On a Novel Security Algorithm for the Encryption of 3 3 Fuzzy Matrices with Rational Entries Based on The Symbolic 2-Plithogenic Integers and El-Gamal Algorithm

Yaser Ahmad Alhasan^1,*, Abuobida Mohammed A. Alfahal¹, Raja Abdullah Abdulfatah¹,

Rozina Ali², Mayas Aljibawi³

¹Deanship of the Preparatory Year, Prince Sattam bin Abdulaziz University, Alkharj, Saudi Arabia

²Department of Mathematics, Faculty of Science, Cairo University, Cairo, Egypt

³Computer Techniques Engineering Department, Al-Mustaqbal University, Hillah 51001, Iraq

Emails: y.alhasan@psau.edu.sa; a.alfahal@psau.edu.sa; r.abdulfatah@psau.edu.sa ; rozyyy123n@gmail.com; mayas.mohammed@uomus.edu.iq

Abstract

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.

Keywords: Symbolic 2-plithogenic integer; fuzzy matrix; fuzzy relation; EL-Gamal crypto-algorithm