一类4-差分置换的构造

CONSTRUCTION OF A CLASS OF DIFFERENTIALLY4-UNIFORM PERMUTATIONS

为了抵抗已知的攻击，用于分组密码S-盒中的多输出布尔函数应具有较好的差分性质，较高的非线性度和较高的代数次数等密码学性质．在某些分组密码中，还要求这些多输出布尔函数是有限域F2n上的置换，这里n为偶数．文章将F2n分为两个子集，通过在这两个子集上分别定义不同置换的方法构造了一类4-差分置换，证明了这类置换具有最优的代数次数，且含有高非线性度的子类．进一步地，通过实例对该函数类与12类4-差分置换进行了CCZ不等价性分析．

To resist against known attacks, multi-output Boolean functions used in the substitution boxes （S-boxes） of block ciphers should have good differentially uniform property, high nonlinearity and algebraic degree. In addition, these functions should be permutations over the finite field F2n in certain block ciphers, where n is an even integer. In this paper, by dividing F2n into two subsets and defining permutations on each of them, we construct a class of differentially 4-uniform permutations. It is proved that each permutation in this class has optimal algebraic degree, and this class contains a subclass consisting of permutations with high nonlinearity. Moreover,presenting some examples, we analyze the CCZ-inequivalence between this class of differentially 4-uniform permutations with twelve known ones.