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QUANTUM NETWORKS: KEY DISTRIBUTION VIA UNTRUSTED NODES

S. P. Kulik, S. N. Molotkov

Published Jan 1, 2025• 1 citation
Publisher

Abstract

The aim of the research is to analyze the secrecy of quantum key distribution through untrusted nodes in quantum networks. Research method: the use of entropy uncertainty relations. Result(s) of the study: the secrecy of quantum key distribution through untrusted nodes in quantum networks is proved. The use of entropy uncertainty relations makes it possible to obtain an accurate solution for the length of the secret key in the single-photon case. A comparison with the exact solution for the BB84 protocol is made and the fundamental difference in the logical structure of proof of the secrecy of keys in these protocols is clearly shown, which, in our opinion, is important for the development of quantum cryptography systems. Scientific novelty: the article proves the secrecy of quantum key distribution through untrusted nodes in quantum networks.

DOI
10.21681/2311-3456-2025-3-90-98

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Abstract A proof of the secrecy of the quantum key distribution through an untrusted node is given. The use of entropy uncertainty relations allows us to obtain an exact solution for the length of the secret key in the single-photon case. Comparison with the exact solution for the BB84 protocol is made and the principal difference in the logical structure of the key secrecy proofs in these protocols is clearly shown, which, in our opinion, is important for the development of quantum cryptography systems.
The proposed article is devoted to the analysis of quantum key distribution protocols based on the Heisenberg uncertainty. The peculiarity of this topic lies in the fact that modern methods of key distribution, which use classical calculations at their core, have significant drawbacks, in contrast to quantum key distribution. This problem concerns all types of algorithms and systems for encrypting secret information, both symmetric encryption with a private key and asymmetric encryption with a public key. An example is that in a communication channel protected by quantum key distributions, it is possible to detect an interceptor between two legal network entities using the principles laid down in quantum physics at the beginning of the last century. Principles and theorems such as the Heisenberg principle, quantum entanglement, superposition, quantum teleportation, and the no-cloning theorem. The field of study of this topic is a promising and rapidly developing area in the field of information security and information protection. There are already created commercial products with the implementation of some of the quantum key distribution protocols. Many of the created products are used in various spheres of human activity. The relevance of applying quantum key distribution protocols under ideal conditions without taking into account errors in the form of quantum noise is analyzed. The implementation of two quantum key distribution protocols based on the Heisenberg uncertainty principle is demonstrated, as well as the results of the appearance of keys and the probability of occurrence of each of them. The purpose of the article is aimed at analyzing and researching quantum key distribution protocols based on Heisenberg uncertainty. The article discusses the advantages and disadvantages of the BB84, B92 quantum key distribution protocols.
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Abstract Basic configuration in quantum cryptography is a point-to-point quantum key distribution. In networks with quantum key distribution, the keys received on different network segments are different. For information encryption between arbitrary network nodes it is necessary to have agreement of the keys distributed in different segments of network through a public classical communication channel. The secrecy criterion for keys independently distributed in different network segments is formulated in terms of the trace distance. These are the so-called ε –secret keys. The paper deals with the issue of the secrecy of the agreed keys. We propose the method of secret keys agreement in which the agreement of two ε 1 , ε 2 –secret keys distributed in different segments leads to a common ( ε 1 + ε 2 ) –secret key. It is shown that in order to agreed common key will be ε –secret, it is sufficient that the keys on the individual segments are ε /2–secret.