Construction of Akushsky Core Functions Without Critical Cores
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 e...
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MDPI AG
2024-10-01
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| author | Vladislav Lutsenko Mikhail Babenko Maxim Deryabin |
| author_facet | Vladislav Lutsenko Mikhail Babenko Maxim Deryabin |
| author_sort | Vladislav Lutsenko |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-decac6a5f8374fa1bf3641eddf83b41f |
| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2024-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-decac6a5f8374fa1bf3641eddf83b41f2024-11-08T14:37:47ZengMDPI AGMathematics2227-73902024-10-011221339910.3390/math12213399Construction of Akushsky Core Functions Without Critical CoresVladislav Lutsenko0Mikhail Babenko1Maxim Deryabin2North Caucasus Center for Mathematical Research, North-Caucasus Federal University, 355017 Stavropol, RussiaNorth Caucasus Center for Mathematical Research, North-Caucasus Federal University, 355017 Stavropol, RussiaSamsung Advanced Institute of Technology, Suwon 16678, Republic of KoreaThe 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.https://www.mdpi.com/2227-7390/12/21/3399residue number systemAkushsky core functioncritical coresmonotonicity of the core functionnon-modular operationsbrute force algorithm |
| spellingShingle | Vladislav Lutsenko Mikhail Babenko Maxim Deryabin Construction of Akushsky Core Functions Without Critical Cores Mathematics residue number system Akushsky core function critical cores monotonicity of the core function non-modular operations brute force algorithm |
| title | Construction of Akushsky Core Functions Without Critical Cores |
| title_full | Construction of Akushsky Core Functions Without Critical Cores |
| title_fullStr | Construction of Akushsky Core Functions Without Critical Cores |
| title_full_unstemmed | Construction of Akushsky Core Functions Without Critical Cores |
| title_short | Construction of Akushsky Core Functions Without Critical Cores |
| title_sort | construction of akushsky core functions without critical cores |
| topic | residue number system Akushsky core function critical cores monotonicity of the core function non-modular operations brute force algorithm |
| url | https://www.mdpi.com/2227-7390/12/21/3399 |
| work_keys_str_mv | AT vladislavlutsenko constructionofakushskycorefunctionswithoutcriticalcores AT mikhailbabenko constructionofakushskycorefunctionswithoutcriticalcores AT maximderyabin constructionofakushskycorefunctionswithoutcriticalcores |