Aim
The purpose of the course is to demonstrate how advanced mathematical theory has important applications in cryptology and security.

Knowledge and understanding
For a passing grade the student must

• be able to describe the role of mathematics in cryptology,

• be able to describe mathematical principles used in various cryptografic primitives,

• be able to describe and compare different solutions to a given cryptologic problem.

Skills and abilities
For a passing grade the student must

• be able to identify and formulate relevant mathematical problems in cryptology,

• be able to describe how difficult mathematical problems can be used to construct cryptographic primitives,

• be able to mathematically analyze possible constructions from a security perspective.

Contents
The course contains a number of mathematical tools with many applications, not only in cryptology and security. Most schemes addressed in the course are standards in different communication systems, e.g., elliptic curve cryptosystems. But few people have the mathematical background to be able to understand how such systems work. We also look at models for proving that a cryptographic scheme or protocol is secure.

The content of the course is more specifically most of the following topics: cryptosystems based on discrete logarithms, elliptic curve cryptography, factoring and the discrete log problem, symmetric ciphers, digital signatures and hash functions, authentication, secret sharing, complexity theory, provable security and random oracles.

Literature
Smart, N., Cryptography: An Introduction, McGraw-Hill, ISBN 0077099877
and some additional lecture notes.