向量Bent函数的进一步研究

A Further Research on Vectorial Bent Functions

向量Bent函数在密码学,编码理论和序列设计等领域应用广泛,是一个重要的研究课题。文章旨在通过对向量Bent函数的研究,得出新的向量Bent函数的构造方法。首先通过对Carlet给出的Bent函数的经典非直和构造的研究,将其推广到向量Bent函数上,并给出构造后函数的谱值公式。然后将布尔函数的级联构造方法推广到向量布尔函数上,通过研究函数间的谱值关系,给出级联4个函数得到的向量布尔函数为向量Bent函数的条件。最后得到3类向量Bent函数的二次构造。

Vectorial Bent function is widely used in cryptography,coding theory,sequence design and other fields,and is an important research topic.This paper aims to obtain a new construction method of vectorial Bent function by studying vectorial Bent function.First,by studying the construction of classical indirect sums of Bent functions given by Carlet,we extend it to vectorial Bent functions,and give the spectral value formula of the constructed functions.Then,the concatenation method of Bent function is extended to vectorial Bent function.By studying the relationship between the spectral values of functions,the condition that vectorial Boolean function obtained by concatenating four functions is vectorial Bent function is given.Finally,the quadratic constructions of three classes of vectorial Bent functions are obtained.