一类动态S盒的构造与差分性质研究

摘要

该文对有限域的逆与仿射变换复合得到的动态S 盒进行了研究。首先给出了动态S 盒变换差分概率的刻画方法，并给出了动态 S 盒变换的差分对应是不可能差分对应的充分必要条件及不可能差分的个数。接着给出了动态S盒变换最大差分概率的上界及可达性。最后利用模拟实验的方法研究了由随机S盒来构造的动态S盒的差分性质。理论和实验分析都表明，这类动态S盒变换具有远好于单个S盒的差分特性。%This paper discusses the dynamic S-boxes using the combination of inversion mapping and an affine transformation over the finite field. First, a definition of differential probability for dynamic S-box is provided. Necessary and sufficient conditions of impossible differentials in dynamic S-box and the number of impossible differentials are presented. Then, an upper bound on the maximum differential probability of dynamic S-box is proved, and the accessibility of this bound is presented. Finally, the differential properties of dynamic S-box consisting of randomly chosen S-boxes are researched by simulation experiments. The theoretical and experimental analyses show that dynamic S-box is better than single S-box in differential properties.