摘要
由于简单、安全且便于高效实现,R-LWE上FHE方案成为目前FHE方案设计的主流。R-LWE上FHE方案基于剩余类环R=Z[x]/(f(x))的多项式扩张因子大小对密文同态操作时的噪声膨胀速度有重要影响。基于对无穷范数意义下多项式环R的扩张因子的研究,给出了几个特殊多项式所对应的具体扩张因子值。证明了系数为零的单项式越多的多项式,其对应的扩张因子越小,系数为0的单项式的幂次越高,其对应的扩张因子越小。该结果可为R-LWE上高效同态密码算法的设计提供理论指导。
Because of the simplicity, security and efficiency R-LWE-based FHE schemes become the mainstream design of FHE. The value of polynomial expansion factor of R-LWE-based FHE for quotient ring R=Z[x]/(f(x))has an important influence on the noise expansion speed for homomorphic operation of ciphertexts. Based on the expansion factor of ∞ norm for different polynomials, the values of expansion factors of ∞ norm over ring R for some special polynomials f(x)are obtained. It proves that the larger numbers of monomials with coefficient being zero for polynomials f(x), the smaller the corresponding expansion factors is. The higher the power of a monomial with a coefficient of 0, the smaller the corresponding expansion factor. The results can provide theoretical guidance for the design of efficient R-LWE-based FHE schemes.
作者
王爱兰
宋巍涛
赵秀凤
WANG Ai-lan;SONG Wei-tao;ZHAO Xiu-feng(Information Engineering University, Zhengzhou 450004, Henan, China)
出处
《山东大学学报（理学版）》
CAS
CSCD
北大核心
2018年第11期78-84,94,共8页
Journal of Shandong University(Natural Science)
基金
国家自然科学基金资助项目(61601515
61672031)
河南省自然科学基金资助项目(162300410332)
