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arXiv:0807.0767 · Quantum Information and Computation

Security of quantum key distribution with bit and basis dependent detector flaws

Lars Lydersen, Johannes Skaar

Published Jan 1, 2010• 32 citations
arXivHTMLPDF

Abstract

We consider the security of the Bennett-Brassard 1984 (BB84) protocol for Quantum Key Distribution (QKD), in the presence of bit and basis dependent detector flaws. We suggest a powerful attack that can be used in systems with detector efficiency mismatch, even if the detector assignments are chosen randomly by Bob. A security proof is provided, valid for any basis dependent, possibly lossy, linear optical imperfections in the channel/receiver/detectors. The proof does not assume the so-called squashing detector model.

DOI
10.26421/qic10.1-2-5

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We consider the security of the Bennett-Brassard 1984 (BB84) protocol for Quantum Key Distribution (QKD), in the presence of bit and basis dependent detector flaws. We suggest a powerful attack that can be used in systems with detector efficiency mismatch, even if the detector assignments are chosen randomly by Bob. A security proof is provided, valid for any basis dependent, possibly lossy, linear optical imperfections in the channel/receiver/detectors. The proof does not assume the so-called squashing detector model.
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.
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.
This paper 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. This proof applies when both the source and the detector have small basis-dependent flaws, as is typical in practical implementations of the protocol. The estimation of the key generation rate in some special cases: sources that emit weak coherent states, detectors with basis-dependent efficiency, and misaligned sources and detectors.
The rules of quantum mechanics makes it possible to exchange a secret key at a distance. This is called quantum key distribution (QKD). In theory the key exchange can be made completely secure. Real QKD implementations however, has numerous imperfections. Luckily one has also been able to prove the security of QKD with a large variety of imperfections. The field of QKD has matured over the recent years, and it has now reached commercial applications with photons as the quantum bits, and optical fibers as the quantum channel. Today there are at least three commercial vendors of QKD-systems. We live in the times of quantum hacking. Researchers has begun the task of breaking the security of QKD-systems. Many new imperfections has been discovered, some of which might be used to break the security of QKD. This thesis is a study of the detector efficiency mismatch loophole. Most QKD-systems require two detectors, and it is virtually impossible to make two identical detectors with the exact same efficiency. What is worse, it turns out that the eavesdropper can often control the relative efficiencies of the two detectors trough some domain, for instance by controlling the timing, the frequency or the spacial mode of the photons. This can in turn be used by the eavesdropper to gain information about the secret key. Previously the best known attack would compromise security if the detector efficiency mismatch of about 1:15. Here the current attacks on systems with detector efficiency mismatch are improved to compromise security for a mismatch of about 1:4. This is less than the mismatch found in a commercial QKD-system, so the attack could in principle be used to eavesdrop on this QKD-system. One might try to close the loophole by modifying the implementation. One suggestion is the four state Bob. The problem is that this patch will in turn open other loopholes, and one of these loopholes reopen the detector efficiency mismatch loophole. One can remove Eves information about the key by doing a sufficient amount of extra privacy amplification. Here a general security bound is presented, quantifying the required amount of extra privacy amplification to remove Eve's information about the key. The proof is more general than the previous security proof, and is valid for any basis dependent, possibly lossy, linear optical imperfections in the channel and receiver/detectors. Since this is more realistic assumptions for a QKD-implementation, the proof represents a major step of closing the loophole in real devices.
The Bennett-Brassard 1984 (BB84) protocol is the most widely implemented quantum key distribution (QKD) scheme. However, despite enormous theoretical and experimental efforts in the past decades, the security of this protocol with imperfect sources has not yet been rigorously established. In this paper, we address this shortcoming and prove the security of the BB84 protocol in the presence of multiple source imperfections, including state preparation flaws and side channels, such as Trojan-horse attacks, mode dependencies and classical correlations between the emitted pulses. To do so, we consider a modified BB84 protocol that exploits the basis mismatched events, which are often discarded in standard security analyses of this scheme; and employ the reference technique, a powerful mathematical tool to accommodate source imperfections in the security analysis of QKD. Moreover, we compare the achievable secret-key rate of the modified BB84 protocol with that of the three-state loss-tolerant protocol, and show that the addition of a fourth state, while redundant in ideal conditions, significantly improves the estimation of the leaked information in the presence of source imperfections, resulting in a better performance. This paper demonstrates the relevance of the BB84 protocol in guaranteeing implementation security, taking us a step further towards closing the existing gap between theory and practice of QKD.
Quantum key distribution (QKD) protocol has been proved to provide unconditionally secure key between two remote legitimate users in theory. Key distribution signals are transmitted in a quantum channel which is established by the calibration process to meet the requirement of high count rate and low error rate. All QKD security proofs implicitly assume that the quantum channel has been established securely. However, the eavesdropper may attack the calibration process to break the security assumption of QKD and provide precondition to steal information about the final key successfully. In this paper, we reveal the security risk of the calibration process of a passive-basis-choice BB84 QKD system by launching a quantum man-in-the-middle attack which intercepts all calibration signals and resends faked ones. Large temporal bit-dependent or basis-dependent detector efficiency mismatch can be induced. Then we propose a basis-dependent detector efficiency mismatch (BEM) based faked states attack on a single photon BB84 QKD to stress the threat of BEM. Moreover, the security of single photon QKD systems with BEM is studied simply and intuitively. Two effective countermeasures are suggested to remove the general security risk of the calibration process.