Mathematical modeling of intellectual and cryptographic protection of authentication keys

Authors

DOI:

https://doi.org/10.20535/2411-1031.2025.13.2.344591

Keywords:

cybersecurity, neural networks, mathematical modeling, intellectual-cryptographic system, preventive response, authentication keys, entropic analysis, adaptive optimization, deep learning

Abstract

The article substantiates the scientific and methodological foundations of mathematical modeling of intellectual-cryptographic systems for preventive response to authentication key compromise threats. A generalized conceptual model is proposed, integrating symmetric encryption mechanisms (in particular, the AES algorithm), steganographic methods for concealing cryptographic parameters, and intelligent attack prediction modules based on deep learning techniques. The developed mathematical framework is grounded in the synthesis of probability theory, information entropy, and adaptive optimization principles, enabling quantitative assessment of compromise risks and the formation of dynamic response strategies under variable threat conditions. Special attention is given to formalizing adaptive adjustment processes of cryptographic complexity levels and degrees of concealment, depending on the results of intelligent traffic analysis and anomaly detection in data transmission channels. Approaches to building energy- and computation-efficient implementations of such systems for embedded and mobile environments with limited resources are also examined. The obtained results establish the scientific basis for developing a new class of intellectual-cryptographic systems capable of self-learning, adaptive security parameter management, and preventive response to potential authentication data compromise threats in a dynamic information environment.

Author Biographies

Yevhen Zhyvylo, National University “Poltava Polytechnic named after Yury Kondratyuk”, Poltava

candidate of sciences in public administration, associate professor, associate professor of the department of computer and information technologies and systems of the Educational and scientific institute of information technologies and robotics

Yurii Kuchma, Limited Liability Company Private Higher Education Institution “University of Modern Technologies”, Kyiv

candidate of technical sciences, associate professor, head of the department of computer systems

References

J. Fridrich, and M. Goljan, “Practical Steganalysis of Digital Images – State of the Art”, in Proc. SPIE 4675, Security and Watermarking of Multimedia Contents IV, San Jose, California, USA, 2002. doi: https://doi.org/10.1117/12.465263.

J. Zhu, R. Kaplan, J. Johnson, and L. Fei-Fei, “HiDDeN: Hiding Data With Deep Networks”, in Proc. Part XV, Computer Vision – ECCV 2018: 15th Eur. Conf., Munich, Germany, 2018, pp. 682-697. doi: https://doi.org/10.1007/978-3-030-01267-0_40.

E. Barker, NIST Special Publication 800-57 Part 1 Revision 5. Recommendation for Key Management: Part 1 – General. USA: NIST, 2020, doi: https://doi.org/10.6028/NIST.SP.800-57pt1r5.

ENISA Threat Landscape 2024, Sep. 2024. [Online]. Available: https://www.enisa.europa.eu/sites/default/files/2024-11/ENISA%20Threat%20Landscape%202024_0.pdf. Accessed on: May 23, 2025.

I. Romashko, and Yu. Kalashnikova, “Cisco SecureX and Zero Trust: modern approaches to cyber defense”, Science and technology today, no. 9 (50), pp. 1475-1489, 2025. doi: https://doi.org/10.52058/2786-6025-2025-9(50)-1475-1489.

S. Kashkevich, A. Shyshatskyi, O. Dmytriieva, Y. Zhyvylo, G. Plekhova, and S. Neronov, “The development of management methods based on bio-inspired algorithms” in Information and control systems: modelling and optimizations. Collective monograph, A. Shyshatskyi, Ed. Kharkiv, Ukraine: Technology Center PC, 2024, pp. 35-69 p. doi: http://doi.org/10.15587/978-617-8360-04-7.

S. Al-Sarawi, M. Anbar, K. Alieyan, and M. Alzubaidi, “Internet of Things (IoT) Communication Protocols: Review”, in Proc. IEEE 8th International Conference on Information Technology (ICIT), 2017, Amman, Jordan, pp. 685-690. doi: https://doi.org/10.1109/ICITECH.2017.8079928.

N. Papernot, P. McDaniel, I. Goodfellow, S. Jha, Z. B. Celik, and A. Swami “Practical Black-Box Attacks against Machine Learning”, in Proc. Asia Conference on Computer and Communications Security (ASIA CCS '17), 2017, Abu Dhabi, UAE, pp. 506-519. doi: https://doi.org/10.1145/3052973.3053009.

M. Koval, O. Sova, O. Orlov, A. Shyshatskyi, Y. Artabaiev, O. Shknai, A. Veretnov, O. Koshlan, Y. Zhyvylo, and I. Zhyvylo, “Improvement of complex resource management of special-purpose communication systems”, Eastern-European Journal of Enterprise Technologies, vol. 5, no. 9 (119): Information and controlling system, pp. 34-44, 2022. doi: https://doi.org/10.15587/1729-4061.2022.266009.

E. Barker, NIST Special Publication 800-175B. Guideline for Using Cryptographic Standards in the Federal Government: Cryptographic Mechanisms. USA: NIST, 2016. doi: http://dx.doi.org/10.6028/NIST.SP.800-175B.

B. Schneier, Applied Cryptography: Protocols, Algorithms, and Source Code in C, 20th Ann. ed. USA: John Wiley & Sons, Inc., 2015.

Q.A. Mahdi et al., “Development of a method of structural-parametric assessment of the object state”, Eastern-European Journal of Enterprise Technologies, vol. 5, no. 4 (113): Mathematics and Cybernetics – applied aspects, pp. 34-44, 2021. doi: https://doi.org/10.15587/1729-4061.2021.240178.

Ye. Zhyvylo, and V. Kuz, “Risk Management of Critical Information Infrastructure: Threats-Vulnerabilities-Consequences”, Theoretical and Applied Cybersecurity: scientific journal, vol. 5, no. 2, pp. 68-80, 2023. doi: https://doi.org/10.20535/tacs.2664-29132023.2.280377.

Ye. Zhyvylo, and D. Shevchenko, “Cybersecurity Risk Assessment and Privacy Control in Government Information Systems”, Coll. of scien. works of the Taras Shevchenko National University of Kyiv, no. 75, pp. 66-76, 2022. doi: https://doi.org/10.17721/2519-481X/2022/75-07.

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Published

2025-11-27

How to Cite

Zhyvylo, Y., & Kuchma, Y. (2025). Mathematical modeling of intellectual and cryptographic protection of authentication keys. Collection "Information Technology and Security", 13(2), 162–177. https://doi.org/10.20535/2411-1031.2025.13.2.344591

Issue

Vol. 13 No. 2 (2025)

Section

CRYPTOLOGY

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