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
Supervisor
Department
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.