基于Binary-LWE噪音控制优化的全同态加密方案与安全参数分析  

A Fully Homomorphic Encryption Scheme Based on Binary-LWE and Analysis of Security Parameters

作　　者：陈智罡[1] 宋新霞[2] 张延红[1] 

机构地区：[1]浙江万里学院计算机与信息学院,浙江宁波315100 [2]浙江万里学院基础学院,浙江宁波315100

出　　处：《四川大学学报（工程科学版）》2015年第2期75-81,共7页Journal of Sichuan University (Engineering Science Edition)

基　　金：宁波市自然科学基金资助项目(2012A610067;2013A610071)

摘　　要：为了对全同态加密方案中的密文噪音进行优化控制,设计了一个基于Binary-LWE的全同态加密方案。同时估计了提出的方案的安全参数,对于指定的安全等级,根据对LWE问题的区分攻击,估计出模q的最大取值。根据噪音增长与模q及电路深度之间的关系,计算方案的具体安全参数。用同样的方法分析了Bra12方案的安全参数,并且与提出的方案的参数进行比较。数据显示提出的方案具有更小的参数尺寸,其密文乘积小于Bra12方案lb2q倍,张量密钥小于Bra12方案lb3q倍,密钥交换矩阵小于Bra12方案lb2q倍。提出的噪音优化控制方法具有通用性,可以用在所有噪音依赖于密钥的基于LWE的全同态加密方案上。To optimize noise management in fully homomorphic encryption scheme,a fully homomorphic encryption scheme with better parameters size was proposed. The security parameters of the scheme were estimated. Given security level,the maximal value of modulus q was got. Then the concert security parameters of the scheme were obtained by the condition of correct decryption among noise growth,circuit depth L and modulus q. The security parameters of Bra12 scheme also was obtained by the same way. The data showed that this scheme has better parameters size. The ciphertext from homomorphic multiplication is smaller by a factor about lb2 q than in Bra12 scheme and the corresponding tensored key is smaller by a factor about lb3 q than in Bra12 scheme. The matrix of key switching is smaller by a factor about lb2 q than in Bra12 scheme. The optimization for noise management is general,which can be used in the fully homomorphic encryption schemes based on LWE in which the noise growth depends on the secret key.

关 键 词：全同态加密 Binary-LWE 噪音控制 安全参数 

分 类 号：TN918.4[电子电信—通信与信息系统]