Syllabus academic year 2007/2008
MATHEMATICAL CRYPTOLOGYEDI075

Higher education credits: 6. Grading scale: TH. Level: A (Second level). Language of instruction: The course will be given in English on demand. Optional for: C4, C4sd, D4, E4, Pi4. Course coordinator: Professor Thomas Johansson, thomas@it.lth.se, Inst f informationsteknologi. Prerequisites: EDI051 Cryptography. Recommended prerequisits: Basic math courses. The course might be cancelled if the numer of applicants is less than 10. Assessment: Written exam and mandatory home exercises. Home page: http://www.it.lth.se/.

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

Skills and abilities
For a passing grade the student must

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.