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arXiv:quant-ph/0508112 · Physical Review A

Security of differential-phase-shift quantum key distribution against individual attacks

Edo Waks A, Hiroki Takesue, Y. Yamamoto

Published Jan 31, 2006• 127 citations
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Abstract

We derive a proof of security for the differential-phase-shift quantum key distribution protocol under the assumption that Eve is restricted to individual attacks. The security proof is derived by bounding the average collision probability, which leads directly to a bound on Eve's mutual information on the final key. The security proof applies to realistic sources based on pulsed coherent light. We then compare individual attacks to sequential attacks and show that individual attacks are more powerful.

DOI
10.1103/physreva.73.012344

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We derive a proof of security for the differential-phase-shift quantum key distribution protocol under the assumption that Eve is restricted to individual attacks. The security proof is derived by bounding the average collision probability, which leads directly to a bound on Eve's mutual information on the final key. The security proof applies to realistic sources based on pulsed coherent light. We then compare individual attacks to sequential attacks and show that individual attacks are more powerful.
Differential phase shift quantum key distribution systems have a high potential for achieving high speed key generation. However, its unconditional security proof is still missing, even though it has been proposed for many years. Here, we prove its security against collective attacks with a weak coherent light source in the noiseless case (i.e., no bit error). The only assumptions are that quantum theory is correct, the devices are perfect and trusted and the key size is infinite. Our proof works on threshold detectors. We compute the lower bound of the secret key generation rate using the information-theoretical security proof method. Our final result shows that the lower bound of the secret key generation rate per pulse is linearly proportional to the channel transmission probability if Bob's detection counts obey the binomial distribution.
Differential phase shift quantum key distribution systems have a high potential for achieving high speed key generation. However, its unconditional security proof is still missing, even though it has been proposed for many years. Here, we prove its security against collective attacks with a weak coherent light source in the noiseless case (i.e. no bit error). The only assumptions are that quantum theory is correct, the devices are perfect and trusted and the key size is infinite. Our proof works on threshold detectors. We compute the lower bound of the secret key generation rate using the information‐theoretical security proof method. Our final result shows that the lower bound of the secret key generation rate per pulse is linearly proportional to the channel transmission probability if Bob’s detection counts obey the binomial distribution.
Quantum key distribution is the art of sharing secret keys between two distant parties, and has attracted a lot of attention due to its unconditional security. Compared with other quantum key distribution protocols, the differential phase shift quantum key distribution protocol has higher efficiency and simpler apparatus. Unfortunately, the unconditional security of differential phase shift quantum key distribution has not been proved. Utilizing the sharp continuity of the von Neuman entropy and some basic inequalities, we estimate the upper bound for the eavesdropper Eve's information. We then prove the lower bound for the security of the differential phase shift quantum key distribution protocol against a one-pulse attack with Devatak—Winter's secret key rate formula.
In this paper, we discuss the security of the differential-phase-shift quantum-key-distribution (DPSQKD) protocol by introducing an improved version of the so-called sequential attack, which was originally discussed by Waks et al. [Phys. Rev. A 73, 012344 (2006)]. Our attack differs from the original form of the sequential attack in that the attacker Eve modulates not only the phases but also the amplitude in the superposition of the single-photon states which she sends to the receiver. Concentrating especially on the ``discretized Gaussian'' intensity modulation, we show that our attack is more effective than the individual attack, which had been the best attack up to present. As a result of this, the recent experiment with communication distance of 100km100\phantom{\rule{0.3em}{0ex}}\mathrm{km}100km reported by Diamanti et al. [Opt. Express 14, 13073 (2006)] turns out to be insecure. Moreover, it can be shown that in a practical experimental setup which is commonly used today, the communication distance achievable by the DPSQKD protocol is less than 95km95\phantom{\rule{0.3em}{0ex}}\mathrm{km}95km.
In this paper, we investigate limitations imposed by sequential attacks on the performance of a differential-phase-shift (DPS) quantum key distribution (QKD) protocol with weak coherent pulses. Specifically, we analyze a sequential attack based on optimal unambiguous discrimination of the relative phases between consecutive signal states emitted by the source. We show that this attack can provide tighter upper bounds for the security of a DPS QKD scheme than those derived from sequential attacks where the eavesdropper aims to identify the state of each signal emitted by the source unambiguously.
In this paper we present limitations imposed by sequential attacks on the maximal distance achievable by a differential‐phase‐shift (DPS) quantum key distribution (QKD) protocol with weak coherent pulses. Specifically, we compare the performance of two possible sequential attacks against DPS QKD where Eve realizes, respectively, optimal unambiguous state discrimination of Alice’s signal states, and optimal unambiguous discrimination of the relative phases between consecutive signal states. We show that the second eavesdropping strategy provides tighter upper bounds for the security of a DPS QKD scheme than the former one.