Efficient Multi-Identity Full Homomorphic Encryption Scheme on Lattice

Abstract

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.

Keywords

• lattice
• full homomorphic encryption
• multi-identity encryption
• LWE problem