SP(Substitution & Permutation)模型是分组密码常用模型之一.该文提出了基于扩散结构特征向量构造SP模型高概率差分传递链和线性逼近链的方法.利用该方法构造了ARIA算法6轮概率为2-168的差分传递链,并构造了仅使用一个S盒的6轮弱化ARIA算法达到概率上界2-144的差分传递链.结果表明,SP模型的设计者应当尽量选择特征向量个数较少且不含低重量特征向量的扩散结构.此外,该文还给出了准对合MDS(Maximum Distance Separable)矩阵及循环移位矩阵的特征值以及特征向量计数公式.%SP (Substitution & Permutation) structure is often used in block ciphers. This paper provides a method which could construct high probability differential trails and linear trails by using characteristic vectors of the diffusion layer. By this method some differential trails of ARIA can be constructed, these trails could reach probability 2-168 for 6 rounds. And for 6 rounds reduced ARIA, who only employs a single S box, some differential trails can be got which could reach the highest probability 2-144. The results show that the SP cipher designers should choose those diffusion layers with fewer characteristic vectors as possible. And diffusion layers should never have low weight characteristic vectors. Additionally, the characteristic value as well as the count value of quasi-involution MDS matrices and cyclic shift matrices are provided.
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