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JOURNALS // Prikladnaya Diskretnaya Matematika. Supplement // Archive

Prikl. Diskr. Mat. Suppl., 2024 Issue 17, Pages 125–129 (Mi pdma661)

Mathematical Foundations of Computer Science and Computer Security

Application of finite dynamic systems for information security

A. V. Zharkova

Saratov State University

Abstract: Graph models occupy an important place in problems related to information security. Finite dynamic system $(\Gamma_G, \alpha)$ is considered, the states of which are all possible orientations of a given graph $G$, and the evolutionary function $\alpha$ transforms a given state $\overrightarrow{G}$ by reversing all arcs in $\overrightarrow{G}$ that go into sinks, and there are no other differences between the given $\overrightarrow{G}$ and the next $\alpha(\overrightarrow{G})$ states. The paper suggests how this system can be used for information security, namely: as a model for ensuring audit and monitoring the state of an object under the influence of threats to its information security, and investigating information security incidents in automated information systems, as a model for managing the continuous operation of systems and system recovery, countering denials of service, as a technology for identifying and authenticating users and subjects of information processes, and an access control system.

Keywords: attractor, authentication, graph, identification, incident, cybersecurity, finite dynamic system, fault-tolerance, evolutionary function.

UDC: 519.1, 004.05

DOI: 10.17223/2226308X/17/31



© Steklov Math. Inst. of RAS, 2026