Graph based codes such as low density parity check (LDPC) codes have been shown promising for the information reconciliation phase in quantum key distribution (QKD). However, existing graph coding schemes have not fully utilized the properties of the QKD channel. In this work, we first investigate the channel statistics for discrete variable (DV) QKD based on energy-time entangled photons. We then establish a so-called balanced modulation scheme that is promising for this channel. Based on the modulation, we propose a joint local-global graph coding scheme that is expected to achieve good error-correction performance.
In time entanglement-based quantum key distribution (QKD), Alice and Bob extract the raw key bits from the (identical) arrival times of entangled photon pairs by time-binning. Each of them individually discretizes time into bins and groups them into frames. They retain only the frames with a single occupied bin. Thus, Alice and Bob can use the position of the occupied bin within a frame to generate random key bits, as in PPM modulation. Because of entanglement, their occupied bins and their keys should be identical. However, practical photon detectors suffer from time jitter errors. These erro…
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…
Information Reconciliation is a mechanism that allows to weed out the discrepancies between two correlated variables. It is an essential component in every key agreement protocol where the key has to be transmitted through a noisy channel. The typical case is in the satellite scenario described by Maurer in the early 90's. Recently the need has arisen in relation with Quantum Key Distribution (QKD) protocols, where it is very important not to reveal unnecessary information in order to maximize the shared key length. In this paper we present an information reconciliation protocol based on a rat…
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.
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).
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…
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…
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…
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 consider a key encapsulation mechanism (KEM) based on Module-LWE where reconciliation is performed on the 8-dimensional lattice $E_8$, which admits a fast CVP algorithm. Our scheme generates 256 bits of key and requires 3 or 4 bits of reconciliation per dimension. We show that it can outperform Kyber in terms of the modulus q with comparable error probability. We prove that our protocol is IND-CPA secure and improves the security level of Kyber by 7.3%.
We consider in this paper the problem of information reconciliation in the context of secret key agreement between two legitimate parties, Alice and Bob. Beginning the discussion with the secret key agreement model introduced by Ahlswede and Csiszár, the channel-type model with wiretapper, we study a protocol based on error correcting codes. The protocol can be adapted to changes in the communication channel extending the original source. The efficiency of the reconciliation is only limited by the quality of the code and, while transmitting more information than needed to reconcile Alice's and…
This paper investigates an efficient and practical information reconciliation method in the case where two parties have access to correlated continuous random variables. We show that reconciliation is a special case of channel coding and that existing coded modulation techniques can be adapted for reconciliation. We describe an explicit reconciliation method based on LDPC codes in the case of correlated Gaussian variables. We believe that the proposed method can improve the efficiency of quantum key distribution protocols based on continuous-spectrum quantum states.
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…
An information reconciliation method for continuous-variable quantum key distribution with Gaussian modulation that is based on non-binary low-density parity-check (LDPC) codes is presented. Sets of regular and irregular LDPC codes with different code rates over the Galois fields $GF(8)$, $GF(16)$, $GF(32)$, and $GF(64)$ have been constructed. We have performed simulations to analyze the efficiency and the frame error rate using the sum-product algorithm. The proposed method achieves an efficiency between $0.94$ and $0.98$ if the signal-to-noise ratio is between $4$ dB and $24$ dB.
Quantum key distribution (QKD) offers a practical solution for secure communication between two distinct parties via a quantum channel and an authentic public channel. In this work, we consider different approaches to the quantum bit error rate (QBER) estimation at the information reconciliation stage of the post-processing procedure. For reconciliation schemes employing low-density parity-check (LDPC) codes, we develop a novel syndrome-based QBER estimation algorithm. The algorithm suggested is suitable for irregular LDPC codes and takes into account punctured and shortened bits. Testing our …
Efficient information reconciliation is crucial in several scenarios, being quantum key distribution a remarkable example. However, efficiency is not the only requirement for determining the quality of the information reconciliation process. In some of these scenarios we find other relevant parameters such as the interactivity or the adaptability to different channel statistics. We propose an interactive protocol for information reconciliation based on low-density parity-check codes. The coding rate is adapted in real time by using simultaneously puncturing and shortening strategies, allowing …
Quantum key distribution (QKD) is a cryptographic system that generates an information-theoretically secure key shared by two legitimate parties. QKD consists of two parts: quantum and classical. The latter is referred to as classical post-processing (CPP). Information reconciliation is a part of CPP in which parties are given correlated variables and attempt to eliminate the discrepancies between them while disclosing a minimum amount of information. The elegant reconciliation protocol known as \emph{Cascade} was developed specifically for QKD in 1992 and has become the de-facto standard for …
Quantum key distribution performs the trick of growing a secret key in two distant places connected by a quantum channel. The main reason is that the legitimate users can bound the information gathered by the eavesdropper. In practical systems, whether because of finite resources or external conditions, the quantum channel is subject to fluctuations. A rate adaptive information reconciliation protocol, that adapts to the changes in the communication channel, is then required to minimize the leakage of information in the classical postprocessing. We consider here the leakage of a rate-adaptive …
The speed at which two remote parties can exchange secret keys over a fixed-length fiber-optic cable in continuous-variable quantum key distribution (CV-QKD) is currently limited by the computational complexity of post-processing algorithms for key reconciliation. Multi-edge low-density parity-check (LDPC) codes with low code rates and long block lengths were proposed for CV-QKD, in order to extend the maximum reconciliation distance between the two remote parties. Key reconciliation over multiple dimensions has been shown to further improve the error-correction performance of multi-edge LDPC …
Cascade is an information reconciliation protocol proposed in the context of secret key agreement in quantum cryptography. This protocol allows removing discrepancies in two partially correlated sequences that belong to distant parties, connected through a public noiseless channel. It is highly interactive, thus requiring a large number of channel communications between the parties to proceed and, although its efficiency is not optimal, it has become the de-facto standard for practical implementations of information reconciliation in quantum key distribution. The aim of this work is to analyze…
We designed high-efficiency error correcting codes allowing to extract an errorless secret key in a continuous-variable quantum key distribution protocol using a Gaussian modulation of coherent states and a homodyne detection. These codes are available for a wide range of signal-to-noise ratios on an AWGN channel with a binary modulation and can be combined with a multidimensional reconciliation method proven secure against arbitrary collective attacks. This improved reconciliation procedure considerably extends the secure range of a continuous-variable quantum key distribution with a Gaussian…
In Part I of this two-part paper on confidential communication over wireless channels, we studied the fundamental security limits of quasi-static fading channels from the point of view of outage secrecy capacity with perfect and imperfect channel state information. In Part II, we develop a practical secret key agreement protocol for Gaussian and quasi-static fading wiretap channels. The protocol uses a four-step procedure to secure communications: establish common randomness via an opportunistic transmission, perform message reconciliation, establish a common key via privacy amplification, and…
Information reconciliation is a crucial procedure in the classical post-processing of quantum key distribution (QKD). Poor reconciliation efficiency, revealing more information than strictly needed, may compromise the maximum attainable distance, while poor performance of the algorithm limits the practical throughput in a QKD device. Historically, reconciliation has been mainly done using close to minimal information disclosure but heavily interactive procedures, like Cascade, or using less efficient but also less interactive -just one message is exchanged- procedures, like the ones based in l…
We define the direct and reverse secret-key capacities of a memoryless quantum channel as the optimal rates that entanglement-based quantum key distribution protocols can reach by using a single forward classical communication (direct reconciliation) or a single feedback classical communication (reverse reconciliation). In particular, the reverse secret-key capacity can be positive for antidegradable channels, where no forward strategy is known to be secure. This property is explicitly shown in the continuous variable framework by considering arbitrary one-mode Gaussian channels.
Although quantum key distribution (QKD) comes from the development of quantum theory, the implementation of a practical QKD system does involve a lot of classical process, such as key reconciliation and privacy amplification, which is called post-processing. Post-processing has been a crucial element to high speed QKD systems, even the bottleneck of it because of its relatively high time consumption. Low density parity check (LDPC) is now becoming a promising approach of overcoming the bottleneck due to its good performance in processing throughput. In this article we propose and simulate an e…
Error correction plays a major role in the reconciliation of continuous variable quantum key distribution (CV-QKD) and greatly affects the performance of the system. CV-QKD requires error correction codes of extremely low rates and high reconciliation efficiencies. There are only very few code designs available in this ultra low rate regime. In this paper, we introduce a method for designing protograph-based ultra low rate LDPC codes using differential evolution. By proposing type-based protographs, a new way of representing low rate protograph-based LDPC codes, we drastically reduce the compl…
Covert and secret quantum key distribution aims at generating information-theoretically secret bits between distant legitimate parties in a manner that remains provably undetectable by an adversary. We propose a framework in which to precisely define and analyze such an operation, and we show that covert and secret key expansion is possible. For fixed and known classical-quantum channels, we develop and analyze protocols based on forward and reverse reconciliation. When the adversary applies the same quantum channel independently on each transmitted quantum state, akin to a collective attack i…
Turbo coding is a powerful class of forward error correcting codes, which can achieve performances close to the Shannon limit. The turbo principle can be applied to the problem of side-information source coding, and we investigate here its application to the reconciliation problem occurring in a continuous-variable quantum key distribution protocol.
