NORX算法中非线性组件的移位参数选取准则研究

NORX算法是进入凯撒竞赛第三轮的15个认证加密候选算法之一,该算法的唯一非线性组件由异或、与和移位操作组成。从非线性逼近和循环分析两个密码学性质研究移位参数的选取准则,证明了可变移位函数的非线性逼近概率为三值函数,并得到了移位参数取1时具有最佳的非线性逼近性质;给出了可变移位函数的循环概率表达式,并证明了对于任意非零的移位参数其最大循环概率均相同。由上述分析结果可知,NORX算法中非线性组件的移位参数取1时达到了最佳的非线性逼近和循环性质。该结果可应用于NORX算法的安全性分析中,同时也能为设计类似算法提供理论指导。

Research on design rationale of the shift parameter in nonlinear component of NORX

NORX is one of the fifteen candidates selected for the third round of the CAESAR (authenticated encryption:security, applicability, and robustness) competition. And its only nonlinear component is made up of XOR, AND and shift operations. The design rationale of the shift parameter of NORX from the perspective of nonlinear approximation and rotational properties were studied. On the one hand, the nonlinear approximation probability of the shift function is theoretically proved to be a three-valued function. When the shift parameter is 1, this function possesses the best nonlinear property. On the other hand, the rotational probability of the shift function is formulated. And it is proved that the maximal rotational probability is the same for all nonzero shift parameters. From the above results, the NORX has the best nonlinear approximation and rotational properties when the shift parameter takes 1. The results can be of reference to the analysis of NORX and can give theoretical guidance when designing similar ciphers.