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).

Lecturers
Kronberg Dmitry Anatolevich
Trushechkin Anton Sergeevich

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