• Offered by Department of Mathematics
  • ANU College ANU Joint Colleges of Science
  • Classification Advanced
    Specialist
  • Course subject Mathematics
  • Areas of interest Mathematics
  • Academic career PGRD
  • Course convener
    • AsPr John Urbas
    • Timothy Trudgian
  • Mode of delivery In Person
  • Co-taught Course
  • Offered in First Semester 2015
    Second Semester 2015
    See Future Offerings

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 (increasingly more sophisticated) 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, highest common factor, prime numbers, prime factorisation, primality testing, congruences, the Chinese remainder theorem, diophantine equations, sums of squares, Euler's function, Fermat's little theorem, quadratic residues, quadratic reciprocity, Pell's equation, continued fractions.

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.

Learning Outcomes

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

On satisfying the requirements of this course, 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

Assessment will be based on:

  • Three assignments (10%; LO 1, 2, 3)
  • Final examination (70%; 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.

Workload

36 lectures and ten tutorials

Requisite and Incompatibility

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

You will need to contact the Department of Mathematics to request a permission code to enrol in this course.

Specialisations

Fees

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

If you are a domestic graduate coursework or international student you will be required to pay tuition fees. Tuition fees are indexed annually. Further information for domestic and international students about tuition and other fees can be found at Fees.

Student Contribution Band:
2
Unit value:
6 units

If you are an undergraduate student and 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). You can find your student contribution amount for each course 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
Domestic fee paying students
Year Fee
2015 $3096
International fee paying students
Year Fee
2015 $4146
Note: Please note that fee information is for current year only.

Offerings, Dates and Class Summary Links

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.

First Semester

Class number Class start date Last day to enrol Census date Class end date Mode Of Delivery Class Summary
3557 16 Feb 2015 06 Mar 2015 31 Mar 2015 29 May 2015 In Person N/A

Second Semester

Class number Class start date Last day to enrol Census date Class end date Mode Of Delivery Class Summary
1872 20 Jul 2015 07 Aug 2015 31 Aug 2015 30 Oct 2015 In Person N/A

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