A Computational-Space-Oriented Reconstruction of Abstract Algebra Teaching in Foundations of Information Security Mathematics

Abstract

Foundations of Information Security Mathematics supports subsequent cryptography courses, yet teaching abstract algebra as an isolated theory often prevents students from relating algebraic structures to cryptographic mechanisms. This paper interprets algebra as the computational spaces of cryptography and reorganizes the course through a requirement-driven structure, where cyclic groups, finite fields, and quotient polynomial rings are introduced as progressively extended environments. A computational-space-oriented pathway is implemented by introducing concepts through cryptographic operations and reinterpreting prior discrete mathematics knowledge. Classroom practice shows a shift from procedural to structural understanding and a unified view of different cryptographic schemes, turning the course from a set of prerequisites into the structural foundation for later study.