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Journal of Experimental and Theoretical Physics Letters

Generalization of a Photon Number Splitting Attack and the Efficiency of Its Application to a Subcarrier Wave Quantum Cryptography Protocol

Dmitry Anatolevich Kronberg

Published Jun 1, 2025• 2 citations
Publisher

Abstract

Coherent state quantum cryptography protocols are of interest due to their easy implementation. However, the security proof of such protocols against all attacks can be tricky because of the attenuation in the communication channel that can be exploited by an eavesdropper. In this work, an attack on the subcarrier wave quantum cryptography protocol has been built, which generalizes the photon number splitting attack. The efficiency of the attack has been analyzed, in particular, for the case where the eavesdropper does not have quantum memory.

DOI
10.1134/s002136402560658x

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Coherent state quantum cryptography protocols are of interest due to their easy implementation. However, the security proof of such protocols against all attacks can be tricky because of the attenuation in the communication channel that can be exploited by an eavesdropper. In this work, an attack on the subcarrier wave quantum cryptography protocol has been built, which generalizes the photon number splitting attack. The efficiency of the attack has been analyzed, in particular, for the case where the eavesdropper does not have quantum memory.
Quantum cryptography allows distributing secure keys between two users so that any performed eavesdropping attempt would be immediately discovered. However, in practice an eavesdropper can obtain key information from multi-photon states when attenuated laser radiation is used as a source of quantum states. In order to prevent actions of an eavesdropper, it is generally suggested to implement special cryptographic protocols, like decoy states or SARG04. In this paper, we describe an alternative method based on monitoring photon number statistics after detection. We provide a useful rule of thumb to estimate approximate order of difference of expected distribution and distribution in case of attack. Formula for calculating a minimum value of total pulses or time-gaps to resolve attack is shown. Also formulas for actual fraction of raw key known to Eve were derived. This method can therefore be used with any system and even combining with mentioned special protocols.
Subcarrier wave quantum key distribution systems demonstrate promising capabilities for secure quantum networking. However for this class of devices no implementation of secure decoy states protocol was developed. It leaves them potentially vulnerable to photon-number splitting attacks on quantum channel and limiting the key distribution distance. We propose a practical solution to this problem by calculating the required parameters of light source and modulation indices for signal and decoy states in a subcarrier wave system and describing the corresponding experimental scheme.
In the last ten years, quantum computing has made substantial progress, presenting a strong challenge to traditional encryption methods that depend on solving discrete algorithmic problems. With the advent of the quantum era, conventional encryption methods are becoming more susceptible to attacks. This paper investigates possible attacks that exploit vulnerabilities in quantum cryptography, specifically investigating weaknesses in quantum key distribution (QKD) systems. The text thoroughly explores advanced attack strategies of photon number splitting highlight the existing vulnerabilities. The goal is to highlight the need for strong safeguards to protect against these threats, which requires continuous research and development to improve the robustness of quantum cryptography algorithms. The experimental investigation includes analyzing crucial parameters, including quantum channel length, loss, QKD protocol, quantum bit error rate (QBER), signal-to-noise ratio (SNR), as well as attack parameters such as probability of photon number splitting (PNS), eavesdropper distance, and detection efficiency. The evaluation includes performance indicators such as secure key rate, quantum bit error rate (QBER) vs distance, vulnerability to photon number splitting (PNS) attacks, and the influence on the pace of key generation.
Decoy-state protocols provide a way to defeat photon-number-splitting attacks in quantum cryptography implemented with weak coherent pulses. We point out that previous security analyses of such protocols relied on assumptions about eavesdropping attacks that considered treating each pulse equally and independently. We give an example to demonstrate that, without such assumptions, the security parameters of previous decoy-state implementations could be worse than the ones claimed. Next we consider more general photon-number-splitting attacks, which correlate different pulses, and give an estimation procedure for the number of single-photon signals with rigorous security statements. The impact of our result is that previous analyses of the number of times a decoy-state quantum cryptographic system can be reused before it makes a weak key must be revised.
Abstract The quantum key distribution protocol utilizing 8 geometrically uniform coherent states is considered. We analyze its security against a generalized photon-number-splitting attack. This protocol allows for several basis configurations, and we demonstrate that one of these configurations is more vulnerable. We also use the previously described methods for attack improvement, namely, modification of observable’s coefficients and using extra photon as assistance for increasing success probability.
A new family of two-parameter quantum key distribution protocols is discussed where eavesdropping is detected by using two parameters: bit error rate Q and photon count rate q in control time slots. When a single-photon source is used and mutually orthogonal states are prepared in each basis, the protocol’s maximum tolerable error rate for secure key distribution is the highest, reaching a theoretical upper limit of 50%. When the signal states emitted by the source of attenuated laser light include multiphoton coherent states, the protocol also guarantees secure key distribution over the longest distance as compared to other quantum cryptography systems, up to the channel length for which the channel losses are sufficiently high that all five-photon pulses can be blocked by an eavesdropper.