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On novel security systems based on the 2-cyclic refined integers and the foundations of 2-cyclic refined number theory

Document Type : Research Paper

Authors

1 Tishreen University, Faculty of Science, Department of Mathematics, Syria.

2 Department of Mathematical Statistics, Faculty of Science, University of Aleppo, Aleppo, Syria.

Abstract

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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References
[1]   Abobala, M. (2020). N-cyclic refined neutrosophic algebraic systems of sub-indeterminacies, an application to rings and modules. International journal of neutrosophic science, 12(2), 81–95. DOI:10.5281/zenodo.4278999
[2]   Smarandache, F. (2015). Symbolic neutrosophic theory. Infinite Study.
[3]   Al Rida Sadiq, B. A. (2022). A contribution to the group of units’ problem in some 2-cyclic refined neutrosophic rings. International journal of neutrosophic science, 18(3), 48–58. DOI:10.54216/IJNS.180304
[4]   Von Shtawzen, O. (2022). Conjectures for invertible diophantine equations of 3-cyclic and 4-cyclic refined integers. Journal of neutrosophic and fuzzy systems, 3, 32–36.
[5]   Basheer, A. A., Ahmad, K. D., & Ali, R. (2022). On some open problems about n-cyclic refined neutrosophic rings and number theory. Journal of neutrosophic and fuzzy systems, 3(2), 37–42.
[6]   Shtawzen, O. V. (2022). On a novel group derived from a generalization of integer exponents and open problems. Galoitica: journal of mathematical structures and applications, 1(1), 12–35. DOI:10.54216/gjmsa.010102
[7]   Othman, K. Ben, Von Shtawzen, O., Khaldi, A., & Ali, R. (2023). On the concept of symbolic 7-plithogenic real matrices. Infinite Study.
[8]   Zayood, K. (2023). On novel public-key cryptosystem using MDS code. CERN European organization for nuclear research, 1. https://doi.org/10.5281/zenodo.7882491
[9]   Zayood, K. (2023). On a novel generalization of the RSA crypto-system. Neoma journal of mathematics and computer science (NJMCS), 1. https://zenodo.org/records/7882515
[10] Merkepci, M., & Sarkis, M. (2022). An application of pythagorean circles in cryptography and some ideas for future non classical systems. Galoitica: journal of mathematical structures and applications, 2(2), 28–30. DOI:10.54216/gjmsa.020205
[11] Abobala, M., & Allouf, A. (2023). On a novel security scheme for the encryption and decryption Of 2×2 fuzzy matrices with rational entries based on the algebra of neutrosophic integers and El-Gamal crypto-system. Neutrosophic sets and systems, 54, 19–32.
[12] Merkepci, M., Abobala, M., & Allouf, A. (2023). The applications of fusion neutrosophic number theory in public key cryptography and the improvement of RSA algorithm. Infinite Study.
[13] Merkepci, M., & Abobala, M. (2023). Security model for encrypting uncertain rational data units based on refined neutrosophic integers fusion and El-Gamal algorithm. Infinite Study.
[14] Alhasan, Y. A., Alfahal, A. M. A., Abdulfatah, R. A., Ali, R., & Aljibawi, M. (2023). On a novel security algorithm for the encryption of 3x3 fuzzy matrices with rational entries based on the symbolic 2- plithogenic integers and El-Gamal algorithm. International journal of neutrosophic science, 21(1), 88–95. DOI:10.54216/IJNS.210108
[15] Taffach, N. M., & Hatip, A. (2023). A brief review on the symbolic 2-plithogenic number theory and algebraic equations. Galoitica: journal of mathematical structures and applications, 5(1), 36–44. DOI:10.54216/gjmsa.050103
[16] Martin, N., & Edalatpanah, S. A. (2023). Application of extended fuzzy ISOCOV methodology in nanomaterial selection based on performance measures. Journal of operational and strategic analytics, 1(2), 55–61. DOI:10.56578/josa010202
[17] Babazadeh, Y., Farahmand, N. F., Pasebani, M., & Matın, Y. A. (2022). Identifying key indicators for developing the use of blockchain technology in financial systems. International journal of research in industrial engineering (2783-1337), 11(3), 244–257.
[18] Sankari, H., & Abobala, M. (2023). On the classification of the group of units of rational and real 2-cyclic refined neutrosophic rings. Neutrosophic sets and systems, 54, 89–100. DOI:10.5281/zenodo.7817657
Journal of Fuzzy Extension and Applications
Volume 5, Issue 1
March 2024
Pages 69-85
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