Course detail

Cryptography

FEKT-MKC-KRYAcad. year: 2022/2023

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..

Language of instruction

Czech

Number of ECTS credits

7

Mode of study

Not applicable.

Guarantor

doc. Ing. Václav Zeman, Ph.D.

Department

Department of Telecommunications (UTKO)

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.

Prerequisites

The subject knowledge on the Bachelor degree level is requested.

Co-requisites

Not applicable.

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.

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.

Work placements

Not applicable.

Aims

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.

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

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)

Recommended reading

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)

Classification of course in study plans

  • Programme MPC-TIT Master's 2 year of study, summer semester, compulsory-optional

Type of course unit

 

Lecture

26 hod., optionally

Teacher / Lecturer

doc. Ing. Václav Zeman, Ph.D.

Syllabus

Introduction to cryptology, substitution and transposition ciphers
Mathematical foundations of cryptology
Cryptographic algorithm types and modes
Secret key encryption, DES data encryption standard
Public key encryption, RSA system
Cryptographic keys and their management
Digital signatures, one-way hash functions
Basic cryptographic protocols and its building blocks
Special algorithms for protocols, identification schemes
Criteria for system security assessment, security implementation principles
Security of data in computer networks
E-commerce security, application of cryptography in electronic publishing
Legislative and ethical protection of data

Laboratory exercise

39 hod., compulsory

Teacher / Lecturer

doc. Ing. Václav Zeman, Ph.D.

Syllabus

Introduction. Information for students about the content of particular laboratory metering assignments, methods of presenting the metering results obtained, organization of work in the laboratory, review exercises and their impact on overall assessment. Safety at work in the laboratory.
Foundations of cryptology, cryptographic algorithm types and modes, digital signatures, basic cryptographic protocols and their building blocks, security of data in computer networks, Internet security.