Mathematical Foundations of Cryptography (WS 2026/27)
Table of Content
Content
This course aims at explaining mathematical concepts underlying many areas in modern-day cryptography, such as the analysis of primitives and protocols, zero knowledge proofs, multiparty computation, and more. The covered mathematical topics include:- A recap of basic concepts from Algebra and Probability Theory, and their application to cryptography.
- Mathematical structures used in classical and post-quantum cryptography, such as lattices.
- Complexity theory and cryptographic hardness problems.
- Probabilistic algorithms and statistical security.
Material
| Date | Who | Lecture 10:00–12:00 (ISEC Seminar room) | Additional Material |
|---|---|---|---|
| 01.10.2026 | All | L1 – Kick-Off: Course introduction & organization | |
| 08.10.2026 | MS | L2 – Algebra 1 (Relations, Groups) | |
| 15.10.2026 | MS | L3 – Algebra 2 (Rings, Fields) | |
| 22.10.2026 | VS | L4 – NTT | |
| 29.10.2026 | FM | L5 – Probabilistic algorithms and Complexity Theory | |
| 05.11.2026 | FL | L6 – Ajtai | |
| 12.11.2026 | FM | L7 – Hardness and Indistinguishability | |
| 19.11.2026 | All | Discussion of Extended Abstracts | |
| 26.11.2026 | FM | L9 – Differential Privacy | |
| 03.12.2026 | FM | L10 – Interactive Proofs | |
| 10.12.2026 | All | L11 – Research talks + question hour | |
| 17.12.2026 | All | L12 – Research talks + question hour | |
| 07.01.2027 | TBD | Guest Lecture | |
| 14.01.2027 | TBD | Guest Lecture | |
| 21.01.2027 | You | Seminar talks (student presentations) | |
| 28.01.2027 | You | Seminar talks (student presentations) | |
| 04.02.2027 | You | Seminar talks (student presentations) |
Deadlines
| Date | Who | What | Additional Material |
|---|---|---|---|
| 12.11.2026 | You | Submit your extended abstract | |
| 03.12.2026 | You | Choose your seminar paper topic | |
| 07.01.2027 | You | Submit your paper draft | |
| 14.01.2027 | Lecturers | Get feedback on your paper draft | |
| 04.02.2027 | You | Submit your final seminar paper |
Administrative Information
Course Mode- The course starts with a series of lectures, where you will get an overview of the course content. Slides or lecture notes from the lecture will be available at the latest just after the lecture.
- Your course contribution consists primarily of writing one short extended abstract and a longer seminar paper, which you also present. These may be on the same topic or on different ones.
- The extended abstract should be handed in in the middle of November, after which you are expected to read the abstracts of the other students because one of the lecture slots will consist of discussions about the topics you have chosen. You are free to choose your own topic or one from a list of suggested topics.
- The seminar paper is a longer report and you will also give a presentation of it to your fellow students. Topics for potential seminar papers related to the contents of each lecture is presented at the end of the given lecture. You are also free to choose your own topic, unrelated to lecture contents.
- Coordinate your topic, for both the paper and the extended abstract, with us before you start working on it.
Extended Abstract
Seminar Paper
- You write a short extended abstract (2-3 pages) about a well-defined topic that is coordinated with us. It can either be some topic you already have an interest in or one from a list of potential topics that we provide.
- The deadline for handing in the abstract is the 12th of November. We then share all of the abstracts with all of the students and you are expected to read the abstracts of the other students before the lecture slot on the 19th of November, where we will discuss the topics of the submitted abstracts.
- During the discussions, we expect the author to very shortly introduce the topic and share insight into how it was to research the topic.
- You write a seminar paper about a well-defined topic that is coordinated with us.
- The deadline for settling on (and coordinating with us) your seminar paper topic is the 3rd of December.
- A very rough guideline is to aim at around 15 pages for the paper, but you're free to hand in both longer and shorter papers, as long as the depth and clarity does not suffer as a result.
- We follow the default TU Graz guidelines on the use of AI-based tools by students.
- Submission deadline for a first draft is the 7th of January.
- You will get feedback on the draft at the latest on the 14th of January.
- After you have gotten feedback, there is a mandatory one-on-one supervision session where we discuss the feedback.
- The final deadline of the paper is then the 4th of February.
Seminar Presentation
- You present your seminar topic in a seminar talk that lasts around 20 minutes, followed by a few minutes for questions.
- The dates for presentations are January 21st, January 28th and February 4th.
- Send us your final presentation slides the day before your presentation.
- Presentation templates can be found here.
Other administrative matters
- We have a channel for the course on the ISEC discord server.
Lecture Dates
| Date | Begin | End | Location | Event | Type | Comment |
|---|---|---|---|---|---|---|
| 2026/10/01 | 08:00 | 10:00 | IFEG042 | CLASS | VU | CLASS/ |
| 2026/10/01 | 08:00 | 10:00 | CCGEG002 | CLASS | VU | CLASS/ |
| 2026/10/08 | 08:00 | 10:00 | IFEG042 | CLASS | VU | CLASS/ |
| 2026/10/08 | 08:00 | 10:00 | CCGEG002 | CLASS | VU | CLASS/ |
| 2026/10/15 | 08:00 | 10:00 | IFEG042 | CLASS | VU | CLASS/ |
| 2026/10/15 | 08:00 | 10:00 | CCGEG002 | CLASS | VU | CLASS/ |
| 2026/10/22 | 08:00 | 10:00 | IFEG042 | CLASS | VU | CLASS/ |
| 2026/10/22 | 08:00 | 10:00 | CCGEG002 | CLASS | VU | CLASS/ |
| 2026/10/29 | 09:00 | 11:00 | IFEG042 | CLASS | VU | CLASS/ |
| 2026/10/29 | 09:00 | 11:00 | CCGEG002 | CLASS | VU | CLASS/ |
| 2026/11/05 | 09:00 | 11:00 | IFEG042 | CLASS | VU | CLASS/ |
| 2026/11/05 | 09:00 | 11:00 | CCGEG002 | CLASS | VU | CLASS/ |
| 2026/11/12 | 09:00 | 11:00 | IFEG042 | CLASS | VU | CLASS/ |
| 2026/11/12 | 09:00 | 11:00 | CCGEG002 | CLASS | VU | CLASS/ |
| 2026/11/19 | 09:00 | 11:00 | IFEG042 | CLASS | VU | CLASS/ |
| 2026/11/19 | 09:00 | 11:00 | CCGEG002 | CLASS | VU | CLASS/ |
| 2026/11/26 | 09:00 | 11:00 | IFEG042 | CLASS | VU | CLASS/ |
| 2026/11/26 | 09:00 | 11:00 | CCGEG002 | CLASS | VU | CLASS/ |
| 2026/12/03 | 09:00 | 11:00 | IFEG042 | CLASS | VU | CLASS/ |
| 2026/12/03 | 09:00 | 11:00 | CCGEG002 | CLASS | VU | CLASS/ |
| 2026/12/10 | 09:00 | 11:00 | IFEG042 | CLASS | VU | CLASS/ |
| 2026/12/10 | 09:00 | 11:00 | CCGEG002 | CLASS | VU | CLASS/ |
| 2026/12/17 | 09:00 | 11:00 | IFEG042 | CLASS | VU | CLASS/ |
| 2026/12/17 | 09:00 | 11:00 | CCGEG002 | CLASS | VU | CLASS/ |
| 2027/01/07 | 09:00 | 11:00 | IFEG042 | CLASS | VU | CLASS/ |
| 2027/01/07 | 09:00 | 11:00 | CCGEG002 | CLASS | VU | CLASS/ |
| 2027/01/14 | 09:00 | 11:00 | IFEG042 | CLASS | VU | CLASS/ |
| 2027/01/14 | 09:00 | 11:00 | CCGEG002 | CLASS | VU | CLASS/ |
| 2027/01/21 | 09:00 | 11:00 | IFEG042 | CLASS | VU | CLASS/ |
| 2027/01/21 | 09:00 | 11:00 | CCGEG002 | CLASS | VU | CLASS/ |
| 2027/01/28 | 09:00 | 11:00 | IFEG042 | CLASS | VU | CLASS/ |
| 2027/01/28 | 09:00 | 11:00 | CCGEG002 | CLASS | VU | CLASS/ |
