In this chapter, we explore the application of the derivative of disproportion functions in developing a cryptographic system and a pattern recognition technique. Firstly, we present an algorithm that utilizes focal functions, known as functions of disproportion, in a cryptographic system. The transmitted symbols are encrypted using the weighted sum of at least two of these functions with randomly generated coefficients. Numerical experiments demonstrate the robustness and reliability of the proposed procedure.

Furthermore, we demonstrate how the derivative of disproportion functions can govern a dynamic process, serving as a tool to identify the form of a real-valued function. This process enables us to determine the class to which the function belongs, independently of its unknown parameter values.