定义了布尔函数的类差分和类差分平衡函数，研究了类差分平衡函数的密码学性质以及构造方法。作为类差分平衡函数的应用，给出了〓上逻辑函数是完全非线性函数的充要条件，并在首先分析得到所有四元类差分平衡函数的基础上，编程搜索出〓上所有的完全非线性函数。

This paper presents the concept of analogous difference of Boolean function, and call the Boolean function an analogue difference balanced function if whose analogous difference is balanced at any nonzero point. The aim of this paper is to study their cryptographic properties and construction methods. Making use of analogue bent functions, the paper proposes an efficient and sufficient condition for a logical function defined on 〓 to be perfect nonlinear, and get all perfect nonlinear functions defined on 〓.