• Offered by Mathematical Sciences Institute
• ANU College ANU Joint Colleges of Science
• Course subject Mathematics
• Areas of interest Mathematics
• Course convener
• AsPr James Borger
• Mode of delivery In Person
• Co-taught Course
• Offered in Second Semester 2025
Number Theory and Cryptography (MATH6114)

The need to protect information being transmitted electronically, such as the widespread use of electronic payment, has transformed the importance of cryptography. Most of the modern types of cryptosystems rely on number theory for their theoretical background. This course introduces elementary number theory, with an emphasis on those parts that have applications to cryptography, and shows how the theory can be applied to cryptography.

Number theory topics will be chosen from: the Euclidean algorithm, greatest common divisor, prime numbers, prime factorisation, primality testing, modular arithmetic, the Chinese remainder theorem, diophantine equations, sums of squares, Euler's function, Fermat's little theorem, primitive roots, quadratic residues, quadratic reciprocity, Pell's equation, continued fractions, Diophantine approximation.

Cryptography topics will be chosen from: symmetric key cryptosystems, including classical examples and a brief discussion of modern systems such as DES and AES, public key systems such as RSA and discrete logarithm systems, cryptanalysis (code breaking) using some of the number theory developed.

Note: Graduate students attend joint classes with undergraduates but are assessed separately. The additional assessment will consist of assignments requiring deeper conceptual understanding and/or a project, and the final exam will contain alternative questions requiring deeper conceptual understanding.

## Learning Outcomes

Upon successful completion, students will have the knowledge and skills to:

1. Solve problems in elementary number theory.
2. Apply elementary number theory to cryptography.
3. Develop a deeper conceptual understanding of the theoretical basis of number theory and cryptography.

## Indicative Assessment

1. Five assignments (50) [LO 1,2,3]
2. Final examination (50) [LO 1,2,3]

The ANU uses Turnitin to enhance student citation and referencing techniques, and to assess assignment submissions as a component of the University's approach to managing Academic Integrity. While the use of Turnitin is not mandatory, the ANU highly recommends Turnitin is used by both teaching staff and students. For additional information regarding Turnitin please visit the ANU Online website.

The expected workload will consist of approximately 130 hours throughout the semester including:

• Face-to face component, which may consist of 3 lectures per week and regular workshops
• Approximately 84 hours of self directed study, which will include preparation for lectures, workshops, and other assessment tasks.

## Inherent Requirements

No course-specific inherent requirements.

## Requisite and Incompatibility

You are not able to enrol in this course if you have completed MATH3301

You will need to contact the Mathematical Sciences Institute to request a permission code to enrol in this course.

## Prescribed Texts

Not required

"Elementary Number Theory", by Kenneth Rosen

## Assumed Knowledge

To enrol in this course you must be studying a Master of Science in Mathematical Sciences or Master of Mathematical Sciences (Advanced).

## Fees

Tuition fees are for the academic year indicated at the top of the page.

Commonwealth Support (CSP) Students
If you have been offered a Commonwealth supported place, your fees are set by the Australian Government for each course. At ANU 1 EFTSL is 48 units (normally 8 x 6-unit courses). More information about your student contribution amount for each course at Fees

Student Contribution Band:
1
Unit value:
6 units

If you are a domestic graduate coursework student with a Domestic Tuition Fee (DTF) place or international student you will be required to pay course tuition fees (see below). Course tuition fees are indexed annually. Further information for domestic and international students about tuition and other fees can be found at Fees.

Where there is a unit range displayed for this course, not all unit options below may be available.

Units EFTSL
6.00 0.12500
Note: Please note that fee information is for current year only.

## Offerings, Dates and Class Summary Links

ANU utilises MyTimetable to enable students to view the timetable for their enrolled courses, browse, then self-allocate to small teaching activities / tutorials so they can better plan their time. Find out more on the Timetable webpage.

The list of offerings for future years is indicative only.
Class summaries, if available, can be accessed by clicking on the View link for the relevant class number.

### Second Semester

Class number Class start date Last day to enrol Census date Class end date Mode Of Delivery Class Summary
7601 21 Jul 2025 28 Jul 2025 31 Aug 2025 24 Oct 2025 In Person N/A