Course detail
Foundations of Cryptography
FEKT-MPA-ZKRAcad. year: 2025/2026
Basic terminology in cryptology, cryptology categorization, algebraic structures used in cryptography. Generation, testing and use of prime numbers. Group arithmetics, bilinear pairing. Complexity theory fundamentals. Computationally hard problems used in cryptography – discrete logarithm, RSA problem, EC discrete logarithm. The overview of basic algorithms used in cryptography. Symmetric and asymmetric cryptosystems (PRESENT, AES, RSA, ECDH, SHA2, 3) and their practical use. Provable security concept – proofs, formal models, zero-knowledge, Sigma-protocols, cryptographic commitments.
Language of instruction
Number of ECTS credits
Mode of study
Guarantor
Department
Offered to foreign students
Entry knowledge
Rules for evaluation and completion of the course
The conditions for the successful course completion are stated in the yearly updated supervisor’s notice.
Aims
Students will obtain theoretical foundations of cryptography and computer security. Based on these foundations, students will be able to analyze and design security solutions for information and communication technologies (ICT). Students will be able to explain basic principles of algebraic structures used in cryptography, basic cryptographic primitives (hashes, RNG, provably secure protocols), basic algorithms and describe the internals of symmetric and asymmetric algorithms. Students will be theoretically prepared for follow-up courses from data transfer and ICT security areas.
Study aids
Prerequisites and corequisites
Basic literature
Oorschot, P. C. v.: Computer Security and the Internet: Tools and Jewels. (EN)
Stallings, W.: Cryptography and Network Security: Principles and Practice. Pearson, 2016, ISBN 978-0134444284 (EN)
Recommended reading
Classification of course in study plans
- Programme MPAD-ACS Master's 2 year of study, winter semester, compulsory
- Programme MPAD-CAN Master's 1 year of study, winter semester, compulsory-optional
- Programme MPA-EAK Master's 2 year of study, winter semester, compulsory-optional
- Programme MPA-MEL Master's 2 year of study, winter semester, compulsory-optional
- Programme MPA-SAP Master's 2 year of study, winter semester, compulsory-optional
- Programme MPAD-CAN Master's 1 year of study, winter semester, compulsory-optional
- Programme MPAD-MEL Master's 2 year of study, winter semester, compulsory-optional
Type of course unit
Lecture
Teacher / Lecturer
Syllabus
1. History and Introduction to cryptography
2. Number Theory and Complexity Theory
3. Basic structures used in cryptography
4. Prime Numbers and their use in cryptography
5. Random Number Generation
6. Asymmetric Cryptography
7. Symmetric Cryptography: Stream Ciphers
8. Symmetric Cryptography: Block Ciphers
9. Elliptic Curve Cryptography
10. Bilinear Pairings in Cryptography
11. Cryptographic protocols 1
12. Cryptography protocols 2
13. Practical authentication