布尔函数扩散性的矩阵刻画
Matrix Description on Propagation Characteristic of Boolean Function
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摘要: 该文利用布尔函数的特征矩阵, 给出了n(3) 元布尔函数在sGFn(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。Abstract: With characteristic matrix of Boolean function, a necessary and sufficient condition is given on a Boolean function satisfying the propagation criterion on vector sGFn(2), which provides n3. On the basis of it, the necessary and sufficient 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.
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