# Seminar Cryptology and Privacy - Mathematical Foundations of Cryptography (WS 2023/24)

### Table of Content

## Content

Mathematics is arguably the backbone of entire field of cryptography. It is the language we use when describing our constructions, it is the tool we use when proving the strength of those constructions and it is the fabric of the very definitions of what we mean when we say something is secure, private, oblivious and so on. In this course we give an introduction to some of the mathematical foundations of cryptography, such as- Algebra (Including Groups, Rings, Fields, Gröbner bases)
- Isogenies
- Probability theory (Including random variables, probability distributions, the central limit theorem, differential privacy)
- Lattices (Including the shortest vector, closest vector and learning-with-errors problems)
- Probabilistic algorithms

## Material

Date | Lecture 10:00–12:00 (IAIK Seminar room) | Who |
---|---|---|

05.10.2023 | Course information and L1 - Algebraic basics (Slides, Jupyter notebook) | KK |

12.10.2023 | L2 – Gröbner Bases (Slides, Jupyter notebook) | KK |

19.10.2023 | L3 – Differential privacy (Lecture Notes) | KK |

09.11.2023 | L4 – Elliptic curves, Isogenies (Slides, Jupyter notebook) | FM |

16.11.2023 | L5 – Probability theory (Lecture Notes) | FM |

23.11.2023 | L6 – Lattices (Lecture Notes) | FM |

30.11.2023 | L7 – Probabilistic algorithms (Lecture Notes) | FM |

## Administrative Information

**Course Mode**

- The course starts with 6 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 of a seminar paper and a presentation. Topics for 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 with us before you start working on it.
- Deadline for choosing topic is the
**30th of November**, but you are allowed to choose before that if you wish.

**Seminar Paper**

- You write a seminar paper about a well-defined topic that is coordinated with us.
- Submission deadline for a first draft is the
**20th of December.** - You will get feedback on the draft at the latest on the
**5th of January.** - The final deadline of the paper is then the
**8th of February.** - Template for the seminar paper can be found here.

**Seminar Presentation**

- You present your seminar topic in a seminar talk that lasts around 30 minutes.
- The dates for presentations are
**January 18th and 25th.** - Send us a draft 1 week before you deliver your presentation.
- Send us your final presentation slides 1 day before your talk.

**Other administrative matters**

- We have a channel for the course on the IAIK discord server.