A New Cryptographic Scheme Using Integral Transform and Matrix Decomposition

Abstract

In this article, we show how to use the Abaoub Shkheam transform and matrix decomposition of the non-singular matrix to increase the security of communication between two people to be more secure. The goal of this research is to create an algorithm for information encryption and decryption using matrix decomposition and Abaoub Shkheam transform. In the first part of the paper for encryption, we take plain text as the original message and convert it to cipher text by applying the Abaoub Shkheam transform of hyperbolic function and lower triangular matrix as the encryption key. In the second part, we used the inverse Abaoub Shkheam transform of a hyperbolic function and upper triangular matrix as the decryption key for decryption. Generalization of the results is also obtained.