一种高效的多身份全同态加密方案  

An efficient multi-identity-based fully homomorphic encryption scheme

作　　者：王威力[1] 胡斌[1] 赵秀凤[1] WANG Wei-li HU Bin ZHAO Xiu-feng(School of Cryptography Engineering, The PLA Information Engineering University, Zhengzhou 450001, Henan, China)

机构地区：[1]解放军信息工程大学密码工程学院,河南郑州450001

出　　处：《山东大学学报（理学版）》2017年第5期85-94,共10页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(61272041);河南省自然科学基金资助项目(162300410332);信息保障技术重点实验室基金资助项目(KJ-15-006)

摘　　要：利用高效的格陷门生成算法构造了身份基加密方案。方案的安全性可归约到标准LWE问题,大大降低了格安全维数,同时降低了密钥规模和计算复杂度。将该方案转化为单身份的全同态加密方案,利用近似奇异向量消除同态运算密钥,运用原象矩阵进行加密,使用子高斯随机变量分析参数,同时将方案的噪声膨胀率由O(n)降为O(n^(0.5))。最后进一步利用扩展密文方法和掩藏方案构造了高效的支持多身份的全同态加密方案。An efficient identity-based encryption scheme is constructed by efficient trapdoor generation algorithm. The security of the scheme can be reduced to the standard LWE problem, which greatly reduces the lattic security dimension and reduces the key scale and computational complexity. In order to convert single-identity-based FHE scheme, the approximate singular vectors, original image matrix and sub Gaussian variable were utilized. What, s more, the noise expansion rate is reduced from O（n） to O（n0. 5）. Finally, we took advantage of extended cipher in conjunction with the masking scheme to construct an efficient multi-identity-based fully homomorphic encryption scheme.

关 键 词：全同态加密 身份基加密 基于身份的全同态加密 LWE问题 

分 类 号：TN918[电子电信—通信与信息系统]