Cryptology and Quantum Computing

Course guarantor:

Lecturer:

Tutor:

Supervisor:

Department of Information Security

Synopsis:

The course covers methods and algorithms of cryptology and their relation to quantum computing. In the first introductory lectures, students will be introduced to the basic principles and algorithms of cryptography. Following these topics, students will be introduced to basic cryptanalytic methods. Then some cryptanalytic algorithms running on quantum computers will be presented. In this context, the problem of security of related cryptographic schemes will be discussed. The next lectures will be devoted to post-quantum algorithms. The last lectures deal with cryptosystems using quantum phenomena.

Requirements:

Syllabus of lectures:

1. Security of cryptographic systems, information theory and complexity theory.

2. Symmetric cryptography - block ciphers, operational modes.

3. Symmetric cryptography - stream ciphers.

4. Asymmetric cryptography - DH, RSA, ElGamal, ECC digital signature.

5. Hash functions, random generators.

6. Linear and differential cryptanalysis.

7. Algebraic cryptanalysis, Groebner bases.

8. Grover's algorithm, Shor's algorithm and its relevance to security.

9. Post-quantum cryptography - multivariate cryptography.

10. Post-quantum cryptography - lattice-based cryptography.

11. Post-quantum cryptography - code-based cryptography (McEliece).

12. Protocols BB84, B92 and Ekert protocol, QKD.

13.Quantum authentication and signature.

Syllabus of tutorials:

Not filled yet.

Study Objective:

The course covers methods and algorithms of cryptology and their relation to quantum computing. In the first introductory lectures, students will be introduced to the basic principles and algorithms of cryptography. Following these topics, students will be introduced to basic cryptanalytic methods. Then some cryptanalytic algorithms running on quantum computers will be presented. In this context, the problem of security of related cryptographic schemes will be discussed. The next lectures will be devoted to post-quantum algorithms. The last lectures deal with cryptosystems using quantum phenomena.

Study materials:

1.

Cox, D. A., Little, J., OShea, D.: Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra

Springer 2013, ISBN 978-3-319-16720-6

2.

Peikert, Ch.: A decade of lattice cryptography. Foundations and trends in theoretical computer science 10, no. 4

Foundations and Trends® in Theoretical Computer Science 2016, https://doi.org/10.1561/0400000074

3.

Swenson, Ch.: Modern cryptanalysis: techniques for advanced code breaking

John Wiley & Sons 2008, ISBN 9781118428627

4.

Aumasson, J. P.: Serious Cryptography: A Practical Introduction to Modern Encryption, 2nd Edition

No Starch Press 2024, ISBN 978-1-59327-826-7

5.

Paar, Ch., Pelzl, J., Preneel, B.: Understanding Cryptography: A Textbook for Students and Practitioners, 1st Edition

Springer 2010, ISBN 978-3-642-04100-6

6.

Zeng, G.: Quantum Private Communication

Springer 2010, ISBN 13: 978-3642032950

Note:

Information about the course and teaching materials can be found at https://courses.fit.cvut.cz/QNI-KKP

Further information:

https://courses.fit.cvut.cz/QNI-KKP

No time-table has been prepared for this course

The course is a part of the following study plans:

• Quantum Informatics (compulsory course in the program)