Mathematical Model of Cyber Risks Management Based on the Expansion of Piecewise Continuous Analytical Approximation Functions of Cyber Attacks in the Fourier Series

Abstract

The comprehensive system of information security of an enterprise includes both tactical aspects of information and strategic priorities, reflecting the information policy and information strategy of the enterprise. Ensuring a given level of cybersecurity requires the identification of threat actors, their purpose, intentions of attacks on the IT infrastructure, and weak points of the enterprise’s information security. To achieve these goals, enterprises need new information security solutions. In this work, a mathematical model of the process of cyber risk management in the enterprise, which is based on the distribution of piecewise continuous analytical approximating functions of cyber attacks in the Fourier series, is obtained. A constant continuous monitoring and conduction of cyber regulatory control of the enterprise on time makes it possible to effectively ensure the cybersecurity of the enterprise in real time—predicting the emergence of cyber threats to some extent—which, in turn, determines the management of cyber risks arising in the field of information security of the enterprise. Such a Fourier series expansion of the piecewise continuous analytical approximating function of the intensity of cyber attacks on damage to standard software, obtained by approximating empirical–statistical slices of the intensity of cyber attacks on damage to standard software for each time period by analytical functions, opens up new mathematical possibilities of transition to systems of regulatory control of cyber threats of the enterprise from discrete to continuous automated process for such types of control.

Keywords

• Fourier series
• cyber threat
• piecewise continuous function
• mathematical model
• information security of an enterprise