Info on CL

Conditions

Cryptology

Subject of the group A for: Informatics
Term: winter
Extent: 3-1
Year: 1st graduate study
Lecturer: prof. RNDr. Otokar Grošek, CSc.

Proportion of final exams in the course completion: 60%.

Keywords: cryptology, block ciphers, public-key cryptography.

Annotation: A content of this course interlace topics from different areas of mathematics and computer science. A good skill in modular arithmetic and preliminary knowledge from group theory, and computer complexity theory is welcome but not required. The aim of this course is to give an overview to block and public-key cryptography.

Syllabus in twelve points:

  1. Permutation as a basic technique for ciphering.
  2. Modular arithmetics.
  3. Basic classical cryptographic systems.
  4. Finite groups, permutation polynomials over Zn.
  5. Shannon's theroy and analysis of classical systems.
  6. Source models, random number generators, statistical tests for random number generators.
  7. Block and stream ciphers.
  8. Block ciphers of the Feistel type.
  9. LUCIFER, DES, BLOWFISH, GOST, IDEA, RIJNDAEL.
  10. Modes of ciphering.
  11. Public-key cryptography.
  12. Knapsack, McEliece, RSA, Goldwasser, EC-systems.

Target: The aim of this course is to give an overview of basic theoretical as well as practical approach to solve problems in cryptography. The first part is devoted to classical ciphers and their solution. The second part is an introduction to some algebraic techniques which allows to design so called block ciphers, as DES, IDEA and RIJNDAEL In the last part, several public-key cryptography techniques are introduced.

Recommended prerequisites: Content of this course interlace topics from different areas of mathematics and computer science. Prerequisites for the course are the following courses: Linear algebra, Probability theory and statistics, Coding theory, Computational complexity. A overview of necessary knowledge of modular arithmetic, group theory, and computer complexity theory is given at the beginning of the course is included.

Bibliography:

foreign:
B. Schneier: Applied Cryptography. J. Wiley and Sons, Inc., 1996.
A.J. Menezes, P.C. van Oorschot, S.A. Vanstone: Handbook of Applied Crytography. http://cacr.math.uwaterloo.ca/hac/.
available in Slovak or Czech:
O. Grošek, Š. Porubský: Šifrovanie - Algoritmy, metódy, prax. GRADA 1992.