Course detail

Mathematical Principles of Cryptographic Algorithms

FSI-9MPK Acad. year: 2022/2023 Summer semester

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

Learning outcomes of the course unit

The algoritmization of some cryptographic problems.

Prerequisites

Basic knowledges of algebra.

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.

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

The study programmes with the given course

Programme D-APM-P: Applied Mathematics, Doctoral, recommended course

Programme D-APM-K: Applied Mathematics, Doctoral, recommended course

Type of course unit

 

Lecture

20 hours, optionally

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.