基于抽象解密结构的全同态加密构造方法分析  

Analysis of Constructing Fully Homomorphic Encryption Based on the Abstract Decryption Structure

作　　者：宋新霞[1] 陈智罡[2,3] SONG Xinxia;CHEN Zhigang(College of Junior, Zhejiang Wanli University, Ningbo 315100, China;College of Electronics and Computer, Zhejiang Wanli University, Ningbo 315100, China;State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences Beijing 100093, China)

机构地区：[1]浙江万里学院基础学院,宁波315100 [2]浙江万里学院电子与计算机学院,宁波315100 [3]中国科学院信息工程研究所信息安全国家重点实验室,北京100093

出　　处：《电子与信息学报》2018年第7期1669-1675,共7页Journal of Electronics & Information Technology

基　　金：浙江省科技厅公益性技术科研项目(2017C33079;LGG18F020001);浙江省自然科学基金(LY17F020002);密码科学技术国家重点实验室开放课题基金;宁波市自然科学基金(2017A610120)~~

摘　　要：为什么能够在格上构造全同态加密?密文矩阵的本质及构造方法是什么?该文提出一个重要的概念:抽象解密结构。该文以抽象解密结构为工具,对目前全同态加密构造方法进行分析,得到抽象解密结构、同态性与噪音控制之间的关系,将全同态加密的构造归结为如何获得最终解密结构的问题,从而形式化地建立全同态加密构造方法。最后对GSW全同态加密方法分析,提出其密文矩阵是由密文向量堆叠而成。基于密文堆叠法,研究密文是矩阵的全同态加密的通用性原因,给出密文矩阵全同态加密与其它全同态加密之间的包含关系。Why can fully homomorphic encryption be constructed based on lattice？ What is the essence and construction of the matrix？ An important concept is proposed： Abstract decryption structure. Based on the abstract decryption structure, the main factors related to the homomorphic encryption are analyzed and relationship between abstract decryption structure, homomorphism and noise control is studied. The construction of the homomorphic encryption is attributed to the problem of how to obtain the final decryption structure. So the formal method of homomorphic encryption can be established. Thus the essential law of the construction method of the homomorphic encryption construction is expounded, which provides the clue and clue for the construction of the new full homomorphic encryption. The general reason of the full homomorphic encryption of the ciphertext matrix from the point of view of the ciphertexts stack method is studied. The relation between the full homomorphic encryption and the other homomorphic encryption is obtained. Finally, this paper gives a general method of constructing fully homomorphic encryption.

关 键 词：全同态加密 构造方法 抽象解密结构 密文堆叠 学习错误问题 

分 类 号：TP309.7[自动化与计算机技术—计算机系统结构]