The existing (fully) homomorphic encryption schemes fail to meet practical needs for poor efficiency. To explore new resolution for better homomorphic encryption schemes, the possibility to construct homomorphism on a public key encryption scheme in literature based on Chinese Residue Theorem (CRT) was studied. The possibility of the original scheme to construct the addition and multiplication homomorphic operations was investigated. The original scheme was proved to be unsuitable for constructing homomorphic addition and multiplication operations. Several problems concerning security and efficiency existing in the original scheme were analyzed. Then a revised scheme with tougher security under proper configurations was given, as well as its correctness verification. After that, analysis on security and computing complexity of the revised scheme was given, emphasizing on its ability against the lattice reduction attack. Afterwards, the feasibility of building homomorphic operations on the revised scheme was studied and the main performance comparison between the original and the revised schemes was constructed. Finally, experience on building homomorphism was summarized and some advice on constructing an ideal (fully) homomorphic encryption scheme was presented.

An improved Differential Evolution (DE) algorithm was proposed to solve the problem of premature convergence and improve the computational efficiency of DE. Firstly, different strategies with different parameter values were adopted to enrich the population diversity. Secondly, a new evaluation index was established to determine the suitable combination to match different phases of the search process. Finally, the evolution process was divided into many subprocesses to eliminate the negative effect of the previously selected combination. The contrast experimental results on ten classical Benchmark functions show that the proposed algorithm has a relatively better performance.