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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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 2783-1442 2717-3453 |