Method for accelerating the calculations of exponent on Galois fields by combining parallel processing and pre-calculations

Authors

DOI:

https://doi.org/10.18372/2073-4751.84.20895

Keywords:

multiplication operation on Galois fields, cryptographic algorithms based on Galois Fields algebra, Galois Fields exponentiation, parallel computing, multi-core microcontrollers

Abstract

Method for exponent calculation on a Galois Field has been developed and researched, with its parallel implementation on an h-core terminal microcontroller for cryptographic applications. The acceleration was achieved due to the following factors: distribution of calculations between h-cores, fast exponentiation to the power of 2k, and simultaneous processing of k digits of the exponent code through the complex use of precomputations. A mathematical proof of the proposed method is given, as well as procedure its operation whose are illustrated be numerical examples.

It has been theoretically proven and experimentally confirmed that on a four-core processor and a fragment size of twenty bits, a 20.34-fold acceleration is achieved compared to the classical method of exponentiation on finite Galois fields.

References

Ruiz A.L. Two Galois Fields Cryptographic Applications / A.L. Ruiz, E. Castillo, L. Parrilla, A. Garsia // Aritmetic and Algebraic Circuits.- 2021.- P.551-565. DOI: 10. 1007/978-3-030-67266-9_12

Марковський О.П. Метод розподіленого обчислення на багатоядерних процесорах експоненти на полях Галуа для криптографічних застосувань/ О.П. Марковський, С.С.Нікольський // Проблеми управління та інформатизації.- 2025.- № 1 (81).- С.59-71. DOI: 10.18372/2073-4751.81.20130

Hachenbergen D., Topic in Galois Fields. / D. Hachenbergen, D. Jungnickel // AACIM.-Vol.29.- Springer International Publishing.- 2020–P.785. DOI: 10.1007/978-3-030-60806-4.

Schneier B. Appllied Cryptography. Protocols, Algorithms and Source Code in C / В. Schneier// Wiley.-2015.-P.784.

Montgomery P. Modular multiplication without trial division / P. Montgomery // Mathematics of Computation. – Vol. 44.- №170. – 1985. – P. 519–521.

Марковський О.П. Метод швидкого експоненціювання на полях Галуа для систем криптографічного захисту інформації / О.П. Марковський, І.В. Дайко // Проблеми управління та інформатизації.- 2024.- № 1 (77).- С.80-88. DOI: 10.18372/2073-4751.77.18660

Al-Mrayt Ghassan Abdel Jalil Halil. Оrganization of fast exponentiation on galois fields for cryptographic data protection systems / Al-Mrayt Ghassan Abdel Jalil Halil , Markovskyi O., Stupak A. // Information, Computing and Intelligent systems. – 2022. – № 3.- P.17-25. DOI: 10.20535/ 2708-4930.3. 2022. 265480.

Dychka I. Method of Performing Operations on the Elements of GF(2m) Using a Sparse Table. / Ivan Dychka, Mykola Onai, Andrii Severin, Cennuo Hu // International Journal of Computer Network and Infor­mation Security(IJCNIS),-2024.- Vol.16, - № 1,- Р.61-72. DOI:10.5815/ijcnis.2024. 01. 05

Wu K.Optimized Design of ECC Point Multiplication Algorithm Over GF(2m) / K. Wu, G. Wei // Proceeding of International Conference on Electronic Engineering and Informatics (EEI), Nanjing, China,- 2019.- P. 420–425. DOI: 10.1109/EEI48997.2019.00097.

Марковський О.П. Метод швидкого обчислення експоненти на полях Галуа GF(2n) для криптографічних застосувань / О.П. Марковський, С.С. Нікольський // Комп’ютерно-інтегровані технології: освіта, наука, виробництво. Луцьк, 2025.- Вип. 58. – C. 188-196. DOI: 10.36910/6775-2524-0560-2925-58-23/

Верба О.А. Метод експоненціювання на полях Галуа для швидкої реалізації криптографічного захисту в IoT / О.А. Верба, С.С.Нікольський // Проблеми управління та інформатизації.- 2024.- № 4 (80).- С.21-31. DOI: 10.18372/2073-4751.80.19767.

Downloads

Published

2025-12-30

How to Cite

Kozachek, M., Verba, O., & Hutsuliak, N. (2025). Method for accelerating the calculations of exponent on Galois fields by combining parallel processing and pre-calculations. Problems of Informatization and Management, 4(84), 48–58. https://doi.org/10.18372/2073-4751.84.20895

Issue

Vol. 4 No. 84 (2025)

Section

Статті

License

The scientific journal adheres to the principles of Open Access and provides free, immediate, and permanent access to all published materials without financial, technical, or legal barriers for readers.

All articles are published in Open Access under the Creative Commons Attribution 4.0 International (CC BY 4.0) license.

Copyright

Authors who publish their works in the journal:

  • retain the copyright to their publications;

  • grant the journal the right of first publication of the article;

  • agree to the distribution of their materials under the CC BY 4.0 license;

  • have the right to reuse, archive, and distribute their works (including in institutional and subject repositories), provided that proper reference is made to the original publication in the journal.