Course detail

Advanced Cryptography

FEKT-DKC-PKRAcad. year: 2023/2024

The subject is focused on the following topics: number theory, group theory, elliptic curve cryptography, cryptographic commitment schemes, interactive proof systems, zero-knowledge protocols, blinded signatures, groups signatures, anonymous credentials, homomorphic encryption, construction of post-quantum cryptography based on lattices, cryptocurrency and blockchain.  

Language of instruction


Number of ECTS credits


Mode of study

Not applicable.

Entry knowledge

Foundations of cryptography in the extent of the Bachelor and Master level programs, e.g. BZKR-IBE a TCPT-IBE. courses

Rules for evaluation and completion of the course

The maximum of 60 points is given upon completion of the individual project. The requirements on the completion of the projects are described in the annual supervisor’s notice.  The maximum of 40 points can be gained during the final exam.
The conditions for the successful course completion are stated in the yearly updated supervisor’s notice.


The goal of the subject is to introduce students the advanced methods of contemporary cryptography, which are necessary for the construction and implementation of modern cryptographic systems. The student will learn fundamental cryptographic primitives, in particular the commitment schemes, group signatures, interactive proof systems, and more advanced cryptographic technologies such as attribute-based credentials, cryptocurrencies and blockchain, post-quantum cryptography.  
Upon the completion of the subject, the students will be able to understand the design of modern cryptographic constructions presented in the form of scientific publications. Student will be able to use basic cryptographic primitives (commitments, proof systems and signature schemes) for the construction of complex schemes. Students will be able to provide a security analysis for designed schemes based on formal models using provable security.

Study aids

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

BURDA, K. Aplikovaná kryptografie. monografie. monografie. Brno: VUTIUM, 2013. 255 s. ISBN: 978-80-214-4612- 0. (CS)
SCHNEIER, Bruce. Applied cryptography: protocols, algorithms, and source code in C. 20th anniversary edition. Indianapolis: Wiley, 2015, xxv, 758 stran : ilustrace. ISBN 978-1-119-09672-6. (EN)

Recommended reading

MENEZES, A. J, Paul C VAN OORSCHOT a Scott A VANSTONE. Handbook of applied cryptography. Boca Raton: CRC Press, c1997. ISBN 0849385237. (EN)

Classification of course in study plans

  • Programme DKC-IBE Doctoral, any year of study, winter semester, compulsory

Type of course unit



39 hours, optionally

Teacher / Lecturer


1. Introductory information to the course
2. Introduction to the basics of cryptographic algorithms
3. Elliptic curve cryptography
4. Commitment Schemes
5. Sigma protocols
6. Blinded digital signature
7. Group signatures
8. Credential Schemes
9. Homomorphic encryption
10. Introduction to Lattice-based Cryptography
11. Post-quantum cryptographic schemes
12. Blockchain and cryptocurrencies
13. Selected topics from modern cryptography