Foundations of Cryptography
FEKT-BZKRAcad. year: 2015/2016
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.
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.
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.
Recommended optional programme components
Recommended or required reading
SINGH, Simon. Kniha kódů a šifer: tajná komunikace od starého Egypta po kvantovou kryptografii. Praha: Dokořán, 2003, 382 s. ISBN 80-865-6918-7.
LEVICKÝ, Dušan. Kryptografia v informačnej bezpečnosti. Košice: Elfa, 2005, 266 s. ISBN 80-808-6022-X.
OCHODKOVÁ, Eliška. Matematické základy kryptografických algoritmů [online]. [cit. 2013-06-11]. Dostupné z: http://mi21.vsb.cz/sites/mi21.vsb.cz/files/unit/mat_zaklady_kryptografickych_algoritmu.pdf
MENEZES, Alfred J. Handbook of applied cryptography. Vyd. 1. Boca Raton: CRC Press, 1997, 780 s. ISBN 08-493-8523-7. Online http://cacr.uwaterloo.ca/hac/.
STALLINGS, William. Cryptography and network security: principles and practice. Seventh edition. xix, 731 pages. ISBN 01-333-5469-5.
GARRETT, Paul. Making, breaking codes: an introduction to cryptology. Vyd. 1. Upper Saddle River: Prentice Hall, 2001, xix, 523 s. ISBN 01-303-0369-0.
BURDA, K. Úvod do kryptografie. Úvod do kryptografie. Brno: Akademické nakladatelství CERM, 2015. ISBN: 978-80-7204-925- 7.
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.
Language of instruction
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
1. Introduction to labs
2. Basic operations and their software implementation
3. Prime number generation and testing
4. Group generation and their properties
5. Discrete logarithm and its usage in cryptography
6. RSA problem and its usage in cryptography
7. Elliptic curves and their usage in cryptography
8. Basic algorithms
9. Basics of cryptography algorithm simulation
10. Simple cryptosystem simulation
11. Modern encryption algorithm simulation
12. Modern authentication algorithm simulation
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.
Classification of course in study plans
- Programme IBEP-T Bachelor's
branch T-IBP , 1. year of study, winter semester, 6 credits, compulsory
- Programme EEKR-B Bachelor's
branch B-TLI , 3. year of study, winter semester, 6 credits, optional specialized
- Programme EEKR-CZV lifelong learning
branch ET-CZV , 1. year of study, winter semester, 6 credits, optional specialized