布尔函数扩散性的矩阵刻画

Matrix Description on Propagation Characteristic of Boolean Function

该文利用布尔函数的特征矩阵,给出了n(≥3)元布尔函数在s∈GFn(2)满足扩散准则的充分必要条件,在此基础上得到了布尔函数满足严格雪崩准则(SAC)的一个充分必要条件和n元平衡布尔函数满足严格雪崩准则、代数次数达到最大且不含有非零线性结构的一个充分必要条件,最后提出了平衡且满足严格雪崩准则的布尔函数的两种特殊的“递补”构造法。

With characteristic matrix of Boolean function, a necessary and sufficient condition is given on a Boolean function satisfying the propagation criterion on vectors S∈GF^n（2）, which provides n ≥ 3. On the basis of it, the necessary and sutTicient conditions are given on a Boolean function satisfying Strict Avalanche Criterion （SAC） and on a balanced SAC function which achieves the maximum degree and no nonzero linear structure. Finally, two special ＂filling vacancies in the proper order ＂methods of construction are presented.