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arXiv:1310.7668 · Journal of Physics A Mathematical and Theoretical

Effect of imperfect Faraday mirrors on the security of a Faraday–Michelson quantum cryptography system

Weilong Wang, Ming Yuan Gao, Zhi Ma

Published Oct 24, 2013• 4 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1088/1751-8113/46/45/455301

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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.
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.
Abstract Passive Faraday-mirror (PFM) attack is based on imperfect Faraday mirrors in practical quantum cryptography systems and a set of three-dimensional Positive Operator-Valued Measure (POVM) operators plays an important role in this attack. In this paper, we propose a simple scheme to implement the POVM in PFM attack on an Faraday–Michelson quantum cryptography system. Since the POVM can not be implemented directly with previous methods, in this scheme it needs to expand the states sent by Alice and the POVM operators in the attack into four-dimensional Hilbert space first, without changing the attacking effect by calculation. Based on the methods proposed by Ahnert and Payne, the linear-optical setup for implementing the POVM operators is derived. At last, the complete setup for realizing the PFM attack is presented with all parameters. Furthermore, our scheme can also be applied to realize PFM attack on a plug-and-play system by changing the parameters in the setup.
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.
Passive Faraday-mirror(PFM) attack is based on imperfect Faraday mirrors in practical quantum cryptography systems and a set of three-dimensional Positive Operator-Valued Measure(POVM) operators plays an important role in this attack.In this paper,we propose a simple scheme to implement the POVM in PFM attack on an FaradayMichelson quantum cryptography system.Since the POVM can not be implemented directly with previous methods,in this scheme it needs to expand the states sent by Alice and the POVM operators in the attack into four-dimensional Hilbert space first,without changing the attacking effect by calculation.Based on the methods proposed by Ahnert and Payne,the linear-optical setup for implementing the POVM operators is derived.At last,the complete setup for realizing the PFM attack is presented with all parameters.Furthermore,our scheme can also be applied to realize PFM attack on a plug-and-play system by changing the parameters in the setup.
Quantum key distribution(QKD) is a major research topic because it provides unconditional security. Unfortunately, many imperfections remain in QKD’s experimental realization. The Faraday–Michelson(FM) QKD system is proposed to eliminate these imperfections using polarization. However, the long arm’s phase modulator(PM) has an unexpected insertion loss, meaning that the state sent is no longer perfect. In this letter, we propose an alternative FM-QKD system structure, and analyze the security and key generation rate in comparison with the original system via different analysis methods. We find an obvious key rate improvement when the PM insertion loss is not extremely small.
Quantum key distribution (QKD) is a major research topic because it provides unconditional security.Unfortunately, many imperfections remain in QKD's experimental realization.The Faraday-Michelson (FM) QKD system is proposed to eliminate these imperfections using polarization.However, the long arm's phase modulator (PM) has an unexpected insertion loss, meaning that the state sent is no longer perfect.In this letter, we propose an alternative FM-QKD system structure, and analyze the security and key generation rate in comparison with the original system via different analysis methods.We find an obvious key rate improvement when the PM insertion loss is not extremely small.