Course detail

Cryptologic Protocol Theory

FEKT-MPA-CPTAcad. year: 2022/2023

The course contains the introduction into advanced cryptography and provides the students with the information about basic cryptographic primitives and schemes. In particular, the commitment schemes, interactive proof systems, zero-knowledge protocols, sigma protocols, interactive and non-interactive proof of knowledge protocols, group signatures and advanced systems like eCash and attribute-based credentials are covered.

Language of instruction


Number of ECTS credits


Mode of study

Not applicable.

Learning outcomes of the course unit

Students will obtain theoretical knowledge of main primitives used in modern cryptography, in particular of commitment schemes, zero-knowledge protocols, sigma-protocols and advanced schemes built using these primitives. After course completion, students will be able to:

Explain in English the principles of cryptographic commitments, zero-knowledge protocols and sigma protocols.
Design the interactive proof of knowledge protocols.
Use the commitment schemes in complex cryptosystems.
Evaluate speed and computational efficiency of standard proof of knowledge protocols.
Explain in English the principles of attribute authentication systems and eCash systems.


Basic knowledge of cryptography as provided in the compulsory subject Foundations of Cryptography, in particular of the asymmetric cryptosystems, is required to enroll the course. Furthermore, the basic knowledge of Czech terminology in cryptography and B1 intermediate English level is required.


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. Teachning methods include lectures and laboratories. Course is taking advantage of e-learning (Moodle) system.

Assesment methods and criteria linked to learning outcomes

The maximum of 40 points is given upon completion of the  tests in laboratories. The requirements on the completion of the tasks in laboratories are described in the annual supervisor’s notice.  The maximum of 60 points can be gained during the final exam.  

Course curriculum

1. Introduction to modern cryptography, Number Theory.
2. Modular arithmetics, Algebraic structures.
3. Basic cryptographic primitives overview.
4. Elliptic curve cryptography.
5. Bilinear pairing.
6. Protocols using bilinear pairing.
7. Commitment schemes.
8. Zero-knowledge protocols.
9. Sigma protocols.
10. Sigma protocols II.
11. Group signatures.
12. Attribute-based credentials. 

Work placements

Not applicable.


The goal of the course is to extend the introductory cryptology courses and to provide students with deeper knowledge of advanced principles of modern cryptology and English terminology. Students will learn the principles of selected building blocks of modern cryptographic protocols and schemes and will be able to understand English information sources during their further studies.

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

MENEZES, A.J. Handbook of applied cryptography. Boca Raton: CRC Press, 1997. Online: (EN)
STALLINGS, W. Cryptography and network security: principles and practice. Seventh edition. (EN)

Recommended reading

Not applicable.


Classification of course in study plans

  • Programme MPA-CAN Master's, 1. year of study, summer semester, compulsory-optional
  • Programme MPAD-CAN Master's, 1. year of study, summer semester, compulsory-optional
  • Programme MPA-TEC Master's, 1. year of study, summer semester, compulsory-optional
  • Programme MPAJ-TEC Master's, 1. year of study, summer semester, compulsory-optional

Type of course unit



26 hours, optionally

Teacher / Lecturer


1. Introduction to modern cryptography.
2. Terminology overview.
3. Basic cryptographic primitives overview.
4. Commitment schemes.
5. Use of cryptographic commitment schemes in protocol construction.
6. Interactive proof systems.
7. Zero-knowledge protocols.
8. Sigma protocols.
9. Sigma protocols II.
10. Interactive and non-interactive proofs of knowledge.
11. Integration of primitives into advanced systems.
12. Group signatures.
13. Attribute-based credentials.

Fundamentals seminar

26 hours, compulsory

Teacher / Lecturer