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:
车小亮, 杨晓元, 申军伟. 一类高阶Bent函数的构造方法[J]. 计算机工程, 2012, 38(14): 122-123.
CHE Xiao-Liang, YANG Xiao-Yuan, SHEN Jun-Wei. Construction Method of A Class of High-rank Bent Function[J]. Computer Engineering, 2012, 38(14): 122-123.