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arXiv:quant-ph/0012078 · Physical Review A

Security of quantum key distribution with entangled photons against individual attacks

Edo Waks A, Assaf J. Zeevi, Y. Yamamoto

Published Apr 25, 2002• 260 citations
arXivHTMLPDF

Abstract

We investigate the security of quantum key distribution with entangled photons, focusing on the two-photon variation of the Bennett-Brassard 1984 (BB84) protocol proposed in 1992 by Bennett, Brasard, and Mermin (BBM92). We present a proof of security which applies to realistic sources, and to untrustable sources which can be placed outside the labs of the two receivers. The proof is restricted to individual eavesdropping attacks, and assumes that the detection apparatus is trustable. We find that the average collision probability for the BBM92 protocol is the same as that of the BB84 protocol with an ideal single-photon source. This indicates that there is no analog in BBM92 to photon splitting attacks, and that the source can be placed between the two receivers without changing the form of the collision probability. We then compare the communication rate of both protocols as a function of distance, and show that BBM92 has potential for much longer communication distances, up to 170 km, in the presence of realistic experimental imperfections. Finally, we propose a scheme based on entanglement swapping that can lead to even longer distance communication. The limiting factor in this scheme is the channel loss, which imposes very slow communication rates at longer distances.

DOI
10.1103/physreva.65.052310

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We investigate the security of quantum key distribution with entangled photons, focusing on the two-photon variation of the Bennett-Brassard 1984 (BB84) protocol proposed in 1992 by Bennett, Brasard, and Mermin (BBM92). We present a proof of security which applies to realistic sources, and to untrustable sources which can be placed outside the labs of the two receivers. The proof is restricted to individual eavesdropping attacks, and assumes that the detection apparatus is trustable. We find that the average collision probability for the BBM92 protocol is the same as that of the BB84 protocol with an ideal single-photon source. This indicates that there is no analog in BBM92 to photon splitting attacks, and that the source can be placed between the two receivers without changing the form of the collision probability. We then compare the communication rate of both protocols as a function of distance, and show that BBM92 has potential for much longer communication distances, up to 170 km, in the presence of realistic experimental imperfections. Finally, we propose a scheme based on entanglement swapping that can lead to even longer distance communication. The limiting factor in this scheme is the channel loss, which imposes very slow communication rates at longer distances.
Quantum key distribution with the Bennett-Brassard 1984 protocol has been shown to be unconditionally secure even using weak coherent pulses instead of single-photon signals. The distances that can be covered by these methods are limited due to the loss in the quantum channel (e.g., loss in the optical fiber) and in the single-photon counters of the receivers. One can argue that the loss in the detectors cannot be changed by an eavesdropper in order to increase the covered distance. Here we show that the security analysis of this scenario is not as easy as is commonly assumed, since already two-photon processes allow eavesdropping strategies that outperform the known photon-number splitting attack. For this reason there is, so far, no satisfactory security analysis available in the framework of individual attacks.
Abstract The single-photon detectionefficiency of the detector unit is crucial for the security of common quantum key distribution protocols like Bennett-Brassard 1984 (BB84). A low value for the efficiency indicates a possible eavesdropping attack that exploits the photon receiver’s imperfections. We present a method for estimating the detection efficiency, and calculate the corresponding secure key generation rate. The estimation is done by testing gated detectors using a randomly activated photon source inside the receiver unit. This estimate gives a secure rate for any detector with non-unity single-photon detection efficiency, both inherit or due to blinding. By adding extra optical components to the receiver, we make sure that the key is extracted from photon states for which our estimate is valid. The result is a quantum key distribution scheme that is secure against any attack that exploits detector imperfections.
We compare the performance of Bennett-Brassard 1984 (BB84) and Scarani-Acin-Ribordy-Gisin 2004 (SARG04) protocols, the latter of which was proposed by V. Scarani et al. [Phys. Rev. Lett. 92, 057901 (2004)]. Specifically, in this paper, we investigate the SARG04 protocol with two-way classical communications and the SARG04 protocol with decoy states. In the first part of the paper, we show that the SARG04 scheme with two-way communications can tolerate a higher bit error rate (19.4% for a one-photon source and 6.56% for a two-photon source) than the SARG04 one with one-way communications (10.95% for a one-photon source and 2.71% for a two-photon source). Also, the upper bounds on the bit error rate for the SARG04 protocol with two-way communications are computed in a closed form by considering an individual attack based on a general measurement. In the second part of the paper, we propose employing the idea of decoy states in the SARG04 scheme to obtain unconditional security even when realistic devices are used. We compare the performance of the SARG04 protocol with decoy states and the BB84 one with decoy states. We find that the optimal mean-photon number for the SARG04 scheme is higher than that of the BB84 one when the bit error rate is small. Also, we observe that the SARG04 protocol does not achieve a longer secure distance and a higher key generation rate than the BB84 one, assuming a typical experimental parameter set.
We prove the security of the Bennett-Brassard (BB84) quantum key distribution protocol in the case where the source and detector are under the limited control of an adversary. Our proof applies when both the source and the detector have small basis-dependent flaws, as is typical in practical implementations of the protocol. We derive a general lower bound on the asymptotic key generation rate for weakly basis-dependent eavesdropping attacks, and also estimate the rate in some special cases: sources that emit weak coherent states with random phases, detectors with basis-dependent efficiency, and misaligned sources and detectors.
The quantum key distribution protocol BB84, published by C. H. Bennett and G. Brassard in 1984, describes how two spatially separated parties can generate a random bit string fully known only to them by transmission of single-qubit quantum states. Any attempt to eavesdrop on the protocol introduces disturbance which can be detected by the legitimate parties. In this Master's Thesis a novel modification to the BB84 protocol is analyzed. Instead of sending single particles one-by-one as in BB84, they are grouped and a non-local transformation is applied to each group before transmission. Each particle is sent to the intended receiver, always delaying the transmission until the receiver has acknowledged the previous particle on an authenticated classical channel, restricting eavesdropping to accessing the quantum transmission one particle at a time. Hence, an eavesdropper cannot undo the non-local transformation perfectly. Even if perfect cloning of quantum states was possible the state of the group could not be cloned. We calculate the maximal information on the established key provided by an intercept-resend attack and the induced disturbance for different transformations. We observe that it is possible to significantly reduce the eavesdropper's maximal information on the key--to one eighth of that in BB84 for a fixed, reasonable amount of disturbance. We also show that the individual access to the particles poses a fundamental restriction to the eavesdropper, and discuss a novel attack type against the proposed protocol.