布尔函数的统计独立性

On the Statistical Independence of Boolean Functions

定义在同一定义域上的两个布尔函数可能存在多种关系,本文研究它们之间的统计独立性,这种性质可以用于布尔置换的构造。本文给出了利用布尔函数的汉明距离判定两个布尔函数是否统计独立的充分必要条件,给出了寻找与某个已知布尔函数统计独立的布尔函数的算法,并分析了这种算法的有效性。

Two Boolean functions defined on the same domain may have veriety of relationships. This paper studies their statistical independence, which is useful in the construction of Boolean permutations. This paper gives a necessary and sufficient condition for judging two Boolean functions to be statistical independent, and gives an algorithm for finding Boolean functions who are statistical independent of the given one, and an analysis of the effectiveness of the algorithm is given.