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Course by A. S. Trushechkin and D. A. Kronberg "Mathematical foundations of quantum cryptography"
September 8–December 22, 2020, Steklov Mathematical Institute, Room. 213 (8 Gubkina)

Quantum cryptography is a modern branch of science where methods of secure communication based on principles of quantum mechanics are studied. Unlike traditional cryptography, in which this problem is solved by means of mathematical transformations of the information, quantum cryptography is based on impossibility (in general) of reading of the information from a quantum information carrier without introducing a noise into it. This makes it possible to detect the fact of eavesdropping before the secure message is transmitted.

Despite the simplicity of this principle, the rigorous proof of the security of quantum cryptography (more precisely, quantum key distribution) requires a complex and beautiful mathematical theory, which is based on theory of discrimination of quantum states, theory of quantum entanglement, theory of quantum error correction (in particular, the fundamental role is played by the so-called phase errors, which are non-classical), quantum entropic measures, in particular entropic uncertainty relations. The aim of this course is to get knowledge to participants about these methods.

Knowledge of mathematical analysis, linear algebra, probability theory is required. Knowledge of quantum mechanics is optional.

The course does not aim at acquaintance with all variety of modern directions in quantum cryptography: with various protocols, problems of practical implementations, etc. The course is restricted to the most widely used (and historically the first) quantum key distribution BB84 protocol (including cases of imperfect devices), but these methods are also applicable to security analysis of other protocols.

After the course, the students will understand the basic methods of security analysis if quantum key distribution protocols, will be able to apply these methods and will understand modern papers devoted to these issues.

Financial support. The course is supported by the Ministry of Science and Higher Education of the Russian Federation (the grant to the Steklov International Mathematical Center, Agreement no. 075-15-2019-1614).

Program

RSS: Forthcoming seminars

Lecturers
Kronberg Dmitry Anatolevich
Trushechkin Anton Sergeevich

Institutions
Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
Steklov International Mathematical Center


Course by A. S. Trushechkin and D. A. Kronberg "Mathematical foundations of quantum cryptography", September 8–December 22, 2020

December 22, 2020 (Tue)
1. Lecture 16. Mathematical foundations of quantum cryptography
A. S. Trushechkin, D. A. Kronberg
December 22, 2020 18:00, Steklov Mathematical Institute, Room. 213 (8 Gubkina)
A. S. Trushechkin, D. A. Kronberg
  

December 15, 2020 (Tue)
2. Lecture 15. Mathematical foundations of quantum cryptography
A. S. Trushechkin, D. A. Kronberg
December 15, 2020 18:00, Steklov Mathematical Institute, Room. 213 (8 Gubkina)
A. S. Trushechkin, D. A. Kronberg
  

December 8, 2020 (Tue)
3. Lecture 14. Mathematical foundations of quantum cryptography
A. S. Trushechkin, D. A. Kronberg
December 8, 2020 18:00, Steklov Mathematical Institute, Room. 213 (8 Gubkina)
A. S. Trushechkin, D. A. Kronberg
  

December 1, 2020 (Tue)
4. Lecture 13. Mathematical foundations of quantum cryptography
A. S. Trushechkin, D. A. Kronberg
December 1, 2020 18:00, Steklov Mathematical Institute, Room. 213 (8 Gubkina)
A. S. Trushechkin, D. A. Kronberg
  

November 24, 2020 (Tue)
5. Lecture 12. Mathematical foundations of quantum cryptography
A. S. Trushechkin, D. A. Kronberg
November 24, 2020 18:00, Steklov Mathematical Institute, Room. 213 (8 Gubkina)
A. S. Trushechkin, D. A. Kronberg
  

November 17, 2020 (Tue)
6. Lecture 11. Mathematical foundations of quantum cryptography
A. S. Trushechkin, D. A. Kronberg
November 17, 2020 18:00, Steklov Mathematical Institute, Room. 213 (8 Gubkina)
A. S. Trushechkin, D. A. Kronberg
  

November 10, 2020 (Tue)
7. Lecture 10. Mathematical foundations of quantum cryptography
A. S. Trushechkin, D. A. Kronberg
November 10, 2020 18:00, Steklov Mathematical Institute, Room. 213 (8 Gubkina)
A. S. Trushechkin, D. A. Kronberg
  

November 3, 2020 (Tue)
8. Lecture 9. Mathematical foundations of quantum cryptography
A. S. Trushechkin, D. A. Kronberg
November 3, 2020 18:00, Steklov Mathematical Institute, Room. 213 (8 Gubkina)
A. S. Trushechkin, D. A. Kronberg
  

October 27, 2020 (Tue)
9. Lecture 8. Mathematical foundations of quantum cryptography
A. S. Trushechkin, D. A. Kronberg
October 27, 2020 18:00, Steklov Mathematical Institute, Room. 213 (8 Gubkina)
A. S. Trushechkin, D. A. Kronberg
  

October 20, 2020 (Tue)
10. Lecture 7. Mathematical foundations of quantum cryptography
A. S. Trushechkin, D. A. Kronberg
October 20, 2020 18:00, Steklov Mathematical Institute, Room. 213 (8 Gubkina)
A. S. Trushechkin, D. A. Kronberg
  

October 13, 2020 (Tue)
11. Lecture 6. Mathematical foundations of quantum cryptography
A. S. Trushechkin, D. A. Kronberg
October 13, 2020 18:00, Steklov Mathematical Institute, Room. 213 (8 Gubkina)
A. S. Trushechkin, D. A. Kronberg
  

October 6, 2020 (Tue)
12. Lecture 5. Mathematical foundations of quantum cryptography
A. S. Trushechkin, D. A. Kronberg
October 6, 2020 18:00, Steklov Mathematical Institute, Room. 213 (8 Gubkina)
A. S. Trushechkin, D. A. Kronberg
  

September 29, 2020 (Tue)
13. Lecture 4. Mathematical foundations of quantum cryptography
A. S. Trushechkin, D. A. Kronberg
September 29, 2020 18:00, Steklov Mathematical Institute, Room. 213 (8 Gubkina)
A. S. Trushechkin, D. A. Kronberg
  

September 22, 2020 (Tue)
14. Lecture 3. Mathematical foundations of quantum cryptography
A. S. Trushechkin, D. A. Kronberg
September 22, 2020 18:00, Steklov Mathematical Institute, Room. 213 (8 Gubkina)
A. S. Trushechkin, D. A. Kronberg
  

September 15, 2020 (Tue)
15. Lecture 2. Mathematical foundations of quantum cryptography
A. S. Trushechkin, D. A. Kronberg
September 15, 2020 18:00, Steklov Mathematical Institute, Room. 213 (8 Gubkina)
A. S. Trushechkin, D. A. Kronberg
  

September 8, 2020 (Tue)
16. Lecture 1. Mathematical foundations of quantum cryptography
A. S. Trushechkin, D. A. Kronberg
September 8, 2020 18:00, Steklov Mathematical Institute, Room. 213 (8 Gubkina)
A. S. Trushechkin, D. A. Kronberg
  
 
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