2026 MAST30035 Number Theory and Cryptography

Many administrative details about the organisation of the subject can (as always) be found in the subject handbook entry.

Consultation hours

  • Mondays 1pm-2pm in Peter Hall room 166
  • Tuesdays 2pm-3pm in Peter Hall room 166
  • Fridays 12pm-1pm in Peter Hall room 166

Lecture notes

General comment: the subject is brand new and is being actively developed as we go. I aim to have reasonably-polished notes available within a couple of days of each lecture.

Chapters:

  1. Elementary number theory (updated: 12 August @ 2pm)
  2. Discrete logarithms
  3. Elliptic curves over finite fields
  4. Lattices
  5. Further topics (if time permits)

Exercises

These are organised in the same manner as the lecture notes:

  1. Elementary number theory (updated: 3 August @ 1pm)
  2. Discrete logarithms
  3. Elliptic curves over finite fields
  4. Lattices
  5. Further topics (if time permits)

Tutorials

Tutorial classes start in week 2 of the semester. The tutorial sheets appear here during the corresponding week, followed by the solutions.

Assignments

The three assignments will be posted both here and on the subject's Canvas page. Your solutions should be submitted via Canvas and Gradescope.

Assignment 1 (worth 10% of final mark)

Here is the pdf file for the first assignment, due Friday 21 August at 23:59. Please read the cover page carefully.

To make copy-and-paste easier: the N in the RSA private key for Assignment Question 1.3 is 613741728013616690147699038703457766174721061233103055423658683990710518710554288157091

Errata for the first assignment

Special consideration

Ed discussion board

Please see the subject's Canvas page for access to the discussion board.

Lecture recordings

Please see the subject's Canvas page for access to the lecture recordings.

Prerequisite knowledge

The main prerequisites for the subject are one of the University of Melbourne's subjects:

For those of you arriving with a different background, this means familiarity with proofs, as well as a solid understanding of linear algebra (which is a prerequisite for all of the above).

Some references

This list is of course not exhaustive.

Note: Many of these references may be accessible via the library system either as electronic resources or physical tomes.

Software

This list is also not exhaustive.

You will want a system that, at the very least, allows you to work easily with arbitrary-sized integers. For later topics, built-in functionality for elliptic curves and lattices may be useful.