Mathematical Foundations of Cryptography (WS 2025/26)
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, Linear Algebra, Algebraic Geometry, and Probability Theory.
- Mathematical structures used in classical cryptography, such as elliptic curves.
- Mathematical structures used in post-quantum cryptography, such as lattices.
- Complexity theory and cryptographic hardness problems.
- Probabilistic algorithms and statistical security.
- Algebraic attacks, in particular polynomial system solving via Gröbner Bases.
Material
| Date | Who | Lecture 10:00–12:00 (ISEC Seminar room) | Additional Material |
|---|---|---|---|
| 02.10.2025 | FM + KK | Kick-Off: Course introduction & organization | |
| 09.10.2025 | FM | Probability theory | |
| 16.10.2025 | FM | Probabilistic computation and complexity | |
| 23.10.2025 | FM | Hardness and indistinguishability | |
| 30.10.2025 | FM | Differential privacy | |
| 06.11.2025 | FM | Computational differential privacy | |
| 13.11.2025 | FM+KK | Discussions of extended abstracts | |
| 20.11.2025 | KK | Algebraic basics 1 | |
| 27.11.2025 | KK | Algebraic basics 2 | |
| 04.12.2025 | KK | Gröbner basis | |
| 11.12.2025 | KK | Lattices | |
| 18.12.2025 | KK | Elliptic curves | |
| 08.01.2026 | FM/KK | tbd | |
| 15.01.2026 | FM/KK | tbd | |
| 22.01.2026 | You | Presentations | |
| 29.01.2026 | You | Presentations |
Deadlines
| Date | Who | What | Additional Material |
|---|---|---|---|
| 06.11.2025 | You | Submit your extended abstract | |
| 13.11.2025 | You | Read extended abstracts of other students | |
| 18.12.2025 | You | Choose your seminar paper topic | |
| 08.01.2026 | You | Submit draft of seminar paper | |
| 15.01.2026 | FM + KK | Give you feedback on the draft | |
| 12.02.2026 | You | Submit your 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 at the start 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 6th 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 13th 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.
- A very rough guideline is to aim at around 15 pages for the paper, but you're free to hand in both significantly longer and significantly shorter papers, as long as the depth and clarity does not suffer as a result.
- Submission deadline for a first draft is the 8th of January.
- You will get feedback on the draft at the latest on the 15th of January.
- The final deadline of the paper is then the 12th of February.
Seminar Presentation
- You present your seminar topic in a seminar talk that lasts 20-25 minutes, followed by a few minutes for questions.
- The date for presentations is January 22nd or 29th.
- 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 |
|---|---|---|---|---|---|---|
| 2025/10/02 | 10:00 | 12:00 | Seminarraum | Abhaltung | VU | fix/ |
| 2025/10/09 | 10:00 | 12:00 | Seminarraum | Abhaltung | VU | fix/ |
| 2025/10/09 | 10:00 | 12:00 | Seminarraum | Abhaltung | VU | fix/ |
| 2025/10/16 | 10:00 | 12:00 | Seminarraum | Abhaltung | VU | fix/ |
| 2025/10/23 | 10:00 | 12:00 | Seminarraum | Abhaltung | VU | fix/ |
| 2025/10/30 | 10:00 | 12:00 | Seminarraum | Abhaltung | VU | fix/ |
| 2025/11/06 | 10:00 | 12:00 | Seminarraum | Abhaltung | VU | fix/ |
| 2025/11/13 | 10:00 | 12:00 | Seminarraum | Abhaltung | VU | fix/ |
| 2025/11/20 | 10:00 | 12:00 | Seminarraum | Abhaltung | VU | fix/ |
| 2025/11/27 | 10:00 | 12:00 | Seminarraum | Abhaltung | VU | fix/ |
| 2025/12/04 | 10:00 | 12:00 | Seminarraum | Abhaltung | VU | fix/ |
| 2025/12/11 | 10:00 | 12:00 | Seminarraum | Abhaltung | VU | fix/ |
| 2025/12/18 | 10:00 | 12:00 | Seminarraum | Abhaltung | VU | fix/ |
| 2026/01/08 | 10:00 | 12:00 | Seminarraum | Abhaltung | VU | fix/ |
| 2026/01/15 | 10:00 | 12:00 | Seminarraum | Abhaltung | VU | fix/ |
| 2026/01/22 | 10:00 | 12:00 | Seminarraum | Abhaltung | VU | fix/ |
| 2026/01/29 | 10:00 | 12:00 | Seminarraum | Abhaltung | VU | fix/ |
