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Journal of Experimental and Theoretical Physics Letters

On a solution to the problem of ensuring the security of quantum cryptography for an infinite communication channel

S. N. Molotkov

Published Aug 1, 2011• 3 citations
Publisher

Abstract

Quantum cryptography involves the fundamental question of the existence of secure protocols of quantum key distribution at any length of a communication channel (at any losses in it). A remarkable feature and novelty of the proposed protocol is that it ensures dual control; first, the intensity of a reference (intense) quantum state is controlled classically before the comparison (measurement) of coherent states from different time windows, and, second, the loss of coherence of a state is detected by interference measurements of an information quantum state and the reference quantum state tested against the conservation of the intensity. Thus, this is the only existing protocol stable to any losses in the communication channel. The length of the communication channel is limited only by dark noise in detectors.

DOI
10.1134/s0021364011120101

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Quantum cryptography involves the fundamental question of the existence of secure protocols of quantum key distribution at any length of a communication channel (at any losses in it). A remarkable feature and novelty of the proposed protocol is that it ensures dual control; first, the intensity of a reference (intense) quantum state is controlled classically before the comparison (measurement) of coherent states from different time windows, and, second, the loss of coherence of a state is detected by interference measurements of an information quantum state and the reference quantum state tested against the conservation of the intensity. Thus, this is the only existing protocol stable to any losses in the communication channel. The length of the communication channel is limited only by dark noise in detectors.
One of the basic results of classical information theory is that error-free information transmission is possible even through an imperfect binary communication channel with noise up to an error of Q c = 1/2. There is a fundamental and applied question of whether quantum-mechanical constraints can ensure error-free classical-information transmission with quantum states and, moreover, guarantee the security of distributed keys up to the theoretical limit in the error Q c. It has been shown that the secure key distribution is possible up to the error Q c in the asymptotic limit of a large number of bases.
The security of cryptographic keys in quantum cryptography systems is guaranteed by fundamental quantum mechanical exclusion principles. A quantum channel through which quantum states are transferred is not controlled and an eavesdropper can perform any modifications with it. The security of quantum key distribution protocols has already been proved [M. Tomamichel et al., Nature Commun. 3 , 634 (2011); S. N. Molotkov, J. Exp. Theor. Phys. 115 , 969 (2012)], including the realistic case of a finite length of transmitted sequences. It is always assumed that the eavesdropper has neither direct nor indirect access to the transmitting and receiving equipment. The real situation is somewhat different. The preparation and detection of quantum states occur according to random sequences that are generated on the transmitter and receiver sides. Detecting electromagnetic radiation generated in these processes, the eavesdropper can obtain additional information on a key. The upper quantum-mechanical bound on the amount of information of the eavesdropper on the key that can be obtained through a side channel has been determined.
Since a source of quantum states is not strictly single-photon and losses exist in a communication channel, an attack with unambiguous measurements is possible, leading to loss of security. The problem of the stability of quantum key distribution protocols in a channel with large losses is still unsolved. A radical solution of this problem has been proposed by completely excluding unambiguous measurements by an eavesdropper. The problem is solved by means of counting of classical reference pulses. The conservation of the number of classical sync pulses results in the impossibility of unambiguous measurements. In this case, losses in the communication channel are considered as a priori unknown and can vary during a series of messages.
Quantum cryptography is an emerging field that ensures secure communication by leveraging principles of quantum mechanics. Unlike classical cryptography methods that rely on mathematical complexity, quantum cryptographic protocols, Quantum Key Distribution (QKD) protocols derive their security from the fundamental laws of physics. Among these, the BB84 protocol is widely recognized for enabling secure key exchange between communicating parties, with any eavesdropping attempts being inherently detectable. The invention of quantum computing poses a significant threat to classical encryption algorithms, and thereby necessitating both post-quantum cryptography and quantum-based approaches. This paper presents a comprehensive overview of quantum cryptography, emphasizing its theoretical principles foundations of quantum cryptography, emphasizing its advantages over traditional encryption methods, implementation challenges, and real-world application. It also outlines the limitations of quantum technology, e.g., hardware limitations and interference by noise, which restrict large-scale application. A detailed comparison between classical, quantum, and hybrid cryptographic approaches is presented to highlight the key advancement, including improved eavesdropping detection, enhanced key generation rates, and security through quantum entanglement. As quantum networks evolve rapidly, quantum cryptography is poised to become a cornerstone of nextgeneration ultra-secure communication systems.
Quantum cryptography was designed to provide a new approach to the problem of distributing keys for private-key cryptography. The principal idea is that security can be ensured by exploiting the laws of quantum physics and, in particular, by the fact that any attempt to measure a quantum state will change it uncontrollably. This change can be detected by the legitimate users of the communication channel and so reveal to them the presence of an eavesdropper. In this paper I explain (briefly) how quantum key distribution works and some of the progress that has been made towards making this a viable technology. With the principles of quantum communication and quantum key distribution firmly established, it is perhaps time to consider how efficient it can be made. It is interesting to ask, in particular, how many bits of information might reasonably be encoded securely on each photon. The use of photons entangled in their time of arrival might make it possible to achieve data rates in excess of 10 bits per photon.