International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/1798 2020 2020 Deanship of the Preparatory Year, Prince Sattam bin Abdulaziz University, Alkharj, Saudi Arabia 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 Department of Mathematics, Faculty of Science, Cairo University, Cairo, Egypt Rozina Ali Computer Techniques Engineering Department, Al-Mustaqbal University, Hillah 51001, Iraq Mayas Aljibawi 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  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 2023 88 95 10.54216/IJNS.210108 https://www.americaspg.com/articleinfo/21/show/1798