Security Of Quantum Key Distribution Research Articles

Symmetry-Protected Privacy: Beating the Rate-Distance Linear Bound Over a Noisy Channel

There are two main factors limiting the performance of quantum key distribution---channel transmission loss and noise. Previously, a linear bound was believed to put an upper limit on the rate-transmittance performance. Remarkably, the recently proposed twin-field and phase-matching quantum key distribution schemes have been proven to overcome the linear bound. In practice, due to the intractable phase fluctuation of optical signals in transmission, these schemes suffer from large error rates, which renders the experimental realization extremely challenging. Here, we close this gap by proving the security based on a different principle---encoding symmetry. With the symmetry-based security proof technique, we can decouple the privacy from the channel disturbance, and eventually remove the limitation of secure key distribution on bit error rates. As a direct application, we show that the phase-matching scheme can yield positive key rates even with high bit error rates up to 50%. In the simulation, with typical experimental parameters, the key rate is able to break the linear bound with an error rate of 13%. Meanwhile, we provide a simple finite-data size analysis for the phase-matching scheme under this symmetry-based analysis, which can break the bound with a reasonable data size of ${10}^{12}$. Encouraged by high loss and error tolerance, we expect the approach based on symmetry-protected privacy will provide a different insight into the security of quantum key distribution.

Leftover Hashing From Quantum Error Correction: Unifying the Two Approaches to the Security Proof of Quantum Key Distribution

We show that the Mayers-Shor-Preskill approach and Renner's approach to proving the security of quantum key distribution (QKD) are essentially the same. We begin our analysis by considering a special case of QKD called privacy amplification (PA). PA itself is an important building block of cryptography, both classical and quantum. The standard theoretical tool used for its security proof is called the leftover hashing lemma (LHL). We present a direct connection between the LHL and the coding theorem of a certain quantum error correction code. Then we apply this result to proving the equivalence between the two approaches to proving the security of QKD.

Finite-key security analysis of the 1-decoy state QKD protocol with a leaky intensity modulator

The finite-key security of the standard three-intensity decoy-state quantum key distribution (QKD) protocol in the presence of information leakage has been analyzed (Wang et al. in New J Phys 20:083027, 2018). On the other hand, the 1-decoy state QKD protocol has been proved to be able to achieve higher secret key rate than the three-intensity decoy-state QKD protocol in the finite-key regime by using only two different intensity settings (Davide et al. in Appl Phys Lett 112:171104, 2018). In this work, we analyze the finite-key security of the 1-decoy state QKD protocol with a leaky intensity modulator, which is used to generate the decoy state. In particular, we simulate the secret key rate under three practical cases of Trojan-horse attacks. Our simulation results demonstrate that the 1-decoy state QKD protocol can be secure over long distances within a reasonable time frame given that the intensity modulator is sufficiently isolated. By comparing the simulation results to those presented in Wang et al. (2018), we find that, as expected, the 1-decoy state QKD protocol is more robust against information leakage from the intensity modulator for all achievable distances.

On the security and confidentiality of quantum key distribution

AbstractCryptography is a scientific method that is used to transmit secret information. In contrast, quantum cryptography depends on physical laws to encrypt information; when the quantum computer appeared, the classic encryption method becomes inefficient. The quantum method is commonly used to distribute keys, a process called as quantum key distribution (QKD). In this paper, we consider the efficiency of the quantum method compared to classical methods. Also, we discuss the security of QKD against several attacks and provide security analysis based on probabilistic models. Additionally, the paper explains how to encrypt random numbers into a sequence of photons using a QKD system for the distribution of a key. This research demonstrates the efficiency and security of QKD in sending and distributing keys between communication parties. Thus, both the sender and the receiver would be able to obtain a security key using the quantum method rather than classical methods.

Secure quantum key distribution with realistic devices

In principle, quantum key distribution (QKD) offers information-theoretic security based on the laws of physics. In practice, however, the imperfections of realistic devices might introduce deviations from the idealized models used in security analyses. Can quantum code-breakers successfully hack real systems by exploiting the side channels? Can quantum code-makers design innovative counter-measures to foil quantum code-breakers? This article reviews theoretical and experimental progress in the practical security aspects of quantum code-making and quantum code-breaking. After numerous attempts, researchers now thoroughly understand and are able to manage the practical imperfections. Recent advances, such as the measurement-device-independent protocol, have closed the critical side channels in the physical implementations, paving the way for secure QKD with realistic devices.

Generalized sequential state discrimination for multiparty QKD and its optical implementation

Sequential state discrimination is a strategy for N separated receivers. As sequential state discrimination can be applied to multiparty quantum key distribution (QKD), it has become one of the relevant research fields in quantum information theory. Up to now, the analysis of sequential state discrimination has been confined to special cases. In this report, we consider a generalization of sequential state discrimination. Here, we do not limit the prior probabilities and the number of quantum states and receivers. We show that the generalized sequential state discrimination can be expressed as an optimization problem. Moreover, we investigate a structure of generalized sequential state discrimination for two quantum states and apply it to multiparty QKD. We demonstrate that when the number of receivers is not too many, generalized sequential state discrimination for two pure states can be suitable for multiparty QKD. In addition, we show that generalized sequential state discrimination for two mixed states can be performed with high optimal success probability. This optimal success probability is even higher than those of quantum reproducing and quantum broadcasting strategy. Thus, generalized sequential state discrimination of mixed states is adequate for performing multiparty QKD. Furthermore, we prove that generalized sequential state discrimination can be implemented experimentally by using linear optics. Finally, we analyze the security of multiparty QKD provided by optimal sequential state discrimination. Our analysis shows that the multiparty QKD guarantees nonzero secret key rate even in low channel efficiency.

Improved quantum de Finetti theorem and its application in quantum key distribution

Quantum de Finetti theorem indicates that a surprising connection exists between the permutation-invariant property of a large system and the independent, identical distribution that describes its subsystems. The theorem is highly nontrivial in that it allows one to infer independence---within a finite error---from symmetry alone, both of which are important and fundamental concepts in physics and mathematics. Here, we present an improved quantum de Finetti theorem that provides a lower error bound, thus establishing an even closer relationship between symmetry and independence than before. As application, we study the security of quantum key distribution under the most general attacks, and show that the key rate is higher than previous ones obtained by existing trace-norm-based de Finetti theorems. Therefore, the application of the quantum de Finetti theorem in quantum information processing, as well as developing the theorem itself, is advanced here.

Quantum signature for designated verifier with strong security

Most of the classical designated verifier signature schemes are insecure against quantum adversary. In this paper, a quantum signature scheme for the designated verifier is proposed. In our scheme, during the initialization phase, the partners share secret keys by performing the quantum key distribution protocol. On the other hand, by performing the quantum direct communication protocol, the key generator center shares secret keys with the signer and the designated verifier, respectively. The key generator center generates a particle sequence of Bell state and distributes the particles between the signer and the designated verifier. During the signature generation phase, the signer encrypts the particle sequence by the secret keys and Hardmard operators. After that, the signer performs the controlled unitary operations on the encrypted particle sequence so as to generate the quantum signature. The designated verifier can simulate the quantum signature by performing the same symmetric signing steps as that performed by the original signer. Hence, the quantum signature signed by the true signer is the same as the one simulated by the receiver, which makes our scheme possess the designated properties. During the signature verification phase, the designated verifier performs the controlled unitary operations on the quantum signature and obtains the quantum ciphertexts. After that, the designated verifier decrypts the quantum ciphertexts by the symmetric secret keys and Hardmard operators so that the quantum signature can be verified. Our signature is secure against forgery attack, inter-resending attacks and Trojan horse attack. Because the trace distance between the density operators of different quantum signatures is zero, the information-theoretical security of our quantum signature scheme can be proved. The unconditionally secure quantum key distribution protocol and the one-time pad encryption algorithm can guarantee the security of the secret keys shared by the partners. What is more, the security assumption about the key generation center is weak. That is, it is not necessary to assume that the key generation center should be fully trusted. On the other hand, in our scheme, the quantum one-way function is not used. To generate a quantum signature, the signer need not prepare for entangled particle sequence. To verify a quantum signature, the verifier need not apply any state comparison to the received particles. The qubit efficiency is 100%. Therefore, our scheme has the advantages in the security and efficiency over the other quantum signature schemes for the designated verifier.

Laser-seeding Attack in Quantum Key Distribution

Quantum key distribution (QKD) based on the laws of quantum physics allows the secure distribution of secret keys over an insecure channel. Unfortunately, imperfect implementations of QKD compromise its information-theoretical security. Measurement-device-independent quantum key distribution (MDI-QKD) is a promising approach to remove all side channels from the measurement unit, which is regarded as the "Achilles' heel" of QKD. An essential assumption in MDI-QKD is however that the sources are trusted. Here we experimentally demonstrate that a practical source based on a semiconductor laser diode is vulnerable to a laser seeding attack, in which light injected from the communication line into the laser results in an increase of the intensities of the prepared states. The unnoticed increase of intensity may compromise the security of QKD, as we show theoretically for the prepare-and-measure decoy-state BB84 and MDI-QKD protocols. Our theoretical security analysis is general and can be applied to any vulnerability that increases the intensity of the emitted pulses. Moreover, a laser seeding attack might be launched as well against decoy-state based quantum cryptographic protocols beyond QKD.

Elimination of Spatial Side-Channel Information for Compact Quantum Key Distribution Senders

For a compact quantum key distribution (QKD) sender for the polarization encoding BB84 protocol, an eavesdropper could take a side-channel attack by measuring the spatial information of photons to infer their polarizations. The possibility of this attack can be reduced by introducing an aperture in the QKD sender, however, the effect of the aperture on the QKD security lacks of quantitative analysis. In this paper, we analyze the mutual information between the actual keys encoded at this QKD sender and the inferred keys at the eavesdropper (Eve), demonstrating the effect of the aperture to eliminate the spatial side-channel information quantitatively. It shows that Eve’s potential on eavesdropping spatial side-channel information is totally dependent on the optical design of the QKD sender, including the source arrangement and the aperture. The height of compact QKD senders with integrated light-emitting diode (LED) arrays could be controlled under several millimeters, showing great potential on applications in portable equipment.

Fading channel estimation for free-space continuous-variable secure quantum communication

We investigate estimation of fluctuating channels and its effect on security of continuous-variable quantum key distribution. We propose a novel estimation scheme which is based on the clusterization of the estimated transmittance data. We show that uncertainty about whether the transmittance is fixed or not results in a lower key rate. However, if the total number of measurements is large, one can obtain using our method a key rate similar to the non-fluctuating channel even for highly fluctuating channels. We also verify our theoretical assumptions using experimental data from an atmospheric quantum channel. Our method is therefore promising for secure quantum communication over strongly fluctuating turbulent atmospheric channels.

Unidimensional continuous-variable quantum key distribution with noisy source

We investigate the security of unidimensional continuous-variable quantum key distribution with source noise at the sender. The source noise is ascribed to the legitimate sides rather than the eavesdropper and modeled as a thermal noise coupled with the signal mode through a beam splitter. The physicality bound and expressions of secret key rate are derived against collective entangling cloner attacks. Simulation results show that with source noise, the security bound of unidimensional protocol can be tightened. Moreover, proper source noise enlarges the security region to a wider range of parameters, thus eliminates potential eavesdropping threats and enhances the feasibility of unidimensional protocol.

Performance Improvement of Underwater Continuous-Variable Quantum Key Distribution via Photon Subtraction

Considering the ocean water’s optical attenuation is significantly larger than that of Fiber Channel, we propose an approach to enhance the security of underwater continuous-variable quantum key distribution (CVQKD). In particular, the photon subtraction operation is performed at the emitter to enhance quantum entanglement, thereby improving the underwater transmission performance of the CVQKD. Simulation results show that the photon subtraction operation can effectively improve the performance of CVQKD in terms of underwater transmission distance. We also compare the performance of the proposed protocol in different water qualities, which shows the advantage of our protocol against water deterioration. Therefore, we provide a suitable scheme for establishing secure communication between submarine and submarine vehicles.

Quantum key distribution with simply characterized light sources

To guarantee the security of quantum key distribution (QKD), security proofs of QKD protocols have assumptions on the devices. Commonly used assumptions are, for example, each random bit information chosen by a sender to be precisely encoded on an optical emitted pulse and the photon-number probability distribution of the pulse to be exactly known. These typical assumptions imposed on light sources such as the above two are rather strong and would be hard to verify in practical QKD systems. The goal of the paper is to replace those strong assumptions on the light sources with weaker ones. In this paper, we adopt the differential-phase-shift (DPS) QKD protocol and drastically mitigate the requirements on light sources, while for the measurement unit, trusted and photon-number-resolving detectors are assumed. Specifically, we only assume the independence among emitted pulses, the independence of the vacuum emission probability from a chosen bit, and upper bounds on the tail distribution function of the total photon number in a single block of pulses for single, two and three photons. Remarkably, no other detailed characterizations, such as the amount of phase modulation, are required. Our security proof significantly relaxes demands for light sources, which paves a route to guarantee implementation security with simple verification of the devices.

Countermeasure against bright-light attack on superconducting nanowire single-photon detector in quantum key distribution.

We present an active anti-latching system for superconducting nanowire single-photon detectors. We experimentally test it against a bright-light attack, previously used to compromise security of quantum key distribution. Although our system detects continuous blinding, the detector is shown to be partially blindable and controllable by specially tailored sequences of bright pulses. Improvements to the countermeasure are suggested.

On the Performance of Quantum Key Distribution FSO Systems Under a Generalized Pointing Error Model

In this letter, the performance of a quantum key distribution (QKD) free-space optical (FSO) system is analyzed while taking a generalized pointing error model into account. More specifically, closed-form expressions for the average received powers at both the legitimate receiver and eavesdropper are derived. In addition, their corresponding asymptotic results valid in the high telescope gain regime are also presented. To capture the secure performance, we also investigate the ratio of received powers at the eavesdropper and at the legitimate receiver. Further, in some special cases, we find the optimal telescope gains for the received powers at both the legitimate receiver and eavesdropper, as well as the power ratio, which is important and useful for a secure QKD FSO system design. Finally, some selected numerical results are presented to illustrate the mathematical formalism and validate the accuracy of the derived analytical expressions.

Attacking a high-dimensional quantum key distribution system with wavelength-dependent beam splitter**Project supported by the National Key Research and Development Program of China (Grant No. 2016YFA0302600) and the National Natural Science Foundation of China (Grant No. 61675235).

The unconditional security of quantum key distribution (QKD) can be guaranteed by the nature of quantum physics. Compared with the traditional two-dimensional BB84 QKD protocol, high-dimensional quantum key distribution (HD-QKD) can be applied to generate much more secret key. Nonetheless, practical imperfections in realistic systems can be exploited by the third party to eavesdrop the secret key. The practical beam splitter has a correlation with wavelength, where different wavelengths have different coupling ratios. Using this property, we propose a wavelength-dependent attack towards time-bin high-dimensional QKD system. What is more, we demonstrate that this attacking protocol can be applied to arbitrary d-dimensional QKD system, and higher-dimensional QKD system is more vulnerable to this attacking strategy.

Intrinsic Mitigation of the After-Gate Attack in Quantum Key Distribution through Fast-Gated Delayed Detection

The information theoretic security promised by quantum key distribution (QKD) holds as long as the assumptions in the theoretical model match the parameters in the physical implementation. The superlinear behaviour of sensitive single-photon detectors represents one such mismatch and can pave the way to powerful attacks hindering the security of QKD systems, a prominent example being the after-gate attack. A longstanding tenet is that trapped carriers causing delayed detection can help mitigate this attack, but despite intensive scrutiny, it remains largely unproven. Here we approach this problem from a physical perspective and find new evidence to support a detector's secure response. We experimentally investigate two different carrier trapping mechanisms causing delayed detection in fast-gated semiconductor avalanche photodiodes, one arising from the multiplication layer, the other from the heterojunction interface between absorption and charge layers. The release of trapped carriers increases the quantum bit error rate measured under the after-gate attack above the typical QKD security threshold, thus favouring the detector's inherent security. This represents a significant step to avert quantum hacking of QKD systems.

Implementation security of quantum key distribution due to polarization-dependent efficiency mismatch

Einstein-Podolsky-Rosen (EPR) steering, as one of the most intriguing phenomenon of quantum mechanics, is a useful quantum resource for quantum communication. Understanding the type of EPR steering in a graph state is the basis for application of it in a quantum network. In this paper, we present EPR steering in a Gaussian weighted graph state, including a linear tripartite and a four-mode square weighted graph state. The dependence of EPR steering on weight factor in the weighted graph state is analyzed. Gaussian EPR steering between two modes of a weighted graph state is presented, which does not exist in the Gaussian cluster state (where the weight factor is unit). For the four-mode square Gaussian weighted graph state, EPR steering between one and its two nearest modes is also presented, which is absent in the four-mode square Gaussian cluster state. We also show that Gaussian EPR steering in a weighted graph state is also bounded by the Coffman-Kundu-Wootters monogamy relation. The presented results are useful for exploiting EPR steering in a Gaussian weighted graph state as a valuable resource in multiparty quantum communication tasks.

Practical security of the continuous-variable quantum key distribution with real local oscillators under phase attack.

Continuous-variable quantum key distribution (CVQKD) with a real local oscillator (LO) is confronted with new security problems due to the reference pulses transmitted together with quantum signals over the insecure quantum channel. In this paper, we propose a method of phase attack on reference pulses of the CVQKD with real LOs. Under the phase attack, the phase drifts of reference pulses are manipulated by eavesdroppers, and then the phase compensation error is increased. Consequently, the secret key rate is reduced due to the imperfect phase compensation for quantum signals. Based on the noise model of imperfect phase compensation, the practical security of the CVQKD under phase attack is analyzed. Besides, we propose an effective method to detect the intensity of phase attack, in which the deviation of phase compensation error on quantum signals and that on reference signals are monitored in real time. The simulation results show that the security analysis is accurate and the method of phase attack detection is feasible.