Aplicação da álgebra moderna nos fundamentos da criptografia-cifras de césar e cifras de hill.

Abstract

Communication is essential in every community and, even before the invention of writing, man used symbols to express his feelings and culture. With the invention of writing, which dates from the fifth century b. C., came the possibility of diffusion of the information. In order to keep the information secret, cryptography emerged, evolving alongside advances in technology. Thus, as in antiquity, the Arabs used a monoalphabetic substitution cipher to protect state secrets, today we use the RSA algorithm in Digital Certificates. With the internet, more and more people are able to access information. Today, encryption is commonplace in our day-to-day lives. The coding processes of the messages sent depend exclusively on mathematical resources, specifically on algebra and number theory. Thus, we will make an introduction to the study of cryptography, based on its foundation, presenting some of the systems that use these resources in the codification of their messages, demonstrating the mathematical concepts applied succinctly, then a description of the first signs of the emergence of cryptography in history, a well as the contributions of cryptography to current scientific and technological development.