Online Undergraduate Seminar: Mathematical Foundations of Cryptography

Previous editions

Semester 2 2019 Lie Groups and Physics

Semester 1 2019 Coxeter Groups and Hecke Algebras

The undergraduate seminar is back! This year the seminar will be aimed at first year students. A seminar is an extracurricular activity in which students work as teams to understand a topic and give a presentation to the larger group about their work and write a little essay about the topics covered. The work of different teams builds on each other, wich will mean that you have to speak to each other. Besides offering the opportunity of studying a topic at greater depth and learning higher level oral and written presentation skills than we cannot easily teach you in a regular class, our seminars have an important social function in the department life. This is where the community comes together as learners and where the different study cohorts really start to take shape.

This year we would like to extend this experience to interested first year students. In a normal year we would love to bring you all together, and we would work on the chalk board. This year, we will be working online. The idea is to get you to work together in groups remotely, under the guidance of some more experienced students and lecturers, so that we have a chance to all grow together as a community, even when we are apart physically.

We have extended this invitation also to a group of students from Tsinghua, who had to cancel their visit to Melbourne in February. We are excited to finally get to meet you.

Our seminar topic will be the mathematics underlying modern cryptography. Participants will prepare their presentations under the guidance of one expert or another, and give a practice talk in advance. Great emphasis is put on clear and compelling exposition. The material is designed for beginners, but students of all levels are welcome to be involved.

If you have a different topic that you are interested in and would like to organize something yourself, please do contact the organizers and we will try to help you make it happen.

This seminar is coorganized by Majid Alamudi, Nora Ganter, Rohan Hitchcock, Adam Walsh, Chengjing Zhang and Gufang Zhao.

Here is the the email list for this seminar, to subscribe, enter enter your email address and then click the link in the confirmation email to subscribe (the website is not very clear on this). If you have questions, contact

Topics are as follows. (The list is likely to evolve once we have an idea of participant numbers).

Week Topics Speaker
4 The Pascal triangle and binomial coefficients factorials and counting. Lemma: p divides "p choose k" when p is a prime. [McC] Fermat's Little Theorem: proof by induction, using Lemma. [Maz,3.2] tba
5 Modular arithmetic and the extended Euclidean algorithm. Bezout's Lemma. Invertibility modulo m. [Maz,5] [Chi, Chapters 2 and 3] tba
6 Euclid's Lemma and Chinese remainder theorem. [Hutz] tba
7 Prime factorization, existence and uniqueness. [Chi, Chapter 4] tba
8 RSA. Prove from Fermat. [Chi, Chapter 9]. tba
9 Groups, cosets, Lagrange's Theorem and Euclid's theorem. [Chi, Chapter 10] tba
10 Discrete logarithm, Part1: ElGamal encryption [She]
11 Discrete logariathm, Part 2: elliptic curve encryption.[Hutz,Chapter 9][She]

[Chi] Lindsey N. Childs: Cryptology and Error Correction -- An Algebraic Introduction and Real World Applications

[Hutz] Benjamin Hutz: An Experimental Introduction to Number Theory

[Maz] David R. Mazur: Combinatorics, A Guided Tour

[McC] John McCleary: Exercises in (Mathematical Style) -- Stories of Binomial Coefficients

[She] Thomas R. Shemanske: Modern Croptography and Elliptic Curves: A Beginner's Guide.