基于错误学习的全同态加密技术研究现状与挑战  

Research Current Status and Challenges of Fully Homomorphic Cryptography Based on Learning with Errors

作　　者：温金明 刘庆[1] 陈洁[3] 吴永东 WEN Jinming;LIU Qing;CHEN Jie;WU Yongdong(College of Information Science and Technology,Jinan University,Guangzhou 510632,China;China State Key Laboratory of Cryptology,Beijing 100878,China;Software Engineering Institute,East China Normal University,Shanghai 200062,China;Guangdong Key Laboratory for Data Security and Privacy Preserving,Guangzhou 510632,China)

机构地区：[1]暨南大学信息科学技术学院,广州510632 [2]密码科学技术国家重点实验室,北京100878 [3]华东师范大学软件工程学院,上海200062 [4]数据安全与隐私保护广东省重点实验室,广州510632

出　　处：《信息网络安全》2024年第9期1328-1351,共24页Netinfo Security

基　　金：国家自然科学基金[11871248,12271215,61932011]。

摘　　要：全同态加密方案是一种具备数据机密性和安全性的加密方案,同时还能够对密文进行计算操作。在云计算时代,全同态加密方案能够满足私有信息检索、多方安全计算等多种应用需求。错误学习与全同态加密的结合,迅速推动了全同态加密方案的发展,并引出了多种技术工具,如密钥交换和模交换等具有理论和实际应用意义的技术。自从2011年基于LWE的全同态加密方案被提出以来,基于LWE类型的方案已成为全同态加密方案的主流方法,并逐步从理论走向实际应用。文章首先介绍全同态加密的基础知识和应用,并对构造方案的数学理论进行详细分析;然后系统梳理了每一代同态加密方案,并给出了每一代方案的典型构造方式;最后探讨了当前基于LWE的全同态加密方案存在的问题以及未来的发展趋势,为后续研究者提供一些参考。Fully homomorphic encryption scheme is an encryption scheme with data confidentiality and security,and it is also able to perform computational operations on the ciphertext.In the era of cloud computing,full homomorphic encryption scheme can meet the needs of private information retrieval,multi-party secure computing and other applications.The combination of the Learning With Errors(LWE)problem and fully homomorphic encryption has rapidly promoted the development of fully homomorphic encryption schemes,and has led to a variety of technological tools,such as key exchange and mode exchange,as well as many technology with theoretical and practical applications.Since the LWE-based fully homomorphic encryption scheme was proposed in 2011,the LWE-type based scheme has become the mainstream method of fully homomorphic encryption scheme,and has gradually moved from theory to practical application.This paper first introduced the basics and applications of full homomorphic encryption,and provided a detailed analysis of the mathematical theory used to construct the scheme;then systematically combed through the development of each generation of homomorphic encryption schemes,and gave the typical construction methods of each generation of schemes;finally,it discussed the problems of the current LWE-based full homomorphic encryption schemes as well as the development trends in the future.This paper analysed and researched the development of LWE-based fully homomorphic encryption in recent years,and provided some references for subsequent researchers.

关 键 词：全同态加密 错误学习 隐私保护 

分 类 号：TP309[自动化与计算机技术—计算机系统结构]