Course detail

Foundations of Cryptography

FEKT-MPA-ZKRAcad. year: 2021/2022

Basic terminology in cryptology, cryptology categorization, algebraic structures used in cryptography. Generation, testing and use of prime numbers. Group arithmetics, bilinear pairing. Complexity theory fundamentals. Computationally hard problems used in cryptography – discrete logarithm, RSA problem, EC discrete logarithm. The overview of basic algorithms used in cryptography. Symmetric and asymmetric cryptosystems (PRESENT, AES, RSA, ECDH, SHA2, 3) and their practical use. Provable security concept – proofs, formal models, zero-knowledge, Sigma-protocols, cryptographic commitments.

Language of instruction

English

Number of ECTS credits

6

Mode of study

Not applicable.

Guarantor

M.Sc. Sara Ricci, Ph.D.

Department

Department of Telecommunications (UTKO)

Offered to foreign students

Of all faculties

Learning outcomes of the course unit

Students will obtain theoretical foundations of cryptography and computer security. Based on these foundations, students will be able to analyze and design security solutions for information and communication technologies (ICT). Students will be able to explain basic principles of algebraic structures used in cryptography, basic cryptographic primitives (hashes, RNG, provably secure protocols), basic algorithms and describe the internals of symmetric and asymmetric algorithms. Students will be theoretically prepared for follow-up courses from data transfer and ICT security areas.

Prerequisites

The course is designed as an introduction to the subject of cryptography thus no prerequisites are required. Only high school knowledge and general PC usage experience is expected.

Co-requisites

Not applicable.

Planned learning activities and teaching methods

Methods of educations are described in the article 7 of the BUT’s Study and Examination Regulation. Techning methods include lectures and laboratories. Course is taking advantage of e-learning (Moodle) system. Students have to deliver 10 assignments during the course.

Assesment methods and criteria linked to learning outcomes

The maximum of 15 points is given upon completion of the theoretical test in laboratories. The correct completion of all tasks in laboratories adds 15 points. The requirements on the completion of the tasks in laboratories are described in the annual supervisor’s notice. The maximum of 70 points can be gained during the final exam.

Course curriculum

1. Introduction to cryptography, history
2. Introduction to number theory
3. Primes and their use in cryptography
4. Basic structures used in cryptography I
5. Basic structures used in cryptography II
6. Modular arithmetic
7. Complexity theory, problem classification
8. Cryptography algorithms I
9. Cryptography algorithms II
10. Practical encryption
11. Practical authentication and digital signature
12. Provable security I
13. Provable security II

Work placements

Not applicable.

Aims

The goal of the course is to provide students with the basic knowledge of cryptography and to provide them with information necessary in more advanced courses in information and communication security. During the course, students will study the theoretical foundations (mainly the algebraic structures and their properties), the most common algorithms and concepts used in modern cryptography.

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

The conditions for the successful course completion are stated in the yearly updated supervisor’s notice.

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Hoffstein, J., Pipher, J., Silverman, J. H.: An introduction to mathematical cryptography. New York: Springer, 2014, ISBN 978-1493917105 (EN)
Oorschot, P. C. v.: Computer Security and the Internet: Tools and Jewels. (EN)
Stallings, W.: Cryptography and Network Security: Principles and Practice. Pearson, 2016, ISBN 978-0134444284 (EN)

Recommended reading

Not applicable.

Elearning

eLearning: currently opened course

Classification of course in study plans

  • Programme MPA-MEL Master's 2 year of study, winter semester, compulsory-optional
  • Programme MPA-EAK Master's 2 year of study, winter semester, compulsory-optional
  • Programme MPAD-MEL Master's 2 year of study, winter semester, compulsory-optional

Type of course unit

 

Lecture

26 hod., optionally

Teacher / Lecturer

M.Sc. Sara Ricci, Ph.D.

Syllabus

1. Úvod do kryptografie, historie
2. Úvod do teorie čísel
3. Prvočísla a jejich využití v kryptografii
4. Základy struktur používaných v kryptografii
5. Základy struktur používaných v kryptografii II
6. Modulární aritmetika
7. Výpočetní problémy, jejich klasifikace a využití
8. Algoritmy pro kryptografii I
9. Algoritmy pro kryptografii II
10. Šifrování v praxi
11. Autentizace a digitální podpis v praxi
12. Prokazatelná bezpečnost I
13. Prokazatelná bezpečnost II

Computer-assisted exercise

39 hod., compulsory

Teacher / Lecturer

M.Sc. Sara Ricci, Ph.D.

Syllabus

1. Úvod do cvičení
2. Základní operace a jejich softwarová implementace
3. Generování a testování prvočísel
4. Generování grup a jejich vlastnosti
5. Diskrétní logaritmus a jeho využití v kryptografii
6. RSA problém a jeho využití v kryptografii
7. Eliptické křivky a jejich využití v kryptografii
8. Základní algoritmy
9. Základy práce v kryptografickém simulačním softwaru
10. Simulace jednoduchých kryptosystémů
11. Simulace moderních šifrovacích algoritmů
12. Simulace moderních autentizačních protokolů

Elearning

eLearning: currently opened course