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Laser Physics Letters

Security analysis of continuous-variable quantum key distribution with imperfect Faraday mirror

Kexin Liang, Zhengwen Cao, Weiqi Liu, Jiayao Wang, Geng Chai, Tongyi Zhang

Published Oct 17, 2019• 2 citations
Publisher

Abstract

Abstract For the practical Faraday mirror (FM) in a continuous-variable quantum key distribution (CVQKD) system there exists a rotation angle deviation that can lead to a loss of photon number when a light message passes through the polarization beam splitter. Here we employ the entanglement-based model to research the influence of the FM’s imperfection. Based on parameter estimation, the imperfection can introduce a loophole for Eve to obtain information. The secret key rate of the CVQKD will be impaired. Finally, a novel method is proposed to ensure system performance by compensating optical power, and we further study the relationship between the secret key rate and the modulation variance.

DOI
10.1088/1612-202x/ab4995

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Abstract For the practical Faraday mirror (FM) in a continuous-variable quantum key distribution (CVQKD) system there exists a rotation angle deviation that can lead to a loss of photon number when a light message passes through the polarization beam splitter. Here we employ the entanglement-based model to research the influence of the FM’s imperfection. Based on parameter estimation, the imperfection can introduce a loophole for Eve to obtain information. The secret key rate of the CVQKD will be impaired. Finally, a novel method is proposed to ensure system performance by compensating optical power, and we further study the relationship between the secret key rate and the modulation variance.
The influence of imperfect Faraday mirror on secret key rate of continuous variable quantum key distribution system in reverse reconciliation is considered with theoretical analysis and numerical simulation.It takes entanglement based scheme.It′s found that Faraday mirror′s imperfection reduces the secret key rate and transmission distance of system.The impact increases if the imperfection turns more serious.Besides it finds using great modulation variance can reduce the impact of Faraday mirror significantly.
In a practical continuous-variable quantum key distribution (CVQKD) system, the optical amplifier can be used to improve the performance of the system by compensating for the imperfections of the detectors. However, the eavesdropper Eve can actively utilize a reverse external magnetic field to deteriorate the performance of the optical amplifier, which may affect the practical security of the system. In this paper, we investigate the practical security of a CVQKD system with an optical amplifier under the effect of the reverse external magnetic field. Based on the investigation of the parameter estimation under the above influence, we find that the evaluation of the secret key rate may be overestimated, which will open a security loophole for Eve to successfully launch an intercept-resend attack in the practical CVQKD system with an optical amplifier. In order to close this security loophole, we can monitor the reverse external magnetic field or change the type of the optical isolator to make the secret key rate of the system evaluated exactly.
The Faraday mirror (FM) plays a very important role in maintaining the stability of two-way plug-and-play quantum key distribution (QKD) systems. However, the practical FM is imperfect, which will not only introduce an additional quantum bit error rate (QBER) but also leave a loophole for Eve to spy the secret key. In this paper we propose a passive Faraday mirror attack in two-way QKD system based on the imperfection of FM. Our analysis shows that if the FM is imperfect, the dimension of Hilbert space spanned by the four states sent by Alice is three instead of two. Thus Eve can distinguish these states with a set of Positive Operator Valued Measure (POVM) operators belonging to three-dimension space, which will reduce the QBER induced by her attack. Furthermore, a relationship between the degree of the imperfection of FM and the transmittance of the practical QKD system is obtained. The results show that the probability that Eve loads her attack successfully depends on the degree of the imperfection of FM rapidly, but the QBER induced by Eve's attack changes slightly with the degree of the FM imperfection.
The one-way Faraday–Michelson system is a very useful practical quantum cryptography system where Faraday mirrors (FMs) play an important role. In this paper we analyze the security of this system against imperfect FMs. We consider the security loophole caused by imperfect FMs in Alice’s and Bob’s security zones. Then we implement a passive FM attack in this system. By changing the values of the imperfection parameters of Alice’s FMs, we calculate the quantum bit error rate between Alice and Bob induced by Eve and the probability that Eve obtains outcomes successfully. It is shown that the imperfection of one of Alice’s two FMs makes the system sensitive to an attack. Finally we give a modified key rate as a function of the FM imperfections. The security analysis indicates that both Alice’s and Bob’s imperfect FMs can compromise the secure key.
In a practical continuous-variable quantum key distribution (CVQKD) system, the optical attenuator can adjust the Gaussian-modulated coherent states and the local oscillator signal to an optimal value for guaranteeing the security of the system and optimizing the performance of the system. However, the performance of the optical attenuator may deteriorate due to the intentional and unintentional damage of the device. In this paper, we investigate the practical security of a CVQKD system with reduced optical attenuation. We find that the secret key rate of the system may be overestimated based on the investigation of parameter estimation under the effects of reduced optical attenuation. This opens a security loophole for Eve to successfully perform an intercept-resend attack in a practical CVQKD system. To close this loophole, we add an optical fuse at Alice's output port and design a scheme to monitor the level of optical attenuation in real time, which can make the secret key rate of the system evaluated precisely. The analysis shows that these countermeasures can effectively resist this potential attack.
Abstract Ideal randomness is one of most important conditions for the implementation of continuous-variable quantum key distribution (CVQKD). However, imperfect randomness may exist in a practical CVQKD system due to imperfections in Gaussian modulation or in random-number generators. Here we propose a weak randomness attack model in practical CVQKD systems to investigate the practical performance of the systems with imperfect randomness, where the prepared coherent states based on nonrandom state modulation are assumed to be known by Eve. Then, we perform parameter estimation and calculate the secret key rate of the system based on the proposed attack model. The simulation results demonstrate that a small imperfect randomness can dramatically reduce the secret key rate of the system, which may seriously limit the practical performance of the system. Therefore, true random numbers and perfect Gaussian modulation are key for practical CVQKD systems.