Miguel Navascues, Frederic Grosshans, Antonio Acin
We analyze the asymptotic security of the family of Gaussian modulated Quantum Key Distribution protocols for Continuous Variables systems. We prove that the Gaussian unitary attack is optimal for all the considered bounds on the key rate when the first and second momenta of the canonical variables involved are known by the honest parties.
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A particularly successful detector blinding attack has been recently demonstrated on various quantum key distribution (QKD) systems, performing for the first time an undetectable and complete recovery of the key. In this paper two original contributions are given to understanding and prevention of this attack.
This is a reply to the comment by Yuan et al. [arXiv:1009.6130v1] on our publication [arXiv:1008.4593].
This is a comment on the publication by Yuan et al. [Appl. Phys. Lett. 98, 231104 (2011); arXiv:1106.2675v1 [quant-ph]].
Security proof for quantum cryptography against entanglement-measurement attack
本文提出利用两种窃听检查方法证明量子密码对抗纠缠测量攻击的安全性，通过最大纠缠态协议演示证明过程。
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 show the detector blinding attack by Lydersen et al [1] will be ineffective on most single photon avalanche photodiodes (APDs) and certainly ineffective on any detectors that are operated correctly. The attack is only successful if a redundant resistor is included in series with the APD, or if the detector discrimination levels are set inappropriately.
In this work we review the security vulnerability of Quantum Cryptography with respect to "man-in-the-middle attacks" and the standard authentication methods applied to counteract these attacks. We further propose a modified authentication algorithm which features higher efficiency with respect to consumption of mutual secret bits.
We introduce a new class of quantum quantum key distribution protocols, tailored to be robust against photon number splitting (PNS) attacks. We study one of these protocols, which differs from the BB84 only in the classical sifting procedure. This protocol is provably better than BB84 against PNS attacks at zero error.
Fuchs et al. [Phys. Rev. A, 1997] suggested an optimal attack on the BB84 protocol, where the necessary and sufficient condition for optimality involves the joint Hilbert space of the sender and the attacker. In this work, we propose a refined optimality criteria involving the Hilbert space of the attacker only. It reveals that the optimal (non-zero) overlaps between the attackers post-interactions states must be equal and numerically same as the difference between the fidelity and the disturbance at the receiving end. That amount turns out to be same as the reduction (factor) in Bell violatio…
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 this paper we review and comment on "A novel protocol-authentication algorithm ruling out a man-in-the-middle attack in quantum cryptography", [M. Peev et al., Int. J. Quant. Inform., 3, 225, (2005)]. In particular, we point out that the proposed primitive is not secure when used in a generic protocol, and needs additional authenticating properties of the surrounding quantum-cryptographic protocol.
If an eavesdropper succeeds in compromising the quantum as well as the classical channels and mimics the receiver "Bob" for the sender "Alice" and vice versa, one defence strategy is the successive, temporally interlocked partial transmission of the entire encrypted message.
A general study of arbitrary finite-size coherent attacks against continuous-variable quantum cryptographic schemes is presented. It is shown that, if the size of the blocks that can be coherently attacked by an eavesdropper is fixed and much smaller than the key size, then the optimal attack for a given signal-to-noise ratio in the transmission line is an individual gaussian attack. Consequently, non-gaussian coherent attacks do not need to be considered in the security analysis of such quantum cryptosystems.
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 consider a variant of the BB84 protocol for quantum cryptography, the prototype of tomographically incomplete protocols, where the key is generated by one-way communication rather than the usual two-way communication. Our analysis, backed by numerical evidence, establishes thresholds for eavesdropping attacks on the raw data and on the generated key at quantum bit error rates of 10% and 6.15%, respectively. Both thresholds are lower than the threshold for unconditional security in the standard BB84 protocol.
This is a study of the security of the Coherent One-Way (COW) protocol for quantum cryptography, proposed recently as a simple and fast experimental scheme. In the zero-error regime, the eavesdropper Eve can only take advantage of the losses in the transmission. We consider new attacks, based on unambiguous state discrimination, which perform better than the basic beam-splitting attack, but which can be detected by a careful analysis of the detection statistics. These results stress the importance of testing several statistical parameters in order to achieve higher rates of secret bits.
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 propose a variational quantum attack algorithm (VQAA) for classical AES-like symmetric cryptography, as exemplified the simplified-data encryption standard (S-DES). In the VQAA, the known ciphertext is encoded as the ground state of a Hamiltonian that is constructed through a regular graph, and the ground state can be found using a variational approach. We designed the ansatz and cost function for the S-DES's variational quantum attack. It is surprising that sometimes the VQAA is even faster than Grove's algorithm as demonstrated by our simulation results. The relationships of the entanglem…
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.
The promise of secure cryptographic quantum key distribution schemes is based on the use of quantum effects in the spin space. We point out that in fact in many current quantum cryptography protocols the space part of the wave function is neglected. However exactly the space part of the wave function describes the behaviour of particles in ordinary real three-dimensional space. As a result such schemes can be secure against eavesdropping attacks in the abstract spin space but could be insecure in the real three-dimensional space. We discuss an approach to the security of quantum key distributi…
We investigate the asymptotic security of one-way continuous variable quantum key distribution against Gaussian two-mode coherent attacks. The one-way protocol is implemented by arranging the channel uses in two-mode blocks. By applying symmetric random permutations over these blocks, the security analysis is in fact reduced to study two-mode coherent attacks and, in particular, Gaussian ones, due to the extremality of Gaussian states. We explicitly show that the use of two-mode Gaussian correlations by an eavesdropper leads to asymptotic secret key rates which are strictly larger than the rat…
Mistrustful cryptography includes important tasks like bit commitment, oblivious transfer, coin flipping, secure computations, position authentication, digital signatures and secure unforgeable tokens. Practical quantum implementations presently use photonic setups. In many such implementations, Alice sends photon pulses encoding quantum states and Bob chooses measurements on these states. In practice, Bob generally uses single photon threshold detectors, which cannot distinguish the number of photons in detected pulses. Also, losses and other imperfections require Bob to report the detected p…
We consider the two-way quantum cryptographic protocol with coherent states assuming direct reconciliation. A detailed security analysis is performed considering a two-mode coherent attack, that represents the residual eavesdropping once the parties have reduced the general attack by applying symmetric random permutations. In this context we provide a general analytical expression for the keyrate, discussing the impact of the residual two-mode correlations on the security of the scheme. In particular we identify the optimal eavesdropping against two-way quantum communication, which is given by…
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.
A new class of quantum cryptography (QC) protocols that are robust against the most general photon number splitting attacks in a weak coherent pulse implementation has been recently proposed. In this article we give a quite exhaustive analysis of several eavesdropping attacks on these schemes. The eavesdropper (Eve) is supposed to have unlimited technological power while the honest parties (Alice and Bob) use present day technology, in particular an attenuated laser as an approximation of a single-photon source. They exploit the nonorthogonality of quantum states for decreasing the information…
Recently, position-based quantum cryptography has been claimed to be unconditionally secure. In contrary, here we show that the existing proposals for position-based quantum cryptography are, in fact, insecure if entanglement is shared among two adversaries. Specifically, we demonstrate how the adversaries can incorporate ideas of quantum teleportation and quantum secret sharing to compromise the security with certainty. The common flaw to all current protocols is that the Pauli operators always map a codeword to a codeword (up to an irrelevant overall phase). We propose a modified scheme lack…
In practical quantum cryptography, the source sometimes produces multi-photon pulses, thus enabling the eavesdropper Eve to perform the powerful photon-number-splitting (PNS) attack. Recently, it was shown by Curty and Lutkenhaus [Phys. Rev. A 69, 042321 (2004)] that the PNS attack is not always the optimal attack when two photons are present: if errors are present in the correlations Alice-Bob and if Eve cannot modify Bob's detection efficiency, Eve gains a larger amount of information using another attack based on a 2->3 cloning machine. In this work, we extend this analysis to all distances…
We examine a situation that $n$ eavesdroppers attack the Bennett-Brassard cryptographic protocol via their own optimal and symmetric strategies. Information gain and mutual information with sender for each eavesdropper are explicitly derived. The receiver's error rate for the case of arbitrary $n$ eavesdroppers can be derived using a recursive relation. Although first eavesdropper can get mutual information without disturbance arising due to other eavesdroppers, subsequent eavesdropping generally increases the receiver's error rate. Other eavesdroppers cannot gain information on the input sign…
An attack on the ``Bennett-Brassard 84''(BB84) quantum key-exchange protocol in which Eve exploits the action of gravitation to infer information about the quantum-mechanical state of the qubit exchanged between Alice and Bob, is described. It is demonstrated that the known laws of physics do not allow to describe the attack. Without making assumptions that are not based on broad consensus, the laws of quantum gravity, unknown up to now, would be needed even for an approximate treatment. Therefore, it is currently not possible to predict with any confidence if information gained in this attack…
The security of a cryptographic key that is generated by communication through a noisy quantum channel relies on the ability to distill a shorter secure key sequence from a longer insecure one. We show that -- for protocols that use quantum channels of any dimension and completely characterize them by state tomography -- the noise threshold for classical advantage distillation is substantially lower than the threshold for quantum entanglement distillation because the eavesdropper can perform powerful coherent attacks. The earlier claims that the two noise thresholds are identical, which were b…
We present a new protocol for practical quantum cryptography, tailored for an implementation with weak coherent pulses. The key is obtained by a very simple time-of-arrival measurement on the data line; an interferometer is built on an additional monitoring line, allowing to monitor the presence of a spy (who would break coherence by her intervention). Against zero-error attacks (the analog of photon-number-splitting attacks), this protocol performs as well as standard protocols with strong reference pulses: the key rate decreases only as the transmission $t$ of the quantum channel. We present…
The use of linearly independent signal states in realistic implementations of quantum key distribution (QKD) enables an eavesdropper to perform unambiguous state discrimination. We explore quantitatively the limits for secure QKD imposed by this fact taking into account that the receiver can monitor to some extend the photon number statistics of the signals even with todays standard detection schemes. We compare our attack to the beamsplitting attack and show that security against beamsplitting attack does not necessarily imply security against the attack considered here.
We study a general family of quantum protocols for position verification and present a new class of attacks based on the Clifford hierarchy. These attacks outperform current strategies based on port-based teleportation for a large class of practical protocols. We then introduce the Interleaved Product protocol, a new scheme for position verification involving only the preparation and measurement of single-qubit states for which the best available attacks have a complexity exponential in the number of classical bits transmitted.
We analyze the security of the two-way continuous-variable quantum key distribution protocol in reverse reconciliation against general two-mode attacks, which represent all accessible attacks at fixed channel parameters. Rather than against one specific attack model, the expression of secret key rates of the two-way protocol are derived against all accessible attack models. It is found that there is an optimal two-mode attack to minimize the performance of the protocol in terms of both secret key rates and maximal transmission distances. We identify the optimal two-mode attack, give the specif…
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.
This is a Reply to the Comment by Lydersen et al. [arXiv: 1106.3756v1].
The phase-coding quantum cryptographic scheme using the homodyne detection and weak coherent state [Hirano et al.,Phys. Rev. A 68, 042331 (2003)] provides the simplest continuous-variable quantum key distribution scheme from the experimental side. However, the inherent loss of the practical system will not only increase the bit error rate (BER) but also affect the security of the final key. In this paper, we propose a single-photon-detection attack, and then the security of the final key will be compromised in some parameter regimes. Our results show that the BER induced by Eve can be lower th…
Quantum cryptographic protocols based on complementarity are nonsecure against attacks in which complementarity is imitated with classical resources. The Kochen-Specker (KS) theorem provides protection against these attacks, without requiring entanglement or spatially separated composite systems. We analyze the maximum tolerated noise to guarantee the security of a KS-protected cryptographic scheme against these attacks, and describe a photonic realization of this scheme using hybrid ququarts defined by the polarization and orbital angular momentum of single photons.
An elementary derivation of best eavesdropping strategies for the 4 state BB84 quantum cryptography protocol is presented, for both incoherent and two--qubit coherent attacks. While coherent attacks do not help Eve to obtain more information, they are more powerful to reveal the whole message sent by Alice. Our results are based on symmetric eavesdropping strategies, which we show to be sufficient to analyze these kind of problems.
We consider a quantum polynomial-time algorithm which solves the discrete logarithm problem for points on elliptic curves over $GF(2^m)$. We improve over earlier algorithms by constructing an efficient circuit for multiplying elements of binary finite fields and by representing elliptic curve points using a technique based on projective coordinates. The depth of our proposed implementation, executable in the Linear Nearest Neighbor (LNN) architecture, is $O(m^2)$, which is an improvement over the previous bound of $O(m^3)$ derived assuming no architectural restrictions.
The goal of two-party cryptography is to enable two parties, Alice and Bob, to solve common tasks without the need for mutual trust. Examples of such tasks are private access to a database, and secure identification. Quantum communication enables security for all of these problems in the noisy-storage model by sending more signals than the adversary can store in a certain time frame. Here, we initiate the study of device-independent protocols for two-party cryptography in the noisy-storage model. Specifically, we present a relatively easy to implement protocol for a cryptographic building bloc…
In practical quantum key distribution, weak coherent state is often used and the channel transmittance can be very small therefore the protocol could be totally insecure under the photon-number-splitting attack. We propose an efficient method to verify the upper bound of the fraction of counts caused by multi-photon pluses transmitted from Alice to Bob, given whatever type of Eve's action. The protocol simply uses two coherent states for the signal pulses and vacuum for decoy pulse. Our verified upper bound is sufficiently tight for QKD with very lossy channel, in both asymptotic case and non-…
We propose a quantum key distribution protocol based on a quantum retrodiction protocol, known as the Mean King problem. The protocol uses a two way quantum channel. We show security against coherent attacks in a transmission error free scenario, even if Eve is allowed to attack both transmissions. This establishes a connection between retrodiction and key distribution.
Strong attacks against quantum key distribution use quantum memories and quantum gates to attack directly the final key. In this paper we extend a novel security result recently obtained, to demonstrate proofs of security against a wide class of such attacks. To reach this goal we calculate information-dependent reduced density matrices, we study the geometry of quantum mixed states, and we find bounds on the information leaked to an eavesdropper. Our result suggests that quantum cryptography is ultimately secure.
Practical implementations of quantum cryptography use attenuated laser pulses as the signal source rather than single photons. The channels used to transmit are also lossy. Here we give a simple derivation of two beam-splitting attacks on quantum cryptographic systems using laser pulses, either coherent or mixed states with any mean photon number. We also give a simple derivation of a photon-number splitting attack, the most advanced, both in terms of performance and technology required. We find bounds on the maximum disturbance for a given mean photon number and observed channel transmission …
Semiconductor avalanche photodiodes (APDs) are commonly used for single photon detection in quantum key distribution. Recently, many attacks using bright illumination have been proposed to manipulate gated InGaAs APDs. In order to devise effective counter-measures, careful analysis of these attacks must be carried out to distinguish between incorrect operation and genuine loopholes. Here, we show that correctly-operated, gated APDs are immune to continuous-wave illumination attacks, while monitoring the photocurrent for anomalously high values is a straightforward counter-measure against attac…
In this letter, first, we investigate the security of a continuous-variable quantum cryptographic scheme with a postselection process against individual beam splitting attack. It is shown that the scheme can be secure in the presence of the transmission loss owing to the postselection. Second, we provide a loss limit for continuous-variable quantum cryptography using coherent states taking into account excess Gaussian noise on quadrature distribution. Since the excess noise is reduced by the loss mechanism, a realistic intercept-resend attack which makes a Gaussian mixture of coherent states g…
A quantum key distribution system may be probed by an eavesdropper Eve by sending in bright light from the quantum channel and analyzing the back-reflections. We propose and experimentally demonstrate a setup for mounting such a Trojan-horse attack. We show it in operation against the quantum cryptosystem Clavis2 from ID~Quantique, as a proof-of-principle. With just a few back-reflected photons, Eve discerns Bob's secret basis choice, and thus the raw key bit in the Scarani-Acín-Ribordy-Gisin 2004 protocol, with higher than 90% probability. This would clearly breach the security of the cryptos…
We describe a cryptographic protocol in which Wheeler's delayed choice experiment is used to generate the key distribution. The protocol, which uses photons polarized only along one axis, is secure against general attacks.
We consider a new type of attack on a coherent quantum key distribution protocol [coherent one-way (COW) protocol]. The main idea of the attack consists in measuring individually the intercepted states and sending the rest of them unchanged. We have calculated the optimum values of the attack parameters for an arbitrary length of a channel length and compared this novel attack with a standard beam-splitting attack.
The phenomenon of quantum erasure has long intrigued physicists, but has surprisingly found limited practical application. Here, we propose an erasure-based protocol for quantum key distribution (QKD) that promises inherent security against detector attacks.
In this paper we analyze the security of the so-called quantum tomographic cryptography with the source producing entangled photons via an experimental scheme proposed in Phys. Rev. Lett. 92, 37903 (2004). We determine the range of the experimental parameters for which the protocol is secure against the most general incoherent attacks.
Quantum cryptography has attracted much recent attention due to its potential for providing secret communications that cannot be decrypted by any amount of computational effort. This is the first analysis of the secrecy of a practical implementation of the BB84 protocol that simultaneously takes into account and presents the {\it full} set of complete analytical expressions for effects due to the presence of pulses containing multiple photons in the attenuated output of the laser, the finite length of individual blocks of key material, losses due to error correction, privacy amplification, con…
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…
It is shown that an existing method to study ideal individual attacks on the BB84 QKD protocol using error discard can be adapted to reconciliation with error correction, and that an optimal attack can be explicitly found. Moreover, this attack fills Luetkenhaus bound, independently of whether error positions are leaked to Eve, proving that it is tight. In addition, we clarify why the existence of such optimal attacks is not in contradiction with the established ``old-style'' theory of BB84 individual attacks, as incorrectly suggested recently in a news feature.
We present a crytographic protocol based upon entangled qutrit pairs. We analyse the scheme under a symmetric incoherent attack and plot the region for which the protocol is secure and compare this with the region of violations of certain Bell inequalities.
In the cryptographic context, an earlier unexplored application of the temporal version of the Bell-type inequality is shown here in the device-independent (DI) scenario. This is done by using the Leggett-Garg inequality (LGI) to demonstrate the security against eavesdropping in a quantum key distribution (QKD) scheme. This typically involves a higher dimensional attack against which the standard BB84 protocol is insecure. For this purpose, we invoke an appropriate form of LGI. While the key generation is done by the usual Bennett-Brassard 1984 (BB84) method, the security check against device …
We present the first device-independent quantum cryptography protocol for continuous variables. Our scheme is based on the Gottesman-Kitaev-Preskill encoding scheme whereby a qubit is embedded in the infinite-dimensional space of a quantum harmonic oscillator. The novel application of discrete-variable device-independent quantum key distribution to this encoding enables a continuous-variable analogue. Since the security of this protocol is based on discrete-variables we inherit by default security against collective attacks and, under certain memoryless assumptions, coherent attacks. We find t…
Quantum cryptography is reviewed, first using entanglement both for the intuition and for the experimental realizations. Next, the implementation is simplified in several steps until it becomes practical. At this point entanglement has disappeared. This method can be seen as a lesson of Applied Physics. Finally, security issues, e.g. photon number splitting attacks, and counter-measures are discussed.
A fully general approach to the security analysis of continuous-variable quantum key distribution (CV-QKD) is presented. Provided that the quantum channel is estimated via the covariance matrix of the quadratures, Gaussian attacks are shown to be optimal against all eavesdropping strategies, including collective and coherent attacks. The proof is made strikingly simple by combining a physical model of measurement, an entanglement-based description of CV-QKD, and a recent powerful result on the extremality of Gaussian states [Phys. Rev. Lett. 96, 080502 (2006)].
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