International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/3899 2020 2020 Department of Mathematics, College of Basic Education, University of Babylon, Hillah, Iraq Sahab Sahab General Directorate of Al-Muthanna Education, Al-Muthanna, Iraq Mohammed Hassan Hamza Department of Mathematics College of Education, University of Al-Qadisiyah, Al-Qadisiya, Iraq Hassan Rashed Yassein 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 2025 113 121 10.54216/IJNS.260411 https://www.americaspg.com/articleinfo/21/show/3899