This course builds on the formal proof techniques and technical content of a foundation course in Discrete Mathematics. The knowledge of finite fields and the introduction to error correcting codes and public key cryptosystems will be used in core MC159 Master of Cyber Security courses INTE2656, INTE2655 and INTE1127.

Two components are introduced: Groups and Codes and Ring and Field Theory for Information Security. Groups and Codes introduces you to the fundamental ideas and applications of group and ring theory, extending your knowledge of basic proof techniques in mathematics and demonstrating the practical application of algebraic theory to error-correction coding for digital communications. In Ring and Field Theory for Information Security, concepts of group theory are particularised to rings and finite fields, where further theory is developed. Applications to private and public key cryptography are covered.