Quantum key distribution (QKD) relies on quantum and classical procedures in order to achieve the growing of a secret random string -the key- known only to the two parties executing the protocol. Limited intrinsic efficiency of the protocol, imperfect devices and eavesdropping produce errors and information leakage from which the set of measured signals -the raw key- must be stripped in order to distill a final, information theoretically secure, key. The key distillation process is a classical one in which basis reconciliation, error correction and privacy amplification protocols are applied to the raw key. This cleaning process is known as information reconciliation and must be done in a fast and efficient way to avoid cramping the performance of the QKD system. Brassard and Salvail proposed a very simple and elegant protocol to reconcile keys in the secret-key agreement context, known as Cascade, that has become the de-facto standard for all QKD practical implementations. However, it is highly interactive, requiring many communications between the legitimate parties and its efficiency is not optimal, imposing an early limit to the maximum tolerable error rate. In this paper we describe a low-density parity-check reconciliation protocol that improves significantly on these problems. The protocol exhibits better efficiency and limits the number of uses of the communications channel. It is also able to adapt to different error rates while remaining efficient, thus reaching longer distances or higher secure key rate for a given QKD system.
We consider an information reconciliation protocol for quantum key distribution (QKD). In order to correct down the error rate, we suggest a method, which is based on symmetric blind information reconciliation for the low-density parity-check (LDPC) codes. We develop a subsequent verification protocol with the use of $ε$-universal hash functions, which allows verifying the identity between the keys with a certain probability.
Information reconciliation protocol has a significant effect on the secret key rate and maximal transmission distance of continuous-variable quantum key distribution (CV-QKD) systems. We propose an efficient rate-adaptive reconciliation protocol suitable for practical CV-QKD systems with time-varying quantum channel. This protocol changes the code rate of multi-edge type low density parity check codes, by puncturing (increasing the code rate) and shortening (decreasing the code rate) techniques, to enlarge the correctable signal-to-noise ratios regime, thus improves the overall reconciliation …
Information reconciliation(IR) is a basic step of quantum key distribution (QKD). Classical message interaction is necessary in a practical IR scheme, and the communication complexity has become a bottleneck of QKD's development. Here we propose a concatenated method of IR scheme which requires only one time one-way communication to achieve any given error rate level. A QKD scheme with the concatenated IR can work without the special interaction of error rate estimation.
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.
We address the security of continuous-variable quantum key distribution with squeezed states upon realistic conditions of noisy and lossy environment and limited reconciliation efficiency. Considering the generalized preparation scheme and clearly distinguishing between classical and quantum resources, we investigate the effect of finite squeezing on the tolerance of the protocol to untrusted channel noise. For a long-distance strongly attenuating channel and the consequent low reconciliation efficiency, we show that feasible limited squeezing is surprisingly sufficient to provide the security…
A big challenge in continuous variable quantum key distribution is to prove security against arbitrary coherent attacks including realistic assumptions such as finite-size effects. Recently, such a proof has been presented in [Phys. Rev. Lett. 109, 100502 (2012)] for a two-mode squeezed state protocol based on a novel uncertainty relation with quantum memories. But the transmission distances were fairly limited due to a direct reconciliation protocol. We prove here security against coherent attacks of a reverse reconciliation protocol under similar assumptions but allowing distances of over 16…
We develop a new approach for asymmetric LDPC-based information reconciliation in order to adapt to the current channel state and achieve better performance and scalability in practical resource-constrained QKD systems. The new scheme combines the advantages of LDPC codes, a priori error rate estimation, rate-adaptive and blind information reconciliation techniques. We compare the performance of several asymmetric and symmetric error correction schemes using real industrial QKD setup. The proposed asymmetric algorithm achieves significantly higher throughput, providing a secret key rate very c…
Reconciliation is a crucial procedure in post-processing of Quantum Key Distribution (QKD), which is used for correcting the error bits in sifted key strings. Although most studies about reconciliation of QKD focus on how to improve the efficiency, throughput optimizations have become the highlight in high-speed QKD systems. Many researchers adpot high cost GPU implementations to improve the throughput. In this paper, an alternative high throughput and efficiency solution implemented in low cost CPU is proposed. The main contribution of the research is the design of a quantized LDPC decoder in…
Information Reconciliation for Continuous-Variable Quantum Key Distribution with $β> 1$ Using Short Blocklength Error Correction Codes: Proposal and Concerns
Eindhoven University of Technology（埃因霍温理工大学）；CubiQ Technologies（CubiQ科技公司）
It is widely accepted in the quantum cryptography community that interactive information reconciliation protocols, such as cascade, are ineffcient due to the communication overhead. Instead, non-interactive information reconciliation protocols based on i.e. LDPC codes or, more recently, polar codes have been proposed. In this work, we argue that interactive protocols should be taken into consideration in modern quantum key distribution systems. In particular, we demonstrate how to improve the performance of cascade by proper implementation and use. Our implementation of cascade reaches a throu…
Information reconciliation (IR), which corrects the errors in the sifted keys, directly determines the secure key rate and the link distance of quantum key distribution (QKD) systems. In this article, we propose an appending information reconciliation (AIR) scheme based on polar codes, which achieves high efficiency and ultra-low failure probability simultaneously, by gradually disclosing the bit values of the polarized channels with high error probability. The experimental results show that the efficiency of the proposed AIR scheme is closer to the Shannon limit, compared with the state-of-th…
Information reconciliation (IR) ensures the correctness of quantum key distribution systems, by correcting the error bits existed in the sifted keys. In this article, we propose a polar codes-based IR scheme with the frozen bits erasure strategy, where an equivalent transmission of sifted keys is conducted, so that the frozen bits in the decoding procedure is erased to 0. Thus, our IR scheme can be implemented efficiently without the assumption of true random numbers. Furthermore, we implement the proposed IR scheme with the fast simplified successive cancellation list decoder and its throughp…
Information reconciliation is crucial for continuous-variable quantum key distribution (CV-QKD) because its performance affects the secret key rate and maximal secure transmission distance. Fixed-rate error correction codes limit the potential applications of the CV-QKD because of the difficulty of optimizing such codes for different low SNRs. In this paper, we propose a rateless reconciliation protocol combined multidimensional scheme with Raptor codes that not only maintains the rateless property but also achieves high efficiency in different SNRs using just one degree distribution. It signi…
An efficient error reconciliation scheme is important for post-processing of quantum key distribution (QKD). Recently, a multi-matrix low-density parity-check codes based reconciliation algorithm which can provide remarkable perspectives for high efficiency information reconciliation was proposed. This paper concerns the improvement of reconciliation performance. Multi-matrix algorithm is implemented and optimized on the graphics processing unit (GPU) to obtain high reconciliation throughput. Experimental results indicate that GPU-based algorithm can highly improve reconciliation throughput to…
Key reconciliation of quantum key distribution (QKD) is the process of correcting errors caused by channel noise and eavesdropper to identify the keys of two legitimate users. Reconciliation efficiency is the most important figure for judging the quality of a reconciliation scheme. To improve reconciliation efficiency, rate-compatible technologies was proposed for key reconciliation, which is denoted as the single-matrix ratecompatible reconciliation (SRCR). In this paper, a recently suggested technique called multi-matrix reconciliation is introduced into SRCR, which is referred to as the mul…
This paper investigates a new information reconciliation method for quantum key distribution in the case where two parties exchange key in the presence of a malevolent eavesdropper. We have observed that reconciliation is a special case of channel coding and for that existing techniques can be adapted for reconciliation. We describe an explicit reconciliation method based on Turbo codes. We believe that the proposed method can improve the efficiency of quantum key distribution protocols based on discrete quantum states.
Quantum key distribution (QKD) is a promising technique for secure communication based on quantum mechanical principles. To improve the secure key rate of a QKD system, most studies on reconciliation primarily focused on improving the efficiency. With the increasing performance of QKD systems, the research priority has shifted to the improvement of both throughput and efficiency. In this paper, we propose a high performance solution of Cascade reconciliation, including a high-throughput-oriented framework and an integrated-optimization-oriented scheme. Benefiting from the fully utilizing compu…
We study the equivalence between a realistic quantum key distribution protocol using coherent states and homodyne detection and a formal entanglement purification protocol. Maximally-entangled qubit pairs that one can extract in the formal protocol correspond to secret key bits in the realistic protocol. More specifically, we define a qubit encoding scheme that allows the formal protocol to produce more than one entangled qubit pair per coherent state, or equivalently for the realistic protocol, more than one secret key bit. The entanglement parameters are estimated using quantum tomography. W…
Reconciliation is an important step to correct errors in Quantum Key Distribution (QKD). In QKD, after comparing basis, two legitimate parties possess two correlative keys which have some differences and they could obtain identical keys through reconciliation. In this paper, we present a new rate compatible reconciliation scheme based on Row Combining with Edge Variation (RCEV) Low Density Parity Check (LDPC) codes which could change code rate adaptively in noisy channel where error rate may change with time. Our scheme is easy to implement and could get good efficiency compared to existing sc…
Information reconciliation (IR) corrects the errors in sifted keys and ensures the correctness of quantum key distribution (QKD) systems. Polar codes-based IR schemes can achieve high reconciliation efficiency, however, the incidental high frame error rate decreases the secure key rate of QKD systems. In this article, we propose a Shannon-limit approached (SLA) IR scheme, which mainly contains two phases: the forward reconciliation phase and the acknowledgment reconciliation phase. In the forward reconciliation phase, the sifted key is divided into sub-blocks and performed with the improved bl…
Aside from significant advancements in the development of optical and quantum components, the performance of practical quantum key distribution systems is largely determined by the type and settings of the error key reconciliation procedure. It is realized through public channel and it dominates the communication complexity of the quantum key distribution process. The practical utilization significantly depends on the computational capacities that are of great importance in satellite-oriented quantum communications. Here we present SarDub19 error key estimation and reconciliation protocol that…
Post-processing is a significant step in quantum key distribution(QKD), which is used for correcting the quantum-channel noise errors and distilling identical corrected keys between two distant legitimate parties. Efficient error reconciliation protocol, which can lead to an increase in the secure key generation rate, is one of the main performance indicators of QKD setups. In this paper, we propose a multi-low-density parity-check codes based reconciliation scheme, which can provide remarkable perspectives for highly efficient information reconciliation. With testing our approach through data…
We discuss the error reconciliation phase in quantum key distribution (QKD) and analyse a simple scheme in which blocks with bad parity (that is, blocks containing an odd number of errors) are discarded. We predict the performance of this scheme and show, using a simulation, that the prediction is accurate.
This paper investigates the design of low-complexity error correction codes for the verification step in continuous variable quantum key distribution (CVQKD) systems. We design new coding schemes based on quasi-cyclic repeat-accumulate codes which demonstrate good performances for CVQKD reconciliation.
Reconciliation is a crucial procedure in post-processing of continuous variable quantum key distribution (CV-QKD) system, which is used to make two distant legitimate parties share identical corrected keys. The adaptive reconciliation is necessary and important for practical systems to cope with the variable channel. Many researchers adopt the punctured LDPC codes to implement adaptive reconciliation. In this paper, a novel rateless reconciliation protocol based on spinal code is proposed, which can achieve a high-efficiency and adaptive reconciliation in a larger range of SNRs. Due to the sho…
This paper investigates a reconciliation method in order to establish an errorless secret key in a QKD protocol. Classical key distribution protocols are no longer unconditionally secure because computational complexity of mathematical problems forced hardships. In this context, QKD protocols offer a highest level of security because they are based on the quantum laws of physics. But, the protocol performances can be lowered by multiples errors. It appears clearly that reconciliation should be performed in such a situation in order to remove the errors as for the legitimate partners. The propo…
We suggest a new protocol for the information reconciliation stage of quantum key distribution based on polar codes. The suggested approach is based on the blind technique, which is proved to be useful for low-density parity-check (LDPC) codes. We show that the suggested protocol outperforms the blind reconciliation with LDPC codes, especially when there are high fluctuations in quantum bit error rate (QBER).
The information reconciliation in a quantum key distribution protocol can be studied separately from other steps in the protocol. The problem of information reconciliation can be reduced to that of distributed source coding. Its solution by LDPC codes is reviewed. We list some obstacles preventing the LDPC-based distributed source coding from becoming a more favorable alternative to the Cascade protocol for information reconciliation in quantum key distribution protocols. This exposition does not require knowledge of the quantum theory.
We present a continuous-variable quantum key distribution protocol combining a discrete modulation and reverse reconciliation. This protocol is proven unconditionally secure and allows the distribution of secret keys over long distances, thanks to a reverse reconciliation scheme efficient at very low signal-to-noise ratio.
We 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 …
Quantum key distribution (QKD) is a quantum-proof key-exchange scheme which is fast approaching the communication industry. An essential component in QKD is the information reconciliation step, which is used for correcting the quantum-channel noise errors. The recently suggested blind reconciliation technique, based on low-density parity-check (LDPC) codes, offers remarkable prospectives for efficient information reconciliation without an a priori error rate estimation. We suggest an improvement of the blind-information-reconciliation protocol promoting a significant increase in the efficiency…
For high-speed quantum key distribution systems, error reconciliation is often the bottleneck affecting system performance. By exchanging common information through a public channel, the identical key can be generated on both communicating sides. However, the necessity to eliminate disclosed bits for security reasons lowers the final key rate. To improve this key rate, the amount of disclosed bits should be minimized. In addition, decreasing the time spent on error reconciliation also improves the key rate. In this paper we introduce a practical method for expeditious error reconciliation impl…
Reconciliation is an essential part of any secret-key agreement protocol and hence of a Quantum Key Distribution (QKD) protocol, where two legitimate parties are given correlated data and want to agree on a common string in the presence of an adversary, while revealing a minimum amount of information. In this paper, we show that for discrete-variable QKD protocols, this problem can be advantageously solved with Low Density Parity Check (LDPC) codes optimized for the BSC. In particular, we demonstrate that our method leads to a significant improvement of the achievable secret key rate, with res…
Several fundamental issues in establishing security in continuous variable quantum key distribution are discussed, in particular on reverse reconciliation and security under heterodyne attack. It appears difficult to derive quantum advantage in a concrete realistic protocol due to source and loss uncertainties, apart from the problem of bounding Eve's information after reconciliation. The necessity of proving robust security for QKD protocols is indicated.
We propose an efficient logical layer-based reconciliation method for continuous-variable quantum key distribution (CVQKD) to extract binary information from correlated Gaussian variables. We demonstrate that by operating on the raw-data level, the noise of the quantum channel can be corrected in the low-dimensional (scalar) space and the reconciliation can be extended to arbitrary dimensions. The CVQKD systems allow an unconditionally secret communication over standard telecommunication networks. To exploit the real potential of CVQKD a robust reconciliation technique is needed. It is current…
The security of quantum key distribution protocols is guaranteed by the laws of quantum mechanics. However, a precise analysis of the security properties requires tools from both classical cryptography and information theory. Here, we employ recent results in non-asymptotic classical information theory to show that one-way information reconciliation imposes fundamental limitations on the amount of secret key that can be extracted in the finite key regime. In particular, we find that an often used approximation for the information leakage during information reconciliation is not generally valid…
In the practical continuous-variable quantum key distribution (CV-QKD) system, the postprocessing process, particularly the error correction part, significantly impacts the system performance. Multi-edge type low-density parity-check (MET-LDPC) codes are suitable for CV-QKD systems because of their Shannon-limit-approaching performance at a low signal-to-noise ratio (SNR). However, the process of designing a low-rate MET-LDPC code with good performance is extremely complicated. Thus, we introduce Raptor-like LDPC (RL-LDPC) codes into the CV-QKD system, exhibiting both the rate compatible prope…
The reconciliation step of continuous-variable quantum key distribution protocols usually involves forward error correction codes. Matching the code rate and the signal-to-noise ratio (SNR) of the quantum channel is required to achieve the high reconciliation efficiencies that are crucial for long distance links. Puncturing and shortening is a way to adapt the code rate to the SNR at the cost of a slightly reduced reconciliation efficiencies. Instead of adapting the code rate to the SNR, we propose to add a controlled amount of artificial noise to the measured data, so that the resulting SNR c…
Joint parameter estimation and multidimensional reconciliation for continuous-variable quantum key distribution
College of Information Science and Technology, Donghua University（东华大学信息科学与技术学院）；Hefei National Laboratory（合肥国家实验室）；State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong University（上海交通大学先进光通信系统网络国家重点实验室）
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…
Implementations of quantum key distribution as available nowadays suffer from inefficiencies due to post processing of the raw key that severely cuts down the final secure key rate. We present a simple model for the error scattering across the raw key and derive "closed form" expressions for the probability of a parity check failure, or experiencing more than some fixed number of errors. Our results can serve for improvement for key establishment, as information reconciliation via interactive error correction and privacy amplification rests on mostly unproven assumptions. We support those hypo…
We describe a new error reconciliation protocol {\it Winnow} based on the exchange of parity and Hamming's ``syndrome'' for $N-$bit subunits of a large data set. {\it Winnow} was developed in the context of quantum key distribution and offers significant advantages and net higher efficiency compared to other widely used protocols within the quantum cryptography community. A detailed mathematical analysis of Winnow is presented in the context of practical implementations of quantum key distribution; in particular, the information overhead required for secure implementation is one of the most im…
We propose a method for extracting an errorless secret key in a continuous-variable quantum key distribution protocol, which is based on Gaussian modulation of coherent states and homodyne detection. The crucial feature is an eight-dimensional reconciliation method, based on the algebraic properties of octonions. Since the protocol does not use any postselection, it can be proven secure against arbitrary collective attacks, by using well-established theorems on the optimality of Gaussian attacks. By using this new coding scheme with an appropriate signal to noise ratio, the distance for secure…
Source noise affects the security of continuous-variable quantum key distribution (CV QKD), and is diffcult to analyze. We propose a model to characterize Gaussian source noise through introducing a neutral party (Fred) who induces the noise with a general unitary transformation. Without knowing Fred's exact state, we derive the security bounds for both reverse and direct reconciliations and show that the bound for reverse reconciliation is tight.
We address the role of the phase-insensitive trusted preparation and detection noise in the security of a continuous-variable quantum key distribution, considering the Gaussian protocols on the basis of coherent and squeezed states and studying them in the conditions of Gaussian lossy and noisy channels. The influence of such a noise on the security of Gaussian quantum cryptography can be crucial, even despite the fact that a noise is trusted, due to a strongly nonlinear behavior of the quantum entropies involved in the security analysis. We recapitulate the known effect of the preparation noi…
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…
