A matemática das criptografias

• Ano de defesa: 2025
• Autor(a) principal: Santos, Aline Márcia dos
• Orientador(a): Rodrigues, Paulo Henrique de Azevedo
• Banca de defesa: Rodrigues, Paulo Henrique de Azevedo , Souza, Mário José de , Silva, Sandro Ricardo Pinto da
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal de Goiás
• Programa de Pós-Graduação: PROFMAT - Programa de Pós-graduação em Matemática em Rede Nacional - Sociedade Brasileira de Matemática (IME)
• Departamento: Instituto de Matemática e Estatística - IME (RMG)
• País: Brasil
• Palavras-chave em Português: Criptografia; Aritmética Modular; Segurança Cibernética; Divisões Euclidianas; Matemática Prática BNCC
• Palavras-chave em Inglês: Cryptography; Modular Arithmetic; Cybersecurity; Euclidean Divisions; Practical Mathematics BNCC
• Área do conhecimento CNPq: CIENCIAS EXATAS E DA TERRA::MATEMATICA
• Link de acesso: https://repositorio.bc.ufg.br/tede/handle/tede/14694

Modular arithmetic is systematically employed in the development of contemporary technologies in order to promote cybersecurity, such as the need for data protection in banking transactions and on social media platforms. Considering the contemporary scenario, in which digital communication is a fundamental element for information security, this study aims to demonstrate to high school mathematics students and teachers a practical application of modular arithmetic in the current context, through the use of cryptography, through a literature review on the topic. Therefore, the work focuses on developing a material specifically aimed at teaching modular arithmetic in high school, in order to validate its practical application. Furthermore, a brief historical analysis is conducted to highlight the recurring use of cryptographic methods in different civilizations. By relating classical content, such as Euclidean divisions, to concrete data protection and information security situations, it was possible to build a bridge between mathematical knowledge and the daily lives of students. Finally, a teaching sequence is proposed with thirteen activities aligned with the National Common Curricular Base. This sequence seeks to optimize mathematical learning by connecting it to practice,in detriment of a teaching method disconnected from reality.