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arXiv:quant-ph/0411041 · Physical Review A

Intercept-resend attacks in the Bennett-Brassard 1984 quantum-key-distribution protocol with weak coherent pulses

Marcos Curty, Norbert Lütkenhaus

Published Jun 1, 2005• 46 citations
arXivHTMLPDF

Abstract

Unconditional security proofs of the Bennett-Brassard 1984 protocol of quantum key distribution have been obtained recently. These proofs cover also practical implementations that utilize weak coherent pulses in the four signal polarizations. Proven secure rates leave open the possibility that new proofs or new public discussion protocols will obtain larger rates over increased distance. In this paper we investigate limits to the error rate and signal losses that can be tolerated by future protocols and proofs.

DOI
10.1103/physreva.71.062301

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Unconditional security proofs of the Bennett-Brassard 1984 protocol of quantum key distribution have been obtained recently. These proofs cover also practical implementations that utilize weak coherent pulses in the four signal polarizations. Proven secure rates leave open the possibility that new proofs or new public discussion protocols will obtain larger rates over increased distance. In this paper we investigate limits to the error rate and signal losses that can be tolerated by future protocols and proofs.
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.
We prove the security of the Bennett-Brassard (BB84) quantum key distribution protocol in the case where the key information is encoded in the relative phase of a coherent-state reference pulse and a weak coherent-state signal pulse, as in some practical implementations of the protocol. In contrast to previous work, our proof applies even if the eavesdropper knows the phase of the reference pulse, provided that this phase is not modulated by the source, and even if the reference pulse is bright. The proof also applies to the case where the key is encoded in the photon polarization of a weak coherent-state pulse with a known phase, but only if the phases of the four BB84 signal states are judiciously chosen. The achievable key generation rate scales quadratically with the transmission in the channel, just as for BB84 with phase-randomized weak coherent-state signals (when decoy states are not used). For the case where the phase of the reference pulse is strongly modulated by the source, we exhibit an explicit attack that allows the eavesdropper to learn every key bit in a parameter regime where a protocol using phase-randomized signals is provably secure.
Quantum key distribution (QKD) protocols are cryptographic techniques with security based only on the laws of quantum mechanics. Two prominent QKD schemes are the Bennett-Brassard 1984 and Bennett 1992 protocols that use four and two quantum states, respectively. In 2000, Phoenix et al. proposed a new family of three-state protocols that offers advantages over the previous schemes. Until now, an error rate threshold for security of the symmetric trine spherical code QKD protocol has been shown only for the trivial intercept-resend eavesdropping strategy. In this Letter, we prove the unconditional security of the trine spherical code QKD protocol, demonstrating its security up to a bit error rate of 9.81%. We also discuss how this proof applies to a version of the trine spherical code QKD protocol where the error rate is evaluated from the number of inconclusive events.
The analysis is based on the error rate and the secure communication rate as functions of distance for three quantum-key-distribution (QKD) protocols: the Bennett–Brassard 1984, the Bennett–Brassard–Mermin 1992, and the coherent differential-phase-shift keying (DPSK) protocols. We consider the secure communication rate of the DPSK protocol against an arbitrary individual attack, including the most commonly considered intercept-resend and photon-number splitting attacks, and concluded that the simple and efficient differential-phase-shift-keying protocol allows for more than 200 km of secure communication distance with high communication rates.
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.