Course detail

# Foundations of Cryptography

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

English

Number of ECTS credits

6

Mode of study

Not applicable.

Offered to foreign students

Of all faculties

Entry knowledge

The course is designed as an introduction to the subject of cryptography thus no prerequisites are required. Only high school knowledge and general PC usage experience is expected.

Rules for evaluation and completion of the course

The maximum of 15 points is given upon completion of the theoretical test in laboratories. The correct completion of all tasks in laboratories adds 15 points. The requirements on the completion of the tasks in laboratories are described in the annual supervisor’s notice. The maximum of 70 points can be gained during the final exam.
The conditions for the successful course completion are stated in the yearly updated supervisor’s notice.

Aims

The goal of the course is to provide students with the basic knowledge of cryptography and to provide them with information necessary in more advanced courses in information and communication security. During the course, students will study the theoretical foundations (mainly the algebraic structures and their properties), the most common algorithms and concepts used in modern cryptography.
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

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Stallings, W.: Cryptography and Network Security: Principles and Practice. Pearson, 2016, ISBN 978-0134444284 (EN)
Hoffstein, J., Pipher, J., Silverman, J. H.: An introduction to mathematical cryptography. New York: Springer, 2014, ISBN 978-1493917105 (EN)
Oorschot, P. C. v.: Computer Security and the Internet: Tools and Jewels. (EN)

Not applicable.

eLearning

Classification of course in study plans

• Programme MPA-MEL 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-EAK Master's, 2. year of study, winter semester, compulsory-optional
• Programme MPA-SAP Master's, 2. year of study, winter semester, compulsory-optional

#### Type of course unit

Lecture

26 hours, optionally

Teacher / Lecturer

Syllabus

1. Introduction to cryptography, history
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

Computer-assisted exercise

39 hours, compulsory

Teacher / Lecturer

eLearning