Course syllabus

Matematisk kryptologi
Mathematical Cryptology

EDIN05, 7,5 credits, A (Second Cycle)

Valid for: 2013/14
Decided by: Education Board A
Date of Decision: 2013-04-15

General Information

Elective for: C4, C4-ks, D4, D4-ks, Pi4, Pi4-pv
Language of instruction: The course will be given in English on demand

Aim

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

Learning outcomes

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.

Competences and skills
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.

Judgement and approach
For a passing grade the 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.

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.

Examination details

Grading scale: TH
Assessment: Written exam and mandatory home exercises.

Admission

Admission requirements:

• EDI051 Cryptography or EDIN01 Cryptography

Required prior knowledge: Basic math courses. Basic programming.
The number of participants is limited to: No
The course overlaps following course/s: EDI075

Reading list

• Smart, N.: Cryptography: An Introduction. McGraw-Hill, ISBN: 0077099877.
• Some additional lecture notes.

Contact and other information

Course coordinator: Professor Thomas Johansson, thomas@eit.lth.se
Course homepage: http://www.eit.lth.se/course/
Further information: With less than 16 participants, the course may be given with reduced teaching and more self studies.