We introduce a constructive method to calculate the achievable secret key rate for a generic class of quantum key distribution protocols, when only a finite number n of signals is given. Our approach is applicable to all scenarios in which the quantum state shared by Alice and Bob is known. In particular, we consider the six state protocol with symmetric eavesdropping attacks, and show that for a small number of signals, i.e. below the order of 10^4, the finite key rate differs significantly from the asymptotic value for n approaching infinity. However, for larger n, a good approximation of the asymptotic value is found. We also study secret key rates for protocols using higher-dimensional quantum systems.
We suggest an attack on a symmetric non-ideal quantum coin-tossing protocol suggested by Mayers Salvail and Chiba-Kohno. The analysis of the attack shows that the protocol is insecure.
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 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.
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…
A symmetric device-independent quantum key distribution (DIQKD) protocol is proposed in this paper, with Holevo limit and subadditivity of von Neumann entropy, one can bound Eve's ability with collective attack. Together with symmetry of this protocol, the state Eve prepared for Alice and Bob, and at the same time, her eavesdropping on Alice's and Bob's measurements can be definitely inferred at the assumption that Eve aims at maximizing her information gain. The optimal state under this circumstance can be solely bounded with Alice and Bob's statistical results on the quantity of Clauser-Horn…
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.
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, security of practically decoy state quantum key distribution under fake state attack is considered. If quantum key distribution is insecure under this type of attack, decoy sources can not also provide it with enough security. Strictly analysis shows that Eve should eavesdrop with the aid of photon-number-resolving instruments. In practical implementation of decoy state quantum key distribution where statistical fluctuation is considered, however, Eve can attack it successfully with threshold detectors.
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 a novel attack on quantum key distribution based on the idea of adaptive absorption [calsam01]. The conditional beam splitting attack is shown to be much more efficient than the conventional beam spitting attack, achieving a performance similar to the, powerful but currently unfeasible, photon number splitting attack. The implementation of the conditional beam splitting attack, based solely on linear optical elements, is well within reach of current technology.
We investigate limitations imposed by sequential attacks on the performance of differential-phase-shift quantum key distribution protocols that use pulsed coherent light. In particular, we analyze two sequential attacks based on unambiguous state discrimination and minimum error discrimination, respectively, of the signal states emitted by the source. Sequential attacks represent a special type of intercept-resend attacks and, therefore, they do not allow the distribution of a secret key.
We propose a double blinding-attack on entangled-based quantum key distribution protocols. The principle of the attack is the same as in existing blinding attack except that instead of blinding the detectors on one side only, Eve is blinding the detectors of both Alice and Bob. In the BBM92 protocol, the attack allows Eve to get a full knowledge of the key and remain undetected even if Alice and Bob are using 100% efficient detectors. The attack can be easily extended to Ekert protocol, with an efficiency as high as 85.3%.
We develop a new method to quantify the secret key rate for permutation-invariant protocols for coherent attacks and finite resources. The method reduces the calculation of secret key rates for coherent attacks to the calculation for collective attacks by bounding the smooth min-entropy of permutation-invariant states via the smooth min-entropy of corresponding tensor-product states. The comparison of the results to the well-known post-selection technique for the BB84 and six-state protocol shows the high relevance of this method. Since our calculation of secret key rates for coherent attacks …
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.
We investigate the security of continuous-variable (CV) quantum key distribution (QKD) using coherent states and reverse reconciliation against Gaussian individual attacks based on an optimal Gaussian $1 \to 2$ cloning machine. We provide an implementation of the optimal Gaussian individual attack. we also find a Bell-measurement attack which works without delayed choice of measurements and has better performance than the cloning attack.
The disturbance effect of a depolarizing channel on the security of the quantum key distribution of the four state BB84 protocol with multiple sequentiel intercept and resend attacks of many eavesdroppers, has been studied. The quantum bit error rate and the mutual information are computed for arbitray number of attacks.
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 propose a way to retrieve the secure key generated by the coherent one way protocol without reading the information transmitted on the quantum channel.
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 introduce new sophisticated attacks with a Hong-Ou-Mandel interferometer against quantum key distribution (QKD) and propose a new QKD protocol grafted with random basis shuffling to block up those attacks. When the polarization basis is randomly and independently shuffled by sender and receiver, the new protocol can overcome the attacks even for not-so-weak coherent pulses. We estimate the number of photons to guarantee the security of the protocol.
Recently, Zhang et al. proposed a single-state semi-quantum key distribution protocol (Int. J. Quantum Inf, 18, 4, 2020) to help a quantum participant to share a secret key with a classical participant. However, this study shows that an eavesdropper can use a double C-NOT attack to obtain parts of the final shared key without being detected by the participants. To avoid this problem, a modification is proposed here.
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 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 propose a new kind of individual attack, based on randomly selected dissipation, on Bennett-Brassard 1984 protocol of practical quantum key distribution (QKD) system with lossy and noisy quantum channel. Since an adversary with super quantum channel can disguise loss and errors induced by his attack as that of the system, he can obtain innegligible amount of information for a practical QKD system, without being detected by legal participants.
Unconditional security of quantum key distribution protocol can be guaranteed by the basic property of quantum mechanics. Unfortunately, the practical quantum key distribution system always have some imperfections, and the practical system may be attacked if the imperfection can be controlled by the eavesdropper Eve. Applying the fatal security loophole introduced by the imperfect beam splitter's wavelength dependent optical property, we propose wavelength-dependent attacking model, which can be applied to almost all practical quantum key distribution systems with the passive state modulation …
An intercept-resend attack on a continuous-variable quantum-key-distribution protocol is investigated experimentally. By varying the interception fraction, one can implement a family of attacks where the eavesdropper totally controls the channel parameters. In general, such attacks add excess noise in the channel, and may also result in non-Gaussian output distributions. We implement and characterize the measurements needed to detect these attacks, and evaluate experimentally the information rates available to the legitimate users and the eavesdropper. The results are consistent with the optim…
To the active basis choice decoy state quantum key distribution systems with detector efficiency mismatch, we present a modified attack strategy, which is based on faked states attack, with quantum nondemolition measurement ability to restress the threat of detector efficiency mismatch. Considering that perfect quantum nondemolition measurement ability dose not exist in real life, we also propose a practical attack strategy using photon number resolving detectors. Theoretical analysis and numerical simulation results show that, without changing the channel, our attack strategies are serious th…
A simple photon-number splitting attack is described which works on any lossy quantum key distribution system with a multi-photon source independently of the mean source photon number, and with no induced error rate. In particular, it cannot be detected by decoy states. The quantitative loss of security is similar when the user employs photon-number resolving detectors or threshold detectors. Numerical values indicate that existing implementations of concrete QKD systems are fundamentally insecure against this attack because a large portion of leaked sifted key bits is not accounted for. The p…
In the classical setting, public-key encryption requires randomness in order to be secure against a forward search attack, whereby an adversary compares the encryption of a guess of the secret message with that of the actual secret message. We show that this is also true in the information-theoretic setting -- where the public keys are quantum systems -- by defining and giving an example of a forward search attack for any deterministic quantum-public-key bit-encryption scheme. However, unlike in the classical setting, we show that any such deterministic scheme can be used as a black box to bui…
In this paper we present the quantum control attack on quantum key distribution systems. The cornerstone of the attack is that Eve can use unitary (polar) decomposition of her positive-operator valued measure elements, which allows her to realize the feed-forward operation (quantum control), change the states in the channel after her measurement and impose them to Bob. Below we consider the general eavesdropping strategy and the conditions those should be satisfied to provide the attack successfully. Moreover we consider several types of the attack, each of them is based on a different type of…
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…
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…
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 …
Security of an ideal system for quantum key distribution can be formally proved. However, technological imperfections of real systems can be misused by an eavesdropper to get information about the key without causing a detectable change in the error rate. An example of this is the blinding attack where the eavesdropper manipulates detectors of the receiving party. To avoid such an attack, technical modifications of the device are usually required. In this paper we show that an extended measurement, similar to the Bell test measurement, can reveal the blinding attack without any modification of…
The Fuchs-Peres-Brandt (FPB) probe realizes the most powerful individual attack on Bennett-Brassard 1984 quantum key distribution (BB84 QKD) by means of a single controlled-NOT (CNOT) gate. This paper describes a complete physical simulation of the FPB-probe attack on polarization-based BB84 QKD using a deterministic CNOT constructed from single-photon two-qubit quantum logic. Adding polarization-preserving quantum nondemolition measurements of photon number to this configuration converts the physical simulation into a true deterministic realization of the FPB attack.
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 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 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.
Security analysis of orthogonal state attack on a high-speed quantum key distribution system
College of Computer Science and Technology, National University of Defense Technology（国防科技大学计算机学院）；School of Automation, Central South University（中南大学自动化学院）；Laboratory of Quantum Information, University of Science and Technology of China（中国科学技术大学量子信息实验室）；Anhui Province Key Laboratory of Quantum Network, University of Science and Technology of China（中国科学技术大学安徽省量子网络重点实验室）；Hefei National Laboratory, University of Science and Technology of China（中国科学技术大学合肥国家实验室）
Quantum cryptography promises security based on the laws of physics with proofs of security against attackers of unlimited computational power. However, deviations from the original assumptions allow quantum hackers to compromise the system. We present a side channel attack that takes advantage of ventilation holes in optical devices to inject additional photons that can leak information about the secret key. We experimentally demonstrate light injection on an ID~Quantique Clavis2 quantum key distribution platform and show that this may help an attacker to learn information about the secret ke…
The differential phase shift quantum key distribution protocol is of high interest due to its relatively simple practical implementation. This protocol uses trains of coherent pulses and allows the legitimate users to resist individual attacks. In this paper, a new attack on this protocol is proposed which is based on the idea of information extraction from the part of each coherent state and then making decision about blocking the rest part depending on the amount of extracted information.
Coherent-one-way (COW) quantum key distribution (QKD) held the promise of distributing secret keys over long distances with a simple experimental setup. Indeed, this scheme is currently used in commercial applications. Surprisingly, however, it has been recently shown that its secret key rate scales at most quadratically with the system's transmittance and, thus, it is not appropriate for long distance QKD transmission. Such pessimistic result was derived by employing a so-called zero-error attack, in which the eavesdropper does not introduce any error, but still the legitimate users of the sy…
The article is focused on research of an attack on the quantum key distribution system and proposes a countermeasure method. Particularly noteworthy is that this is not a classic attack on a quantum protocol. We describe an attack on the process of calibration. Results of the research show that quantum key distribution systems have vulnerabilities not only in the protocols, but also in other vital system components. The described type of attack does not affect the cryptographic strength of the received keys and does not point to the vulnerability of the quantum key distribution protocol. We al…
In this paper, we report the first quantum key-recovery attack on a symmetric block cipher design, using classical queries only, with a more than quadratic time speedup compared to the best classical attack. We study the 2XOR-Cascade construction of Gaži and Tessaro (EUROCRYPT~2012). It is a key length extension technique which provides an n-bit block cipher with 5n/2 bits of security out of an n-bit block cipher with 2n bits of key, with a security proof in the ideal model. We show that the offline-Simon algorithm of Bonnetain et al. (ASIACRYPT~2019) can be extended to, in particular, attack …
Unconditional security proofs of various quantum key distribution (QKD) protocols are built on idealized assumptions. One key assumption is: the sender (Alice) can prepare the required quantum states without errors. However, such an assumption may be violated in a practical QKD system. In this paper, we experimentally demonstrate a technically feasible "intercept-and-resend" attack that exploits such a security loophole in a commercial "plug & play" QKD system. The resulting quantum bit error rate is 19.7%, which is below the proven secure bound of 20.0% for the BB84 protocol. The attack we ut…
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…
I present an eavesdropping on the protocol proposed by W.-H. Kye, et al. [Phys. Rev. Lett. 95, 040501 (2005)]. I show how an undetectable Eve can steal the whole information by labeling and then measuring the photons prepared by the user Alice.
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…
In this paper, we discuss the security of the differential-phase-shift quantum key distribution (DPSQKD) protocol by introducing an improved version of the so-called sequential attack, which was originally discussed by Waks et al. Our attack differs from the original form of the sequential attack in that the attacker Eve modulates not only the phases but also the amplitude in the superposition of the single-photon states which she sends to the receiver. Concentrating especially on the "discretized gaussian" intensity modulation, we show that our attack is more effective than the individual att…
To protect practical quantum key distribution (QKD) against photon-number-splitting attacks, one could measure the coherence of the received signals. One prominent example that follows this approach is coherent-one-way (COW) QKD, which is commercially available. Surprisingly, however, it has been shown very recently that its secret key rate scales quadratically with the channel transmittance, and, thus, this scheme is unsuitable for long-distance transmission. This result was derived by using a zero-error attack, which prevents the distribution of a secure key without introducing any error. He…
Quantum Key Distribution or QKD provides symmetric key distribution using the quantum mechanics/channels with new security properties. The security of QKD relies on the difficulty of the quantum state discrimination problem. We discover that the recent developments in $\mathcal{PT}$ symmetry can be used to expedite the quantum state discrimination problem and therefore to attack the BB84 QKD scheme. We analyze the security of the BB84 scheme and show that the attack significantly increases the eavesdropping success rate over the previous Hermitian quantum state discrimination approach. We desi…
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.
An eavesdropper Eve may probe a quantum key distribution (QKD) system by sending a bright pulse from the quantum channel into the system and analyzing the back-reflected pulses. Such Trojan-horse attacks can breach the security of the QKD system if appropriate safeguards are not installed or if they can be fooled by Eve. We present a risk analysis of such attacks based on extensive spectral measurements, such as transmittance, reflectivity, and detection sensitivity of some critical components used in typical QKD systems. Our results indicate the existence of wavelength regimes where the attac…
The quantum security of lightweight block ciphers is receiving more and more attention. However, the existing quantum attacks on lightweight block ciphers mainly focused on the quantum exhaustive search, while the quantum dedicated attacks combined with classical cryptanalysis methods haven't been well studied. In this paper, we study quantum key recovery attack on SIMON block cipher using Quantum Amplitude Amplification algorithm in Q1 model. At first, we reanalyze the quantum circuit complexity of quantum master key exhaustive search on SIMON block cipher. The Clifford gates count is estimat…
Quantum key distribution can be performed with practical signal sources such as weak coherent pulses. One example of such a scheme is the Bennett-Brassard protocol that can be implemented via polarization of the signals, or equivalent signals. It turns out that the most powerful tool at the disposition of an eavesdropper is the photon-number splitting attack. We show that this attack can be extended in the relevant parameter regime such as to preserve the Poissonian photon number distribution of the combination of the signal source and the lossy channel.
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…
We review the study on a two way quantum key distribution protocol given imperfect settings through a simple analysis of a toy model and show that it can outperform a BB84 setup. We provide the sufficient condition for this as a ratio of optimal intensities for the protocols.
