This paper reviewed the development of homomorphic encryption. It summarized five typical public key homomorphic eneryption scheme and two kinds of typical fully homomorphic encryption scheme, and analyzed the design method of fully homomorphic eneryption algorithm. It also analyzed deeply for fully homomorphic encryption from security. This paper compared the four kinds of fully homomorphic encryption algorithm. It pointed out the key problems of fully homomorphic encryption that needed to be researched at present. It can pr...