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.
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