aspg-21-3899-1792500399 20261020124639 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group International Journal of Neutrosophic Science IJNS 2692-6148 2690-6805 2025 26 4 Sahab Mohsen Abboud Department of Mathematics, College of Basic Education, University of Babylon, Hillah, Iraq Mohammed Hassan Hamza General Directorate of Al-Muthanna Education, Al-Muthanna, Iraq Hassan Rashed Yassein Department of Mathematics College of Education, University of Al-Qadisiyah, Al-Qadisiya, Iraq HXDTRU is a multidimensional public key encryption system with sixteen encrypted data vectors at each step. In this work, we propose HXDHS, an improved version of HXDTRU based on hexadecnion algebra with neutrosophic integer coefficients, as well as a new mathematical construction includes three private keys with one public key to enhance the security and robustness of the public-key system. HXDHS is suitable for applications that require concurrent operation from multiple sources. 2025 113 121 3899 https://creativecommons.org/licenses/by/4.0/ 10.54216/IJNS.260411 https://www.americaspg.com/journal/21/article/3899 https://www.americaspg.com/storage/61749757949.pdf