- Lecturer: Dominique Unruh
- Room: 220 (Paabel)
- Time: Thursday, 10:15-11:45 (starting Feb 16)
- Whiteboard photos: Dropbox folder

This course covers basic mathematical background knowledge and skills which you will need in courses on Cryptology. More specifically the course is divided into the following nine sections:

- Probability (Attach:01-probability.pdf)
- Divisibility and modular arithmetic (Attach:02-modarith.pdf). In the reading material, you do not have to learn the following parts (they will also not be covered in the lecture):
- Abstract view on divisibility in Section 1 (groups, monoids, etc.). We will only consider divisibility on natural numbers.
- Proofs of the various claims in the reading material
- Section 7 (residue classes)

- Further concepts in number theory (CRT, Euler's phi function) (Attach:03-crt-and-phi.pdf)
- Asymptotic Notation (Attach:04-asymptotics.pdf)
- Finite Fields (Attach:05-finite-fields.pdf)
- Linear Algebra (Attach:06-linear-algebra.pdf)
- The Discrete Logarithm (Attach:07-discrete-logarithm.pdf)
- Integer Factorization
- Primality Testing

There will be an additional topic of your own choice, we will discuss what it will be later in the course.

As **homework assignments**, for each of these sections, you will be asked to

- read and comprehend a homework text document (will be made available here);
- solve all the exercises contained in that document to make sure that you are sufficiently familiar with what you have read, and to prepare for the quizzes and the final exam;
- understand how the concepts are useful in cryptography (e.g. how it relates to Cryptology I);

**In class**, you will

- be required to take nine short quizzes, one for each section, comprising a few easy questions about the respective section;
- have the opportunity to discuss what you have read and the solutions to the exercises.

Obtaining at least 50% of the marks on the total of these quizzes qualifies you to participate in the final exam. Quizzes about different sections may have different amounts of marks, i.e., not all quizzes count the same.

In the **final exam**, you will have to

- solve problems similar to the exercises in the homework documents.