Matematisk kryptologi

**Valid from:** Spring 2013**Decided by:** FN1/Anders Gustafsson**Date of establishment:** 2013-06-07

**Division:** Electrical and Information Technology**Course type:** Course given jointly for second and third cycle**The course is also given at second-cycle level with course code:** EDIN05**Teaching languages:** English, Swedish

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 doctoral student must

- •be able to describe the role of mathematics in cryptology,
- •be able to explain mathematical principles used in various cryptografic primitives,
- •be able to describe and compare different solutions to a given cryptologic problem.

*Competences and Skills*

For a passing grade the doctoral 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.

*Judgement and Approach*

For a passing grade the doctoral student must

- •be able to classify the level of difficulty of problems related to the his/her own level of knowledge,
- •be aware of how problems and their parameters are connected to different security levels.

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. 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.

Smart, N.: Cryptography: An introduction (tredje upplagan tillgänglig för nedladdning). McGraw-Hill. ISBN 0077099877.

Some additional lecture notes.

**Types of instruction:** Lectures, exercises, project

**Examination formats:** Written exam, written assignments.
Written exam and mandatory home exercises.**Grading scale:** Failed, pass**Examiner:**

**Admission requirements:** EDI051 Cryptography OR EDIN01 Cryptography**Assumed prior knowledge:** Basic math courses. Basic programming.

Course coordinator: Professor Thomas Johansson

**Course coordinator:** Thomas Johansson `<thomas.johansson@eit.lth.se>`