On Two Novel Generalized Versions of Diffie-Hellman Key Exchange Algorithm Based on Neutrosophic and Split-Complex Integers and their Complexity Analysis

Dima; Talat; Ahmed Soiman Rashed; Ali; Hussein; Abdallah

doi:https://doi.org/10.54216/IJNS.250201

Full Length Article

Volume 25 • Issue 2 • PP: 01-10 • 2025

On Two Novel Generalized Versions of Diffie-Hellman Key Exchange Algorithm Based on Neutrosophic and Split-Complex Integers and their Complexity Analysis

Dima Alrwashdeh ^1*

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,

Talat Alkhouli ²

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,

Ahmed Soiman Rashed Alhawiti ³

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,

Ali Allouf ⁴

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,

Hussein Edduweh ⁵

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,

Abdallah Al-Husban ⁶

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¹Department of Information Technology, School of Information Technology and System, the University of Jordan, Aqaba, Jordan

²Applied Science Department, Aqaba University College, Al-Balqa Applied University, Jordan

³Department of General Studies, Technical College of Haql, Tabuk, Kingdom of Saudi Arabia

⁴Tishreen University, Faculty Of computer engineering and automation, Latakia, Syria

⁵Department of Mathematics, the University of Texas at Arlington, Arlington, TX 76019-0407, USA

⁶Department of Mathematics, Faculty of Science and Technology, Irbid National University, P.O. Box: 2600 Irbid, Jordan

* Corresponding Author.

DOI https://doi.org/10.54216/IJNS.250201

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Received: January 29, 2024 Revised: April 28, 2024 Accepted: July 20, 2024

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Abstract

The objective of this paper is to build the Split-Complex version of Diffie-Hellman key Exchange Algorithm, where we use the mathematical foundations of Split-Complex Number Theory and Integers, such as congruencies, raising a split-complex integer to a power of split-complex integer to build novel algorithms for key Exchange depending of famous Diffie-Hellman algorithm. Additionally, we present the proposed version of the Diffie-Hellman algorithm based on neutrosophic number theory. Also, we analyze the complexity of the novel algorithms with many examples that explain their applied validity.

Keywords

Split-Complex Cryptography Split-Complex Diffie-Hellman Hellman key Exchange Algorithms Neutrosophic Diffie-Hellman

References

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Alrwashdeh, Dima, Alkhouli, Talat, Alhawiti, Ahmed Soiman Rashed, Allouf, Ali, Edduweh, Hussein, Al-Husban, Abdallah. "On Two Novel Generalized Versions of Diffie-Hellman Key Exchange Algorithm Based on Neutrosophic and Split-Complex Integers and their Complexity Analysis." International Journal of Neutrosophic Science, vol. Volume 25, no. Issue 2, 2025, pp. 01-10. DOI: https://doi.org/10.54216/IJNS.250201

Alrwashdeh, D., Alkhouli, T., Alhawiti, A., Allouf, A., Edduweh, H., Al-Husban, A. (2025). On Two Novel Generalized Versions of Diffie-Hellman Key Exchange Algorithm Based on Neutrosophic and Split-Complex Integers and their Complexity Analysis. International Journal of Neutrosophic Science, Volume 25(Issue 2), 01-10. DOI: https://doi.org/10.54216/IJNS.250201

Alrwashdeh, Dima, Alkhouli, Talat, Alhawiti, Ahmed Soiman Rashed, Allouf, Ali, Edduweh, Hussein, Al-Husban, Abdallah. "On Two Novel Generalized Versions of Diffie-Hellman Key Exchange Algorithm Based on Neutrosophic and Split-Complex Integers and their Complexity Analysis." International Journal of Neutrosophic Science Volume 25, no. Issue 2 (2025): 01-10. DOI: https://doi.org/10.54216/IJNS.250201

Alrwashdeh, D., Alkhouli, T., Alhawiti, A., Allouf, A., Edduweh, H., Al-Husban, A. (2025) 'On Two Novel Generalized Versions of Diffie-Hellman Key Exchange Algorithm Based on Neutrosophic and Split-Complex Integers and their Complexity Analysis', International Journal of Neutrosophic Science, Volume 25(Issue 2), pp. 01-10. DOI: https://doi.org/10.54216/IJNS.250201

Alrwashdeh D, Alkhouli T, Alhawiti A, Allouf A, Edduweh H, Al-Husban A. On Two Novel Generalized Versions of Diffie-Hellman Key Exchange Algorithm Based on Neutrosophic and Split-Complex Integers and their Complexity Analysis. International Journal of Neutrosophic Science. 2025;Volume 25(Issue 2):01-10. DOI: https://doi.org/10.54216/IJNS.250201

D. Alrwashdeh, T. Alkhouli, A. Alhawiti, A. Allouf, H. Edduweh, A. Al-Husban, "On Two Novel Generalized Versions of Diffie-Hellman Key Exchange Algorithm Based on Neutrosophic and Split-Complex Integers and their Complexity Analysis," International Journal of Neutrosophic Science, vol. Volume 25, no. Issue 2, pp. 01-10, 2025. DOI: https://doi.org/10.54216/IJNS.250201

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