O uso da criptografia no ensino de matrizes: contribuições a partir da cifra de hill

Abstract

This work presents a proposal for teaching Mathematics in Middle and High School based on the study of cryptography, focusing on the César, Vigenère and Hill ciphers. The choice of this theme is grounded in the interdisciplinary potential of cryptography, which allows the integration of mathematical, historical, literary and technological concepts, promoting a more meaningful and investigative learning process. The mathematical topics addressed include congruences and operations with remainders, linear systems, matrices, determinants, inverse matrices, and modular arithmetic applied to matrices, although modular arithmetic is a topic traditionally associated with higher education, it is approached in a subtle and contextualized manner, in accordance with the competencies and skills established by the Base Nacional Comum Curricular (BNCC). As an educational product, a didactic material was developed that can be used independently of the dissertation, containing definitions, examples, activities, and historical contextualization, allowing each activity to be applied individually or combined into a didactic sequence. It is expected that this proposal contributes to Mathematics education by highlighting concrete applications of mathematical concepts and fostering students, logical reasoning and quick thinking.