“Quantum cryptography (program of the Faculty of Physics)” - course 12,160 rubles. from MSU, training 15 weeks. (4 months), Date: December 2, 2023.

Professor, leading researcher at the Center for Quantum Technologies, Faculty of Physics, Moscow State University named after M.V. Lomonosov

Position: Professor, Department of Supercomputers and Quantum Information Science, Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University

Lecture 1. A brief excursion into the history of cryptography. What is quantum cryptography and what problems does it solve? Disposable keys. Shannon's criterion of absolute secrecy. Current advances in quantum cryptography.

Lecture 2. Fundamentals of the mathematical apparatus of quantum information science: description of quantum states of individual and composite quantum systems, pure, mixed states, quantum entanglement, orthogonal and generalized measurements, purification of quantum states, the no-copy theorem, transformations of quantum systems, completely positive display.

Lecture 3. Measures of proximity of quantum states used in quantum cryptography protocols.

Lecture 4. Basic protocols of quantum communications and their description: quantum teleportation, ultra-dense coding, quantum key distribution. Main quantum key distribution protocols: BB84, B92, E91, SARG04, phase-time coding, differential phase coding, relativistic quantum distribution of keys through open space with and without clock synchronization at the receiving and transmitting points side.

Lecture 5. Continuation. Basic protocols for quantum key distribution and their implementation.

Lecture 6. Basic concepts of classical information theory. Shannon and Renyi entropies and their properties. Conditional, mutual information, typical sequences, source coding theorems, forward and inverse coding theorems for a noisy channel, capacity

Lecture 7. Continuation – basic concepts of classical information theory. Examples.

Lecture 8. Von Neumann entropy, basic properties and use in quantum information theory. The concept of quantum communication channels. Classical capacity of a quantum communication channel. Individual and collective measurements in quantum cryptography.

Lecture 9. Continued -- Fundamental Holevo bound for the reachable bound of classical information. Multiplicity of eavesdropper attacks, connection of attacks with the capacity of a quantum channel.

Lecture 10. Basic properties of quantum Renyi entropies (min and max entropies). Smoothed min and max entropies, chain rules, changes in min and max entropies under the action of a superoperator, properties of min and max entropies for composite quantum systems.

Lecture 11. Entropy relations of uncertainties in quantum cryptography, connection with min and max Renyi entropies.

Lecture 12. Key secrecy criterion in quantum cryptography based on trace distance. Universal hash functions of the second kind, use in security enhancement procedures. Left over hash Lemma.

Lecture 13. Proof of the secrecy of quantum key distribution using the BB84 protocol as an example, based on entropy uncertainty relations (the case of a strictly single-photon source of information states).

Lecture 14. Analysis of the cryptographic strength of implementations of quantum cryptography systems with non-ideal sources of quantum states, detectors and a quantum communication channel with losses. Attack with splitting by the number of photons, attack with measurements with a certain outcome, transparent attack with a beam splitter.

Lecture 15. Continuation – modification of quantum cryptography protocols taking into account attacks related to the non-strict one-photonity of the source of information states. An example is a method with trap states (Decoy State method).

Lecture 16. Relationship between the quantum security criterion based on the trace distance and the Shannon criterion based on the complexity of key enumeration.

Lecture 17. About quantum random number generators. Sources of quantum randomness, post-processing methods - randomness extraction. Examples of implementation.