PS类Bent函数的一种构造方法

One Method for Constructing Bent Functions of Class PS

PS类bent函数类是所有 2 (n/2 ) -1或 2 (n/2 ) -1+1个Fn2 的“不交的”n2 维子空间的指示函数的模 2和所组成的函数的集合 .这些函数具有很好的代数结构并在密码学中有很多应用 .如何来刻画PSbent函数的代数范式一直是公开的难题 .构造PS类bent函数关键在于如何将Fn2 划分为 2 n/2 +1个 n2 维子空间 .本文给出一种划分的方法 ,从而构造出PS类bent函数 ,并给出了对应的代数范式 .

The class of PS bent functions is one interesting class of bent functions, they have good algebraic structure and have many applications in cryptography. They are also useful for studying the general structure of bent functions. Unfortunately, the construction of PS bent functions is theoretic, it is still an open problem to characterize the algebraic normal forms of PS bent functions. We study the properties of such functions, and one method to construct PS bent functions and the corresponding algebraic normal forms are provided.