A matemática presente no desenvolvimento da criptografia. / Lucas Purificação Mendes de Souza

Abstract

Although little is imagined and understood, cryptography has been widely used since the dawn of history in order to keep various information secret, since human beings have always had, for various reasons, the need to maintain the security and privacy of messages. As time went on, various methods of hiding a message were developed, the processes of encoding and decoding messages became more and more vital. For this, cryptography (the art of coding a message) had to evolve since it continued to be something essential for humanity and, in order for this evolution to become possible, several concepts of Mathematics were used. This work intends to show the use, importance, the presence of Mathematics in the dynamics and reliability of keeping secret messages for different civilizations throughout human history. For this, a bibliographical study was used, seeking to observe what other authors addressed on the subject. As well as practical demonstrations regarding the functionality of the methods covered. In this research, several coding methods were found used throughout its trajectory, and, over time, several new methods were created, or improved old methods, which are increasingly complex, given the fact that cryptanalysis (an area responsible for analyzing decoding methods with the aim of unveiling the patterns and secrets that the messages contained) also showed constant evolution. However, even with all the development of cryptanalysis, there have always been efficient coding methods, and currently the method that fulfills its function with greater security is the RSA method, which uses mathematical concepts, which involves the set of integers and their properties as a basis for its operation. What stands out: the product of <big= prime numbers, modular congruence, among others