ISSN 1000-1239 CN 11-1777/TP

• 信息安全 •

一个LWE上的短公钥多位全同态加密方案

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

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.