NTRU型无需密钥交换的全同态加密方案  

NTRU-type fully homomorphic encryption scheme without key switching

作　　者：宋新霞[1] 陈智罡[2] 周国民[3] SONG Xin-xia CHEN Zhi-gang ZHOU Guo-min(College of Junior, Zhejiang Wanli University, Ningbo 315100, China College of Electronic and Computer, Zhejiang Wanli University, Ningbo 315100, China Department of Computer and Information Technology, Zhejiang Police College, Hangzhou 310053, China)

机构地区：[1]浙江万里学院基础学院,浙江宁波315100 [2]浙江万里学院电子与计算机学院,浙江宁波315100 [3]浙江警察学院计算机与信息技术系,浙江杭州310053

出　　处：《网络与信息安全学报》2017年第1期39-45,共7页Chinese Journal of Network and Information Security

基　　金：浙江省自然科学基金资助项目(No.LYNF020002);浙江省公益性技术应用研究计划基金资助项目(No.2017C33079);NSFC-浙江两化融合联合基金资助项目(No.U1509219);宁波市自然科学基金资助项目(No.2016A610226)~~

摘　　要：详细分析了环LWE上NTRU基本加密方案的噪声特性与同态性,引出了"零次同态加密"的概念,并且说明了环LWE上NTRU基本加密方案是一个零次同态加密。提出了2个同态加密方案,展示了如何基于NTRU零次同态加密,设计NTRU型BGN同态加密方案与全同态加密方案。在该NTRU型全同态加密方案中,其密钥在密文计算中始终保持不变,因此,无需密钥交换就获得了一个全同态加密方案。此外,该NTRU型全同态加密的密文是一个向量,相比密文是矩阵的GSW全同态加密方案,具有存储与传输上的优势。In order to construct a fully homomorphic encryption scheme based on NTRU cryptosystem from ring learning with errors, noise growth and homomorphic property in the NTRU cryptosystem were analyzed. The concept of zero homomorphic encryption was introdced and that the NTRU cryptosystem was zero homomorphic en- cryption was shown. A BGN homomorphic encryption scheme and a fully homomorphic encryption scheme were proposed based on the NTRU cryptosystem. In the proposed NTRU-type fully homomorphic encryption scheme, the secret key doesn＇t change in homomorphic multiplications. Thus a fully homomorphic encryption scheme can be obtained without key switching that was used in the previous fully homomorphic encryption schemes. Moreover, the cipbertext is a vector in the proposed NTRU-type fully homomorphic encryption scheme which has the advantage of storage and transmission compared to GSW fully homomorphic encryption scheme where the ciphertext is a matrix.

关 键 词：全同态加密 NTRU加密 环LWE问题 密钥交换 BGN同态加密 

分 类 号：TP309.7[自动化与计算机技术—计算机系统结构]