Basics of Cryptography

Syllabus of lectures:
1. Cryptography and its role in IT security. Basic concepts: security services, mechanisms, threats, attacks, risks, vulnerabilities and their examples.
2. Classical (historical) cryptography I. Examples of ciphers and their principles.
3. Classical (historical) cryptography II. Examples of ciphers and their principles in today's context.
4. Cryptanalysis - Methods and types of attacks on classical cipher. Ciphertext only attack.
5. Mathematical foundations of cryptographic algorithms I (congruence, modular arithmetic, primes).
6. Mathematical foundations of cryptographic algorithms II (algebraic structures (groups, fields)).
7. Modern cryptographic algorithms - symmetric cryptography. Basic principles, examples of algorithms (DES, AES) and ways of using them (modes of operation). Applications in protocols.
8. Modern cryptographic algorithms - asymmetric cryptography. Basic principles, examples of algorithms (RSA, Diffie-Hellman). Applications inprotocols.
9. Modern cryptographic algorithms - hash function. Principles and algorithms. Applications in protocols.
10. Modern Cryptographic Algorithms - Digital Signature. Principles and algorithms. Applications in protocols.
11. Pseudorandom Generators (PRNG). Principles and their applications for cryptographic purposes.
12. Authentication protocols and cryptographic algorithms.
13. Related legislation, standards.

Syllabus of seminars:
The seminars will take place in a computer classroom. They will include both the practical implementation of simple cryptographic algorithms and their demonstration in existing tools and aplications. The focus will also be on the mathematical principles of cryptography.
1. Basic cryptographic concepts and principles - practice, examples
2. Classical cryptography I.
3. Classical cryptography II.
4. Simulation of simple cryptanalytical attacks.
5. Practice of mathematical principles of algorithms discussed - modular arithmetic.
6. Algebraic structures.
7. Theory of Numbers.
8. Symmetric cryptography.
9. Asymmetric cryptography.
10. Hash functions.
11. OpenSSL, PGP.
12. PRNG.
13. Practical examples of security applications and protocols.