Volume 27 • Issue 2 • PP: 195-203 • 2026
A Novel Application of Symbolic 2-Plithogenic Integers and Refined Neutrosophic Numbers in Public Key Encryption Based On Hexadecnion Algebra
Open Access & Copyright
© 2026 The Author(s). Published by ASPG. This article is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
View PDF Abstract
In this work, we use the symbolic 2-plithogenic integers and refined neutrosophic numbers to get a generalized version of HXDTRU with a strict approach includes three symbolic 2-plithogenic and refined neutrosophic private keys with one public symbolic 2-pithogenic and refined neutrosophic key to improve the security. In addition, we analyse the complexity of the generalized systems numerically.
Keywords
References
[1] J. Hoffstein, J. Pipher, and J. H. Silverman, "NTRU: A ring-based public key cryptosystem," in Proc. Int. Algorithmic Number Theory Symp., 1998, pp. 267–288.
[2] Y. A. Alhasan et al., "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," Int. J. Neutrosophic Sci., vol. 21, no. 1, pp. 88–95, 2023, doi: 10.54216/IJNS.210108.
[3] Allouf, "A Review on the Neutrosophic Number Theory Based Cryptography and Neutrosophic Public Key Crypto-Systems," Int. J. Adv. Appl. Comput. Intell, pp. 30-35, 2024, doi: https://doi.org/10.54216/IJAACI.060103.
[4] M. Abobala, H. Sankari, and M. B. Zeina, "On Novel Security Systems Based on the 2-Cyclic Refined Integers and the Foundations of 2-Cyclic Refined Number Theory," J. Fuzzy Extension Appl., 2024.
[5] M. Abobala and A. Allouf, "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 Syst., vol. 54, 2023.
[6] H. R. Yassein and N. M. Al-Saidi, “HXDTRU cryptosystem based on hexadecnion algebra,” in Proc. 5th Int. Cryptol. Inf. Secur. Conf., Kota Kinabalu, Malaysia, 2016, vol. 31.
[7] Z. Djedid et al., "On solutions of differential and integral equations using new fixed point results in cone Eb-metric spaces," Partial Differ. Equations Appl. Math., vol. 8, p. 100559, 2023.
[8] D. Alrwashdeh et al., "On Two Novel Generalized Versions of Diffie-Hellman Key Exchange Algorithm Based on Neutrosophic and Split-Complex Integers and their Complexity Analysis," Int. J. Neutrosophic Sci., pp. 01-10, 2025, doi: https://doi.org/10.54216/IJNS.250201.
[9] F. Smarandache, Plithogeny, Plithogenic Set, Logic, Probability, and Statistics. Brussels, Belgium: Pons Editions, 2017.
[10] R. Saadeh et al., "Linear Fractional Differential Equations for Modeling Nonlinear Hydro Environmental Phenomena," Eng. Lett, vol. 33, no. 6, 2025.
[11] M. Celik and A. Hatip, "On The Refined AH-Isometry And Its Applications In Refined Neutrosophic Surfaces," Galoisica J. Math. Struct. Appl., 2022.
[12] E. O. Adeleke, A. A. A. Agboola, and F. Smarandache, "Refined Neutrosophic Rings I", Int. J. Neutrosophic Sci., vol. 2, no. 2, pp. 77-81, 2020.
Cite This Article
Choose your preferred format
Publisher's Note
The statements, opinions, and data presented in this article are solely those of the author(s) and do not necessarily represent those of ASPG, the journal, or its editors. ASPG and the editors disclaim responsibility for any harm arising from the use of any ideas, methods, instructions, or products described in this article, to the fullest extent permitted by applicable law.