NTRU型无需密钥交换的全同态加密方案

doi:10.11959/j.issn.2096-109x.2017.00117

网络与信息安全学报 ›› 2017, Vol. 3 ›› Issue (1): 39-45.doi: 10.11959/j.issn.2096-109x.2017.00117

NTRU型无需密钥交换的全同态加密方案

宋新霞¹,陈智罡²(),周国民³

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

修回日期:2016-10-30 出版日期:2017-01-15 发布日期:2020-03-20
作者简介:宋新霞（1973-），女，陕西户县人，浙江万里学院副教授，主要研究方向为代数密码。|陈智罡（1972-），男，四川资中人，博士，浙江万里学院副教授，主要研究方向为全同态加密、格公钥密码学。|周国民（1971-），男，浙江义乌人，浙江警察学院副教授，主要研究方向为网络安全与执法。
基金资助:
：浙江省自然科学基金资助项目(LYNF020002);；浙江省公益性技术应用研究计划基金资助项目(2017C33079);NSFC—浙江两化融合联合基金资助项目(U1509219);宁波市自然科学基金资助项目(2016A610226)

NTRU-type fully homomorphic encryption scheme without key switching

Xin-xia SONG¹,Zhi-gang CHEN²(),Guo-min ZHOU³

¹ College of Junior, Zhejiang Wanli University, Ningbo 315100, China
² College of Electronic and Computer, Zhejiang Wanli University, Ningbo 315100, China
³ Department of Computer and Information Technology, Zhejiang Police College, Hangzhou 310053, China

Revised:2016-10-30 Online:2017-01-15 Published:2020-03-20
Supported by:
Zhejinag Provincial Natural Science Foundation of China(LYNF020002);The Public Projects of ZhejiangProvince(2017C33079);NSFC-Zhejiang Joint Fund for the Integration of Industrialization Information(U1509219);Ningbo Natural Science Foundation(2016A610226)

摘要/Abstract

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。

关键词: 全同态加密, NTRU加密, 环LWE问题, 密钥交换, BGN同态加密

Abstract:

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 con-cept 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 ciphertext 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.

Key words: fully homomorphic encryption, NTRU cryptosystem, ring learning with errors, key switching, BGN homomorphic encryption

中图分类号:

TP309.7

宋新霞,陈智罡,周国民. NTRU型无需密钥交换的全同态加密方案[J]. 网络与信息安全学报, 2017, 3(1): 39-45.

Xin-xia SONG,Zhi-gang CHEN,Guo-min ZHOU. NTRU-type fully homomorphic encryption scheme without key switching[J]. Chinese Journal of Network and Information Security, 2017, 3(1): 39-45.

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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

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