摘要： 提出一类高阶Bent函数的构造方法，将级联后的Bent序列转化为矩阵形式，对矩阵作任意行列置换，得到一类新的Bent序列，根据Bent序列的性质，对2个已知的 元Bent函数进行Kronecker积运算，由此构造一个 元的Bent函数，同理对 个 元Bent函数进行Kronecker积运算，构造 元高阶Bent函数，并对构造的 元Bent函数进行矩阵变换，得到数量更多的高阶Bent函数。

关键词: 密码学, 布尔函数, 级联Bent函数, 矩阵变换, Kronecker积运算, 高阶Bent函数

Abstract: Construction Method of A Class of High-rank Bent FunctionA construction method of high-rank Bent function is researched in this article. By translating the cascading Bent sequence into the matrices and using the random cortege permutation to change the matrices, a kind of new Bent sequences are achieved. According to the properties of Bent sequence, a new Bent function with 2n-variables is constructed from two known n-variables Bent functions by the method of Kronecker product operation. Extend the conclusion, a new Bent function with mn-variables is constructed from m known n-variables Bent functions via the Kronecker product operation. And much more high-rank Bent sequences are got through matrix transformation of the mn-variables Bent function.

Key words: cryptography, Boolean function, cascading Bent function, matrix transformation, Kronecker product operation, high-rank Bent function

中图分类号: 

• TP309