ISSN 1000-1239 CN 11-1777/TP

• 信息安全 •

### 全同态加密研究动态及其应用概述

1. 1(北京大学北京国际数学研究中心 北京 100871);2(清华大学微电子学研究所 北京 100084) (liumj9705@pku.edu.cn)
• 出版日期: 2014-12-01
• 基金资助:
基金项目：国家“九七三”重点基础研究发展计划基金项目(2013CB834201)；信息保障技术重点实验室开放基金项目(KJ-13-101)；中国博士后科学基金面上项目(2013M540786)；“十二五”国家密码发展基金密码理论课题(MMJJ201401009)；国家自然科学基金项目(61402252)

### Fully Homomorphic Encryption and Its Applications

Liu Mingjie1, Wang An2

1. 1(Beijing International Center for Mathematical Research, Peking University, Beijing 100871); 2(Institute of Microelectronics, Tsinghua University, Beijing 100084)
• Online: 2014-12-01

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.