On novel security systems based on the 2-cyclic refined integers and the foundations of 2-cyclic refined number theory
Integers play a basic role in the structures of asymmetric crypto-algorithms. Many famous public key crypto-schemes use the basics of number theory to share keys and decrypt and encrypt messages and multimedia. As a novel trend in the world of cryptography, non-classical integer systems, such as neu...
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| Format: | Article |
| Language: | English |
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Ayandegan Institute of Higher Education,
2024-03-01
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| Series: | Journal of Fuzzy Extension and Applications |
| Subjects: | |
| Online Access: | https://www.journal-fea.com/article_188610_01287a9dd768b182af73dae66faed762.pdf |
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| _version_ | 1832577810888130560 |
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| author | Mohammad Abobala Hasan Sankari Mohamed Zeina |
| author_facet | Mohammad Abobala Hasan Sankari Mohamed Zeina |
| author_sort | Mohammad Abobala |
| collection | DOAJ |
| description | Integers play a basic role in the structures of asymmetric crypto-algorithms. Many famous public key crypto-schemes use the basics of number theory to share keys and decrypt and encrypt messages and multimedia. As a novel trend in the world of cryptography, non-classical integer systems, such as neutrosophic or plithogenic integers, are used for encryption and decryption. The objective of this paper is to provide the basic foundations of 2-cyclic refined number theory and linear Diophantine equations in two variables by building suitable algebraic isomorphism between the 2-cyclic refined integer ring and a subring of the direct product of Z with itself three times. Also, this work presents two novel crypto schemes for the encryption and decryption of data and information based on the algebraic properties of 2-cyclic refined integers, where improved versions of the El-Gamal crypto-scheme and RSA algorithm will be established through the view of the algebra and number theory of 2-cyclic refined integers. On the other hand, we illustrate some examples and tables to show the validity and complexity of the novel algorithms. |
| format | Article |
| id | doaj-art-55218417007d4515910cc85567eb4098 |
| institution | Kabale University |
| issn | 2783-1442 2717-3453 |
| language | English |
| publishDate | 2024-03-01 |
| publisher | Ayandegan Institute of Higher Education, |
| record_format | Article |
| series | Journal of Fuzzy Extension and Applications |
| spelling | doaj-art-55218417007d4515910cc85567eb40982025-01-30T15:07:00ZengAyandegan Institute of Higher Education,Journal of Fuzzy Extension and Applications2783-14422717-34532024-03-0151698510.22105/jfea.2024.423818.1321188610On novel security systems based on the 2-cyclic refined integers and the foundations of 2-cyclic refined number theoryMohammad Abobala0Hasan Sankari1Mohamed Zeina2Tishreen University, Faculty of Science, Department of Mathematics, Syria.Tishreen University, Faculty of Science, Department of Mathematics, Syria.Department of Mathematical Statistics, Faculty of Science, University of Aleppo, Aleppo, Syria.Integers play a basic role in the structures of asymmetric crypto-algorithms. Many famous public key crypto-schemes use the basics of number theory to share keys and decrypt and encrypt messages and multimedia. As a novel trend in the world of cryptography, non-classical integer systems, such as neutrosophic or plithogenic integers, are used for encryption and decryption. The objective of this paper is to provide the basic foundations of 2-cyclic refined number theory and linear Diophantine equations in two variables by building suitable algebraic isomorphism between the 2-cyclic refined integer ring and a subring of the direct product of Z with itself three times. Also, this work presents two novel crypto schemes for the encryption and decryption of data and information based on the algebraic properties of 2-cyclic refined integers, where improved versions of the El-Gamal crypto-scheme and RSA algorithm will be established through the view of the algebra and number theory of 2-cyclic refined integers. On the other hand, we illustrate some examples and tables to show the validity and complexity of the novel algorithms.https://www.journal-fea.com/article_188610_01287a9dd768b182af73dae66faed762.pdf2-cyclic refined integersrsael-gamalsecurity system |
| spellingShingle | Mohammad Abobala Hasan Sankari Mohamed Zeina On novel security systems based on the 2-cyclic refined integers and the foundations of 2-cyclic refined number theory Journal of Fuzzy Extension and Applications 2-cyclic refined integers rsa el-gamal security system |
| title | On novel security systems based on the 2-cyclic refined integers and the foundations of 2-cyclic refined number theory |
| title_full | On novel security systems based on the 2-cyclic refined integers and the foundations of 2-cyclic refined number theory |
| title_fullStr | On novel security systems based on the 2-cyclic refined integers and the foundations of 2-cyclic refined number theory |
| title_full_unstemmed | On novel security systems based on the 2-cyclic refined integers and the foundations of 2-cyclic refined number theory |
| title_short | On novel security systems based on the 2-cyclic refined integers and the foundations of 2-cyclic refined number theory |
| title_sort | on novel security systems based on the 2 cyclic refined integers and the foundations of 2 cyclic refined number theory |
| topic | 2-cyclic refined integers rsa el-gamal security system |
| url | https://www.journal-fea.com/article_188610_01287a9dd768b182af73dae66faed762.pdf |
| work_keys_str_mv | AT mohammadabobala onnovelsecuritysystemsbasedonthe2cyclicrefinedintegersandthefoundationsof2cyclicrefinednumbertheory AT hasansankari onnovelsecuritysystemsbasedonthe2cyclicrefinedintegersandthefoundationsof2cyclicrefinednumbertheory AT mohamedzeina onnovelsecuritysystemsbasedonthe2cyclicrefinedintegersandthefoundationsof2cyclicrefinednumbertheory |