МАТЕМАТИЧНА МОДЕЛЬ СИМТЕРИЧНОЇ КРИПТОГРАФІЧНОЇ СИСТЕМИ ЗАХИСТУ МОВНОЇ ІНФОРМАЦІЇ НА ОСНОВІ ДИФЕРЕНЦІАЛЬНИХ ПЕРЕТВОРЕНЬ

Автор(и)

  • Ольга Грищук Національний авіаційний університет, Національний університет оборони України https://orcid.org/0000-0001-6957-4748

DOI:

https://doi.org/10.28925/2663-4023.2024.25.401409

Ключові слова:

mathematical model, symmetric cryptographic system, speech information, differential transformations, Fredholm integral equation of the first kind

Анотація

Among known cryptographic systems, in practice, symmetric cryptographic systems are most often used to protect speech information. Such systems, when encrypting speech information, implement stream encryption of outgoing traffic. At the same time, the rapid development of quantum and post-quantum technologies, methods and means of cryptanalysis determines the urgent need for their further development. One of the promising approaches, which is not sufficiently covered in the professional literature today, is considered to be an approach based on the methods of integral cryptography. According to the basic principles of integral cryptography, a mathematical model in the form of an integral Fredholm equation of the first kind can be used as the basis of a cryptographic algorithm for a symmetric cryptographic system of speech information protection. The main difference and at the same time the advantage of cryptographic systems based on Fredholm integral equations of the first kind is their guaranteed theoretical and practical cryptographic stability. The guaranteed theoretical cryptographic stability and speed of such a symmetric cryptographic system is provided by the application of the method of differential transformations of Academician of the National Academy of Sciences of Ukraine G. Pukhov. Practical crypto-resistance is ensured by the practical unsolvability of the inverse incorrect decryption problem. It is suggested to use the regularization method of Professor A. Tikhonov to decipher the cyphergram obtained from speech information. Thus, the proposed mathematical model of a symmetric cryptographic system based on differential transformations is a further development of modern information technologies for cryptographic protection of speech information in Ukraine.

Завантаження

Дані завантаження ще не доступні.

Посилання

Toledano, S. A. (2024). Critical Infrastructure Security: Cybersecurity lessons learned from real-world breaches. Birmingham: Packt Publishing.

Huiqin, X. (2024). Quantum Truncated Differential and Boomerang Attack. Symmetry, 16(9), 1–27.

Boudot, F. (2020). Comparing the difficulty of factorization and discrete logarithm: a 240-digit experiment. Advances in Cryptology – CRYPTO 2020, 62–91.

Schneier, B. (2003). Applied cryptography. Protocols, algorithms, source texts in C language. Triumph.

Usmonov, M. (2021). Asymmetric Cryptosystems. International Journal of Academic Engineering Research, 5(1), 6–9.

Deep, G. M. (2024). Keys and Symmetric Cryptography. Techsar Pvt. Ltd.

Kizza, J. M. (2024). Computer Network Security Protocols. Guide to Computer Network Security. Springer, 409–441.

Marković, M. R. (2024). Analysis of packet switching in VoIP telephony at the command post of tactical level units. Military technical courier, 72(1), 409–434.

Merzlykin, P. V. (2018). Cryptographic algorithm based on the system of tyurmites. Actual issues of ensuring cyber security and information protection: collection of theses of reports IV International. science and practice conf, 86–92.

Yong, Z. A. (2017). Chaotic System Based Image Encryption Scheme with Identical Encryption and Decryption Algorithm. Chinese Journal of Electronics, 26(5), 1022–1031.

Gorbenko, I. (2017). Study of the possibility of using and advantages of post-quantum algorithms depending on the conditions of application. East European Journal of Advanced Technologies, 2(9(86)), 21–32.

Hryshchuk, R. V. (2019). Generalized model of the Fredholm cryptosystem. Cybersecurity: education, science, technology, 4, 14–23.

Bronshpak, G. (2014). New generation cryptography: Integral equations as an alternative to algebraic methodology. Applied Electronics, 3, 337–349.

Okhrimenko, M. G. (2008). Methods of solving incorrectly set problems. Center for Educational Literature.

Tikhonov, A. N. (1979). Methods for solving ill-posed problems. Science: Main editorial office of physical and mathematical literature.

Pavlenko, P. M. (2017). Mathematical modeling of systems and processes. NAU.

Korchenko, O. (2022). Comparative analysis of mathematical models of speech information. Information security, 28(2), 48–56.

Shannon, C. E. (1949). Communication Theory of Secrecy Systems. Bell System Technical Journal, 656–715.

Pukhov, G. E. (1986). Differential transformations and mathematical modeling of physical processes: monograph. Nauk. dumka.

Downloads


Переглядів анотації: 29

Опубліковано

2024-09-25

Як цитувати

Грищук, О. (2024). МАТЕМАТИЧНА МОДЕЛЬ СИМТЕРИЧНОЇ КРИПТОГРАФІЧНОЇ СИСТЕМИ ЗАХИСТУ МОВНОЇ ІНФОРМАЦІЇ НА ОСНОВІ ДИФЕРЕНЦІАЛЬНИХ ПЕРЕТВОРЕНЬ. Електронне фахове наукове видання «Кібербезпека: освіта, наука, техніка», 1(25), 401–409. https://doi.org/10.28925/2663-4023.2024.25.401409