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International Journal of Neutrosophic Science

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International Journal of Neutrosophic Science

Volume 25 , Issue 2 , PP: 01-10, 2025 | Cite this article as | XML | Html | PDF | Full Length Article

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 * , Talat Alkhouli 2 , Ahmed Soiman Rashed Alhawiti 3 , Ali Allouf 4 , Hussein Edduweh 5 , Abdallah Al-Husban 6

  • 1 Department of Information Technology, School of Information Technology and System, the University of Jordan, Aqaba, Jordan - (d.rawashdeh@ju.edu.jo)
  • 2 Applied Science Department, Aqaba University College, Balqa Applied University, Jordan - (Talat.khouli@bau.edu.jo)
  • 3 Department of General Studies, Technical College of Haql, Tabuk, Kingdom of Saudi Arabia - (ahmed.a13@tvtc.gov.sa)
  • 4 Tishreen University, Faculty Of computer engineering and automation, Latakia, Syria - (Ali.allouf@gmail.com)
  • 5 Department of Mathematics, the University of Texas at Arlington, Arlington, TX 76019-0407, USA - (Husseinsaid.edduweh@mavs.uta.edu)
  • 6 Department of Mathematics, Faculty of Science and Technology, Irbid National University, P.O. Box: 2600 Irbid, Jordan - (dralhosban@inu.edu.jo)

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

    Received: January 29, 2024 Revised: April 28, 2024 Accepted: July 20, 2024
    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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    [2]          Merkepci, M., and Abobala, M., “On Some Novel Results about Split-Complex Numbers, the Diagonalization Problem and Applications to Public Key Asymmetric Cryptography", Journal of Mathematics, Hindawi, 2023.

    [3]          S. A. Aparna J R, "Image Watermarking using Diffie Hellman Key Exchange," in International Conference on Information and Communication Technologies, Kochi, India, 2015.

    [4]          https://www.bsi.bund.de/EN/Themen/Unternehmen-und-Organisationen/Informationen-und Empfehlungen/ Kryptografie/ KI-in-der-Kryptografie/ki-in-der-kryptografie_node.html.  Last visted: 6/17/2024.

    [5]          Abobala, M., and Allouf, A., " 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, vol.54, 2023.

    [6]          Merkepci, M., Abobala, M., and Allouf, A., " The Applications of Fusion Neutrosophic Number Theory in Public Key Cryptography and the Improvement of RSA Algorithm ", Fusion: Practice and Applications, 2023.

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    [9]          Mohammad Abobala, Hasan Sankari, and Mohamed Bisher 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, 2024.

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    [11]       Shihadeh, A., Matarneh, K. A. M., Hatamleh, R., Hijazeen, R. B. Y., Al-Qadri, M. O., & Al-Husban, A. (2024). An Example of Two-Fold Fuzzy Algebras Based On Neutrosophic Real Numbers. Neutrosophic Sets and Systems, 67, 169-178.‏

    [12]       Abdallah Shihadeh, Khaled Ahmad Mohammad Matarneh, Raed Hatamleh, Mowafaq Omar Al-Qadri, Abdallah Al-Husban. (2024). On The Two-Fold Fuzzy n-Refined Neutrosophic Rings For 2 ≤3. Neutrosophic Sets and Systems, 68, 8-25.‏

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    Cite This Article As :
    Alrwashdeh, Dima. , Alkhouli, Talat. , Soiman, Ahmed. , 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. , no. , 2025, pp. 01-10. DOI: https://doi.org/10.54216/IJNS.250201
    Alrwashdeh, D. Alkhouli, T. Soiman, 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, (), 01-10. DOI: https://doi.org/10.54216/IJNS.250201
    Alrwashdeh, Dima. Alkhouli, Talat. Soiman, Ahmed. 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 , no. (2025): 01-10. DOI: https://doi.org/10.54216/IJNS.250201
    Alrwashdeh, D. , Alkhouli, T. , Soiman, 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 , () , 01-10 . DOI: https://doi.org/10.54216/IJNS.250201
    Alrwashdeh D. , Alkhouli T. , Soiman 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. (): 01-10. DOI: https://doi.org/10.54216/IJNS.250201
    Alrwashdeh, D. Alkhouli, T. Soiman, 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, vol. , no. , pp. 01-10, 2025. DOI: https://doi.org/10.54216/IJNS.250201

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