ISSN 1000-1239 CN 11-1777/TP

Journal of Computer Research and Development ›› 2016, Vol. 53 ›› Issue (10): 2216-2223.doi: 10.7544/issn1000-1239.2016.20160431

Special Issue: 2016网络空间共享安全研究进展专题

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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.

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

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