Methodology of processing multi-digit numbers in asymmetric cryptosystems

Authors

  • Михайло Миколайович Касянчук Ternopil National Economic University
  • Микола Петрович Карпінський University of Bielsko-Biala
  • Світлана Володимирівна Казмірчук National Aviation University

DOI:

https://doi.org/10.18372/2410-7840.21.13764

Keywords:

asymmetric cryptosystems, multi-digit numbers, modular multiplication, modular exponentiation, vector-modular method, system of residual classes, methodology of processing multi-digit numbers

Abstract

To date, an increase in the key length inevitably leads to an increase in computational volumes to protect information flows using asymmetric cryptosystems, where the most common operations there is the modular multiplication and modular exponentiation. Existing methods and algorithms for performing above-mention operations are based on positional numerical systems that are characterized by considerable time complexity due to the limited possibilities of parallelizing the computation process, which leads to a decrease in their performance. Using of new approaches, in particular, the vector-modular method of modular multiplication and exponential, as well as the system of residual classes, will allow expanding the functionality of computing systems to encrypt / decrypt information. To this goal, a methodology which allows to increase the speed of asymmetric cryptosystems is proposed, and the basic mechanism of which is grounded on the eight stages: the formation of a plurality of open-ended blocks, the formation of requirements for cryptosystem parameters and information security, the choice of an asymmetric cryptosystem, the formation of a set of basic operations, the choice of the method of operations execution , the choice of the form of the system of residual classes, the choice of methods for constructing perfect and modified perfect forms of the system of residual classes, the implementation of basic asymmetries cryptosystems based on these approaches. The proposed methodology can reduce the temporal complexity, increase the speed of algorithms, specialized software and hardware during the processing of multi-digit numbers in asymmetric cryptosystems.

Author Biographies

Михайло Миколайович Касянчук, Ternopil National Economic University

PhD in Physics and Mathematics, Associate Professor, Associate Professor of Department of Cybersecurity, Ternopil National Economic University

Микола Петрович Карпінський, University of Bielsko-Biala

Dr.Sc., Professor, Chairman of Department of Computer Science and Automatics University of Bielsko-Biala

Світлана Володимирівна Казмірчук, National Aviation University

Dr Eng (Information security), Head of Computerised Information Security Systems Academic Department, National Aviation University

References

М. Касянчук, "Теорія та математичні закономірності досконалої форми системи залишкових класів", Праці Міжнародного симпозіуму "Питання оптимізації обчислень (ПОО–ХХХV)", Т. 1. Київ–Кацивелі, С. 306-310, 2009.

М. Касянчук, І. Якименко, О. Волинський, І. Пітух, "Теорія алгоритмів RSA та Ель–Гамаля в розмежованій системі числення Радемахера–Крестенсона", Вісник Хмельницького національного університету. Технічні науки, №3, С. 265-273, 2011.

Я. Николайчук, М. Касянчук, І. Якименко, С. Івасьєв, "Ефективний метод модулярного множення

в теоретико-числовому базисі Радемахера–Крестенсона", Вісник Національного університету «Львівська політехніка». Комп’ютерні системи та мережі,

№ 806, С. 195-199, 2014.

V. Adki, S. Hatkar, "A Survey on Cryptography Techniques", International Journal of Advanced Research in Computer Science and Software Engineering, Vol. 6, No. 6,

pp. 469-475, 2016.

P. Ananda Mohan, Residue Number Systems: Theory and

Applications, Birkhäuser, 2016, 351 p.

M. Deryabin, N. Chervyakov, A. Tchernykh, M. Babenko, M. Shabalina, "High Performance Parallel

Computing in Residue Number System", International

Journal of Combinatorial Optimization Problems and

Informatics, Vol. 9, No 1, pp. 62-67, 2018.

M. Kasianchuk, Ya. Nykolaychuk, I. Yakymenko,

"Theory and Methods of Constructing of Modules

System of the Perfect Modified Form of the System

of Residual Classes", Journal of Automation and Information Sciences, Vol. 48, No 8, pp. 56-63, 2016.

D. Kozaczko, S. Ivasiev, I. Yakymenko, M. Kasianchuk, "Vector Module Exponential in the Remaining

Classes System", Proceedings of the 2015 IEEE 8th

International Conference on Intelligent Data Acquisition and

Advanced Computing Systems: Technology and Applications

(IDAACS–2015), Warsaw (Poland), V. 1, pp. 161-

, 2015.

A. Okeyinka, "Computational Speeds Analysis of

RSA and ElGamal Algorithms", Proceedings of the World

Congress on Engineering and Computer Science (WCECS

, San Francisco (USA), V. I, pp. 237-242, 2015.

W. Stallings, Cryptography and Network Security: Principles

and Practice, 5th Prentice Hall Press Upper Saddle

River, NJ, USA, 2010, 719 p.

Published

2019-06-27

Issue

Section

Articles