Course detail
Foundations of Cryptography
FEKT-MPA-ZKRAcad. year: 2024/2025
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
Elearning
Classification of course in study plans
- 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-MEL Master's 2 year of study, winter semester, compulsory-optional
- Programme MPA-CAN Master's 1 year of study, winter semester, compulsory-optional
- Programme MPAD-CAN Master's 1 year of study, winter semester, compulsory-optional
Type of course unit
Lecture
Teacher / Lecturer
Syllabus
2. Introduction to number theory
3. Primes and their use in cryptography
4. Basic structures used in cryptography I
5. Basic structures used in cryptography II
6. Modular arithmetic
7. Complexity theory, problem classification
8. Cryptography algorithms I
9. Cryptography algorithms II
10. Practical encryption
11. Practical authentication and digital signature
12. Provable security I
13. Provable security II
Elearning