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 〓.