一类多输出Bent函数的构造

Construction of a Class of Multi-output Bent Functions

推广了半Bent函数的概念,提出了多输出半Bent函数的概念,并由此给出了多输出Bent函数的一种构造方法.该方法通过级联两个多输出半Bent函数得到多输出Bent函数.与原有的方法相比,该方法具有结构简单、使用方便的优点.用此方法可构造具有任意偶数个变元的多输出Bent函数.此外,还给出了多输出半Bent函数的一种构造方法.除了可用于构造多输出Bent函数外,多输出半Bent函数还可应用于多输出前馈网等方面.

The concept of semi-bent functions is generalized. Meanwhile, the concept of multi-output semi-bent functions is introduced. Based on the new concept, a method of construct ing multi-output Bent functions is presented. In the method, a multi-output Bent function is constructed by concatenating two multi-output semi-Bent functions. Compared with the existing methods, our newly proposed method has a simple structure and is convenient to use. With this new method, multi-output Bent functions with arbitrary even variables can be constructed. Moreover, a method of constructing multi-output semi-Bent functions is proposed. Besides, applications in the construction of multi-output Bent functions, multi-output semi-Bent functions can also be applied in multi-output feedforward networks.