广义向量Bent函数

Generalized Vector Bent Functions

该文完善并拓展了Nyberg(1991)的关于广义向量Bent函数性质的结论,相应于Nyberg给出的正则广义向量Bent函数,提出了'负则的广义向量Bent函数'的概念;得到有偶数个输入的负则的广义向量Bent函数输出维数也不大于输入维数的一半:证明了奇数个输入的正则和负则的广义向量Bent函数都不存在,这些结果的给出,可使密码设计者避免一味去寻找某类不存在的函数。该文还给出了广义向量Bent函数的一种递归构造法。

This paper generalizes the conclusion of Perfect nonlinear S-boxes by Nyberg(1991), and introduces the conception of inverse regular generalized vector Bent function. It shows that for inverse regular generalized vector Bent functionf(m)(x) with even variables, m is no more than half of n. It also shows that when the input dimension n is odd, the regular generalized vector Bent function and the inverse regular generalized vector Bent function do not exist. This may prevent the cryptology designer from seeking the inexistent function. A method for recursively constructing vector generalized Bent function is presented.