A Fully Homomorphic Encryption Scheme with Better Key Size

• Published in: China communications Vol. 11; no. 9; pp. 82 - 92
• Main Authors: Chen, Zhigang, Wang, Jian, Zhang, Zengnian, Song, Xinxia
• Format: Journal Article
• Language: English
• Published: China Institute of Communications 01.09.2014; College of Computer Science and Technology, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, P.R.China; College of Computer and Information, Zhejiang Wanli University, Zhejiang NingBo 315100, P.R.China; Information Security Group, Royal Holloway, University of London,UK%College of Computer Science and Technology, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, P.R.China%Faculty of Electronic and Information Engineering, Zhejiang Wanli University, Zhejiang NingBo 315100, P.R.China%College of Junior.Zhejiang Wanli University, Zhejiang Ningbo 31510, P.R.China
• Subjects: Computer security; concert parameters; Encryption; Error analysis; fully homomorphic encryption; learning with error; Public key encryption; 主要尺寸; 二进制; 交换矩阵; 加密方案; 同态加密; 安全性; 组密钥; 音乐会; public key encryption; learning with error; fully homomorphic encryption; concert parameters
• ISSN: 1673-5447
• DOI: 10.1109/CC.2014.6969773

Fully homomorphic encryption is faced with two problems now. One is candidate fully homomorphic encryption schemes are few. Another is that the efficiency of fully homomorphic encryption is a big question. In this paper, we propose a fully homomorphic encryption scheme based on LWE, which has better key size. Our main contributions are： （1） According to the binary-LWE recently, we choose secret key from binary set and modify the basic encryption scheme proposed in Linder and Peikert in 2010. We propose a fully homomorphic encryption scheme based on the new basic encryption scheme. We analyze the correctness and give the proof of the security of our scheme. The public key, evaluation keys and tensored ciphertext have better size in our scheme. （2） Estimating parameters for fully homomorphic encryption scheme is an important work. We estimate the concert parameters for our scheme. We compare these parameters between our scheme and Bral2 scheme. Our scheme have public key and private key that smaller by a factor of about logq than in Bral2 scheme. Tensored ciphertext in our scheme is smaller by a factor of about log2q than in Bral2 scheme. Key switching matrix in our scheme is smaller by a factor of about log3q than in Bra12 scheme.