MSE Master of Science in Engineering

# The Swiss engineering master's degree

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
Cryptography and Coding Theory (FTP_CryptCod)

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++, Python, Sage)
 Week Contents (Order and weighting may be adapted) 1 Algebraic basics: modular arithmetic, Euclidean algorithm, extended Euclidean algorithm, Bezout theorem, Fermat Euler theorem, Chinese Remainder theorem 2 3 Asymmetric (public key) cryptography: Diffie Hellman key exchange, RSA algorithm, digital signatures 4 5 Algebraic basics: polynomials and finite fields 6 Symmetric (secret key) cryptography: review of important examples (substitution cipher, transposition cipher, product cipher, block cipher,etc.) 7 Symmetric (secret key) cryptography: Hash functions,  Data Encryption Standard (DES), Advanced Encryption Standard (AES), Chacha20, modes of operation, authenticated encryption 8 Elliptic Curve Diffie Hellman (ECDH), digital signatures 9 10 One-time pad (OTP), Modern Topics in Cryptography, TLS and X509v3 11 Error-correcting codes: Cyclic codes, Reed-Solomon, BCH, Convolutional Codes, Turbo 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
• ZĂ©mor, Gilles: Cours de cryptographie, Cassini, 2000, ISBN: 2-84225-020-6