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arXiv:1701.04168 · Physical Review A

Finite-key analysis for quantum key distribution with weak coherent pulses based on Bernoulli sampling

Shun Kawakami, Toshihiko Sasaki, Masato Koashi

Published Jul 5, 2017• 4 citations
arXivHTMLPDF

Abstract

An essential step in quantum key distribution is the estimation of parameters related to the leaked amount of information, which is usually done by sampling of the communication data. When the data size is finite, the final key rate depends on how the estimation process handles statistical fluctuations. Many of the present security analyses are based on the method with simple random sampling, where hypergeometric distribution or its known bounds are used for the estimation. Here we propose a concise method based on Bernoulli sampling, which is related to binomial distribution. Our method is suitable for the Bennett-Brassard 1984 (BB84) protocol with weak coherent pulses [C. H. Bennett and G. Brassard, Proceedings of the IEEE Conference on Computers, Systems and Signal Processing (IEEE, New York, 1984), Vol. 175], reducing the number of estimated parameters to achieve a higher key generation rate compared to the method with simple random sampling. We also apply the method to prove the security of the differential-quadrature-phase-shift (DQPS) protocol in the finite-key regime. The result indicates that the advantage of the DQPS protocol over the phase-encoding BB84 protocol in terms of the key rate, which was previously confirmed in the asymptotic regime, persists in the finite-key regime.

DOI
10.1103/physreva.96.012305

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An essential step in quantum key distribution is the estimation of parameters related to the leaked amount of information, which is usually done by sampling of the communication data. When the data size is finite, the final key rate depends on how the estimation process handles statistical fluctuations. Many of the present security analyses are based on the method with simple random sampling, where hypergeometric distribution or its known bounds are used for the estimation. Here we propose a concise method based on Bernoulli sampling, which is related to binomial distribution. Our method is suitable for the Bennett-Brassard 1984 (BB84) protocol with weak coherent pulses [C. H. Bennett and G. Brassard, Proceedings of the IEEE Conference on Computers, Systems and Signal Processing (IEEE, New York, 1984), Vol. 175], reducing the number of estimated parameters to achieve a higher key generation rate compared to the method with simple random sampling. We also apply the method to prove the security of the differential-quadrature-phase-shift (DQPS) protocol in the finite-key regime. The result indicates that the advantage of the DQPS protocol over the phase-encoding BB84 protocol in terms of the key rate, which was previously confirmed in the asymptotic regime, persists in the finite-key regime.
Quantum key distribution (QKD) allows two distant parties to share a secret key and realizes a communication with information-theoretic security by combining it with one-time-pad encryption.Since the Bennett-Brassard 1984 (BB84) protocol was proposed, a large number of researches on QKD have been conducted from both aspects of theory and implementations.For implementations of QKD, weak coherent pulses (WCP) are heavily used as optical signals because they are easily generated by typical lasers and attenuators.The security for QKD with WCP has been also studied along the development of the implementations.In this thesis, the security analysis of the QKD with WCP is considered and further developed from two aspects.First, the security of the differential-quadrature-phase-shift (DQPS) protocol is proved.The DQPS protocol has essentially the same set up as the phase-encoding BB84 (PE-BB84) protocol, which is one of the most frequently demonstrated protocols.Since the known proof techniques for the BB84 protocol is not directly applicable, a modified approach is developed which is suitable for the DQPS protocol.As a result, the advantage of the DQPS protocol in the key generation rate over the PE-BB84 protocol is shown in the asymptotic limit where the size of communication data is assumed to be infinite.Second, a new method for security analysis with finite-key size is proposed as a suitable method for QKD protocols using WCP.Differently from the current method based on simple random sampling, the proposed method relies on Bernoulli sampling, which is associated with binomial distribution.The security of the BB84 protocol is proved by using the Bernoulli-sampling method, enabling a simpler analysis with a smaller number of parameters to be estimated compared to the method with simple random sampling.The required number of detected signals to generate a secret key is shown to be smaller than 10 4 , which is drastic improvement from the number ∼ 10 7 obtained in the previous result.The proposed method is also applied to the DQPS protocol, and its advantage over the PE-BB84 protocol is certified even in the finite-key regime.i
One of the simplest methods for implementing quantum key distribution over fiber-optic communication is the Bennett-Brassard 1984 protocol with phase encoding (PE-BB84 protocol), in which the sender uses phase modulation over double pulses from a laser and the receiver uses a passive delayed interferometer. Using essentially the same setup and by regarding a train of many pulses as a single block, one can carry out the so-called differential-quadrature-phase-shift (DQPS) protocol, which is a variant of differential-phase-shift (DPS) protocols. Here we prove the security of the DQPS protocol based on an adaptation of proof techniques for the BB84 protocol, which inherits the advantages arising from the simplicity of the protocol, such as accommodating the use of threshold detectors and simple off-line calibration methods for the light source. We show that the secure key rate of the DQPS protocol in the proof is eight-thirds as high as the rate of the PE-BB84 protocol.
Abstract Quantum key distribution (QKD) is a secure communication method that relies on the inherent randomness of quantum mechanics to ensure information-theoretic security. The first and most widely used QKD protocol is BB84, and the proof of BB84's security is vital. The Discrete Phase Randomized BB84 protocol is a variant of the decoy BB84 protocol. It has been proven to be promising in the development of high-speed QKD systems. However, it still lacks an analysis with a finite number of pulses. This paper presents a comprehensive security analysis of the discrete phase BB84 protocol, using two different methods under different conditions. The analysis involves simulations and optimizations to determine the optimal parameter settings. It is confirmed that for typical scenarios, if the number of discrete phases exceeds 30, one can calculate the key rate by assuming that a continuous phase randomization process was in operation. On the other hand, for a relatively smaller number of discrete values, we have developed a numerical method to calculate the key rate. We have confirmed that its performance is reduced but still acceptable with a finite number of pulses.
This paper presents a quantum key distribution (QKD) protocol named differential-quadrature-phase-shift (DQPS) QKD. A transmitter sends a coherent pulse train in which each pulse is phase modulated by ${0,\ensuremath{\pi}}$ ${\ensuremath{\pi}/2,3\ensuremath{\pi}/2}$, and a receiver measures it with either one of two asymmetric Mach-Zehnder interferometers having phase biases of 0 and $\ensuremath{\pi}/2$, respectively. This scheme is devised such that the idea of the conventional Bennett-Brassard 1984 protocol (BB84) is introduced to differential-phase-shift (DPS) QKD. Simulations show that the proposed scheme is robust against a sequential attack that is crucial eavesdropping to DPS-QKD.
We present a tight security analysis of the Bennett–Brassard 1984 protocol taking into account the finite-size effect of key distillation and achieving unconditional security. We begin by presenting a concise analysis utilizing the normal approximation of the hypergeometric function. Next we show that a similar tight bound can also be obtained by a rigorous argument without relying on any approximation. In particular, for the convenience of experimentalists who wish to evaluate the security of their quantum key distribution systems, we also give the explicit procedures of our key distillation and show how to calculate the secret key rate and the security parameter from a given set of experimental parameters. In addition to the exact values of key rates and security parameters, we also describe how to obtain their rough estimates using the normal approximation.
A quantum key distribution (QKD) scheme named differential-quadrature-phase-shift (DQPS) QKD is presented. A transmitter sends a weak coherent pulse train with a phase of {0, π}{ π/2. 3π /2} for each pulse, and a receiver measures it with either one of two delay interferometers respectively having bias phases of 0 and π/2. The scheme introduces the idea of the BB84 protocol into differential-phase-shift (DPS) QKD, making the system robust against a sequential attack, and may guarantee the unconditional security as in BB84.