基于素数幂次阶分圆环的NTRU型全同态加密方案  

NTRU Type Fully Homomorphic Encryption Scheme over Prime Power Cyclotomic Rings

作　　者：秦小月 黄汝维[1] 杨波 QIN Xiao-yue;HUANG Ru-wei;YANG Bo(School of Computer and Electronic Information,Guangxi University,Nanning 530004,China)

机构地区：[1]广西大学计算机与电子信息学院,南宁530004

出　　处：《计算机科学》2022年第5期341-346,共6页Computer Science

基　　金：国家自然科学基金(62062009)。

摘　　要：全同态加密支持在不解密的情况下对密文进行任意运算,为云计算的隐私安全提供了一种保护,但目前使用近似特征向量法构造的全同态加密方案需要进行复杂的矩阵乘法计算,存在计算复杂、无法抵御子域攻击等问题。文中使用素数幂次阶分圆环代替2的幂次阶分圆环,提出了一种新的全同态加密方案,并通过修改密文形式以及解密结构有效避免了同态乘法中复杂的矩阵乘法计算。与同类方案相比,所提方案在效率上至少提升了lφ(x)/2d倍,并满足IND-CPA安全。Full homomorphic encryption(FHE)supports arbitrary computation on the ciphertext without the requirement of decryption,which provides protection for privacy security in cloud computing.However,the current FHE scheme constructed using the approximate eigenvector method requires complex matrix multiplications,which is computationally complicated and cannot resist subfield attacks.In this paper,a new FHE scheme was proposed by using the power-of-prime cyclotomic ring instead of a power-of-two cyclotomic ring,and the complex matrix multiplications in homomorphic multiplications were effectively avoided by modifying the ciphertext form and decryption structure.Compared with similar schemes,the proposed scheme improves the efficiency at least by a factor of lφ(x)/2d and is secure against IND-CPA attacks.

关 键 词：素数幂次阶分圆环 全同态加密 IND-CPA安全 

分 类 号：TP309[自动化与计算机技术—计算机系统结构]