Algorithms of findings of perfect shape modules of remaining classes system

M Kasianchuk, I Yakymenko, I Pazdriy… - The experience of …, 2015 - ieeexplore.ieee.org
Present paper shows that the system of residual classes is quite promising for usage in
modern computing systems, especially for performing operations with multi-digit numbers …

Vector module exponential in the remaining classes system

D Kozaczko, S Ivasiev, I Yakymenko… - 2015 IEEE 8th …, 2015 - ieeexplore.ieee.org
This paper contains the elaboration of the effective remaining classes system method based
on vector-modular multiplication which allows to decrease the time-complication and to …

Encryption Using Residue Number System: Research Trends and Future Challenges

R Shevchuk, I Yakymenko… - 2024 14th International …, 2024 - ieeexplore.ieee.org
This paper presents a comprehensive knowledge mapping and in-depth analysis of the
application of residue number system in encryption technique research to understand better …

Theoretical foundations of the modified perfect form of residue number system

YM Nykolaychuk, MM Kasianchuk… - Cybernetics and Systems …, 2016 - Springer
The paper presents the theoretical foundations of the modified perfect form of residue
number system. The method is developed to select a set of three modules, which form …

High-performance coprocessors for arithmetic and logic operations of multi-bit cores for vector and scalar supercomputers

Y Nykolaychuk, V Hryha, N Vozna… - 2022 12th …, 2022 - ieeexplore.ieee.org
The relevance of solving the priority improvement problem for functional and computational
components of microelectronics for arithmetic and logic unit (ALU) of modern …

Symmetric Encryption Algorithms in a Polynomial Residue Number System

I Yakymenko, M Karpinski, R Shevchuk… - Journal of Applied …, 2024 - Wiley Online Library
In this paper, we develop the theoretical provisions of symmetric cryptographic algorithms
based on the polynomial residue number system for the first time. The main feature of the …

Finding the inverse of a polynomial modulo in the ring z [x] based on the method of undetermined coefficients

R Shevchuk, I Yakymenko, M Karpinski… - Computer …, 2024 - journals.agh.edu.pl
This paper presents the theoretical foundations of finding the inverse of a polynomial
modulo in the ring Z [x] based on the method of undetermined coefficients. The use of the …

Експериментальне дослідження програмної реалізації методів пошуку оберненого елемента за модулем

ММ Касянчук, ІЗ Якименко, СВ Івасьєв… - Інформатика та …, 2017 - irbis-nbuv.gov.ua
Знаходження мультиплікативного оберненого елемента за модулем дуже часто є
необхідною умовою для розв'язування багатьох задач сучасної теорії чисел …

Algorithms for solving problems of cryptographic protection of color image pixels in the Rademacher's basis and residue number systems

NY Vozna, YM Nykolaychuk, OI Volynskyi - Cybernetics and Systems …, 2019 - Springer
This paper substantiates the urgency of developing theoretical foundations, methods, and
algorithms for cryptographic protection of color image pixels using problem-oriented …

Multiple error detection and correction based on modular arithmetic correcting codes

V Yatskiv, T Tsavolyk… - 2015 IEEE 8th International …, 2015 - ieeexplore.ieee.org
In this paper we proposed correcting codes-based on modular arithmetic-to improve the
data transmission robustness in wireless sensor networks. We developed a new method …