Usage of hypercomplex numbers in a cryptographic key agreement protocol based on neural networks

  • Pavel P. Urbanovich Belarusian State Technological University, 13a Svyardlova Street, Minsk 220006, Belarus; The John Paul II Catholic University of Lublin, 14 Racławickie Alley, Lublin 20-950, Poland
  • Nadzeya P. Shutko Belarusian State Technological University, 13a Svyardlova Street, Minsk 220006, Belarus

Abstract

We analyse the features of the structural and functional organisation of two interacting neural networks based on the known architecture in the form of a tree parity machine (TPM) using algebras of real and hypercomplex numbers. Such machines are used as an alternative to the Diffie – Hellman algorithm to generate a shared secret cryptographic key between two parties. The main elements of mathematical models of TPMs, operating on the basis of the listed algebras, are considered. The features of the software implementation of a system simulator based on interacting TРMs are described, and the results of using the developed tool for analysing the dynamics of processes in the system under consideration are presented. Mutual learning and data exchange of two TРMs are realised based on the transmission control and Internet protocols (TCP/IP). The synchronisation state of the networks is determined by the equality of the hashes that each party calculates based on the secure hash algorithm. A hash size of 512 bits are generated by transforming the string representation of the current input vector of neuron weights. The effectiveness of possible attempts by a third party to synchronise with two legitimate TPMs operating on the basis of algebras of hypercomplex numbers is assessed.

Author Biographies

Pavel P. Urbanovich, Belarusian State Technological University, 13a Svyardlova Street, Minsk 220006, Belarus; The John Paul II Catholic University of Lublin, 14 Racławickie Alley, Lublin 20-950, Poland

doctor of science (engineering), full professor; professor at the department of information systems and technologies, faculty of information technologies, Belarusian State Technological University, and visiting professor at the John Paul II Catholic University of Lublin

Nadzeya P. Shutko, Belarusian State Technological University, 13a Svyardlova Street, Minsk 220006, Belarus

PhD (engineering), docent; associate professor at the department of informatics and web-design, faculty of information technologies

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Published
2024-08-01
Keywords: neural cryptography, tree parity machines, hypercomplex numbers, networks mutual learning
Supporting Agencies The authors express their gratitude to the director of the Institute of Mathematics, Computer Science and Landscape Design of the John Paul II Catholic University of Lublin doctor of science M. Plonkowski for the help and information provided, which contributed to the improvement of the article content.
How to Cite
Urbanovich, P. P., & Shutko, N. P. (2024). Usage of hypercomplex numbers in a cryptographic key agreement protocol based on neural networks. Journal of the Belarusian State University. Mathematics and Informatics, 2, 81-92. Retrieved from https://journals.bsu.by/index.php/mathematics/article/view/5869
Issue
No 2 (2024): Journal of the Belarusian State University. Mathematics and Informatics
Section
Theoretical Foundations of Computer Science

Copyright (c) 2024 Journal of the Belarusian State University. Mathematics and Informatics

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