Reconciliation Protocol Research Articles

Low-complexity adaptive reconciliation protocol for continuous-variable quantum key distribution

In continuous-variable quantum key distribution systems, reconciliation is a crucial step that significantly affects the secret key rate (SKR). The rateless protocol based on Raptor codes can achieve high reconciliation efficiency at low signal-to-noise ratios (SNRs). However, the high complexity of low-density parity-check (LDPC) codes used for the precoding in Raptor codes limits the speed of reconciliation. In this paper, we propose an adaptive reconciliation protocol by modifying Raptor codes. The length of random binary sequences is increased because we remove the LDPC precoding that adds redundancy. The modified Raptor codes reduce the complexity of encoding with better performance. The proposed protocol gives a reconciliation efficiency higher than 98.1% in the SNR below −20 dB and maintains a certain SKR in long-distance transmission.

Distributional Transform Based Information Reconciliation

In this paper, we present an information reconciliation protocol designed for Continuous-Variable QKD using the Distributional Transform. By combining tools from copula and information theory, we present a method for extracting independent symmetric Bernoulli bits for Gaussian-modulated CVQKD protocols, which we called the Distributional Transform Expansion (DTE). We derived the expressions for the maximum reconciliation efficiency for both homodyne and heterodyne measurements, which, for the last, is achievable with an efficiency greater than 0.9 at a signal-to-noise ratio lower than -3.6 dB.

GenSync: A New Framework for Benchmarking and Optimizing Reconciliation of Data

In the set reconciliation problem, remote parties seek to reconcile similar sets of data according to an efficiency objective, such as minimizing communication or computation. Though investigated for many individual distributed applications, this problem still lacks a holistic treatment, and this is the aim of this work. Specifically, we design and analyze GenSync, a unified set reconciliation framework that incorporates several state-of-the-art set reconciliation protocols with an integrated testbed. We compare and analyze the various protocols and offer general guidelines for selecting a good protocol for a given application. Through extensive experiments, we demonstrate that the optimal choice of protocol is highly sensitive to several parameters, including network properties (e.g., bandwidth and latency) and computing power. Notably, none of our framework’s protocols are universally dominant under diverse conditions, and a poor protocol choice may lead to a 5x hit in performance. To demonstrate our framework, we measure the effects of protocol choice in reconciling memory pools of adjacent Bitcoin nodes.

Optimised Multithreaded CV-QKD Reconciliation for Global Quantum Networks

Designing a practical Continuous Variable (CV) Quantum Key Distribution (QKD) system requires an estimation of the quantum channel characteristics and the extraction of secure keys based on a large number of distributed quantum signals. On standard processors, it can take hours to reconcile the required number of quantum signals. This problem is exacerbated for Low Earth Orbit (LEO) satellite CV-QKD, where the satellite flyover time is less than a few minutes. A potential solution is massive parallelisation of the classical reconciliation where a large-code block is subdivided into many shorter blocks for individual decoding. However, the penalty of this procedure on the important final secured key rate is non-trivial to determine and hitherto has not been formally analysed. In this work, we fill this important knowledge gap via detailed analyses and experimental verification of a CV-QKD sliced reconciliation protocol that uses large block-length low-density parity-check decoders. Our new solution results in a significant increase in the final key rate relative to non-optimised reconciliation. In addition, it allows for the acquisition of quantum secured messages between terrestrial stations and LEO satellites within a flyover timescale even using off-the-shelf processors. Our work allows for optimised global quantum networks secured via fundamental physics.

MCFsyn: A Multi-Party Set Reconciliation Protocol With the Marked Cuckoo Filter

Multi-party set reconciliation is a key component in distributed and networking systems. It naturally contains two dimensions, i.e., set representation and reconciliation protocol. However, existing sketch data structures are insufficient to satisfy the new needs brought by the multi-party scenario simultaneously, including space-efficiency, mergeability, and completeness. The current reconciliation protocols, on the other hand, fail to achieve the global optimization of communication cost. To this end, in this article, we propose the marked cuckoo filter (MCF), a data structure for representing set members. Grounded on MCF, we implement the MCFsyn protocol to reconcile multiple sets. MCFsyn aggregates and distributes sets information represented by MCFs along with an underlying minimum spanning tree among the participants. The participants then identify the different elements by traversing the overall MCF which contains the information of all elements in the union set. For the identified missing elements, MCFsyn helps the participants to choose the optimal senders to fetch with the minimum communication cost. Comprehensive evaluations indicate that MCFsyn significantly outperforms existing alternatives in terms of both reconciliation accuracy and communication cost.

High-Efficient Syndrome-Based LDPC Reconciliation for Quantum Key Distribution.

Quantum key distribution (QKD) is a promising technique to share unconditionally secure keys between remote parties. As an essential part of a practical QKD system, reconciliation is responsible for correcting the errors due to the quantum channel noise by exchanging information through a public classical channel. In the present work, we propose a novel syndrome-based low-density parity-check (LDPC) reconciliation protocol to reduce the information leakage of reconciliation by fully utilizing the syndrome information that was previously wasted. Both theoretical analysis and simulation results show that our protocol can evidently reduce the information leakage as well as the number of communication rounds.

An Improved Slice Reconciliation Protocol for Continuous-Variable Quantum Key Distribution.

Reconciliation is an essential procedure for continuous-variable quantum key distribution (CV-QKD). As the most commonly used reconciliation protocol in short-distance CV-QKD, the slice error correction (SEC) allows a system to distill more than 1 bit from each pulse. However, the quantization efficiency is greatly affected by the noisy channel with a low signal-to-noise ratio (SNR), which usually limits the secure distance to about 30 km. In this paper, an improved SEC protocol, named Rotated-SEC (RSEC), is proposed through performing a random orthogonal rotation on the raw data before quantization, and deducing a new estimator for the quantized sequences. Moreover, the RSEC protocol is implemented with polar codes. The experimental results show that the proposed protocol can reach up to a quantization efficiency of about 99%, and maintain at around 96% even at the relatively low SNRs , which theoretically extends the secure distance to about 45 km. When implemented with the polar codes with a block length of 16 Mb, the RSEC achieved a reconciliation efficiency of above 95%, which outperforms all previous SEC schemes. In terms of finite-size effects, we achieved a secret key rate of bits/pulse at a distance of 33.93 km (the corresponding SNR value is 1). These results indicate that the proposed protocol significantly improves the performance of SEC and is a competitive reconciliation scheme for the CV-QKD system.

A novel error correction protocol for continuous variable quantum key distribution

Reconciliation is a key element of continuous-variable quantum key distribution (CV-QKD) protocols, affecting both the complexity and performance of the entire system. During the reconciliation protocol, error correction is typically performed using low-density parity-check (LDPC) codes with a single decoding attempt. In this paper, we propose a modification to a conventional reconciliation protocol used in four-state protocol CV-QKD systems called the multiple decoding attempts (MDA) protocol. MDA uses multiple decoding attempts with LDPC codes, each attempt having fewer decoding iteration than the conventional protocol. Between each decoding attempt we propose to reveal information bits, which effectively lowers the code rate. MDA is shown to outperform the conventional protocol in regards to the secret key rate (SKR). A 10% decrease in frame error rate and an 8.5% increase in SKR are reported in this paper. A simple early termination for the LDPC decoder is also proposed and implemented. With early termination, MDA has decoding complexity similar to the conventional protocol while having an improved SKR.

A continuous variable quantum key distribution protocol based on multi-dimensiondata reconciliation with Polar code

The continuous variable quantum key distribution protocol (CV-QKD) has the advantages of easy generation of quantum signals, convenient measurement and high communication capacity. However, the multi-dimensional data reconciliation is mainly implemented by binary LDPC code as quantum error correction code, which is greatly affected by complex environments and the bit error rate is high. In order to solve this problem, acontinuous variable quantum key distribution protocol based onmulti-dimension data reconciliation with Polar code, that can be applied to long-distance transmission in power systems, is proposed. First, we prepare an EPR quantum state, and perform heterodyne detection on one of the quantum states, and obtain the values of two orthogonal components at the same time which is the coherent state of the information carrier. Then the continuous variable quantum key distribution is realized by six steps (i.e., quantum state preparation, gaussian random detection, data filtering, calculation of bit error rate, data reconciliation, privacy amplification).In data reconciliation, we use Polar code as the error correction code and use reverse coding technology to achieve key error correction, which can effectively improve the negotiation efficiency. Numerical simulation verifies the feasibility of the protocol, and the protocol is more efficient than the multi-dimensiondata reconciliation protocol based on LDPC code under the same conditions.

Randomized View Reconciliation in Permissionless Distributed Systems

In a sybil attack , an adversary creates many fake identities/nodes and have them join the system. Computational puzzles have long been investigated as a possible sybil defense: nodes that fail to solve the puzzle in time will no longer be accepted by other nodes. However, a malicious node can behave in such a way that it is accepted by some honest nodes but not other honest nodes. This results in different honest nodes having different views on which set of nodes constitute the system. Such view divergence , unfortunately, breaks the overarching assumption required by many existing security protocols. Partly spurred by the growing popularity of Bitcoin, researchers have recently formalized the above view divergence problem and proposed interesting solutions (which we call view reconciliation protocols ). All existing view reconciliation protocols so far have a similar $\Theta (N)$ time complexity, with $N$ being the number of honest nodes in the system. As this paper’s main contribution, we propose a novel view reconciliation protocol whose time complexity is only $\Theta ({\ln N}/{\ln \ln N})$ . To achieve such an exponential improvement, we aggressively exploit randomization. The hidden constant factor in the asymptotic complexity of our protocol, however, is considerably larger than in previous protocols. Concrete numerical comparisons show that our protocol is more suitable for large-scale systems, while existing protocols are better for smaller-scale systems.

Novel reconciliation protocol based on spinal code for continuous-variable quantum key distribution

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 for practical systems to cope with the variable channel. Many researchers adopt fixed-rate error correction codes to implement adaptive reconciliation, such as the punctured LDPC code; however such protocol can achieve high efficiency only in a small range of signal-to-noise ratios (SNRs). In this paper, the spinal-based rateless reconciliation protocol for CV-QKD is first proposed. The proposed adaptive reconciliation protocol can achieve high efficiency in a much larger range of SNRs. Because the protocol we propose uses the code with short length and simple encoding/decoding structure, the design and implementation complexities of our protocol are greatly decreased. Meanwhile, its parallel attribute makes it suitable for hardware implementation, which means it has the potential of achieving high-throughput reconciliation. Moreover, the security of proposed protocol is investigated and proved. Experimental results show that the reconciliation efficiency of the spinal-based protocol maintains around $$95\%$$ in a larger SNR range (0,0.5), and even exceeds $$96.5\%$$ at extremely low SNR ( $$\le 0.032$$ ) with quite low frame error rate (FER) ( $$\le 5.2\%$$ ). Both the theoretical analysis and experimental results demonstrate that the proposed adaptive reconciliation protocol is a suitable candidate for the long-distance CV-QKD systems.

KEHKey

For kinetic-powered body area networks, we explore the feasibility of converting energy harvesting patterns for device authentication and symmetric secret keys generation continuously. The intuition is that at any given time, multiple wearable devices harvest kinetic energy from the same user activity, such as walking, which allows them to independently observe a common secret energy harvesting pattern not accessible to outside devices. Such continuous KEH-based authentication and key generation is expected to be highly power efficient as it obviates the need to employ any extra sensors, such as accelerometer, to precisely track the walking patterns. Unfortunately, lack of precise activity tracking introduces bit mismatches between the independently generated keys, which makes KEH-based authentication and symmetric key generation a challenging problem. We propose KEHKey, a KEH-based authentication and key generation system that employs a compressive sensing-based information reconciliation protocol for wearable devices to effectively correct any mismatches in generated keys. We implement KEHKey using off-the-shelf piezoelectric energy harvesting products and evaluate its performance with data collected from 24 subjects wearing the devices on different body locations including head, torso and hands. Our results show that KEHKey is able to generate the same key for two KEH-embedded devices at a speed of 12.57 bps while reducing energy consumption by 59% compared to accelerometer-based methods, which makes it suitable for continuous operation. Finally, we demonstrate that KEHKey can successfully defend against typical adversarial attacks. In particular, KEHKey is found to be more resilient to video side channel attacks than its accelerometer-based counterparts.

EnQuad: A Publicly-Available Simulator for Quantum Key Distribution Protocols

Abstract In this paper, we present EnQuad Version 1.0: a high-speed and expandable simulator for Quantum Key Distribution (QKD) protocols. Surpassing available simulators, EnQuad does not only simulate a QKD stack, but also does security testing and guides the researcher on which reconciliation protocol should be used in his experimental setup. On the top of that, it recommends changes for the researcher to satisfy security or a given target key-rate if any of them is not already fulfilled. Although EnQuad V1.0 is concerned with depolarizing channels and Individual Intercept-and-Resend attacks, EnQuad is featured with 24 parameters and 9 modular functions so that it could be expanded to a wide range of QKD protocols. In addition, we validated EnQuad outcomes against a comparable simulator and against theory. Furthermore, a set of 11 experiments showed that EnQuad runs 6.12× to 12.2× faster than a comparable simulator. EnQuad was implemented in MATLAB and the code is available online.

Blind information reconciliation with variable step sizes for quantum key distribution

Quantum key distribution (QKD) generates symmetric keys between two authenticated parties with the guarantee of information-theoretically security. A vital step in QKD to obtain fully-matched key between two parties is information reconciliation. The blind reconciliation protocol provides a useful tool that corrects the mismatch in a wide range of qubit error rate (QBER) but without a prior error estimation. However, there is a contradiction between the reconciliation efficiency and the processing time in this protocol. In this work, we propose a blind reconciliation protocol with variable step sizes to relieve this contradiction. The analysis and simulation results show that the improved protocol inherits all the advantages of the original blind reconciliation protocol and can obtain better reconciliation efficiency with less operation time. The improved blind reconciliation protocol enhances the final secret key rate and accelerates the processing speed of a QKD system.

Continuous-Variable Quantum Key Distribution with Rateless Reconciliation Protocol

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 significantly decreases the complexity of optimization and increases the robustness of the system. Using this protocol, the CV-QKD system can operate with the optimal modulation variance which maximizes the secret key rate. Simulation results show that the proposed protocol can achieve reconciliation efficiency of more than 95% within the range of SNR from -20 dB to 0 dB. It also shows that we can obtain a high secret key rate at arbitrary distances in a certain range and achieve a secret key rate of about 5*10^(-4) bits/pulse at a maximum distance of 132 km (corresponding SNR is -20dB) that is higher than previous works. The proposed protocol can maintain high efficient key extraction under the wide range of SNRs and paves the way toward the practical application of CV-QKD systems in flexible scenarios.

A Hybrid Information Reconciliation Method for Physical Layer Key Generation.

Physical layer key generation (PKG) has become a research focus as it solves the key distribution problem, which is difficult in traditional cryptographic mechanisms. Information reconciliation is a critical process in PKG to obtain symmetric keys. Various reconciliation schemes have been proposed, including the error detection protocol-based approach (EDPA) and error correction code-based approach (ECCA). Both EDPA and ECCA have advantages and drawbacks, regarding information leakage, interaction delay, and computation complexity. In this paper, we choose the BBBSS protocol from EDPA and BCH code from ECCA as a case study, analyzing their comprehensive efficiency performance versus pass number and bit disagreement ratio (BDR), respectively. Next, we integrate the strength of the two to design a new hybrid information reconciliation protocol (HIRP). The design of HIRP consists of three main phases, i.e., training, table lookup, and testing. To comprehensively evaluate the reconciliation schemes, we propose a novel efficiency metric to achieve a balance of corrected bits, information leakage, time delay, and computation time, which represents the effectively corrected bits per unit time. The simulation results show that our proposed method outperforms other reconciliation schemes to improve the comprehensive reconciliation efficiency. The average improvement in efficiency is 2.48 and 22.36 times over the BBBSS and BCH code, respectively, when the range of the BDR is from 0.5% to 11.5%. Compared to the BBBSS protocol and the BCH code, HIRP lies at a mid-level in terms of information leakage and computation time cost. Besides, with the lowest time delay cost, HIRP reaches the highest reconciliation efficiency.

Multi-matrix error estimation and reconciliation for quantum key distribution.

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. By testing our approach through data simulation, we show that the proposed scheme combining multi-syndrome-based error rate estimation allows for a more accurate estimation of the error rate as compared with random sampling and single-syndrome estimation techniques before the error correction, as well as a significant increase in the efficiency of the procedure without compromising security and sacrificing reconciliation efficiency.

Symmetric Blind Information Reconciliation and Hash-function-based Verification for Quantum Key Distribution

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 $\epsilon$-universal hash functions, which allows verifying the identity between the keys with a certain probability.

Improved reconciliation with polar codes in quantum key distribution

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 all QKD implementations. However, the protocol is highly interactive. Thus, other protocols based on linear block codes such as Hamming codes, low-density parity-check (LDPC) codes, and polar codes have been researched. In particular, reconciliation using LDPC codes has been mainly studied because of its outstanding performance. Nevertheless, with small block size, the bit error rate performance of polar codes under successive-cancellation list (SCL) decoding with a cyclic redundancy check (CRC) is comparable to state-of-the-art turbo and LDPC codes. In this study, we demonstrate the use of polar codes to improve the performance of information reconciliation in a QKD system with small block size. The best decoder for polar codes, a CRC-aided SCL decoder, requires CRC-precoded messages. However, messages that are sifted keys in QKD are obtained arbitrarily as a result of a characteristic of the QKD protocol and cannot be CRC-precoded. We propose a method that allows arbitrarily obtained sifted keys to be CRC precoded by introducing a virtual string. Thus the best decoder can be used for reconciliation using polar codes and improves the efficiency of the protocol.

Optimized CASCADE protocol for efficient information reconciliation

CASCADE protocol is an error detection and correction (EDC) method proposed firstly for use in quantum key distribution (QKD) systems. It is used to detect and correct all the errors in keys transmitted over a noisy quantum channel. This is done by sending some redundant information about the key to receiver as usual. However, just as differently, this extra information is sent over another noiseless classical channel after the quantum transmission is completely finished. Briefly, all the errors in noisy quantum communication are detected and corrected by a later noiseless classical communication using CASCADE protocol. In QKD literature, this EDC process is also called as information reconciliation (IR) or secret key reconciliation (SKR). For an IR protocol in QKD, one of the main performance measures is efficiency which depends on the amount of redundant information sent to make EDC possible. Since this extra information is transmitted over public channels, everyone can get it easily. Because this can damage the secrecy of keys that must be kept secret from third parties, more efficient, that is revealing less information about keys, IR methods are needed. In this paper, we present more efficient implementations of CASCADE protocol, using some inherent information already available in the protocol, exactly known bits and already known parities. This information is used in error detection and correction steps of the protocol to decrease the redundancy in redundant information. Our experiments have shown that the resulting protocols have higher efficiency than both all the previous CASCADE versions and several other more recently proposed IR methods.