- Code MATH3301
- Unit Value 6 units
- Offered by Department of Mathematics
- ANU College ANU Joint Colleges of Science
- Course subject Mathematics
- Areas of interest Mathematics
- Academic career UGRD
- Timothy Trudgian
- Mode of delivery In Person
Second Semester 2014
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.
Honours Pathway Option (HPO):
Students who take the HPO will complete extra work of a more theoretical nature. The assignments will be replaced by alternative assignments and the final exam will contain alternative questions requiring deeper conceptual understanding.
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. (HPO only) Develop a deeper conceptual understanding of the theoretical basis of number theory and cryptography
Assessment will be based on:
- Three assignments (10%; LO 1, 2, & 3 for HPO)
- Final examination (70%; LO 1, 2, & 3 for HPO)
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36 lectures and 10 tutorials
Requisite and Incompatibility
Tuition fees are for the academic year indicated at the top of the page.
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- Student Contribution Band:
- 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.
- Domestic fee paying students
- International fee paying students
Offerings, Dates and Class Summary Links
Class summaries, if available, can be accessed by clicking on the View link for the relevant class number.
|Class number||Class start date||Last day to enrol||Census date||Class end date||Mode Of Delivery||Class Summary|
|7321||21 Jul 2014||01 Aug 2014||31 Aug 2014||30 Oct 2014||In Person||N/A|