International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/4059 2020 2020 Department of Science, Applied Science Private University, Jordan Gharib Gharib Department of Mathematics, Zarqa University, Zarqa , Jordan Gharib M. Gharib Faculty of Information Technology, Abu Dhabi University, Abu Dhabi, United Arab Emirates Fadil A. Jaradat Faculty of Computer Studies, Arab Open University, Saudi Arabia Ahmad A. Abubaker The University of Jordan, Aqaba, Department of computer information systems, Jordan Ahmed Atallah Alsaraireh 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. 2026 2026 195 203 10.54216/IJNS.270217 https://www.americaspg.com/articleinfo/21/show/4059