aspg-21-1798-1791468693 20261008141133 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group International Journal of Neutrosophic Science IJNS 2692-6148 2690-6805 2023 21 1 Yaser Ahmad Alhasan Deanship of the Preparatory Year, Prince Sattam bin Abdulaziz University, Alkharj, Saudi Arabia Abuobida Mohammed A. Alfahal Deanship of the Preparatory Year, Prince Sattam bin Abdulaziz University, Alkharj, Saudi Arabia Raja Abdullah Abdulfatah Deanship of the Preparatory Year, Prince Sattam bin Abdulaziz University, Alkharj, Saudi Arabia Rozina Ali Department of Mathematics, Faculty of Science, Cairo University, Cairo, Egypt Mayas Aljibawi Computer Techniques Engineering Department, Al-Mustaqbal University, Hillah 51001, Iraq Mathematical cryptography applies special properties of integers and number theory in encrypting and decrypting messages in our world which is increasingly in demand for information security, especially for social media and multimedia. The objective of this work is to generalize El-Gamal crypto algorithm to be applied by using symbolic 2-plithogenic integers instead of classical integers. Also, we apply the novel algorithm to the encryption and the decryption of square style='mso-bidi-font-style:normal'> 10.0pt;font-family:"Cambria Math",serif;mso-bidi-font-family:"Times New Roman"; mso-bidi-theme-font:major-bidi;mso-ansi-language:EN-GB;mso-bidi-language:AR-SY'>3×3 fuzzy matrices with rational entries, and fuzzy relations which can be represented as fuzzy matrices with rational entries. In addition, many examples with numerical data will be presented. 2023 88 95 1798 https://creativecommons.org/licenses/by/4.0/ 10.54216/IJNS.210108 https://www.americaspg.com/journal/21/article/1798 https://www.americaspg.com/storage/81749432774.pdf