NTRU型无需密钥交换的全同态加密方案

宋新霞; 陈智罡; 周国民

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

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NTRU型无需密钥交换的全同态加密方案

学术论文 | 更新时间：2024-06-03

- 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
- 网络与信息安全学报 2017年3卷第1期页码：39-45
- 作者机构：
  
  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
- 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。" ]
- 基金信息：
  
  ：浙江省自然科学基金资助项目;Zhejinag Provincial Natural Science Foundation of China(LYNF020002);；浙江省公益性技术应用研究计划基金资助项目;The Public Projects of ZhejiangProvince(2017C33079);NSFC—浙江两化融合联合基金资助项目;NSFC-Zhejiang Joint Fund for the Integration of Industrialization Information(U1509219);宁波市自然科学基金资助项目;Ningbo Natural Science Foundation(2016A610226)
- DOI：10.11959/j.issn.2096-109x.2017.00117
  中图分类号： TP309.7
- 网络首发：2017-01，
  
  纸质出版：2017-01-15
- 稿件说明：
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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]. Journal of network and information security, 2017, 3(1): 39-45.
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. DOI： 10.11959/j.issn.2096-109x.2017.00117.

Xin-xia SONG, Zhi-gang CHEN, Guo-min ZHOU. NTRU-type fully homomorphic encryption scheme without key switching[J]. Journal of network and information security, 2017, 3(1): 39-45. DOI： 10.11959/j.issn.2096-109x.2017.00117.

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。

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.

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references

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