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.
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 toit , which results in that the number of learning with errors samples decrease from 2n\ogqton + 1. Weprove that our fully homomorphic encryption scheme is feasible and its security relies on the hardnessof learning with errors problem. In addition, we adapt the optimization for the process of keyswitching 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 logg than the one in BGH13 scheme.
作者
陈智罡
宋新霞
赵秀凤
Chen Zhigang;Song Xinxia;Zhao Xiufeng(C o)
出处
《计算机研究与发展》
EI
CSCD
北大核心
2016年第10期2216-2223,共8页
Journal of Computer Research and Development
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)~~
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
fully homomorphic encryption
learning with errors (LWE)
multi-bit plaintext
concert security parameters
lattice-based cryptography
