Each module contains 3 ECTS. You choose a total of 10 modules/30 ECTS in the following module categories:
- 12-15 ECTS in technical scientific modules (TSM)
TSM modules teach profile-specific specialist skills and supplement the decentralised specialisation modules. - 9-12 ECTS in fundamental theoretical principles modules (FTP)
FTP modules deal with theoretical fundamentals such as higher mathematics, physics, information theory, chemistry, etc. They will teach more detailed, abstract scientific knowledge and help you to bridge the gap between abstraction and application that is so important for innovation. - 6-9 ECTS in context modules (CM)
CM modules will impart additional skills in areas such as technology management, business administration, communication, project management, patent law, contract law, etc.
In the module description (download pdf) you find the entire language information per module divided into the following categories:
- instruction
- documentation
- examination
This course provides the mathematical fundamentals of cryptography and coding theory and illustrates them with numerous practical examples.
Prerequisites
No particular prerequisites are required, but fundamental interest in practical applications of mathematics!
Learning Objectives
This course provides advanced methods of applied algebra and number theory and concentrates on their practical applications in cryptography and coding theory.
Contents of Module
- Algebra: algebraic structures (proups, fields), modular arithmetic, Chinesise remainder theorem, constuction and fundamental properties of finite fields (Galois fields GF (pm)), applications to cryptography and coding theory
- Algorithms in number theory (primality tests, integer factorization methods, elliptic curves), applications to cryptography and coding theory
- Use of a development environment (Java, C, C++)
Week |
Contents (Order and weighting may be adapted) |
1 |
Algebraic basics: |
2 | |
3 |
Asymmetric (public key) cryptography: |
4 | |
5 |
Algebraic basics: polynomials and finite fields |
6 |
Symmetric (secret key) cryptography: |
7 |
Symmetric (secret key) cryptography: Hash functions, Data Encryption Standard (DES), Advanced Encryption Standard (AES), modes of operation, authenticated encryption |
8 |
Elliptic Curve Diffie Hellman (ECDH), digital signatures |
9 | |
10 |
One-time pad (OTP), Quantum Cryptography |
11 |
Error-correcting codes: |
12 | |
13 | |
14 |
Teaching and Learning Methods
- Lectures with practical application examples
- Exercices with solutions allowing knowledge application and deepening
Literature
- Buchmann, Johannes: Introduction to Cryptography, 2nd. ed., Springer Verlag, 2004, ISBN: 978-0-387-21156-5
- Stinson, Douglas: Cryptography: Theory and Practice, 3rd ed., Chapman & Hall, 2005, ISBN: 978-1-584-88508-5
- Zémor, Gilles: Cours de cryptographie, Cassini, 2000, ISBN: 2-84225-020-6
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