Course detail

Mathematical Principles of Cryptographic Algorithms

FSI-9MPK Acad. year: 2024/2025 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

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.

The study programmes with the given course

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

Programme D-APM-P: 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.