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.
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Requisite and Incompatibility
Incompatible: MATH3301.
You will need to contact the Mathematical Sciences Institute to request a permission code to enrol in this course.
Referenced entries (1)
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- MATH3301 · 2027 · saved source not linked
Learning Outcomes
Upon successful completion, students will have the knowledge and skills to:
Solve problems in elementary number theory.
Apply elementary number theory to cryptography.
Develop a deeper conceptual understanding of the theoretical basis of number theory and cryptography.
Published offerings
Future offerings are indicative. Only recognised 2027 sessions with a published class number are offered in the enrolment demo.
| Year | Session | Class number | Class start date | Last day to enrol | Census date | Class end date | Mode Of Delivery | Class Summary |
|---|---|---|---|---|---|---|---|---|
| 2027 | Second Semester | 9041 | 26 Jul 2027 | 02 Aug 2027 | 31 Aug 2027 | 29 Oct 2027 | In Person | N/A |
| 2028 | Second Semester | 9966 | 24 Jul 2028 | 31 Jul 2028 | 31 Aug 2028 | 27 Oct 2028 | In Person | N/A |
Complete offering text
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. 2027 2028 Second Semester Class number Class start date Last day to enrol Census date Class end date Mode Of Delivery Class Summary 9041 26 Jul 2027 02 Aug 2027 31 Aug 2027 29 Oct 2027 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 9966 24 Jul 2028 31 Jul 2028 31 Aug 2028 27 Oct 2028 In Person N/A
Source evidence (1 saved copy)
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