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Issue 12, 2025
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International year of quantum science and technology. Reviews of topical problems


Vernam's, Kotelnikov's, and Shannon's one-time pad and quantum cryptography

†  a, ‡  a, b, c, d
a Academy of Cryptography of the Russian Federation, PO Box 100, Moscow, 119331, Russian Federation
b Osipyan Institute of Solid State Physics, Russian Academy of Sciences, Akademika Osip'yana str. 2, Chernogolovka, Moscow Region, 142432, Russian Federation
c Faculty of Computational Mathematics and Cybernetics of Lomonosov Moscow State University, Leninskie Gory 1, build. 52, Moscow, 119991, Russian Federation
d Quantum Technology Center of Lomonosov Moscow State University, Leninskie Gory 1, build. 35, Moscow, 119991, Russian Federation

Quantum cryptography — quantum key distribution (QKD) — was one of the first fields of study of quantum information theory. It reached a mature scientific level and has been implemented in commercial systems for secure quantum communications. The key distribution problem is the central issue of symmetric cryptography. Quantum cryptography solves this problem on the basis of the fundamental laws of nature: the principles of quantum mechanics. Quantum key distribution is essentially matching two independent random sequences on the transmitting and receiving sides by exchanging quantum states. Required in addition to the quantum channel is an authentic classical communication channel. Both communication channels are open and vulnerable to a perpetrator's attack. To ensure the authenticity of the classical channel at initial system startup, a seed key is required, which is used to provide information-theoretic authentication. In essence, quantum cryptography systems are mechanisms for expanding this seed key. Subsequent sessions generate a quantum key, part of which is used for authentication, while another part is employed for other cryptographic purposes, such as encryption. An issue fundamental for quantum cryptography is the number of quantum key distribution sessions that can be conducted from the initial system launch until a new system reboot, when the cryptographic properties of the quantum keys reach a critical level, after which they can no longer be used for cryptographic purposes, and a new system reboot is needed. Although a number of reviews on quantum cryptography are currently available, this issue has not been discussed in detail. It is shown that for realistic parameters of quantum cryptography systems that are currently achievable, a QKD system can operate for virtually any length of time before the next reboot. This implies that QKD systems can implement a 'one-time pad' — a set of one-time keys using only a single seed key. A brief historical overview is also presented, outlining some facts little known to the general public. This review, which is intended for a general audience, is comprehensible to undergraduate and graduate students who have completed university courses on quantum information science. The authors hope that it will provide a deeper understanding of the cryptographic underpinnings of state-of-the-art quantum key distribution systems.

Fulltext pdf (998 KB)
Fulltext is also available at DOI: 10.3367/UFNe.2025.07.039972
Keywords: quantum cryptography, one-time pad, secure communications, authentication
PACS: 03.67.Dd, 03.67.Hk, 89.70.−a (all)
DOI: 10.3367/UFNe.2025.07.039972
URL: https://ufn.ru/en/articles/2025/10/a/
Citation: Arbekov I M, Molotkov S N "Vernam's, Kotelnikov's, and Shannon's one-time pad and quantum cryptography" Phys. Usp. 68 963–986 (2025)
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Received: 13th, January 2025, revised: 28th, July 2025, 28th, July 2025

Оригинал: Арбеков И М, Молотков С Н «Одноразовый блокнот Вернама, Котельникова, Шеннона и квантовая криптография» УФН 195 1021–1046 (2025); DOI: 10.3367/UFNr.2025.07.039972

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