一类新的基于元胞自动机的S盒的密码学性质研究

Research on cryptographic properties of a new S-box based on cellular automaton

通过实验找到了一类新的基于元胞自动机的S盒,分析了该S盒的置换性质,证明了其仅在规模为5时是一个置换。通过构造差分矩阵的方法给出了该S盒的非平凡差分转移概率与差分矩阵的秩之间的关系,从而得到其取值范围。证明了对输入差分进行循环移位不改变其对应的非平凡差分转移概率,从而给出其在规模为5时取最大和最小非平凡差分转移概率的充要条件,彻底解决了此时该S盒的差分对应的结构和计数问题。

A new S-box based on cellular automata was found by experiments. The permutation properties of the S-box were analyzed, which proved that the S-box was a permutation only when the size of lattice was 5. Then the relation be- tween the nontrivial difference transition probability of the S-box and the rank of the difference matrix was proved by constructing the difference matrix. And it was proved that the cyclic shift of input differential would not change the cor-responding nontrivial differential transition probability, and obtained the sufficient and necessary conditions about the maximum and minimum nontrivial differential transition probabilities when the size of lattice was 5. Then the problem of the difference distribution of the S-box in this situation is completely solved.