Security of quantum key distribution against sophisticated attacks is among the most important issues in quantum information theory. In this work we prove security against a very important class of attacks called collective attacks (under a compatible noise model) which use quantum memories and gates, and which are directed against the final key. Although attacks stronger than the collective attacks can exist in principle, no explicit example was found and it is conjectured that security against collective attacks implies also security against any attack.
In this paper, we give a simple proof of the fact that the optimal collective attacks against continous-variable quantum key distribution with a Gaussian modulation are Gaussian attacks. Our proof makes use of symmetry properties of the quantum key distribution protocol in phase-space.
We derive a proof of security for the Differential Phase Shift Quantum Key Distribution (DPSQKD) protocol under the assumption that Eve is restricted to individual attacks. The security proof is derived by bounding the average collision probability, which leads directly to a bound on Eve's mutual information on the final key. The security proof applies to realistic sources based on pulsed coherent light. We then compare individual attacks to sequential attacks and show that individual attacks are more powerful.
We present strong attacks against quantum key distribution schemes which use quantum memories and quantum gates to attack directly the final key. We analyze a specific attack of this type, for which we find the density matrices available to the eavesdropper and the optimal information which can be extracted from them. We prove security against this attack and discuss security against any attack allowed by the rules of quantum mechanics.
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 consider the collective eavesdropping of the BB84 and six-state protocols. Since these protocols are symmetric in the eigenstates of conjugate bases, we consider collective attacks having the same kind of symmetry. We then show how these symmetric collective attacks are sufficiently strong in order to minimize the Devetak-Winter rates. In fact, it is quite easy to construct simple examples able to reach the unconditionally-secure key-rates of these protocols.
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…
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.
We present the optimal collective attack on a Quantum Key Distribution (QKD) protocol in the "device-independent" security scenario, where no assumptions are made about the way the QKD devices work or on what quantum system they operate. Our main result is a tight bound on the Holevo information between one of the authorized parties and the eavesdropper, as a function of the amount of violation of a Bell-type inequality.
In this paper, we briefly show how the quantum key distribution with blind polarization bases [Kye et al., Phys. Rev. Lett. 95, 040501 (2005)] can be made secure against the invisible photon attack.
Unconditional security of the BB84 quantum key distribution protocol has been proved by exploiting the fundamental laws of quantum mechanics, but the practical quantum key distribution system maybe hacked by considering the imperfect state preparation and measurement respectively. Until now, different attacking schemes have been proposed by utilizing imperfect devices, but the general security analysis model against all of the practical attacking schemes has not been proposed. Here, we demonstrate that the general practical attacking schemes can be divided into the Trojan horse attack, strong …
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.
In this paper, we briefly show how the quantum key distribution with blind polarization bases [Kye et al., Phys. Rev. Lett. 95, 040501 (2005)] can be made secure against the impersonation attack.
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.
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 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.
I prove the security of quantum key distribution against individual attacks for realistic signals sources, including weak coherent pulses and downconversion sources. The proof applies to the BB84 protocol with the standard detection scheme (no strong reference pulse). I obtain a formula for the secure bit rate per time slot of an experimental setup which can be used to optimize the performance of existing schemes for the considered scenario.
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…
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…
It is shown that the effect of transmission loss has often not been properly taken into account in the security proofs on quantum key distribution. A class of general attacks to be called probabilistic re-sends attack is described that has not been accounted for, which is a generalization of the well-known unique state determination attack. In the case of the four-state single-photon BB84 protocol, it is shown in detail how such attacks are not accounted for in the known security proofs against the simplest individual attacks.
Counterfactual quantum cryptography (CQC), recently proposed by Noh, is featured with no transmission of signal particles. This exhibits evident security advantage, such as its immunity to the well known PNS attack. In this paper, the theoretical security of CQC protocol against the general intercept-resend attacks is proved by bounding the information of an eavesdropper Eve more tightly than in Yin's proposal[Phys. Rev. A 82, 042335 (2010)]. It is also showed that practical CQC implementations may be vulnerable when equipped with imperfect apparatuses, by proving that a negative key rate can …
We investigate a new strategy for incoherent eavesdropping in Ekert's entanglement based quantum key distribution protocol. We show that under certain assumptions of symmetry the effectiveness of this strategy reduces to that of the original single qubit protocol of Bennett and Brassard.
In Gaussian quantum key distribution eavesdropping attacks are conventionally modeled through the universal entangling cloner scheme, which is based on the premise that the whole environment is under control of the adversary, i.e., the eavesdropper purifies the system. This assumption implies that the eavesdropper has either access to an identity (noiseless) channel or infinite amount of entanglement in order to simulate such an identity channel. In this work, we challenge the necessity of this assumption, and we propose a teleportation-based eavesdropping attack, where the eavesdropper is not…
Recently, Yang et al. (Quantum Inf Process 18, 74, 2019) proposed a two-party quantum key agreement protocol over a collective noisy channel. They claimed that their quantum key agreement protocol can ensure both of the participants have equal influence on the final shared key. However, this study shows that the participant who announces the permutation operation can manipulate the final shared key by himself/herself without being detected by the other. To avoid this loophole, an improvement is proposed here.
The potential weakness of the Y-00 direct encryption protocol when the encryption box ENC in Y-00 is not chosen properly is demonstrated in a fast correlation attack by S. Donnet et al in Phys. Lett. A 35, 6 (2006) 406-410. In this paper, we show how this weakness can be eliminated with a proper design of ENC. In particular, we present a Y-00 configuration that is more secure than AES under known-plaintext attack. It is also shown that under any ciphertext-only attack, full information-theoretic security on the Y-00 seed key is obtained for any ENC when proper deliberate signal randomization i…
In the quantum version of a Trojan-horse attack, photons are injected into the optical modules of a quantum key distribution system in an attempt to read information direct from the encoding devices. To stop the Trojan photons, the use of passive optical components has been suggested. However, to date, there is no quantitative bound that specifies such components in relation to the security of the system. Here, we turn the Trojan-horse attack into an information leakage problem. This allows us quantify the system security and relate it to the specification of the optical elements. The analysis…
In this paper, two information leakage resistant quantum dialogue (QD) protocols over a collective-noise channel are proposed. Decoherence-free subspace (DFS) is used to erase the influence from two kinds of collective noise, i.e., collective-dephasing noise and collective-rotation noise, where each logical qubit is composed of two physical qubits and free from noise. In each of the two proposed protocols, the secret messages are encoded on the initial logical qubits via two composite unitary operations. Moreover, the single-photon measurements rather than the Bell-state measurements or the mo…
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…
We investigate limitations imposed by detector dead-times on the performance of sequential attacks against a differential-phase-shift (DPS) quantum key distribution (QKD) protocol with weak coherent pulses. In particular, we analyze sequential attacks based on unambiguous state discrimination of the signal states emitted by the source and we obtain ultimate upper bounds on the maximal distance achievable by a DPS QKD scheme both in the so-called trusted and untrusted device scenarios, respectively.
Most security proofs of quantum key distribution (QKD) disregard the effect of information leakage from the users' devices, and, thus, do not protect against Trojan-horse attacks (THAs). In a THA, the eavesdropper injects strong light into the QKD apparatuses, and then analyzes the back-reflected light to learn information about their internal setting choices. Only a few recent works consider this security threat, but predict a rather poor performance of QKD unless the devices are strongly isolated from the channel. Here, we derive finite-key security bounds for decoy-state-based QKD schemes i…
This is a brief comment on the Letter by Balygin and his coworkers [Laser Phys. Lett. 15, 095203 (2018)]. We point out an error that invalidates the Letter's conclusions.
In a recent paper [Z. J. Zhang and Z. X. Man, Phys. Rev. A 72, 022303(2005)], a multiparty quantum secret sharing protocol based on entanglement swapping was presented. However, as we show, this protocol is insecure in the sense that an unauthorized agent group can recover the secret from the dealer. Hence, we propose an improved version of this protocol which can stand against this kind of attack.
We consider a subcarrier wave quantum key distribution (QKD) system, where the quantum en- coding is carried by weak sidebands generated to a coherent optical beam by means of an electrooptic phase modulation. We study the security of two protocols, B92 and BB84, against one of the most powerful attacks on the systems of this class: the collective beam splitting attack. We show that a subcarrier wave QKD system with realistic parameters is capable of distributing a cryptographic key over large distances. We show also that a modification of the BB84 protocol, with discrimina- tion of only one s…
Recently, we have shown the advantages of two-way quantum communications in continuous variable quantum cryptography. Thanks to this new approach, two honest users can achieve a non-trivial security enhancement as long as the Gaussian interactions of an eavesdropper are independent and identical. In this work, we consider asymmetric strategies where the Gaussian interactions can be different and classically correlated. For several attacks of this kind, we prove that the enhancement of security still holds when the two-way protocols are used in direct reconciliation.
Evaluating the theoretical limit of the amount of information Eve can steal from a quantum key distribution protocol under given conditions is one of the most important things that need to be done in security proof. In addition to source loopholes and detection loopholes, channel attacks are considered to be the main ways of information leakage, while collective attacks are considered to be the most powerful active channel attacks. Here we deduce in detail the capability limit of Eve's collective attack in non-entangled quantum key distribution, like BB84 and measurement-device-independent pro…
It is of folkloric belief that the security of classical cryptographic protocols is automatically broken if the Adversary is allowed to perform superposition queries and the honest players forced to perform actions coherently on quantum states. Another widely held intuition is that enforcing measurements on the exchanged messages is enough to protect protocols from these attacks. However, the reality is much more complex. Security models dealing with superposition attacks only consider unconditional security. Conversely, security models considering computational security assume that all suppos…
We provide a simple description of the most general collective Gaussian attack in continuous-variable quantum cryptography. In the scenario of such general attacks, we analyze the asymptotic secret-key rates which are achievable with coherent states, joint measurements of the quadratures and one-way classical communication.
The Quantum Key Distribution (QKD) protocol BB84 has been proven secure against several important types of attacks: the collective attacks and the joint attacks. Here we analyze the security of a modified BB84 protocol, for which information is sent only in the z basis while testing is done in both the z and the x bases, against collective attacks. The proof follows the framework of a previous paper (Boyer, Gelles, and Mor, 2009), but it avoids the classical information-theoretical analysis that caused problems with composability. We show that this modified BB84 protocol is as secure against c…
Quantum Cryptography uses the counter-intuitive properties of Quantum Mechanics for performing cryptographic tasks in a secure and reliable way. The Quantum Key Distribution (QKD) protocol BB84 has been proven secure against several important types of attacks: collective attacks and joint attacks. Here we analyze the security of a modified BB84 protocol, for which information is sent only in the z basis while testing is done in both the z and the x bases, against collective attacks. The proof follows the framework of a previous paper (Boyer, Gelles, and Mor, 2009), but it avoids a classical in…
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.
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…
Here, we investigate the security of the practical one-way CVQKD and CV-MDI-QKD systems under laser seeding attack. In particular, Eve can inject a suitable light into the laser diodes of the light source modules in the two kinds of practical CVQKD systems, which results in the increased intensity of the generated optical signal. The parameter estimation under the attack shows that the secret key rates of these two schemes may be overestimated, which opens a security loophole for Eve to successfully perform an intercept-resend attack on these systems. To close this loophole, we propose a real-…
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…
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 …
