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 gives a loss limit in the presence of any excess Gaussian noise.
We use the probability of error as a measure of distinguishability between two pure and two mixed symmetric coherent states in the context of continuous variable quantum cryptography. We show that the two mixed symmetric coherent states (in which the various components have the same real part) never give an eavesdropper more information than two pure coherent states.
Weak coherent states as a photon source for quantum cryptography have limit in secure data rate and transmission distance because of the presence of multi-photon events and loss in transmission line. Two-photon events in a coherent state can be taken out by a two-photon interference scheme. We investigate the security issue of utilizing this modified coherent state in quantum cryptography. A 4 dB improvement in secure data rate or a nearly two-fold increase in transmission distance over the coherent state are found. With a recently proposed and improved encoding strategy, further improvement i…
A setup for discriminating between arbitrary two coherent states of a single light mode with the highest success rate allowed by quantum mechanics is presented. Its application to time-multiplexed quantum key distribution is discussed.
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 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.
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.
All incoherent as well as 2- and 3-qubit coherent eavesdropping strategies on the 6 state protocol of quantum cryptography are classified. For a disturbance of 1/6, the optimal incoherent eavesdropping strategy reduces to the universal quantum cloning machine. Coherent eavesdropping cannot increase Eve's Shannon information, neither on the entire string of bits, nor on the set of bits received undisturbed by Bob. However, coherent eavesdropping can increase as well Eve's Renyi information as her probability of guessing correctly all bits. The case that Eve delays the measurement of her probe u…
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 consider one of the quantum key distribution protocols recently introduced in Ref. [Pirandola et al., Nature Physics 4, 726 (2008)]. This protocol consists in a two-way quantum communication between Alice and Bob, where Alice encodes secret information via a random phase-space displacement of a coherent state. In particular, we study its security against a specific class of individual attacks which are based on combinations of Gaussian quantum cloning machines.
In order to beat any type of photon-number-splitting attack, we propose a protocol for quantum key distributoin (QKD) using 4 different intensities of pulses. They are vacuum and coherent states with mean photon number $μ,μ'$ and $μ_s$. $μ_s$ is around 0.55 and this class of pulses are used as the main signal states. The other two classes of coherent states ($μ,μ'$) are also used signal states but their counting rates should be studied jointly with the vacuum. We have shown that, given the typical set-up in practice, the key rate from the main signal pulses is quite close to the theoretically …
We investigate the performance of continuous variable quantum key distribution scheme in a practical setting. More specifically, we take non-ideal error reconciliation procedure into account. The quantum channel connecting the two honest parties is assumed to be lossy but noiseless. Secret key rates are given for the case that the measurement outcomes are postselected or a reverse reconciliation scheme is applied. The reverse reconciliation scheme loses its initial advantage in the practical setting. If one combines postselection with reverse reconciliation however, much of this advantage can …
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 propose several methods for quantum key distribution (QKD) based upon the generation and transmission of random distributions of coherent or squeezed states, and we show that they are are secure against individual eavesdropping attacks. These protocols require that the transmission of the optical line between Alice and Bob is larger than 50 %, but they do not rely on "non-classical" features such as squeezing. Their security is a direct consequence of the no-cloning theorem, that limits the signal to noise ratio of possible quantum measurements on the transmission line. Our approach can als…
The safety of a quantum key distribution system relies on the fact that any eavesdropping attempt on the quantum channel creates errors in the transmission. For a given error rate, the amount of information that may have leaked to the eavesdropper depends on both the particular system and the eavesdropping strategy. In this work, we discuss quantum cryptographic protocols based on the transmission of weak coherent states and present a new system, based on a symbiosis of two existing ones, and for which the information available to the eavesdropper is significantly reduced. This system is there…
The Differential-Phase-Shift (DPS) and the Coherent-One-Way (COW) are among the most practical protocols for quantum cryptography, and are therefore the object of fast-paced experimental developments. The assessment of their security is also a challenge for theorists: the existing tools, that allow to prove security against the most general attacks, do not apply to these two protocols in any straightforward way. We present new upper bounds for their security in the limit of large distances ($d \gtrsim 50$km with typical values in optical fibers) by considering a large class of collective attac…
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 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.
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…
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 discuss several methods for unambiguous state discrimination of N symmetric coherent states using linear optics and photodetectors. One type of measurements is shown to be optimal in the limit of small photon numbers for any N. For the special case of N=4 this measurement can be fruitfully used by the receiving end (Bob) in an implementation of the BB84 quantum key distribution protocol using faint laser pulses. In particular, if Bob detects only a single photon the procedure is equivalent to the standard measurement that he would have to perform in a single-photon implementation of BB84, i…
We investigate the security against collective attacks of a continuous variable quantum key distribution scheme in the asymptotic key limit for a realistic setting. The quantum channel connecting the two honest parties is assumed to be lossy and imposes Gaussian noise on the observed quadrature distributions. Secret key rates are given for direct and reverse reconciliation schemes including postselection in the collective attack scenario. The effect of a non-ideal error correction and two-way communication in the classical post-processing step is also taken into account.
We consider the distinguishability of Gaussian states from the view point of continuous-variable quantum cryptography using post-selection. Specifically, we use the probability of error to distinguish between two pure coherent (squeezed) states and two particular mixed symmetric coherent (squeezed) states where each mixed state is an incoherent mixture of two pure coherent (squeezed) states with equal and opposite displacements in the conjugate quadrature. We show that the two mixed symmetric Gaussian states (where the various components have the same real part) never give an eavesdropper more…
Quantum computing had a profound impact on cryptography. Shor's discovery of an efficient quantum algorithm for factoring large integers implies that many existing classical systems based on computational assumptions can be broken, once a quantum computer is built. It is therefore imperative to find other means of implementing secure protocols. This thesis aims to contribute to the understanding of both the physical limitations, as well as the possibilities of cryptography in the quantum setting. In particular, we investigate several questions that are crucial to the security of quantum protoc…
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 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…
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…
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.
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.
We discuss quantum key distribution protocols using quantum continuous variables. We show that such protocols can be made secure against individual gaussian attacks regardless the transmission of the optical line between Alice and Bob. This is achieved by reversing the reconciliation procedure subsequent to the quantum transmission, that is, using Bob's instead of Alice's data to build the key. Although squeezing or entanglement may be helpful to improve the resistance to noise, they are not required for the protocols to remain secure with high losses. Therefore, these protocols can be impleme…
A number of questions associated with practical implementations of quantum cryptography systems having to do with unconditional secrecy, computational loads and effective secrecy rates in the presence of perfect and imperfect sources are discussed. The different types of unconditional secrecy, and their relationship to general communications security, are discussed in the context of quantum cryptography. In order to actually carry out a quantum cryptography protocol it is necessary that sufficient computational resources be available to perform the various processing steps, such as sifting, er…
We propose a new coherent state quantum key distribution protocol that eliminates the need to randomly switch between measurement bases. This protocol provides significantly higher secret key rates with increased bandwidths than previous schemes that only make single quadrature measurements. It also offers the further advantage of simplicity compared to all previous protocols which, to date, have relied on switching.
In this paper we investigate the security of a quantum cryptographic scheme which utilizes balanced homodyne detection and weak coherent pulse (WCP). The performance of the system is mainly characterized by the intensity of the WCP and postselected threshold. Two of the simplest intercept/resend eavesdropping attacks are analyzed. The secure key gain for a given loss is also discussed in terms of the pulse intensity and threshold.
We study the impact of finite-size effects on the security of thermal one-way quantum cryptography. Our approach considers coherent/squeezed states at the preparation stage, on the top of which the sender adds trusted thermal noise. We compute the key rate incorporating finite-size effects, and we obtain the security threshold at different frequencies. As expected finite-size effects deteriorate the performance of thermal quantum cryptography. Our analysis is useful to quantify the impact of this degradation on relevant parameters like tolerable attenuation, transmission frequencies at which o…
The application in cryptography of quantum algorithms for prime factorization fostered the interest in quantum computing. However, quantum computers, and particularly quantum annealers, can also be helpful to construct secure cryptographic keys. Indeed, finding robust Boolean functions for cryptography is an important problem in sequence ciphers, block ciphers, and hash functions, among others. Due to the super-exponential size $\mathcal{O}(2^{2^n})$ of the associated space, finding $n$-variable Boolean functions with global cryptographic constraints is computationally hard. This problem has a…
BBN, Harvard, and Boston University are building the DARPA Quantum Network, the world's first network that delivers end-to-end network security via high-speed Quantum Key Distribution, and testing that Network against sophisticated eavesdropping attacks. The first network link has been up and steadily operational in our laboratory since December 2002. It provides a Virtual Private Network between private enclaves, with user traffic protected by a weak-coherent implementation of quantum cryptography. This prototype is suitable for deployment in metro-size areas via standard telecom (dark) fiber…
We report an experimental quantum key distribution that utilizes balanced homodyne detection, instead of photon counting, to detect weak pulses of coherent light. Although our scheme inherently has a finite error rate, it allows high-efficiency detection and quantum state measurement of the transmitted light using only conventional devices at room temperature. When the average photon number was 0.1, an error rate of 0.08 and "effective" quantum efficiency of 0.76 were obtained.
We consider two-way continuous-variable quantum key distribution, studying its security against general eavesdropping strategies. Assuming the asymptotic limit of many signals exchanged, we prove that two-way Gaussian protocols are immune to coherent attacks. More precisely we show the general superadditivity of the two-way security thresholds, which are proven to be higher than the corresponding one-way counterparts in all cases. We perform the security analysis first reducing the general eavesdropping to a two-mode coherent Gaussian attack, and then showing that the superadditivity is achiev…
We present a bidirectional quantum communication system based on optical phase conjugation for achieving fully autocompensating high-dimensional quantum cryptography. We prove that random phase shifts and couplings among 2N spatial and polarization optical modes described by SU(2N) transformations due to perturbations are autocompensated after a single round trip between Alice and Bob. Bob can use a source of single photons or, alternatively, coherent states and then Alice attenuates them up to a single photon level, and thus non-perturbated 1-qudit states are generated for high-dimensional QK…
We introduce new quantum key distribution protocols using quantum continuous variables, that are secure against individual attacks for any transmission of the optical line between Alice and Bob. In particular, it is not required that this transmission is larger than 50 %. Though squeezing or entanglement may be helpful, they are not required, and there is no need for quantum memories or entanglement purification. These protocols can thus be implemented using coherent states and homodyne detection, and they may be more efficient than usual protocols using quantum discrete variables.
We demonstrate that secure quantum key distribution systems based on continuous variables implementations can operate beyond the apparent 3 dB loss limit that is implied by the beam splitting attack . The loss limit was established for standard minimum uncertainty states such as coherent states. We show that by an appropriate postselection mechanism we can enter a region where Eve's knowledge falls behind the information shared between Alice and Bob even in the presence of substantial losses.
The significance of quantum computation for cryptography is discussed. Following a brief survey of the requirements for quantum computational hardware, an overview of the ion trap quantum computation project at Los Alamos is presented. The physical limitations to quantum computation with trapped ions are analyzed and an assessment of the computational potential of the technology is made.
The large-alphabet quantum cryptography protocol based on the two-mode coherently correlated multi-photon beams is proposed. The alphabet extension for the protocol is shown to result in the increase of the QKD effectiveness and security.
We provide a complete proof of the security of quantum cryptography against any eavesdropping attack including coherent measurements even in the presence of noise. Polarization-based cryptographic schemes are shown to be equivalent to EPR-based schemes. We also show that the performance of a noisy channel approaches that of a noiseless one as the error rate tends to zero. (i.e., the secrecy capacity $C_s (ε) \to C_s (0)$ as $ε\to 0$.) One implication of our results is that one can {\it double} the efficiency of a most well-known quantum cryptographic scheme proposed by Bennett and Brassard sim…
In this thesis we explore the benefits of relativistic constraints for cryptography. We first revisit non-communicating models and its applications in the context of interactive proofs and cryptography. We propose bit commitment protocols whose security hinges on communication constraints and investigate its limitations. We explain how some non-communicating models can be justified by special relativity and study the limitations of such models. In particular, we present a framework for analysing security of multiround relativistic protocols. The second part of the thesis is dedicated to analys…
The use of quantum bits (qubits) in cryptography holds the promise of secure cryptographic quantum key distribution schemes. Unfortunately, the implemented schemes can be totally insecure. We provide a thorough investigation of security issues for practical quantum key distribution, taking into account channel losses, a realistic detection process, and modifications of the ``qubits'' sent from the sender to the receiver. We first show that even quantum key distribution with perfect qubits cannot be achieved over long distances when fixed channel losses and fixed dark count errors are taken int…
Quantum Cryptography is on the verge of commercial application. One of its greatest limitations is over long distance - secret key rates are low and the longest fibre over which any key has been exchanged is currently 100 km. We investigate the quantum relay, which can increase the maximum distance at which quantum cryptography is possible. The relay splits the channel into sections, and sends a different photon across each section, increasing the signal to noise ratio. The photons are linked as in teleportation, with entangled photon pairs and Bell measurements. We show that such a scheme cou…
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 …
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…
We present a generalized tomographic quantum key distribution protocol in which the two parties share a Bell diagonal mixed state of two qubits. We show that if an eavesdropper performs a coherent measurement on many quantum ancilla states simultaneously, classical methods of secure key distillation are less effective than quantum entanglement distillation protocols. We also show that certain Bell diagonal states are resistant to any attempt of incoherent eavesdropping.
We prove that the teleportation based quantum cryptography protocol presented in [Opt. Commun. 283, 184 (2010)], which is built using only orthogonal states encoding the classical bits that are teleported from Alice to Bob, is asymptotically secure against all types of individual and collective attacks. We then investigate modifications to that protocol leading to greater secret-key rates and to security against coherent attacks. In other words, we show an unconditional secure quantum key distribution protocol that does not need non-orthogonal quantum states to encode the bits of the secret ke…
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…
Position-based quantum cryptography (PBQC) allows a party to use its geographical location as its only credential to implement various cryptographic protocols. Such a protocol may lead to important applications in practice. Although it has been shown that any PBQC protocol is breakable if the adversaries pre-share an arbitrarily large entangled state, the security of PBQC in the bounded-quantum-storage model is still an open question. In this paper, we study the performance of various PBQC protocols over a lossy channel under the assumption that no entanglement is pre-shared between adversarie…
In this thesis we study the finite-size analysis of two continuous-variables quantum key distribution schemes. The first one is the one-way protocol using Gaussian modulation of thermal states and the other is the measurement-device-independent protocol. To do so, we adopt an efficient channel parameter estimation method based on the assumption of the Gaussian variables and the central limit theorem introduced by Ruppert et al. [Phys. Rev. A 90, 062310 (2014)]. Furthermore, we present a composable security analysis of the measurement device independent protocol for coherent attacks with a chan…
The problem of unconditional security of quantum cryptography (i.e. the security which is guaranteed by the fundamental laws of nature rather than by technical limitations) is one of the central points in quantum information theory. We propose a relativistic quantum cryptosystem and prove its unconditional security against any eavesdropping attempts. Relativistic causality arguments allow to demonstrate the security of the system in a simple way. Since the proposed protocol does not employ collective measurements and quantum codes, the cryptosystem can be experimentally realized with the prese…
In state-of-the-art quantum key distribution (QKD) systems, the main limiting factor in increasing the key generation rate is the timing resolution in detecting photons. Here, we present and experimentally demonstrate a strategy to overcome this limitation, also for high-loss and long-distance implementations. We exploit the intrinsic wavelength correlations of entangled photons using wavelength multiplexing to generate a quantum secure key from polarization entanglement. The presented approach can be integrated into both fiber- and satellite-based quantum-communication schemes, without any ch…
A highly attenuated laser pulse which gives a weak coherent state is widely used in quantum key distribution (QKD) experiments. A weak coherent state has multi-photon components, which opens up a security loophole to the sophisticated eavesdropper. With a small adjustment of the hardware, we prove that the decoy state method can close this loophole and substantially improve the QKD performance. We also propose a few practical decoy state protocols, study statistical fluctuations and perform experimental demonstrations. Moreover, we apply the methods from entanglement distillation protocols bas…
The security of source has become an increasingly important issue in quantum cryptography. Based on the framework of measurement-device-independent quantum-key-distribution (MDI-QKD), the source becomes the only region exploitable by a potential eavesdropper (Eve). Phase randomization is a cornerstone assumption in most discrete-variable (DV-) quantum communication protocols (e.g., QKD, quantum coin tossing, weak coherent state blind quantum computing, and so on), and the violation of such an assumption is thus fatal to the security of those protocols. In this paper, we show a simple quantum h…
