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arXiv:quant-ph/0602113 · Physical Review A

Practical evaluation of security for quantum key distribution

Masahito Hayashi

Published Aug 7, 2006• 66 citations
arXivHTMLPDF

Abstract

Many papers have proven the security of quantum key distribution (QKD) systems in the asymptotic framework. The degree of the security has not been discussed in the finite coding-length framework, sufficiently. However, to guarantee any implemented QKD system required, it is needed to evaluate a protocol with a finite coding length. For this purpose, we derive a tight upper bound of the eavesdropper's information. This bound is better than existing bounds. We also obtain the exponential rate of the eavesdropper's information. Further, we approximate our bound by using the normal distribution.

DOI
10.1103/physreva.74.022307

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Many papers have proven the security of quantum key distribution (QKD) systems in the asymptotic framework. The degree of the security has not been discussed in the finite coding-length framework, sufficiently. However, to guarantee any implemented QKD system required, it is needed to evaluate a protocol with a finite coding length. For this purpose, we derive a tight upper bound of the eavesdropper's information. This bound is better than existing bounds. We also obtain the exponential rate of the eavesdropper's information. Further, we approximate our bound by using the normal distribution.
Quantum key distribution (QKD) enables secure information exchange with untrusted quantum links between remote communication parties. A central task in the studies of QKD protocols is security analysis, which aims at deriving the length of the final key such that it is secure regardless of the eavesdropper's computational power. In literature, the security analysis has been done both analytically and numerically. Compared to analytical methods which tend to require techniques specific to each QKD protocol, numerical ones are more general since they can be directly applied to many QKD protocols with little adaptation. However, current numerical methods are carried out based on some assumptions such as working in the asymptotic limit and collective attacks from eavesdroppers. In this work, we remove these assumptions and develop a numerical finite-size security analysis against general attacks for a large class of QKD protocols. We also give an example of applying the method to the recent phase-matching QKD protocol with a simplified protocol design. Our result shows that the finite-size key rate can surpass the linear key-rate bound with a practical QKD system operated for only several hours.
Decoy state method quantum key distribution (QKD) is one of the promising practical solutions to BB84 QKD with coherent light pulses. In the real world, however, statistical fluctuations with the finite code length cannot be negligible, and the securities of theoretical and experimental researches of the decoy method state QKD so far are based on the asymptotic GLLP's formula which guarantees only that the limit of eavesdropper's information becomes zero as the code length approaches infinity. In this paper, we propose a substantially improved decoy state QKD in the framework of the finite code length and derive the upper bound of eavesdropper's information in the finite code length decoy state QKD with arbitrary number of decoy states of different intensities incorporating the finite statistics. We also show the performance of our decoy QKD and optimal values of parameters by numerical simulation.
Information-theoretical security of quantum key distribution (QKD) has been convincingly proven in recent years and remarkable experiments have shown the potential of QKD for real-world applications. Due to its unique capability of combining high key rate and security in a realistic finite-size scenario, the efficient version of the BB84 QKD protocol endowed with decoy states has been subject of intensive research. Its recent experimental implementation finally demonstrated a secure key rate beyond 1 Mb/s over a 50 km of optical fiber. However, the achieved rate holds under the restrictive assumption that the eavesdropper performs collective attacks. Here, we review the protocol and generalize its security. We exploit a map by Ahrens to rigorously upper bound the hypergeometric distribution resulting from a general eavesdropping. Despite the extended applicability of the new protocol, its key rate is only marginally smaller than its predecessor in all cases of practical interest.
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Due to its ability to tolerate high channel loss, decoy-state quantum key distribution (QKD) has been one of the main focuses within the QKD community. Notably, several experimental groups have demonstrated that it is secure and feasible under real-world conditions. Crucially, however, the security and feasibility claims made by most of these experiments were obtained under the assumption that the eavesdropper is restricted to particular types of attacks or that the finite-key effects are neglected. Unfortunately, such assumptions are not possible to guarantee in practice. In this work, we provide concise and tight finite-key security bounds for practical decoy-state QKD that are valid against general attacks.