Course detail


FEKT-MPA-KRIAcad. year: 2020/2021

Probability and information theory, Shannon's theory of secrecy. Computational complexity and number theory and its applications in cryptography. Turing machines and their variants, propositional logic, formal system of propositional logic, provability in propositional logic. Algebra and basic types, algebraic structures used in cryptography. Elliptic curve. Bilinear pairings and the use of cryptography, lattice, modern symmetric and asymmetric cryptographic systems. Quantum computational number theory, quantum resistant cryptography..

Learning outcomes of the course unit

Students will be introduced to applications of cryptographic mechanisms and methods in IT. They will learn the principles of information system security. On completion of the course, students will be able to explain the principles of modern symmetric and asymmetric cryptography.


The subject knowledge on the Bachelor degree level is requested.


Not applicable.

Recommended optional programme components

Not applicable.

Recommended or required reading

Song Y. Yan. Computational Number Theory and Modern Cryptography, 2013, ISBN: 978-1-118-18858-3 (EN)
Lawrence C. Washington. Elliptic Curves: Number Theory and Cryptography, Chapman and Hall/CRC, 2008, ISBN 9781420071467 (EN)
Cameron, P.J. Sets, Logic and Categories, Springer-Verlag, 2000, ISBN 1852330562 (EN)
Biggs, N.L. Discrete Mathematics, Oxford Science Publications, 1999, ISBN 0198534272 (EN)

Planned learning activities and teaching methods

Techning methods include lectures, computer laboratories and practical laboratories. Course is taking advantage of e-learning (Moodle) system. Teaching methods depend on the type of course unit as specified in article 7 of the BUT Rules for Studies and Examinations.

Assesment methods and criteria linked to learning outcomes

Evaluation of study results follows the Rules for Studies and Examinations of BUT and the Dean's Regulation complementing the Rules for Studies and Examinations of BUT.
Up to 30 points are given for work in laboratory.
Up to 70 points are given for the final examination.

Language of instruction


Work placements

Not applicable.

Course curriculum

1. Probability theory and information theory, Shannon’s theory of secrecy systems, entropy, mutual information.
2. Complexity theory, Number theory, complexity classes.
3. Propositional logic, formulas and their truth, formal system of propositional logic, provability in propositional logic, the use of cryptography.
4. Universal algebras and their basic types, algebraic methods, subalgebras, homomorphisms and isomorphisms, congruences and direct products of algebras.
5. Congruences on groups and rings, normal subgroups and ideals, polynomial rings, divisibility in integral domains.
6. Field theory, minimal fields, extension of fields, finite fields.
7. ECC.
8. Bilinear pairings in cryptography.
9. Lattice, LLL algorithm.
10. Modern cryptography systems I.
11. Modern cryptography systems II.
12. Quantum computational number theory, quantum resistant cryptography.


The objective of this course is to provide students with detailed theoretical and practical knowledge on which they are built modern cryptographic systems designed to protect information technology.

Specification of controlled education, way of implementation and compensation for absences

The content and forms of instruction in the evaluated course are specified by a regulation issued by the lecturer responsible for the course and updated for every academic year.

Classification of course in study plans

  • Programme MPA-EAK Master's, 2. year of study, summer semester, 7 credits, compulsory

Type of course unit



26 hours, optionally

Teacher / Lecturer

Laboratory exercise

39 hours, compulsory

Teacher / Lecturer