Abstract: With the development of Internet, especially, the occurrence of the concept of cloud computing, there is an increasing demand for the search and process of encrypted data, which makes the fully homomorphic encryption become more and more important. The concept of fully homomorphic encryption was first introduced by Rivest et al. in 1970s. How to construct such schemes is a hard problem for cryptographers. Until 2009, Gentry presented the first fully homomorphic schemes based on ideal lattice, which is a breakthrough in this field. After that, many cryptographers have done some interesting work which promote the fully homomorphric schemes to be practical in future. Fully homomorphric encryption becomes a very trendy topic in cryptography. This paper discusses the main progress on fully homomorphric schemes including the first homomorphic encryption introduced by Gentry and its optimizations, as well as the fully homorphric schemes based on integer and learning with errors problem (LWE problem). Then, the general application framework of fully homomorphic scheme is provided. Cloud computing, electronic voting and digital watermarking are taken as examples to introduce the significant value of application of fully homomorphric encryption.

Key words: cryptography, public-key cryptography, fully homomorphric encryption, cloud computing, information security