一个LWE上的短公钥多位全同态加密方案

发布时间：2019-06-07 15:25

【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2nlogq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.
[Abstract]:At present, the efficiency of full homomorphism encryption needs to be improved urgently. In order to improve the efficiency of full homomorphism encryption, a short public key multi-bit full homomorphism encryption scheme on LWE (learning with errors) is proposed. In the scheme, the LWE sample is selected from the discrete Gao Si distribution, and Gao Si noise is added to it, which leads to the decrease of LWE sample from 2nlogq to n 1, which makes the public key length of the scheme shorter. The noise growth analysis and security proof of the scheme are given in detail. In addition, the current key exchange technology is optimized, and the formal description of the optimized version of key exchange is given for multi-bit homomorphism encryption. Finally, according to the practical application of full homomorphism encryption, the method of analyzing the specific security parameters of full homomorphism encryption is given. The specific security parameters of the scheme and the BGH13 scheme are analyzed. The data show that the specific parameter length of the scheme is better than that of the BGH13 scheme.
【作者单位】：浙江万里学院电子与计算机学院;浙江万里学院基础学院;信息工程大学三院;
【基金】：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)~~
【分类号】：TN918.4

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