Security of practical continuous-variable quantum key distribution is addressed and a security analysis framework, which does not rely on phase-space symmetries of signal states and correlations, is developed. In a general purification-based approach, following optimality of Gaussian collective attacks, it is suggested to find an equivalent generally mixed two-mode state shared between the trusted parties and then purifying it using Bloch-Messiah decomposition. This allows to assess security of the schemes with arbitrary parameters, which can be typically expected in experiments. It also allows to theoretically predict the role of asymmetries of signals and correlations on security of the protocols. The method can be used for security analysis of practical continuous-variable schemes directly from the measured data without any symmetrization assumptions.
Quantum key distribution (QKD) protocols make it possible for two parties to generate a secret shared key. One of the most important QKD protocols, BB84, was suggested by Bennett and Brassard in 1984. Various proofs of unconditional security for BB84 have been suggested, but the first security proofs were not composable. Here we improve a security proof of BB84 given by [Biham, Boyer, Boykin, Mor, and Roychowdhury, J. Cryptology, 19(4):381-439, 2006] to be composable and match the state-of-the-art results for BB84, and we extend it to prove unconditional security of several variants of the BB8…
Several fundamental issues in establishing security in continuous variable quantum key distribution are discussed, in particular on reverse reconciliation and security under heterodyne attack. It appears difficult to derive quantum advantage in a concrete realistic protocol due to source and loss uncertainties, apart from the problem of bounding Eve's information after reconciliation. The necessity of proving robust security for QKD protocols is indicated.
We consider a recently proposed entity authentication protocol, in which a physical unclonable key is interrogated by random coherent states of light, and the quadratures of the scattered light are analysed by means of a coarse-grained homodyne detection. We derive a sufficient condition for the protocol to be secure against an emulation attack, in which an adversary knows the challenge-response properties of the key, and moreover he can access the challenges during the verification. The security analysis relies on Holevo's bound and Fano's inequality, and suggests that the protocol is secure …
Quantum Key Distribution (QKD) in principle offers unconditional security based on the laws of physics. Continuous variable (CV) quantum key distribution has the potential for high-key-rate and low-cost implementations using standard telecom components. Despite tremendous theoretical and experimental progress in continuous-variable quantum key distribution, the security has not been rigorously established for most current continuous-variable quantum key distribution systems that have imperfections. Among the imperfections, intensity fluctuation is a significant principal problem affecting secu…
Rigorous mathematical proofs of the security of continuous-variable quantum key distribution (CV QKD) have been obtained recently. Unfortunately, these security proofs rely on assumptions that are hardly met in experimental practice. Here I investigate these issues in detail, and discuss experimentally-friendly workarounds to assess the security of CV QKD. The aim of this paper is to show that there are hidden and unsolved issues and to indicate possible partial solutions. To provide a complete and rigorous mathematical security proof is out of the scope of this contribution.
We analyze the security against collective attacks for a homodyne-based continuous-variable quantum key distribution protocol using binary coherent states and postselection. We derive a lower bound of the secret key rate in an asymptotic scenario, and numerically optimize it for the case of a symmetric Gaussian channel.
We provide a security analysis of continuous-variable quantum key distribution (CVQKD) with discrete modulation against general attacks in a realistic finite-size regime. To realize this goal, we first prove security of the continuous-variable quantum key distribution protocol with discrete modulation against collective attacks by using the reliable tomography of the covariance matrix, leading to the reliable and tight error bounds in the derived confidence regions. Combining the proof with de Finetti reduction, the discrete-modulation-based continuous-variable quantum key distribution (DM-CVQ…
We investigate the security of continuous-variable (CV) quantum key distribution (QKD) using coherent states in the presence of quadrature excess noise. We consider an eavesdropping attack which uses a linear amplifier and beam splitter. This attack makes a link between beam-splitting attack and intercept-resend attack (classical teleportation attack). We also show how postselection loses its efficiency in a realistic channel.
We extend the security proof for continuous variable quantum key distribution protocols using post selection to account for arbitrary eavesdropping attacks by employing the concept of an equiv- alent protocol where the post-selection is implemented as a projective quantum measurement. We demonstrate that the security can be calculated using only experimentally accessible quantities and finally explicitly evaluate the performance for the case of a noisy Gaussian channel in the limit of unbounded key length.
We present a continuous-variable quantum key distribution protocol combining a discrete modulation and reverse reconciliation. This protocol is proven unconditionally secure and allows the distribution of secret keys over long distances, thanks to a reverse reconciliation scheme efficient at very low signal-to-noise ratio.
We give the first composable security proof for continuous-variable quantum key distribution with coherent states against collective attacks. Crucially, in the limit of large blocks the secret key rate converges to the usual value computed from the Holevo bound. Combining our proof with either the de Finetti theorem or the Postselection technique then shows the security of the protocol against general attacks, thereby confirming the long-standing conjecture that Gaussian attacks are optimal asymptotically in the composable security framework. We expect that our parameter estimation procedure, …
Proving the unconditional security of a quantum key distribution (QKD) scheme is a highly challenging task as one needs to determine the most efficient attack compatible with experimental data. This task is even more demanding for continuous-variable QKD as the Hilbert space where the protocol is described is infinite dimensional. A very natural way to address this problem is to make an extensive use of the symmetries of the protocols. In this article, we investigate a symmetry in phase space that is particularly relevant to continuous-variable QKD, and explore the way towards a new quantum de…
We discuss a quantum key distribution scheme in which small phase and amplitude modulations of CW light beams carry the key information. The presence of EPR type correlations provides the quantum protection. We identify universal constraints on the level of shared information between the intended receiver (Bob) and any eavesdropper (Eve) and use this to make a general evaluation of security. We identify teleportation as an optimum eavesdropping technique.
In comparison to conventional discrete-variable (DV) quantum key distribution (QKD), continuous-variable (CV) QKD with homodyne/heterodyne measurements has distinct advantages of lower-cost implementation and affinity to wavelength division multiplexing. On the other hand, its continuous nature makes it harder to accommodate to practical signal processing, which is always discretized, leading to lack of complete security proofs so far. Here we propose a tight and robust method of estimating fidelity of an optical pulse to a coherent state via heterodyne measurements. We then construct a binary…
We investigate the performance of Gaussianmodulated coherent-state QKD protocols in the presence of canonical attacks, which are collective Gaussian attacks resulting in Gaussian channels described by one of the possible canonical forms. We present asymptotic key rates and then we extend the results to the finite-size regime using a recently-developed toolbox for composable security.
We present a general framework encompassing a number of continuous-variable quantum key distribution protocols, including standard one-way protocols, measurement-device-independent protocols as well as some two-way protocols, or any other continuous-variable protocol involving only a Gaussian modulation of coherent states and heterodyne detection. The main interest of this framework is that the corresponding protocols are all covariant with respect to the action of the unitary group $U(n)$, implying that their security can be established thanks to a Gaussian de Finetti reduction. In particular…
We give an achievable secret key rate of a binary modulated continuous variable quantum key distribution schemes in the collective attack scenario considering quantum channels that impose arbitrary noise on the exchanged signals. Bob performs homodyne measurements on the received states and the two honest parties employ a reverse reconciliation procedure in the classical post-processing step of the protocol.
In this paper, we generalize a secured direct communication process between N users with partial and full cooperation of quantum server. The security analysis of authentication and communication processes against many types of attacks proved that the attacker cannot gain any information during intercepting either authentication or communication processes. Hence, the security of transmitted message among N users is ensured as the attacker introduces an error probability irrespective of the sequence of measurement.
We present here an information theoretic study of Gaussian collective attacks on the continuous variable key distribution protocols based on Gaussian modulation of coherent states. These attacks, overlooked in previous security studies, give a finite advantage to the eavesdropper in the experimentally relevant lossy channel, but are not powerful enough to reduce the range of the reverse reconciliation protocols. Secret key rates are given for the ideal case where Bob performs optimal collective measurements, as well as for the realistic cases where he performs homodyne or heterodyne measuremen…
Measurement-device-independent quantum key distribution protocol, whose security analysis does not rely on any assumption on the detection system, can immune the attacking against detectors. We give a first composable security analysis for continuous-variable measurement-device-independent quantum key distribution using squeezed states against general coherent attacks. The security analysis is derived based on the entanglement-based scheme considering finite size effect. A version of entropic uncertainty relation is exploited to give a lower bound on the conditional smooth min-entropy by trust…
We prove the security of Gaussian continuous-variable quantum key distribution against arbitrary attacks in the finite-size regime. The novelty of our proof is to consider symmetries of quantum key distribution in phase space in order to show that, to good approximation, the Hilbert space of interest can be considered to be finite-dimensional, thereby allowing for the use of the postselection technique introduced by Christandl, Koenig and Renner (Phys. Rev. Lett. 102, 020504 (2009)). Our result greatly improves on previous work based on the de Finetti theorem which could not provide security f…
Continuous-variable quantum key distribution exploits coherent measurements of the electromagnetic field, i.e., homodyne or heterodyne detection. The most advanced security proofs developed so far relied on idealised mathematical models for such measurements, which assume that the measurement outcomes are continuous and unbounded variables. As physical measurement devices have finite range and precision, these mathematical models only serve as an approximation. It is expected that, under suitable conditions, the predictions obtained using these simplified models are in good agreement with the …
Security bounds for key distribution protocols using coherent and squeezed states and homodyne measurements are presented. These bounds refer to (i) general attacks and (ii) collective attacks where Eve interacts individually with the sent states, but delays her measurement until the end of the reconciliation process. For the case of a lossy line and coherent states, it is first proven that a secure key distribution is possible up to 1.9 dB of losses. For the second scenario, the security bounds are the same as for the completely incoherent attack.
Security of a continuous-variable quantum key distribution protocol based on noisy coherent states and channel is analyzed. Assuming the noise of coherent states is induced by Fred, a neutral party relative to others, we prove that the prepare and measurement scheme and entanglement-based scheme are equivalent. Then, we show that this protocol is secure against Gaussian collective attacks even if the channel is lossy and noisy, and further, a lower bound to the secure key rate is derived.
We present a rigorous security analysis of Continuous-Variable Measurement-Device Independent Quantum Key Distribution (CV MDI QKD) in a finite size scenario. The security proof is obtained in two steps: by first assessing the security against collective Gaussian attacks, and then extending to the most general class of coherent attacks via the Gaussian de Finetti reduction. Our result combines recent state-of-the-art security proofs for CV QKD with new findings about min-entropy calculus and parameter estimation. In doing so, we improve the finite-size estimate of the secret key rate. Our conc…
Establishing the security of continuous-variable quantum key distribution against general attacks in a realistic finite-size regime is an outstanding open problem in the field of theoretical quantum cryptography if we restrict our attention to protocols that rely on the exchange of coherent states. Indeed, techniques based on the uncertainty principle are not known to work for such protocols, and the usual tools based on de Finetti reductions only provide security for unrealistically large block lengths. We address this problem here by considering a new type of Gaussian de Finetti reduction, t…
Continuous-variable quantum key distribution (CV-QKD) has many practical advantages including compatibility with current optical communication technology. Implementation using heterodyne measurements is particularly attractive since it eliminates the need for active phase locking of the remote pair of local oscillators, but the full security of CV QKD with discrete modulation was only proved for a protocol using homodyne measurements. Here we propose an all-heterodyne CV-QKD protocol with binary modulation and prove its security against general attacks in the finite-key regime. Although replac…
In this paper, using the full security framework for continuous variable quantum key distribution (CV-QKD), we provide a composable security proof for the CV-QKD system in a realistic implementation. We take into account equipment losses and contributions from various components of excess noise and evaluate performance against collective and coherent attacks assuming trusted hardware noise. The calculation showed that the system remains operable at channel losses up to 10.2 dB in the presence of collective attacks and up to 7.5 dB in the presence of coherent ones.
Phase reference calibration is a necessary procedure in practical continuous-variable measurement-device-independent quantum key distribution (CV-MDI-QKD) for the need of Bell-State Measurement (BSM). However, the phase reference calibration may become imperfect in practical applications. We explored the practical security of CV-MDI-QKD with imperfect phase reference calibration under realistic conditions of lossy and noisy quantum channel. Specifically, a comprehensive framework is developed to model and characterize the imperfection of practical phase reference calibration operation, which i…
We present the first protocol for oblivious transfer that can be implemented with an optical continuous-variable system, and prove its security in the noisy-storage model. This model allows security to be achieved by sending more quantum signals than an attacker can reliably store at one specific point during the protocol. Concretely, we determine how many signals need to be sent in order to achieve security by establishing a trade-off between quantum uncertainty generated in the protocol and the classical capacity of the memory channel. As our main technical tool, we study and derive new unce…
The original two-way continuous-variable quantum-key-distribution (CV QKD) protocols [S. Pirandola, S. Mancini, S. Lloyd, and S. L. Braunstein, Nature Physics 4, 726 (2008)] give the security against the collective attack on the condition of the tomography of the quantum channels. We propose a family of new two-way CV QKD protocols and prove their security against collective entangling cloner attacks without the tomography of the quantum channels. The simulation result indicates that the new protocols maintain the same advantage as the original two-way protocols whose tolerable excess noise su…
The need for secrecy and security is essential in communication. Secret sharing is a conventional protocol to distribute a secret message to a group of parties, who cannot access it individually but need to cooperate in order to decode it. While several variants of this protocol have been investigated, including realizations using quantum systems, the security of quantum secret sharing schemes still remains unproven almost two decades after their original conception. Here we establish an unconditional security proof for continuous variable entanglement-based quantum secret sharing schemes, in …
We establish a lower bound on the asymptotic secret key rate of continuous-variable quantum key distribution with a discrete modulation of coherent states. The bound is valid against collective attacks and is obtained by formulating the problem as a semidefinite program. We illustrate our general approach with the quadrature phase-shift keying (QPSK) modulation scheme and show that distances over 100 km are achievable for realistic values of noise. We also discuss the application to more complex quadrature amplitude modulations (QAM) schemes. This work is a major step towards establishing the …
The ability to distribute secret keys between two parties with information-theoretic security, that is, regardless of the capacities of a malevolent eavesdropper, is one of the most celebrated results in the field of quantum information processing and communication. Indeed, quantum key distribution illustrates the power of encoding information on the quantum properties of light and has far reaching implications in high-security applications. Today, quantum key distribution systems operate in real-world conditions and are commercially available. As with most quantum information protocols, quant…
Continuous-variable quantum key distribution (CV QKD) protocols with discrete modulation are interesting due to their experimental simplicity and their great potential for massive deployment in the quantum-secured networks, but their security analysis is less advanced than that of Gaussian modulation schemes. In this work, we apply a numerical method to analyze the security of discrete-modulation protocols against collective attacks in the asymptotic limit, paving the way for a full security proof with finite-size effects. While our method is general for discrete-modulation schemes, we focus o…
A quantum random-number generator (QRNG) can theoretically generate unpredictable random numbers with perfect devices and is an ideal and secure source of random numbers for cryptography. However, the practical implementations always contain imperfections, which will greatly influence the randomness of the final output and even open loopholes to eavesdroppers. Recently, Thewes et al. experimentally demonstrated a continuous-variable eavesdropping attack, based on heterodyne detection, on a trusted continuous-variable QRNG in Phys. Rev. A 100, 052318 (2019), yet like in many other practical con…
Prepare and measure quantum key distribution protocols can be decomposed into two basic steps: delivery of the signals over a quantum channel and distillation of a secret key from the signal and measurement records by classical processing and public communication. Here we formalize the distillation process for a general protocol in a purely quantum-mechanical framework and demonstrate that it can be viewed as creating an ``effective'' quantum channel between the legitimate users Alice and Bob. The process of secret key generation can then be viewed as entanglement distribution using this chann…
We consider continuous-variable quantum key distribution with discrete-alphabet encodings. In particular, we study protocols where information is encoded in the phase of displaced coherent (or thermal) states, even though the results can be directly extended to any protocol based on finite constellations of displaced Gaussian states. In this setting, we provide a composable security analysis in the finite-size regime assuming the realistic but restrictive hypothesis of collective Gaussian attacks. Under this assumption, we can efficiently estimate the parameters of the channel via maximum like…
We investigate the composable security of unidimensional contin- uous variable quantum key distribution (UCVQKD), which is based on the Gaussian modulation of a single quadrature of the coherent-state of light, aiming to provide a simple implementation of key distribution compared to the symmetrically modulated Gaussian coherent-state protocols. This protocol neglects the necessity in one of the quadrature modulation in coherent-states and hence reduces the system complexity. To clarify the influence of finite-size effect and the cost of performance degeneration, we establish the relation- shi…
A quantum key distribution (QKD) system must fulfill the requirement of universal composability to ensure that any cryptographic application (using the QKD system) is also secure. Furthermore, the theoretical proof responsible for security analysis and key generation should cater to the number $N$ of the distributed quantum states being finite in practice. Continuous-variable (CV) QKD based on coherent states, despite being a suitable candidate for integration in the telecom infrastructure, has so far been unable to demonstrate composability as existing proofs require a rather large $N$ for su…
We consider discrete-modulation protocols for continuous-variable quantum key distribution (CV-QKD) that employ a modulation constellation consisting of a finite number of coherent states and that use a homodyne or a heterodyne-detection receiver. We establish a security proof for collective attacks in the asymptotic regime, and we provide a formula for an achievable secret-key rate. Previous works established security proofs for discrete-modulation CV-QKD protocols that use two or three coherent states. The main constituents of our approach include approximating a complex, isotropic Gaussian …
In a previous paper certain measurable criteria have been derived, that are sufficient to demonstrate the existence of Einstein-Podolsky-Rosen (EPR) correlations for measurements with continuous variable outcomes. Here it is shown how such EPR criteria, which do not demand perfect EPR correlations, can be used to prove the extent of security for continuous variable quantum cryptographic schemes (in analogy to that proposed by Ekert) where Alice and Bob hope to construct a secure sequence of values from measurements performed on continuous-variable EPR-correlated fields sent from a distant sour…
We provide a security analysis for continuous variable quantum key distribution protocols based on the transmission of squeezed vacuum states measured via homodyne detection. We employ a version of the entropic uncertainty relation for smooth entropies to give a lower bound on the number of secret bits which can be extracted from a finite number of runs of the protocol. This bound is valid under general coherent attacks, and gives rise to keys which are composably secure. For comparison, we also give a lower bound valid under the assumption of collective attacks. For both scenarios, we find po…
Despite tremendous theoretical and experimental progress in continuous variable (CV) quantum key distribution (QKD), its security has not been rigorously established for practical systems with multiple imperfections. The idea of tagging is widely used in security proofs of discrete variable quantum key distribution with imperfect devices. In this paper, we generalize the tagging idea from discrete variable to continuous variable. Based on untagged signals, we prove the security of the imperfect quantum key distribution system in the most conservative case. By introducing a generic imperfection…
Recently in 2018, Niu et al. proposed a measurement-device-independent quantum secure direct communication protocol using Einstein-Podolsky-Rosen pairs and generalized it to a quantum dialogue protocol (Niu et al., Science bulletin 63.20, 2018). By analyzing these protocols we find some security issues in both these protocols. In this work, we show that both the protocols are not secure against information leakage, and a third party can get half of the secret information without any active attack. We also propose suitable modifications of these protocols to improve the security.
We introduce a ternary quantum key distribution (QKD) protocol and asymptotic security proof based on three coherent states and homodyne detection. Previous work had considered the binary case of two coherent states and here we nontrivially extend this to three. Our motivation is to leverage the practical benefits of both discrete and continuous (Gaussian) encoding schemes creating a best-of-both-worlds approach; namely, the postprocessing of discrete encodings and the hardware benefits of continuous ones. We present a thorough and detailed security proof in the limit of infinite signal states…
The practical homodyne detector model of continuous-variable quantum key distribution models the inherent imperfections of the practical homodyne detector, namely the limited detection efficiency and the electronic noise, into trusted loss. However, the conventional practical homodyne detector model is valid only when both the imperfections of the practical homodyne detector are calibrated. In this paper, we show a modified practical homodyne detector model that can model the imperfections separately. The phase-sensitive amplifier is further applied to compensate the imperfections of the pract…
We propose a scheme for the secure direct communication based on the entangled phase-coherent states, which shows an elevated level of confidentiality. The protocol gives a simultaneous security control for every bit of transferred information. The security-check-per-bit is provided by sending an additional mode to prove the legitimate parties' authenticity. Other benefit include increased transfer rate, since a separate control sequences is unnecessary. We study the security of the scheme for both ideal and realistic quantum channel. The protocol shows a robust security and prepares 50% proba…
