Course Unit
Catalogue
Algebraic methods in cryptography
- Unit Coordinator: dr inż. Witold Tomaszewski
- Programme: RealMaths
- ECTS Credits: 4
- Semester: 1
- Year: 2
- Campus: Silesian University of Technology
- Language: English
- Aims:
The aim of the course is to familiarize students with various aspects of modern cryptography, using number theory, modular arithmetic, group theory and the theory of rings and fields
Content:
1. Number theory algorithms: Euclidean algorithm, Diophantine equations, Chinese remainder theorem.
2. Elements of group theory and commutative ring theory.
3. Modular arithmetic.
4. Classical ciphers: Caesar cipher, affine cipher, Vigenère cipher, matrix ciphers.
5. Public-key cryptography.
6. Selected cryptographic protocols.
7. Finite fields: constructions, properties and arithmetic.
8. Applications of finite fields in cryptography.
9. Elliptic-curve cryptography.
- Content:
1. Number theory algorithms: Euclidean algorithm, Diophantine equations, Chinese remainder theorem.
2. Elements of group theory and commutative ring theory.
3. Modular arithmetic.
4. Classical cyphers: Caesar cypher, affine cypher, Vigenère cypher, matrix cyphers.
5. Public-key cryptography.
6. Selected cryptographic protocols.
7. Finite fields: constructions, properties and arithmetic.
8. Applications of finite fields in cryptography.
9. Elliptic-curve cryptography.
