Czech

Not applicable.

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.

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.

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 10 points are given for work in laboratory.
Up to 20 points individual project.
Up to 70 points are given for the final examination.

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.

Not applicable.

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.

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.

Not applicable.

Not applicable.

Burda, K. Aplikovaná kryptografie, 2013, ISBN: 978-80-214-4612-0 (EN)
Song Y. Yan. Computational Number Theory and Modern Cryptography, 2013, ISBN: 978-1-118-18858-3 (EN)

Biggs, N.L. Discrete Mathematics, Oxford Science Publications, 1999, ISBN 0198534272 (EN)
Cameron, P.J. Sets, Logic and Categories, Springer-Verlag, 2000, ISBN 1852330562 (EN)
Lawrence C. Washington. Elliptic Curves: Number Theory and Cryptography, Chapman and Hall/CRC, 2008, ISBN 9781420071467 (EN)
Procházka, L. Algebra, Academia, Praha, 1990 (CS)