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arXiv:2312.16206

The Security Analysis of Continuous-Variable Quantum Key Distribution under Limited Eavesdropping with Practical Fiber

Sheng Liu, Lu Fan, Zhengyu Li, Qiang Zhou, Yunbo Li, Dong Wang, Dechao Zhang, Yichen Zhang, Han Li

Published Dec 23, 2023• 2 citations
arXivHTMLPDF

Abstract

Research on optimal eavesdropping models under practical conditions will help to evaluate realistic risk when employing quantum key distribution (QKD) system for secure information transmission. Intuitively, fiber loss will lead to the optical energy leaking to the environment, rather than harvested by the eavesdropper, which also limits the eavesdropping ability while improving the QKD system performance in practical use. However, defining the optimal eavesdropping model in the presence of lossy fiber is difficult because the channel is beyond the control of legitimate partners and the leaked signal is undetectable. Here we investigate how the fiber loss influences the eavesdropping ability based on a teleportation-based collective attack model which requires two distant stations and a shared entanglement source. We find that if the distributed entanglement is limited due to the practical loss, the optimal attack occurs when the two teleportation stations are merged to one and placed close to the transmitter site, which performs similar to the entangling-cloning attack but with a reduced wiretapping ratio. Assuming Eve uses the best available hollow-core fiber, the secret key rate in the practical environment can be 20%~40% higher than that under ideal eavesdropping. While if the entanglement distillation technology is mature enough to provide high quality of distributed entanglement, the two teleportation stations should be distantly separated for better eavesdropping performance, where the eavesdropping can even approach the optimal collective attack. Under the current level of entanglement purification technology, the unavoidable fiber loss can still greatly limit the eavesdropping ability as well as enhance the secret key rate and transmission distance of the realistic system, which promotes the development of QKD systems in practical application scenarios.

DOI
10.48550/arxiv.2312.16206

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Research on optimal eavesdropping models under practical conditions will help to evaluate realistic risk when employing quantum key distribution (QKD) system for secure information transmission. Intuitively, fiber loss will lead to the optical energy leaking to the environment, rather than harvested by the eavesdropper, which also limits the eavesdropping ability while improving the QKD system performance in practical use. However, defining the optimal eavesdropping model in the presence of lossy fiber is difficult because the channel is beyond the control of legitimate partners and the leaked signal is undetectable. Here we investigate how the fiber loss influences the eavesdropping ability based on a teleportation-based collective attack model which requires two distant stations and a shared entanglement source. We find that if the distributed entanglement is limited due to the practical loss, the optimal attack occurs when the two teleportation stations are merged to one and placed close to the transmitter site, which performs similar to the entangling-cloning attack but with a reduced wiretapping ratio. Assuming Eve uses the best available hollow-core fiber, the secret key rate in the practical environment can be 20%~40% higher than that under ideal eavesdropping. While if the entanglement distillation technology is mature enough to provide high quality of distributed entanglement, the two teleportation stations should be distantly separated for better eavesdropping performance, where the eavesdropping can even approach the optimal collective attack. Under the current level of entanglement purification technology, the unavoidable fiber loss can still greatly limit the eavesdropping ability as well as enhance the secret key rate and transmission distance of the realistic system, which promotes the development of QKD systems in practical application scenarios.
Research on optimal eavesdropping models under practical conditions will help to evaluate realistic risk when employing a quantum key distribution system for secure information transmission. Intuitively, fiber loss will lead to the optical energy leaking to the environment, rather than harvested by the eavesdropper, which also limits the eavesdropping ability while improving the quantum key distribution system performance in practical use. However, defining the optimal eavesdropping model in the presence of lossy fiber is difficult because the channel is beyond the control of legitimate partners and the leaked signal is undetectable. Here we investigate how the fiber loss influences the eavesdropping ability based on a teleportation-based collective attack model, which requires two distant stations and a shared entanglement source. We find that if the distributed entanglement is limited due to the practical loss, the optimal attack occurs when the two teleportation stations are merged to one and placed close to the transmitter site, which performs similar to the entangling-cloning attack but with a reduced wiretapping ratio. Assuming Eve uses the best available hollow-core fiber, the secret key rate in the practical environment can be 20--40% higher than that under ideal eavesdropping. While if the entanglement distillation technology is mature enough to provide high quality of distributed entanglement, the two teleportation stations should be distantly separated for better eavesdropping performance, where the eavesdropping can even approach the optimal collective attack. Under the current level of entanglement purification technology, the unavoidable fiber loss can still greatly limit the eavesdropping ability as well as enhance the secret key rate and transmission distance of the realistic system, which promotes the development of quantum key distribution systems in practical application scenarios.
We develop a physical model to describe the signal transmission for a continuous-variable quantum key distribution scheme and investigate its security against a couple of eavesdropping attacks assuming that the eavesdropper’s power is partly restricted owing to today’s technological limitations. We consider an eavesdropper performing quantum optical homodyne measurement on the signal obtained by a type of beamsplitting attack. We also consider the case in which the eavesdropper Eve is unable to access a quantum memory and she performs heterodyne measurement on her signal without performing a delayed measurement. Our formulation includes a model in which the receiver’s loss and noise are unaccessible by the eavesdropper. This setup enables us to investigate the condition that Eve uses a practical fiber differently from the usual beamsplitting attack where she can deploy a lossless transmission channel. The secret key rates are calculated in both the direct and reverse reconciliation scenarios.
In Gaussian quantum key distribution eavesdropping attacks are conventionally modeled through the universal entangling cloner scheme, which is based on the premise that the whole environment is under control of the adversary, i.e., the eavesdropper purifies the system.This assumption implies that the eavesdropper has either access to an identity (noiseless) channel or an infinite amount of entanglement in order to simulate such an identity channel.In this work we challenge the necessity of this assumption and we propose a teleportation-based eavesdropping attack, where the eavesdropper is not assumed to have access to the shared channel, that represents the unavoidable noise due to the environment.Under collective measurements, this attack reaches optimality in the limit of an infinite amount of entanglement, while for finite entanglement resources it outperforms the corresponding optimal individual attack.We also calculate the minimum amount of distributed entanglement that is necessary for this eavesdropping scheme, since we consider it as the operationally critical quantity capturing the limitations of a realistic attack.We conclude that the fact that an infinite amount of entanglement is required for an optimal collective eavesdropping attack signifies the robustness of Gaussian quantum key distribution.
Quantum cryptography provides absolute security against an all-powerful eavesdropper (Eve). However, in practice Eve's resources may be restricted to a limited aperture size so that she cannot collect all paraxial light without alerting the communicating parties (Alice and Bob). In this paper we study a quantum wiretap channel in which the connection from Alice to Eve is lossy, so that some of the transmitted quantum information is inaccessible to both Bob and Eve. For a pureloss channel under such restricted eavesdropping, we show that the key rates achievable with a two-mode squeezed vacuum state, heterodyne detection, and public classical communication assistance-given by the Hashing inequality-can exceed the secret key distillation capacity of the channel against an omnipotent eavesdropper. We report upper bounds on the key rates under the restricted eavesdropping model based on the relative entropy of entanglement, which closely match the achievable rates. For the pure-loss channel under restricted eavesdropping, we compare the secret-key rates of continuous-variable (CV) quantum key distribution (QKD) based on Gaussian-modulated coherent states and heterodyne detection with the discrete variable (DV) decoystate BB84 QKD protocol based on polarization qubits encoded in weak coherent laser pulses.
The theory of quantum cryptography aims to guarantee unconditional information-theoretic security against an omnipotent eavesdropper. In many practical scenarios, however, the assumption of an all-powerful adversary is excessive and can be relaxed considerably. In this paper we study secret-key distillation across a lossy and noisy quantum wiretap channel between Alice and Bob, with a separately parameterized realistically lossy quantum channel to the eavesdropper Eve. We show that under such restricted eavesdropping, the key rates achievable can exceed the secret-key-distillation capacity against an unrestricted eavesdropper in the quantum wiretap channel. Furthermore, we show upper bounds on the key rates based on the relative entropy of entanglement. This simple restricted eavesdropping model is widely applicable, for example, to free-space quantum optical communication, where realistic collection of light by Eve is limited by the finite size of her optical aperture. Future work will include calculating bounds on the amount of light Eve can collect under various realistic scenarios.
Quantum cryptographic protocols are typically analyzed by assuming that potential opponents can carry out all physical operations, an assumption which grants capabilities far in excess of present technology. Adjusting this assumption to reflect more realistic capabilities is an attractive prospect, but one that can only be justified with a rigorous, quantitative framework that relates adversarial restrictions to the protocol's security and performance. We investigate the effect of limitations on the eavesdropper's (Eve's) ability to make a coherent attack on the security of continuous-variable quantum key distribution (CV-QKD). We consider a realistic attack in which the total decoherence induced during the attack is modeled by a Gaussian channel. Based on our decoherence model, we propose an optimal hybrid attack, which allows Eve to perform a combination of both coherent and individual attacks simultaneously. We evaluate the asymptotic and composable finite-size security of a heterodyne CV-QKD protocol against such hybrid attacks in terms of Eve's decoherence. We show that when the decoherence is greater than a threshold value, Eve's most effective strategy is reduced to the individual attack. Thus, if we are willing to assume that the decoherence caused by the memory and the collective measurement is large enough, it is sufficient to analyze the security of the protocol only against individual attacks, which significantly improves the CV-QKD performance in terms of both the key rate and maximum secure transmission distance.