Course detail

Mathematical Principles of Cryptographic Algorithms

FSI-9MPKAcad. year: 2023/2024

Basic mathematical principles of asymmetric cryptography. The RSA system. The cryptography based on elliptic curves (ECC). Finite field arithmetics and some results of number theory. Algorithms.

Language of instruction


Number of ECTS credits


Mode of study

Not applicable.

Entry knowledge

Basic knowledges of algebra.

Rules for evaluation and completion of the course

The examination checks up knowledge of basic definitions and theorems and practical skills for solutions of cryptographic tasks.
Lectures: recommended


Fundamentals of problems of assymetric cryptography with emphasis to the ECC system.
The algoritmization of some cryptographic problems.

Study aids

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Darrel Hankerson, Alfred Menezes, and Scott Vanstone: Guide to Elliptic Curve Cryptography, Springer-Verlag Professional Computing Series, ISBN: 0-387-95273-X, 2004.

Recommended reading

Not applicable.

Classification of course in study plans

  • Programme D-APM-K Doctoral, 1. year of study, summer semester, recommended
  • Programme D-APM-P Doctoral, 1. year of study, summer semester, recommended

Type of course unit



20 hours, optionally

Teacher / Lecturer


1.-2. Introduction to asymmetric cryptography.
3.-4. The system RSA.
5.-6. Finite fields.
7.-8. Elliptic curves.
9.-10. Some results of Number theory.
11. The system ECC.
12.-13. The order of elliptic curves and the algorithm development.