Course detail

Mathematical Principles of Cryptographic Algorithms

FSI-9MPKAcad. year: 2020/2021

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.

Learning outcomes of the course unit

The algoritmization of some cryptographic problems.


Basic knowledges of algebra.


Not applicable.

Recommended optional programme components

Not applicable.

Recommended or required reading

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

Planned learning activities and teaching methods

The course is taught through lectures explaining the basic principles and theory of the discipline.

Assesment methods and criteria linked to learning outcomes

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

Language of instruction

Czech, English

Work placements

Not applicable.


Fundamentals of problems of assymetric cryptography with emphasis to the ECC system.

Specification of controlled education, way of implementation and compensation for absences

Lectures: recommended

Classification of course in study plans

  • Programme D-APM-K Doctoral, 1. year of study, summer semester, 0 credits, recommended

  • Programme D4P-P Doctoral

    branch D-APM , 1. year of study, summer semester, 0 credits, 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.