Mathematical Principles of Cryptographic Algorithms (FSI-9MPK)

Academic year 2022/2023
Supervisor: doc. RNDr. Miroslav Kureš, Ph.D.  
Supervising institute: ÚM all courses guaranted by this institute
Teaching language: Czech or English
Aims of the course unit:
Fundamentals of problems of assymetric cryptography with emphasis to the ECC system.
Learning outcomes and competences:
The algoritmization of some cryptographic problems.
Prerequisites:
Basic knowledges of algebra.
Course contents:
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.
Teaching methods and criteria:
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.
Controlled participation in lessons:
Lectures: recommended
Type of course unit:
    Lecture  10 × 2 hrs. optionally                  
Course curriculum:
    Lecture 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.
Literature - fundamental:
1. Darrel Hankerson, Alfred Menezes, and Scott Vanstone: Guide to Elliptic Curve Cryptography, Springer-Verlag Professional Computing Series, ISBN: 0-387-95273-X, 2004.
The study programmes with the given course:
Programme Study form Branch Spec. Final classification   Course-unit credits     Obligation     Level     Year     Semester  
D-APM-K combined study --- -- DrEx 0 Recommended course 3 1 S
D-APM-P full-time study --- -- DrEx 0 Recommended course 3 1 S