Course detail

Mathematical Principles of Cryptographic Algorithms

FSI-9MPKAcad. year: 2024/2025

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)

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

Aims

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