectiveness of extirpation-based key derivation algorithm, the overhead of the system and the privacy security of the framework. Finally, we summarize our work and introduce our future research directions.

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