MATHEMATICAL METHODS IN CIBERNETIC SECURITY: GRAPHS AND THEIR APPLICATION IN INFORMATION AND CYBERNETIC SECURITY

Abstract

This article is devoted to the problem of applying graph theory in cybersecurity systems and is an overview. Widespread penetration of mathematical methods in the development of information technology characterizes the current stage of our society. Among the mathematical methods used in information and cyber security, a large niche is graph technology. A streamlined system of special terms and symbols of graph theory allows you to easily and easily describe complex and subtle things both geometrically and algebraically. A graph is a mathematical model of a wide variety of objects, phenomena, and the relationships between them. This justifies the choice and relevance of this study. The article outlines the main elements of graph theory, the wide scope of their implementation and provides a historical perspective on the development of this theory. The analysis of scientific works allowed to determine the main directions of application of properties, characteristics of graphs and graph algorithms in information and cyber security. Among them are studies related to the use of graphs in information systems and programming; with modeling, analysis and application of attack graphs; with cryptographic transformations; with the construction of a decision tree in decision-making tasks in conditions of risk and uncertainty. It is proved that the ability to operate with the methods of graph technologies contributes to the development of software and hardware for information protection. The considered approaches to the application of graph theory in information and cyber security can be implemented during the study of the discipline "Special methods in security systems: discrete mathematics" for students majoring in 125 Cybersecurity, as well as in training in research or course work or thesis. By increasing the professional orientation of training, future cybersecurity workers gain a thorough knowledge of fundamental disciplines.