ISSN 1000-1239 CN 11-1777/TP

计算机研究与发展 ›› 2016, Vol. 53 ›› Issue (10): 2216-2223.doi: 10.7544/issn1000-1239.2016.20160431

所属专题: 2016网络空间共享安全研究进展专题

• 信息安全 • 上一篇    下一篇

一个LWE上的短公钥多位全同态加密方案

陈智罡1,宋新霞2,赵秀凤3   

  1. 1(浙江万里学院电子与计算机学院 浙江宁波 315100); 2(浙江万里学院基础学院 浙江宁波 315100); 3(信息工程大学三院 郑州 450001) (zhig.chen@foxmail.com)
  • 出版日期: 2016-10-01
  • 基金资助: 
    浙江省自然科学基金项目(LY17F020002);NSFC-浙江两化融合联合基金项目(U1509219);宁波市自然科学基金项目(2016A610226) This work was supported by the Natural Science Foundation of Zhejiang Province of China (LY17F020002), the NSFC-Zhejiang Joint Fund for the Integration of Industrialization Informatization (U1509219), and the Ningbo Natural Science Foundation (2016A610226).

A Multi-Bit Fully Homomorphic Encryption with Better Key Size from LWE

Chen Zhigang1, Song Xinxia2, Zhao Xiufeng3   

  1. 1(College of Electronic and Computer, Zhejiang Wanli University, Ningbo, Zhejiang 315100); 2(College of Junior,Zhejiang Wanli University, Ningbo, Zhejiang 315100); 3(The Third School, Information Engineering University, Zhengzhou 450001)
  • Online: 2016-10-01

摘要: 目前全同态加密的效率亟待提高,为了提高全同态加密的效率,提出一个LWE(learning with errors)上的短公钥多位全同态加密方案.方案中从离散高斯分布上选取LWE样例,并且将高斯噪音与之相加,导致LWE样例从 2n log q下降到n+1,使得方案的公钥长度变短.详细给出了该方案的噪音增长分析与安全性证明;此外,对目前密钥交换技术进行了优化,并且针对多位全同态加密,给出了密钥交换优化版本的形式化描述;最后,针对目前全同态加密的实践应用,给出了分析全同态加密具体安全参数的方法.分析了该方案与BGH13方案的具体安全参数,数据显示该方案的具体参数长度要优于BGH13方案.

关键词: 全同态加密, 学习错误问题, 多位明文, 具体安全参数, 格密码

Abstract: The efficiency of fully homomorphic encryption is a big question at present. To improve the efficiency of fully homomorphic encryption, we use the technique of packed ciphertexts to construct a multi-bit fully homomorphic encryption based on learning with errors (LWE) problem. Our scheme has a short public key. Since our fully homomorphic encryption scheme builds on the basic encryption scheme that chooses learning with errors samples from Gaussian distribution and add Gaussian error to it, which results in that the number of learning with errors samples decrease from 2n log q to n+1. We prove that our fully homomorphic encryption scheme is feasible and its security relies on the hardness of learning with errors problem. In addition, we adapt the optimization for the process of key switching from BGH13 and formal this new process of key switching for multi-bit fully homomorphic encryption. At last, we analyze the concert parameters and compare these parameters between our scheme and BGH13 scheme. The data show that our scheme has smaller public key by a factor of about log q than the one in BGH13 scheme.

Key words: fully homomorphic encryption, learning with errors (LWE), multi-bit plaintext, concert security parameters, lattice-based cryptography

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