山东大学学报 (理学版) ›› 2018, Vol. 53 ›› Issue (11): 78-84.doi: 10.6040/j.issn.1671-9352.0.2017.370
王爱兰,宋巍涛,赵秀凤
WANG Ai-lan, SONG Wei-tao, ZHAO Xiu-feng
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。
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