Course Title: Algebra for Information Security

Part A: Course Overview

Course Title: Algebra for Information Security

Credit Points: 12.00

Terms

Course Code

Campus

Career

School

Learning Mode

Teaching Period(s)

MATH2148

City Campus

Undergraduate

145H Mathematical & Geospatial Sciences

Face-to-Face

Sem 1 2006,
Sem 1 2007,
Sem 1 2008,
Sem 1 2009,
Sem 1 2010,
Sem 1 2011,
Sem 1 2012,
Sem 1 2013,
Sem 1 2014,
Sem 1 2015,
Sem 1 2016

MATH2148

City Campus

Undergraduate

171H School of Science

Face-to-Face

Sem 1 2017,
Sem 1 2018,
Sem 1 2019,
Sem 1 2020,
Sem 1 2021

MATH2172

City Campus

Postgraduate

145H Mathematical & Geospatial Sciences

Face-to-Face

Sem 1 2007,
Sem 1 2008,
Sem 1 2009,
Sem 1 2010,
Sem 1 2011,
Sem 1 2012,
Sem 1 2013,
Sem 1 2014,
Sem 1 2015,
Sem 1 2016

MATH2172

City Campus

Postgraduate

171H School of Science

Face-to-Face

Sem 1 2017,
Sem 1 2018,
Sem 1 2019,
Sem 1 2020,
Sem 1 2021

Course Coordinator: Dr Graham Clarke

Course Coordinator Phone: +61 3 9925 3225

Course Coordinator Email: g.clarke@rmit.edu.au

Course Coordinator Location: B015-03-014

Course Coordinator Availability: By arrangement


Pre-requisite Courses and Assumed Knowledge and Capabilities

An introductory course in Discrete Mathematics such as MATH1150 or an equivalent.


Course Description

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 INTE1124, INTE1125 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. 


Objectives/Learning Outcomes/Capability Development

 

This course contributes to the following Program Learning Outcomes for MC159 Master of Applied Science (Information Security and Assurance)

Knowledge and Technical Competence

  • The ability to use the appropriate and relevant, fundamental and applied mathematical and statistical knowledge, methodologies and modern computational tools.

Problem-solving

  • The ability to bring together and flexibly apply knowledge to characterise, analyse and solve a wide range of problems
  • An understanding of the balance between the complexity / accuracy of the mathematical / statistical models used and the timeliness of the delivery of the solution.


On completion of this course you should be able to

  1. Construct logically valid proofs for mathematical propositions.
  2. Recognise algebraic systems as having a group, ring or field structure.
  3. Use group and ring properties to construct error correcting codes including cyclic codes.
  4. Apply finite field properties to construct public key cryptosystems.


Overview of Learning Activities

All learning activities are student-centred, designed to interest and motivate you to be actively involved in your study. More specifically your learning activities consist of: 

  • Reading the current section of the lecture notes prior to each class. 
  • Viewing the video on each recorded topic. 
  • Joining the online classes where the subject matter of the lecture notes and videos will be illustrated with demonstrations and examples. 
  • Participating in the online classes by working through examples set as class exercises, which are designed to build your capacity to solve problems, think critically and analytically, and obtain further practice in the application of theory and procedures. These classes are open-book and you are encouraged to work collaboratively with your peers and, if necessary, to seek help from the instructor before completing your individual solutions. 
  • In addition to the in-class activities, students will have the opportunity to develop greater understanding of the concepts in this course through their reading, discussion with other students and with the lecturer, and private study. 
  • Assignments, in-class assessments and class exercises will enable you to gauge your progress and provide you with feedback on your understanding of the course material. 


Overview of Learning Resources

You will have access to class lecture notes. There is no prescribed text. You will be expected to expand on the subject matter provided as lecture notes in class. This will take the form of accessing various external and internal resources, such as the library and the Internet. The general topic area for search is ‘abstract algebra’. 

Canvas: This course is supported online using Canvas, which gives access to important announcements, a discussion forum, staff contact details, the teaching schedule, assessment timelines, lecture notes and practice questions and answers. You are advised to read your student EMS email daily for important announcements. You should also visit the course Canvas site at least once a day for important announcements regarding the course and course-related documents. 

A library subject guide is available at: 

http://rmit.libguides.com/mathstats 


Overview of Assessment

Assessment Tasks:

 

Assessment Task 1: In-class discipline-based summative assessments  

Weighting 50%  

This assessment task supports CLOs 1—4. 

 

Assessment Task 2: Individual assignments 

Weighting 50%  

This assessment task supports CLOs 1—4.