Course detail

Mathematical Principles of Cryptographic Algorithms

FSI-9MPKAcad. year: 2022/2023

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

Czech

Mode of study

Not applicable.

Guarantor

doc. RNDr. Miroslav Kureš, Ph.D.

Department

Institute of Mathematics (ÚM)

Learning outcomes of the course unit

The algoritmization of some cryptographic problems.

Prerequisites

Basic knowledges of algebra.

Co-requisites

Not applicable.

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.

Course curriculum

Not applicable.

Work placements

Not applicable.

Aims

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

Recommended optional programme components

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

Type of course unit

 

Lecture

20 hod., optionally

Teacher / Lecturer

doc. RNDr. Miroslav Kureš, Ph.D.

Syllabus

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.