Xiang-Bin Wang, Cheng-Zhi Peng, Jun Zhang, Jian-Wei Pan
We show the unconditional security of decoy-state method quantum cryptography with whatever intensity error pattern provided that the error is not too large. Our result immediately applies to the existing experimental data. Our result is not limitted to coherent states.
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Experimental one-way decoy pulse quantum key distribution running continuously for 60 hours is demonstrated over a fiber distance of 20km. We employ a decoy protocol which involves one weak decoy pulse and a vacuum pulse. The obtained secret key rate is on average over 10kbps. This is the highest rate reported using this decoy protocol over this fiber distance and duration.
We analyse the finite-size security of the efficient Bennett-Brassard 1984 protocol implemented with decoy states and apply the results to a gigahertz-clocked quantum key distribution system. Despite the enhanced security level, the obtained secure key rates are the highest reported so far at all fibre distances.
Quantum key distribution establishes a secret string of bits between two distant parties. Of concern in weak laser pulse schemes is the especially strong photon number splitting attack by an eavesdropper, but the decoy state method can detect this attack with current technology, yielding a high rate of secret bits. In this Letter, we develop rigorous security statements in the case of finite statistics with only a few decoy states, and we present the results of simulations of an experimental setup of a decoy state protocol that can be simply realized with current technology.
Decoy-state protocols provide a way to defeat photon-number splitting attacks in quantum cryptography implemented with weak coherent pulses. We point out that previous security analyses of such protocols relied on assumptions about eavesdropping attacks that considered treating each pulse equally and independently. We give an example to demonstrate that, without such assumptions, the security parameters of previous decoy-state implementations could be worse than the ones claimed. Next we consider more general photon-number splitting attacks, which correlate different pulses, and give an estima…
This paper provides a formula for the sacrifice bit-length for privacy amplification with the Bennett-Brassard 1984 protocol for finite key lengths when we employ the decoy method. Using the formula, we can guarantee the security parameter for realizable quantum key distribution system. The key generation rates with finite key lengths are numerically evaluated. The proposed method improves the existing key generation rate even in the asymptotic setting.
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 cod…
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 pro…
We propose the improved decoy state quantum key distribution incorporating finite statistics due to the finite code length and report on its demonstration. In our experiment, four different intensities including the vacuum state for optimal pulses are used and the key generation rate of 200 bps is achieved in the 20 km telecom optical fiber transmission keeping the eavesdropper's mutual information with the final key less than 2^{-9}.
The decoy-state method is a standard enhancement to quantum key distribution (QKD) protocols that has enabled countless QKD experiments with inexpensive light sources. However, new technological advancements might require further theoretical study of this technique. In particular, the decoy-state method is typically described under the assumption of a Poisson statistical distribution for the number of photons in each QKD pulse. This is a practical choice, because prepare-and-measure QKD is often implemented with attenuated lasers, which produce exactly this distribution. However, sources that …
Quantum cryptography or, more precisely, quantum key distribution (QKD), is one of the advanced areas in the field of quantum technologies. The confidentiality of keys distributed with the use of QKD protocols is guaranteed by the fundamental laws of quantum mechanics. This paper is devoted to the decoy state method, a countermeasure against vulnerabilities caused by the use of coherent states of light for QKD protocols whose security is proved under the assumption of single-photon states. We give a formal security proof of the decoy state method against all possible attacks. We compare two wi…
Protocol-level description and self-contained security proof of decoy-state BB84 QKD protocol
本文提出诱骗态BB84 QKD协议的流程图描述，并在通用可组合框架内给出自包含的信息论安全性证明，严格论证了密钥率及正确性和保密性参数，推动QKD系统正式认证。
Improved security bounds against the Trojan-Horse attack in decoy-state quantum key distribution
针对量子特洛伊木马攻击，提出一种数值方法以改进诱骗态QKD系统的安全界，显著提升最终密钥和传输距离，为实际系统安全提供新工具。
In this paper, security of practically decoy state quantum key distribution under fake state attack is considered. If quantum key distribution is insecure under this type of attack, decoy sources can not also provide it with enough security. Strictly analysis shows that Eve should eavesdrop with the aid of photon-number-resolving instruments. In practical implementation of decoy state quantum key distribution where statistical fluctuation is considered, however, Eve can attack it successfully with threshold detectors.
Security of the decoy-state BB84 protocol with imperfect state preparation
本研究分析了在不完美强度和偏振调制导致源缺陷的情况下，高效诱骗态BB84量子密钥分发协议的安全性，并探讨了非泊松光子数统计与基依赖性，且得到了实验表征支持。
Finite-key security analysis of the decoy-state BB84 QKD with passive measurement
本文提出有限密钥下基于被动测量的诱骗态BB84 QKD协议的安全性证明，推导出闭合形式的秘密密钥率公式，并通过模拟验证被动测量不影响密钥生成效率。
Finite-key security analysis of decoy-state QKD with source and detector imperfections
提出一种综合解析有限密钥安全性证明，同时考虑发射器和接收器的多种实际缺陷，包括态制备缺陷、比特和基矢侧信道泄漏与相关性、设置无关强度波动及探测效率失配。
The BB84 quantum key distribution (QKD) combined with decoy-state method is currently the most practical protocol, which has been proved secure against general attacks in the finite-key regime. Thereinto, statistical fluctuation analysis methods are very important in dealing with finite-key effects, which directly affect secret key rate, secure transmission distance and even the most important security. There are two tasks of statistical fluctuation in decoy-state BB84 QKD. One is the deviation between expected value and observed value for a given expected value or observed value. The other is…
A rigorous and complete security proof of decoy-state BB84 quantum key distribution
本文提出了一种通用框架，用于严格证明decoy-state BB84 QKD协议的安全性，并整合了多种QKD安全分析技术。
To beat PNS attack, decoy state quantum key distribution (QKD) based on coherent state has been studied widely. We present a decoy state QKD protocol with modified coherent state (MCS). By destruction quantum interference, MCS with fewer multi-photon events can be get, which may improve key bit rate and security distance of QKD. Through numerical simulation, we show about 2-dB increment on security distance for BB84 protocol.
Quantum key distribution (QKD) promises provably secure communications. In order to improve the secret key rate, combining a biased basis choice with the decoy-state method is proposed. Concomitantly, there is a basis-independent detection efficiency condition, which usually cannot be satisfied in a practical system, such as the time-phase encoding. Fortunately, this flaw has been recently removed theoretically and experimentally using the fact that the expected yields of single-photon states prepared in two bases stay the same for a given measurement basis. However, the security proofs do not…
Security formulas of quantum key distribution (QKD) with imperfect resources are obtained for finite-length code when the decoy method is applied. This analysis is useful for guaranteeing the security of implemented QKD systems. Our formulas take into account the effect of the vacuum state and dark counts in the detector. We compare the asymptotic key generation rate in presence of dark counts with that without.
Security of decoy-state quantum key distribution with correlated intensity fluctuations
本文针对诱骗态QKD中强度相关性导致的安全性证明难题，提出将Cauchy-Schwarz约束与细粒度诱骗态分析相结合的方法，显著提升密钥率并使可达到距离翻倍，同时证明精确表征强度波动相关性可接近理想密钥率。
In quantum key distribution, measurement-device-independent and decoy-state techniques enable the two cooperative agents to establish a shared secret key using imperfect measurement devices and weak Poissonian sources, respectively. Investigations so far are not comprehensive as they restrict to less than or equal to four decoy states. Moreover, many of them involves pure numerical studies. Here I report a general security proof that works for any fixed number of decoy states and any fixed raw key length. The two key ideas involved here. The first one is the repeated application of the inversi…
Twin-Field quantum key distribution (TF-QKD) and its variants, e.g. Phase-Matching QKD, Sending-or-not-sending QKD, and No Phase Post-Selection TFQKD promise high key rates at long distance to beat the rate distance limit without a repeater. The security proof of these protocols are based on decoy-state method, which is usually performed by actively modulating a variable optical attenuator together with a random number generator in practical experiments, however, active-decoy schemes like this may lead to side channel and could open a security loophole. To enhance the source security of TF-QKD…
In this work, we incorporate decoy-state analysis into a well-established numerical framework for key rate calculation, and apply the numerical framework to decoy-state BB84 and measurement-device-independent (MDI) QKD protocols as examples. Additionally, we combine with these decoy-state protocols what is called "fine-grained statistics", which is a variation of existing QKD protocols that makes use of originally discarded data to get a better key rate. We show that such variations can grant protocols resilience against any unknown and slowly changing rotation along one axis, similar to refer…
A consolidated and accessible security proof for finite-size decoy-state quantum key distribution
本文提供了一个严谨且全面的安全性证明，针对有限大小1诱骗态和2诱骗态BB84协议，解决了之前工作中关于固定长度处理和接受测试处理的重要技术问题，统一了多个工作的概念，深入讨论了底层假设并解决了技术不一致问题。
Quantum Key Distribution (QKD) is an innovative quantum communications protocol which exploits the laws of quantum mechanics to generate unconditionally secure cryptographic keying material between two geographically separated parties. The unique nature of QKD shows promise for high-security applications such as those found in banking, government, and military environments. However, QKD systems contain implementation non-idealities which can negatively impact their performance and security.In particular, QKD systems often employ the decoy state protocol to improve system throughput and mitigat…
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 Mbps over a 50 km optical fiber. However the achieved rate holds under the restrictive assumpt…
The performance of a QKD implementation is determined by the tightness of the underlying security analysis. In particular, the security analyses determines the key-rate, i.e., the amount of cryptographic key material that can be distributed per time unit. Nowadays, the security analyses of various QKD protocols are well understood. It is known that optimal protocol parameters, such as the number of decoy states and their intensities, can be found by solving a nonlinear optimization problem. The complexity of this optimization problem is typically handled by making an number of heuristic assump…
Quantum key distribution (QKD) utilizes the laws of quantum mechanics to achieve information-theoretically secure key generation. This field is now approaching the stage of commercialization, but many practical QKD systems still suffer from security loopholes due to imperfect devices. In fact, practical attacks have successfully been demonstrated. Fortunately, most of them only exploit detection-side loopholes which are now closed by the recent idea of measurement-device-independent QKD. On the other hand, little attention is paid to the source which may still leave QKD systems insecure. In th…
UAV-Deployed OAM-BB84 QKD: Turbulence- and Misalignment-Resilient Decoy-State Finite-Key Security with AI-Assisted Calibration
本研究提出了一种基于无人机的OAM-BB84量子密钥分发方案，通过AI辅助校准提高湍流和对准抗性，实现更高效的安全密钥率。
Decoy state quantum key distribution (QKD) has been proposed as a novel approach to improve dramatically both the security and the performance of practical QKD set-ups. Recently, many theoretical efforts have been made on this topic and have theoretically predicted the high performance of decoy method. However, the gap between theory and experiment remains open. In this paper, we report the first experiments on decoy state QKD, thus bridging the gap. Two protocols of decoy state QKD are implemented: one-decoy protocol over 15km of standard telecom fiber, and weak+vacuum protocol over 60km of s…
Security of decoy-state quantum key distribution with correlated bit-and-basis encoders
本文提出一种有限密钥安全性证明，针对一般相干攻击，考虑了Alice比特-基编码引入的相关性，仅部分表征相关性以提升实际应用的安全性。
There has been much interest in quantum key distribution. Experimentally, quantum key distribution over 150 km of commercial Telecom fibers has been successfully performed. The crucial issue in quantum key distribution is its security. Unfortunately, all recent experiments are, in principle, insecure due to real-life imperfections. Here, we propose a method that can for the first time make most of those experiments secure by using essentially the same hardware. Our method is to use decoy states to detect eavesdropping attacks. As a consequence, we have the best of both worlds--enjoying uncondi…
Rényi security framework against coherent attacks applied to decoy-state QKD
本文提出了一个适用于相干攻击下固定和可变长度QKD协议的有限尺寸安全性证明框架，通过引入夹心条件Rényi熵评估等新数值技术，实现了更广的适用范围和更优的密钥率，特别是在小块尺寸下表现突出。
We present a general theorem for the efficient verification of the lower bound of single-photon transmittance. We show how to do decoy-state quantum key distribution efficiently with large random errors in the intensity control. In our protocol, the linear terms of fluctuation disappear and only the quadratic terms take effect. We then show the unconditional security of decoy-state method with whatever error pattern in intensities of decoy pulses and signal pulses provided that the intensity of each decoy pulse is less than $μ$ and the intensity of each signal pulse is larger than $μ'$.
Quantum key distribution (QKD) is a technology that allows two users to exchange keys securely. The decoy state technique enhances the technology, ensuring keys can be shared at high bit rates over long distances with information theoretic security. However, imperfections in the implementation, known as side-channels, threaten the perfect security of practical QKD protocols. Intensity modulators are required for high-rate decoy state QKD systems, although these are unstable and can display a side channel where the intensity of a pulse is dependent on the previous pulse. Here we demonstrate the…
The decoy state protocol has been considered to be one of the most important methods to protect the security of quantum key distribution (QKD) with a weak coherent source. Here we test two experimental approaches to generating the decoy states with different intensities: modulation of the pump current of a semiconductor laser diode, and external modulation by an optical intensity modulator. The former approach shows a side-channel in the time domain that allows an attacker to distinguish s signal state from a decoy state, breaking a basic assumption in the protocol. We model a photon-number-sp…
Photon number resolving detectors can enhance the performance of many practical quantum cryptographic setups. In this paper, we employ a simple method to estimate the statistics provided by such a photon number resolving detector using only a threshold detector together with a variable attenuator. This idea is similar in spirit to that of the decoy state technique, and is specially suited for those scenarios where only a few parameters of the photon number statistics of the incoming signals have to be estimated. As an illustration of the potential applicability of the method in quantum communi…
Secure key rate of decoy-state quantum key distribution protocols has been improved with biased basis choice, however, the security standards and parameters of current protocols are different. As a result, we cannot give an accurate key rate comparison between different kinds of protocols. Taking the schemes based on different formula of secure key rate as examples, we give a fair comparison between typical protocols under universal composable security standard. Through analyzing the relationship of security parameters in post-processing stage and final secure key, we achieve the unified quant…
Twin-Field (TF) quantum key distribution (QKD) represents a novel QKD approach whose principal merit is to beat the point-to-point private capacity of a lossy quantum channel, thanks to performing single-photon interference in an untrusted node. Indeed, recent security proofs of various TF-QKD type protocols have confirmed that the secret key rate of these schemes scales essentially as the square root of the transmittance of the channel. Here, we focus on the TF-QKD protocol introduced by Curty et al, whose secret key rate is nearly an order of magnitude higher than previous solutions. Its sec…
Improved finite-size effects in QKD protocols with applications to decoy-state QKD
本文通过精细化集中不等式和改进二阶修正项，提出了更紧致的QKD有限尺寸安全性证明，并将其应用于诱骗态BB84协议及相干攻击场景。
In recent years, there has been a great effort to prove the security of quantum key distribution (QKD) with a minimum number of assumptions. Besides its intrinsic theoretical interest, this would allow for larger tolerance against device imperfections in the actual implementations. However, even in this device-independent scenario, one assumption seems unavoidable, that is, the presence of a protected space devoid of any unwanted information leakage in which the legitimate parties can privately generate, process and store their classical data. In this paper we relax this unrealistic and hardly…
We simulate quantum key distribution (QKD) experimental setups and give out some improvement for QKD procedures. A new data post-processing protocol is introduced, mainly including error correction and privacy amplification. This protocol combines the ideas of GLLP and the decoy states, which essentially only requires to turn up and down the source power. We propose a practical way to perform the decoy state method, which mainly follows the idea of Lo's decoy state. A new data post-processing protocol is then developed for the QKD scheme with the decoy state. We first study the optimal expecte…
We report here a complete experimental realization of one-way decoy-pulse quantum key distribution, demonstrating an unconditionally secure key rate of 5.51 kbps for a 25.3 km fibre length. This is two orders of magnitudes higher than the value that can be obtained with a non-decoy system. We introduce also a simple test for detecting the photon number splitting attack and highlight that it is essential for the security of the technique to fully characterize the source and detectors used.
We analyze the security of the efficient two-party quantum private comparison protocol with decoy photons and two-photon entanglement. It is shown that the compromised third party (TP) can obtain the final comparison result without introducing any detectable errors in the standard semi-honest model. The attack strategy is discussed in detail and an improvement of this protocol is demonstrated. The idea of our attack might be instructive for the cryptanalysis of quantum cryptographic schemes.
The measurement-device-independent quantum key distribution (MDI-QKD) possesses the highest security among all practical quantum key distribution protocols. However, existing multi-intensity decoy-state methods may cause loopholes when modulating light intensities with practical devices. In this paper, we propose a passive decoy-state MDI-QKD protocol based on a novel structure of heralded single-photon sources. It does not need to modulate the light source into different intensities and thus can avoid leaking modulation information of decoy states to eavesdroppers, enhancing the security of p…
Decoy State Quantum Key Distribution (QKD), being capable of beating PNS attack and uncon- ditionally secure, have become an attractive one recently. But, in many QKD systems, disturbances of transmission channel make quantum bit error rate (QBER) increase which limits both security distance and key bit rate of real-life decoy state QKD systems. We demonstrate the two-intensity decoy QKD with one-way Faraday-Michelson phase modulation system, which is free of channel dis- turbance and keeps interference fringe visibility (99%) long period, near 130KM single mode optical fiber in telecom (1550 …
The decoy-state method is widely used in practical quantum key distribution systems to replace ideal single photon sources with realistic light sources by varying intensities. Instead of active modulation, the passive decoy-state method employs built-in decoy states in a parametric down-conversion photon source, which can decrease the side channel information leakage in decoy state preparation and hence increase the security. By employing low dark count up-conversion single photon detectors, we have experimentally demonstrated the passive decoy-state method over a 50-km-long optical fiber and …
From Received Power to Certified Secret Keys: A General Method for Bridging Classical FSO Link Budgets and Decoy-State QKD
本文提出一种通用接口，将经典自由空间光链路预算与诱骗态量子密钥分发相连接，实现从接收功率到可认证密钥的转换，并通过数值模拟给出不同大气条件下的性能预测。
Imperfect Phase-Randomisation and Generalised Decoy-State Quantum Key Distribution
该研究将诱骗态分析推广至不完美相位随机化激光源，并开发理论工具证明独立非同分布脉冲协议的安全性，定量展示其对关键速率的影响。
Analytical bounds for decoy-state quantum key distribution with discrete phase randomization
本研究推导了在离散相位随机化设置下BB84和测量设备无关QKD协议的密钥生成率分析界限，以提高安全性证明的效率。
Twin-field quantum key distribution (TF-QKD), which is immune to all possible detector side channel attacks, enables two remote legitimate users to perform secure communications without quantum repeaters. With the help of a central node, TF-QKD is expected to overcome the linear key-rate constraint using current technologies. However, the security of the former TF-QKD protocols relies on the hypothesis of infinite-key and stable sources. In this paper, we present the finite-key analysis of a practical decoy-state twin-field quantum key distribution with variant statistical fluctuation models. …
Security of quantum key distribution with intensity correlations
针对高速诱骗态QKD中脉冲强度相关性泄露强度设置信息的问题，提出一种仅需量化相关范围和最大相对偏差两个参数的通用安全性分析技术，并给出渐近密钥率公式的非标准推导。
In this paper, a photon-number-resolving decoy state quantum key distribution scheme is presented based on recent experimental advancements. A new upper bound on the fraction of counts caused by multiphoton pulses is given. This upper bound is independent of intensity of the decoy source, so that both the signal pulses and the decoy pulses can be used to generate the raw key after verified the security of the communication. This upper bound is also the lower bound on the fraction of counts caused by multiphoton pulses as long as faint coherent sources and high lossy channels are used. We show …
We propose an efficient four-intensity decoy-state BB84 protocol and derive concise security bounds for this protocol with the universally composable finite-key analysis method. Comparing with the efficient three-intensity protocol, we find that our efficient four-intensity protocol can increase the secret key rate by at least $30\%$. Particularly, this increasing rate of secret key rate will be raised as the transmission distance increases. At a large transmission distance, our efficient four-intensity protocol can improve the performance of quantum key distribution profoundly.
Quantum key distribution with decoherence-free subspaces has been proposed to overcome the collective noise to the polarization modes of photons flying in quantum channel. Prototype of this scheme have also been achieved with parametric-down conversion source. However, a novel type of photon-number-splitting attack we proposed in this paper will make the practical implementations of this scheme insecure since the parametric-down conversion source may emit multi-photon pairs occasionally. We propose decoy states method to make these implementations immune to this attack. And with this decoy sta…
For quantum key distribution (QKD) using spontaneous parametric-down-conversion sources (SPDCSs), the passive decoy-state protocol has been proved to be efficiently close to the theoretical limit of an infinite decoy-state protocol. In this paper, we apply a tight finite-key analysis for the passive decoy-state QKD using SPDCSs. Combining the security bound based on the uncertainty principle with the passive decoy-state protocol, a concise and stringent formula for calculating the key generation rate for QKD using SPDCSs is presented. The simulation shows that the secure distance under our for…
The existing theory of decoy-state quantum cryptography assumes the exact control of each states from Alice's source. Such exact control is impossible in practice. We develop the theory of decoy-state method so that it is unconditionally secure even there are state errors of sources, if the range of a few parameters in the states are known. This theory simplifies the practical implementation of the decoy-state quantum key distribution because the unconditional security can be achieved with a slightly shortened final key, even though the small errors of pulses are not corrected.
Imperfect preparation and Trojan attack on the phase modulator in the decoy-state BB84 protocol
本研究分析诱骗态BB84协议在相位调制器木马攻击下的安全性，推广攻击模型至任意探测态，引入保守泄漏界限，并证明量子硬币不平衡低且超100公里距离仍有非零安全密钥率。
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