On A Novel Security Scheme for The Encryption and Decryption Of 2×2 Fuzzy Matrices with Rational Entries Based on The Algebra of Neutrosophic Integers and El-Gamal Crypto-System

Abstract

The main goal behind mathematical cryptography is to keep messages and
multimedia messages secret at a time when modern means of communication have
spread and become very diverse.
Fuzzy matrices as strong tools which was defined to deal with incomplete and
uncertain data and many relationships in real life problems especially those which
are related to images and graphs, may considered as important subjects for secret
information and communication.
The aim of this research paper is to present a new model and method for encrypting
2×2 fuzzy matrices using the basic concepts in neutrosophic number theory and El
Gamal algorithm in cryptography, where we generalize El Gamal algorithm to
become applicable to the ring of neutrosophic integer numbers that represents the
studied fuzzy matrices.
On the other hand, we study the applications of the novel algorithm to the
encryption and decryption of some fuzzy relations represented in terms of fuzzy
functions. In addition, we illustrate many examples to clarify the validity of the new
algorithm