Vector Cryptography System: An Approach for the Analysis of Linear Arithmetic Spaces

This paper proposes the development of mathematical reasoning in undergraduate students through vector cryptography implemented in a software system. Mathematical reasoning is a cognitive function that could be improved using symmetric encryption techniques such as Hill Cipher, which implements the operations of the linear arithmetic spaces. The goal of this research project is that undergraduate students can learn, understand and apply abstract linear algebra theorems in cryptography context. It is intend to use neurosciences tools to validate the proposed method. The electric brain activity can be measured using electroencephalography (EEG) to obtain neural recruitment while solving complex mathematical problems.