Applications of matrix algebra in encryption by transposition

Abstract

Since the beginning of communication in humanity has seen the need to convey messages in a way that are
hidden for those who are not the recipient. Message encryption methodologies have been developed since ancient
times, which has allowed various methods and mathematical algorithms, in fact some of them at present have not yet
been fully deciphered. In this article we develop a methodology and algorithm that models the encryption through
the transposition system known as double transposition through the mathematical foundations of linear algebra. An
application of an encryption method is established, based on the PALU special matrix factorization, leaving the door
open for new methodologies by factorizations of different order and complexity according to the matrix algebra.