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arXiv:1305.5986 · Physical Review A

Single-photon-detection attack on the phase-coding continuous-variable quantum cryptography

Shi‐Hai Sun, Mu-Sheng Jiang, Lin-Mei Liang

Published Jul 5, 2012• 3 citations
arXivHTMLPDF

Abstract

The phase-coding quantum cryptographic scheme using the homodyne detection and weak coherent state [Hirano et al., Phys. Rev. A 68, 042331 (2003)] provides the simplest continuous-variable quantum key distribution scheme from the experimental side. However, the inherent loss of the practical system will not only increase the bit error rate (BER) but also affect the security of the final key. In this paper, we propose a single-photon-detection attack, and then the security of the final key will be compromised in some parameter regimes. Our results show that the BER induced by Eve can be lower than the inherent BER induced by the loss of the system in some parameter regimes. Furthermore, our attack gives the maximal communication distance of this scheme for given experimental parameters.

DOI
10.1103/physreva.86.012305

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The phase-coding quantum cryptographic scheme using the homodyne detection and weak coherent state [Hirano et al., Phys. Rev. A 68, 042331 (2003)] provides the simplest continuous-variable quantum key distribution scheme from the experimental side. However, the inherent loss of the practical system will not only increase the bit error rate (BER) but also affect the security of the final key. In this paper, we propose a single-photon-detection attack, and then the security of the final key will be compromised in some parameter regimes. Our results show that the BER induced by Eve can be lower than the inherent BER induced by the loss of the system in some parameter regimes. Furthermore, our attack gives the maximal communication distance of this scheme for given experimental parameters.
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Quantum continuous variables (CV) have been explored as an alternative to qubits for quantum key distribution (QKD). More specifically, protocols using coherent states and homodyne or heterodyne measurements have been proposed and experimentally demonstrated (Grosshans et al., 2003). Relying on technologies allowing much higher rates than allowed by the single photon detectors used in qubit based QKD, those protocols are the only ones which could allow key rates in the GHz range in the foreseeable future. Furthermore, their security proofs have recently been extendend to generic attacks in the case of gaussian modulation. However, to our knowledge, all security analyses up to know have implicitely assumed Bob's measurement setup to use a homo- or heterodyne detection with an external classical phase reference, while the experimental realizations use a lightbeam for this role. This beam doesn't carry any information useful to the spy, and any attack on its phase could equally be carried on the signal beam. However, the intensity of this beam is used in experimental implementations to calibrate the quantum noise level. This calibration is then used to determine the channel gain, which is an important parameter of Eve's attack. We show that this allows Eve to implement an intercepte resend attack forbiding QKD as soon as the losses are above 3dB. We also give simple countermeasures to this new class of attacks.
Quantum key distribution is a technique in which secret key bits are encoded into quantum states which are transmitted over a quantum channel, e.g. an optical link, so that the security is guaranteed by the laws of quantum physics. Most experimental realizations to date have relied on discrete protocols, involving ideally single-photons states (or, in practice, strongly attenuated light pulses) as well as single-photon detectors. In this chapter, we present an overview of the recent continuous-variable quantum cryptosystems, which instead rely on continuously-modulated Gaussian states (e.g. coherent states) and homodyne detection. The series of security proofs of these protocols against increasingly powerful attacks will be reviewed. A particular emphasis will be put on the op-timality of Gaussian attacks in this context, which holds provided that the second-order moments of the relevant variables are monitored.
We discuss the unconditional security of a quantum key distribution protocol in which bit values are encoded in the phase of a weak coherent-state pulse relative to a strong reference pulse, which is essentially the one proposed by Bennett in 1992 (the B92 scheme). In the BB84 protocol with a perfect single photon source, the key rate decreases linearly with the transmission η of the channel. If we simply replace this source with a weak coherent-state pulse, the key rate drops more rapidly (as O(η)) since the presence of multiple photons favors the eavesdropper, Eve. The B92 protocol, if modified to be encoded on the polarization of a single photon, also shows O(η) dependence. This comes from Eve’s option of sending the vacuum state, which is always registered as an inconclusive result and never causes bit errors. In the original B92 scheme with phase coding, Eve has no such option replacing the weak pulse by the vacuum cannot avoid errors completely, thanks to the strong reference pulse. This should make the scheme stronger against the loss in the channel even coherent-state pulses from conventional lasers are used. We have obtained an unconditional security proof allowing the presence of small bit errors, and confirmed the above observation in a rigorous way. The key rate is found to drop linearly with the transmission η, and it is lower than the BB84 with a perfect single-photon source only by a constant.
We discuss the unconditional security of a quantum key distribution protocol in which bit values are encoded in the phase of a weak coherent-state pulse relative to a strong reference pulse, which is essentially the one proposed by Bennett in 1992 (the B92 scheme). In the BB84 protocol with a perfect single photon source, the key rate decreases linearly with the transmission T of the channel. If we simply replace this source with a weak coherent-state pulse, the key rate drops more rapidly (as O(η2)) since the presence of multiple photons favors the eavesdropper, Eve. The B92 protocol, if modified to be encoded on the polarization of a single photon, also shows O(η2) dependence. This comes from Eve's option of sending the vacuum state, which is always registered as an inconclusive result and never causes bit errors. In the original B92 scheme with phase coding, Eve has no such option--replacing the weak pulse by the vacuum cannot avoid errors completely, thanks to the strong reference pulse. This should make the scheme stronger against the loss in the channel even coherent-state pulses from conventional lasers are used. We have obtained an unconditional security proof allowing the presence of small bit errors, and confirmed the above observation in a rigorous way. The key rate is found to drop linearly with the transmission η, and it is lower than the BB84 with a perfect single-photon source only by a constant.
We provide a security analysis for continuous variable quantum key distribution protocols based on the transmission of two-mode squeezed vacuum states measured via homodyne detection. We employ a version of the entropic uncertainty relation for smooth entropies to give a lower bound on the number of secret bits which can be extracted from a finite number of runs of the protocol. This bound is valid under general coherent attacks, and gives rise to keys which are composably secure. For comparison, we also give a lower bound valid under the assumption of collective attacks. For both scenarios, we find positive key rates using experimental parameters reachable today.