La inversa de Moore-Penrose en matrices rectangulares de Fibonacci y sus aplicaciones en la criptografía

Abstract

This monograph focuses on the study of the Moore-Penrose inverse, analyzing its properties and its application in the field of cryptography, taking as a reference the work titled "The Moore-Penrose inverse of the rectangular Fibonacci matrix and applications to the cryptology," published in the journal Advances and Applications in Discrete Mathematics by Suleyman Aydinyuz and Mustafa Acsci. The main objective of this work is to investigate how, through the use of rectangular Fibonacci matrices and this pseudoinverse, it is possible to design an effective method for encoding and decoding messages. Throughout the development of the study, different encryption and decryption techniques will be addressed, evaluating how this approach can be optimized and made more effective for future cryptographic applications. The aim is to complement the results of the aforementioned authors by adding some constraints to achieve more robust encoding and decoding. This analysis will be supported by tools from number theory and matrix algebra, as well as by computational simulations carried out in Python, which will provide practical validation of the theoretical results obtained.