一类CI-SAC布尔函数的存在性及其构造

The Existence and Construction of a Kind of CI-SAC Boolean Function

相关免疫且满足严格雪崩准则的布尔函数称为CI-SAC函数。本文利用特征矩阵给出了一类布尔函数为平衡且代数次数达到最大的CI-SAC函数的一个充分必要条件,也就通过特征矩阵给出了具有这类"综合优良性"的布尔函数的一种简单易行的构造方法。

The Boolean function is called CI-SAC function if it is correlation immunity and satisfies strict avalanche criterion. By characteristic matrix, this paper gives a necessary and sufficient condition on a kind of CI-SAC function which is balanced and achieves the maximum degree. At the same time, a simple and feasible method is presented for constructing this excellent function.