Criptografia e a Matemática

• Ano de defesa: 2021
• Autor(a) principal: Oliveira, Vinícius Matos de
• Orientador(a): Santos, Naldisson dos
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Programa de Pós-Graduação: Mestrado Profissional em Matemática
• Palavras-chave em Português: Matemática; Números primos; Congruências e restos; Criptografia; Congruências; Sistema RSA
• Palavras-chave em Inglês: Prime numbers; Congruences; Cryptography; RSA system
• Área do conhecimento CNPq: CIENCIAS EXATAS E DA TERRA::MATEMATICA
• Link de acesso: http://ri.ufs.br/jspui/handle/riufs/15776

The present dissertation aims to align the mathematical knowledge to the RSA encryption system theme. Initially, a historical line is made on the evolution of cryptography, showing the need for rulers, kings, commanders to pass confidential information throughout history. Next, the essential mathematical knowledge is studied to understand the most used cryptographic system today: the RSA system. Among this mathematical knowledge, prime numbers stand out in basic arithmetic, and the congruence system in the modular arithmetic. Soon after, it is demonstrated how works the system Encryption RSA, as well as is guaranteed enormous difficulty in breaking the message encrypted from the prime numbers chosen for its composition.