Description:

Students will learn the essentials of cryptanalysis and the mathematical principles of constructing symmetric and asymmetric ciphers. They will know the mathematical principles of random number generators. They will have an overview of cryptanalysis methods, elliptic curve cryptography and quantum cryptography, which they can apply to the integration of their own systems or to the creation of their own software solutions.

Contents:

1. Mathematical fundamentals of cryptanalysis of cyphers.
2. Random number generators.
3. Symmetric cryptography (block and stream encryption).
4. Asymmetric cryptography.
5. Unidirectional functions, hash functions.
6. Implementation of individual protocols.
7. Linear cryptanalysis.
8. Differential cryptanalysis.
9. Algebraic cryptanalysis.
10. Eliptic curves and their properties.
11. [2] Algorithms and cryptosystems based on elliptic curves.
12. Quantum computing and cryptography.

Seminar contents:

1. Mathematical fundamentals of cryptanalysis of cyphers.
2. Random number generators.
3. Symmetric cryptography (block and stream encryption).
4. Asymmetric cryptography.
5. Unidirectional functions, hash functions.
6. Implementation of individual protocols.
7. Linear cryptanalysis.
8. Differential cryptanalysis.
9. Algebraic cryptanalysis.
10. Eliptic curves and their properties.
11. [2] Algorithms and cryptosystems based on elliptic curves.
12. Quantum computing and cryptography.

Recommended literature:

1. Menezes, A., Oorschot, P., Vanstone, S. ''Handbook of Applied Cryptography''. CRC Press, 1996. ISBN 0849385237.
2. Gregory, V., B., ''Algebraic Cryptanalysis'', Springer, 2009, ISBN: 978-0-387-88756-2.
3. Daemen, J.., Rijmen, V.: ''The Design of Rijndael: AES - The Advanced Encryption Standard'', Springer, 2002, ISBN: 3-540-42580-2.
4. Gruska, J., ''Quantum computing'', McGraw-Hill Companies, 1999, ISBN: 0-07-709503-0.

Keywords:

cryptology, cryptography, cryptanalysis, linear cryptanalysis, differential cryptanalysis

Abbreviations used:

Semester:

• W ... winter semester (usually October - February)
• S ... spring semester (usually March - June)
• W,S ... both semesters

Mode of completion of the course:

• A ... Assessment (no grade is given to this course but credits are awarded. You will receive only P (Passed) of F (Failed) and number of credits)
• GA ... Graded Assessment (a grade is awarded for this course)
• EX ... Examination (a grade is awarded for this course)
• A, EX ... Examination (the award of Assessment is a precondition for taking the Examination in the given subject, a grade is awarded for this course)

Weekly load (hours per week):

• P ... lecture
• C ... seminar
• L ... laboratory
• R ... proseminar
• S ... seminar