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Search Results (4)

Search Parameters:
Keywords = Akushsky Core Function

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16 pages, 1175 KB  
Article
Construction of Akushsky Core Functions Without Critical Cores
by Vladislav Lutsenko, Mikhail Babenko and Maxim Deryabin
Mathematics 2024, 12(21), 3399; https://doi.org/10.3390/math12213399 - 30 Oct 2024
Viewed by 990
Abstract
The residue number system is widely used in cryptography, digital signal processing, image processing systems, and other areas where high-performance computing is required. One of the main tools used in the residue number system is the Akushsky core function. However, its use is [...] Read more.
The residue number system is widely used in cryptography, digital signal processing, image processing systems, and other areas where high-performance computing is required. One of the main tools used in the residue number system is the Akushsky core function. However, its use is limited due to the existence of so-called critical cores. This study aims to develop Akushsky core functions that effectively eliminate the occurrence of critical cores, thereby enhancing their applicability in real-world scenarios. We introduce a fundamental approach to critical core detection that reduces the average time for critical core detection by 99.48% compared to the brute force algorithm. The results of our analysis indicate not only a substantial improvement in the speed of core detection but also an enhancement in the overall performance of systems utilizing the Akushsky core function. Our findings provide important insights into optimizing residue number systems and encourage further exploration into advanced computational techniques within this domain. Full article
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15 pages, 2343 KB  
Article
Algorithm for Determining the Optimal Weights for the Akushsky Core Function with an Approximate Rank
by Egor Shiriaev, Nikolay Kucherov, Mikhail Babenko, Vladislav Lutsenko and Safwat Al-Galda
Appl. Sci. 2023, 13(18), 10495; https://doi.org/10.3390/app131810495 - 20 Sep 2023
Cited by 4 | Viewed by 1604
Abstract
In this paper, a study is carried out related to improving the reliability and fault tolerance of Fog Computing systems. This work is a continuation of previous studies. In the past, we have developed a method of fast operation for determining the sign [...] Read more.
In this paper, a study is carried out related to improving the reliability and fault tolerance of Fog Computing systems. This work is a continuation of previous studies. In the past, we have developed a method of fast operation for determining the sign of a number in the Residue Number System based on the Akushsky Core Function. We managed to increase the efficiency of calculations by using the approximate rank of a number. However, this result is not final. In this paper, we consider in detail the methods and techniques of the Akushsky Core Function. During research, it was found that the so-called weights can be equal to random variables. Based on the data obtained, we have developed a method for determining the optimal weights for the Akushsky Core Function. The result obtained allows you to obtain a performance advantage due to the preliminary identification of optimal weights for each set of moduli. Full article
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14 pages, 1249 KB  
Article
Fast Operation of Determining the Sign of a Number in RNS Using the Akushsky Core Function
by Egor Shiriaev, Nikolay Kucherov, Mikhail Babenko and Anton Nazarov
Computation 2023, 11(7), 124; https://doi.org/10.3390/computation11070124 - 28 Jun 2023
Cited by 4 | Viewed by 2161
Abstract
This article presents a study related to increasing the performance of distributed computing systems. The essence of fog computing lies in the use of so-called edge devices. These devices are low-power, so they are extremely sensitive to the computational complexity of the methods [...] Read more.
This article presents a study related to increasing the performance of distributed computing systems. The essence of fog computing lies in the use of so-called edge devices. These devices are low-power, so they are extremely sensitive to the computational complexity of the methods used. This article is aimed at improving the efficiency of calculations while maintaining an appropriate level of reliability by applying the methods of the Residue Number System (RNS). We are investigating methods for determining the sign of a number in the RNS based on the core function in order to develop a new, fast method. As a result, a fast method for determining the sign of a number based on the Akushsky core function, using approximate calculations, is obtained. Thus, in the course of this article, a study of methods for ensuring reliability in distributed computing is conducted. A fast method for determining the sign of a number in the RNS based on the core function using approximate calculations is also proposed. This result is interesting from the point of view of nebulous calculations, since it allows maintaining high reliability of a distributed system of edge devices with a slight increase in the computational complexity of non-modular operations. Full article
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14 pages, 945 KB  
Article
Improved Modular Division Implementation with the Akushsky Core Function
by Mikhail Babenko, Andrei Tchernykh and Viktor Kuchukov
Computation 2022, 10(1), 9; https://doi.org/10.3390/computation10010009 - 13 Jan 2022
Cited by 5 | Viewed by 3196
Abstract
The residue number system (RNS) is widely used in different areas due to the efficiency of modular addition and multiplication operations. However, non-modular operations, such as sign and division operations, are computationally complex. A fractional representation based on the Chinese remainder theorem is [...] Read more.
The residue number system (RNS) is widely used in different areas due to the efficiency of modular addition and multiplication operations. However, non-modular operations, such as sign and division operations, are computationally complex. A fractional representation based on the Chinese remainder theorem is widely used. In some cases, this method gives an incorrect result associated with round-off calculation errors. In this paper, we optimize the division operation in RNS using the Akushsky core function without critical cores. We show that the proposed method reduces the size of the operands by half and does not require additional restrictions on the divisor as in the division algorithm in RNS based on the approximate method. Full article
(This article belongs to the Special Issue Advanced Information, Computation, and Control Systems for Distributed Environments)
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