中文摘要：

随着互联网的发展,尤其是云计算概念的诞生,人们在加密数据搜索与处理等方面的需求日益增加,使得全同态加密变得愈加重要.全同态加密的思想是20世纪70年代Rivest等人首次提出的,如何构造满足全同态性质的体制一直是困扰密码学家的难题,直到2009年Gentry基于理想格提出了第1个全同态加密体制使得该方面的研究取得突破性进展.随后许多密码学家在全同态加密方案的研究上作出了有意义的工作,促进了全同态加密向实用化的发展.对全同态加密的研究动态进行了概要的介绍,包括Gentry提出的第1个全同态加密方案及其优化;基于整数的全同态加密方案;基于LWE问题的全同态加密方案等.随后探讨了全同态加密的一般性应用框架,并以云计算、电子投票、数字水印3个应用为例,介绍了全同态加密的重要应用价值.

英文摘要：

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 homomorphie 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.