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Acta Sinica Quantum Optica

Reconciliation of Quantum Gaussian Distributed Key based on Turbo Codes

郭大波 Guo Dabo, 张宁 Zhang Ning, 刘纲 LIU Gang

Published Jan 1, 2013• 1 citation
Publisher

Abstract

Two legitimate users of an encryption system,Alice and Bob,want to acquire the key from the related Gaussian continuous variables X and Y transferred through a quantum channel,by exchanging parts of information through an ideal public authorized channel,and they get consistent binary keys from the inconsistent X and Y.This process is referred to reconciliation.This paper builds a reconciliation scheme for continuous-variables quantum key distribution using Turbo codes as the primitive code,on the basis of Sliced Error Correction(SEC) and Multi Level coding/Multi Stage Decoding(MLC/MSD).Parity bits of Turbo code are employed as the redundant information in the Slepian-Wolf encoding and decoding scheme.The simulation results show that the reconciliation convergences when the SNR is 7dB above whilst the block size is 20000.

DOI
10.3788/asqo20131901.0032

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Two legitimate users of an encryption system,Alice and Bob,want to acquire the key from the related Gaussian continuous variables X and Y transferred through a quantum channel,by exchanging parts of information through an ideal public authorized channel,and they get consistent binary keys from the inconsistent X and Y.This process is referred to reconciliation.This paper builds a reconciliation scheme for continuous-variables quantum key distribution using Turbo codes as the primitive code,on the basis of Sliced Error Correction(SEC) and Multi Level coding/Multi Stage Decoding(MLC/MSD).Parity bits of Turbo code are employed as the redundant information in the Slepian-Wolf encoding and decoding scheme.The simulation results show that the reconciliation convergences when the SNR is 7dB above whilst the block size is 20000.
The party Alice in a cryptograph system transmits coherent quantum signals to the party Bob,obtaining a series of correlated continuous Gaussian variables.The process to distill a binary key out of the correlated Gaussian variables that they share is called continuous-variable quantum key distribution(CVQKD).Reconciliation in CVQKD,i.e.,to correct differences between the correlated variables,is the key issue discussed in the paper.Based on both sliced error correction(SEC) protocol and multilevel coding/multistage decoding(MLC/MSD),reconciliation is implemented by LDPC code-based Slepian-Wolf CODEC.According to the proposed multilevel Tanner graph which depicts message transition of information,multistage iterative intrinsic and extrinsic information belief-propagation(LLR-BP) update formulae are derived.Three decoding modes of MSD are compared experimentally in convergence and performance.Simulation results show that the proposed algorithm can reconcile reliably 10000 continuous quantum variables with efficiency of 92.3% when SNR of the channel is above 2.5 dB.
Quantum Key Distribution (QKD) is a communication method which exchanges secret keys using cryptographic protocols involving elements from quantum science. Continuous Variable (CV) QKD is a method to implement key exchange using sampling of Gaussian signals. Reconciliation in CV-QKD is fundamentally realized via coding of the Alice or Bob binary labels of the Gaussian samples using either one-way or interactive communications between the parties, Alice and Bob, over a public authenticated channel. We assume that the communication is performed through an Optical Wireless (OW) or Free Space Optics (FSO) channel. In that case the received signal suffers from stochastic fading due to pointing jitter or atmospheric turbulence. As a result of the channel fading and noise Alice and Bob Gaussian samples will not match. Information Reconciliation (IR) is the phase of the CV-QKD protocol that makes sure that Alice and Bob agree on a common and identical labeling of their samples, i.e. agree on a common stream of bits that we denote as “reconciled key.” The information reconciliation in CV-QKD could be done by one-way or two-way channel coding to correct the actual labels so that they do match. To do so Bob generates a sequence of parity bits using a systematic code. These bits are sent to Alice over an authenticated public channel. Alice then uses her own sequence of labels she obtains after quantization with the redundancy provided by Bob to recover Bob’s binary sequence. In this work we analyze the problem of information reconciliation for continuous variable quantum key distribution over a free space optics channel.
Abstract Quantum key distribution (QKD) is the most mature application of quantum information technology. Information reconciliation is a crucial step in QKD and significantly affects the final secret key rates shared between two legitimate parties. We analyze and compare various construction methods of low-density parity-check (LDPC) codes and design high-performance irregular LDPC codes with a block length of 10 6 . Starting from these good codes and exploiting the slice reconciliation technique based on multilevel coding and multistage decoding, we realize high-efficiency Gaussian key reconciliation with efficiency higher than 95% for signal-to-noise ratios above 1. Our demonstrated method can be readily applied in continuous variable QKD.
Abstract In Quantum Key Distribution (QKD), two users extract a shared secret key using a quantum communication channel in the presence of an eavesdropper. Among QKD protocols, the ones based on Energy-Time (ET) entanglement of photons have been studied extensively due to their ability to generate high key rates from the arrival times of entangled photons. For the information reconciliation (IR) stage of ET-QKD protocols (where the users communicate using a classical channel in order to reconcile differences in their data), a scheme called multi-level coding (MLC) was proposed by Zhou et al. in prior work. The MLC scheme splits the raw key symbols into bit layers and utilizes binary Low-Density Parity-Check (LDPC) codes to encode each layer. Although binary LDPC codes are able to offer low complexity decoding for IR, they have poor error-correcting performance compared to their non-binary counterparts, thus leading to low key rates. Additionally, existing LDPC codes do not fully utilize the properties of the QKD channel to optimize the key rates. In this paper, we mitigate the above issues by proposing a flexible protocol for IR in ET-QKD systems called Non-Binary Multi-Level Coding NB-MLC(a) which is parameterized by a positive integer a. The NB-MLC(a) protocol is a generalization of the MLC scheme and utilizes NB-LDPC codes from a Galois field of size 2^a. We show that by using a small value of a, the NB-MLC(a) protocol significantly improves the key rate without much increase in complexity. To further improve the key rates of the NB-MLC(a) protocol, we propose i) a joint rate and degree distribution optimization (JRDO) algorithm to design the NB-LDPC codes for the protocol; ii) an interleaved decoding and communication (IDC) scheme to decode the different layers of the NB-MLC(a) protocol. The JRDO algorithm is designed to use the QKD channel information and we show that it results in a higher key rate than codes used in prior work. Additionally, the IDC scheme improves the key rate compared to the decoding and communication methods utilized previously in literature. Overall, the NB-MLC(a) protocol that uses JRDO LDPC codes and the IDC scheme results in a significant 40 − 60% improvement in key rates compared to prior work for ET-QKD systems.
Continuous-variable quantum key distribution (QKD) utilizes an ensemble of coherent states of light to distribute secret encryption keys between two parties. An essential ingredient of the QKD protocol is highly efficient information reconciliation. To achieve highly efficient reconciliation, error-correcting codes with a low channel coding rate are inevitable in the most common schemes of multilevel coding and multistage decoding (MLC-MSD) and multidimensional reconciliation. Multiedge-type (MET) low-density parity-check (LDPC) codes are well suited for highly efficient reconciliation at low rates. Here, we calculate the optimal channel coding rates in the MLC-MSD scheme for reverse reconciliation, introduce the concept of generalized extrinsic information transfer charts for MET-LDPC codes, which constitute a simple and fast asymptotic analysis tool, and present a set of MET-LDPC codes with asymptotic efficiency >97>97%>97 for channel coding rates 0.1, 0.05, 0.02, and 0.01. We believe that our codes will find wide application in implementations of continuous-variable quantum key distribution based on Gaussian modulation.
The well-known multidimensional reconciliation is a significant stage of a continuous-variable quantum key distribution (CVQKD) system, which uses ddd-dimensional rotations to build a virtual channel between authenticated parties, Alice and Bob. Generally, a block low-density parity-check code with a belief-propagation (BP) iterative decoding algorithm, which is optimized for an additive white Gaussian noise channel, is always used in multidimensional reconciliation for the CVQKD system. In this paper, we study the signal-to-noise ratio (SNR) of the virtual channel of multidimensional reconciliation in CVQKD and prove that the noise of the virtual channel follows the Student's ttt-distribution. Therefore, we propose a ttt-BP decoding algorithm, which can be better applied to multidimensional reconciliation. Simulation results show that the frame error rate (FER) with the proposed ttt-BP decoding algorithm is superior to that with the conventional BP decoding algorithm applied to multidimensional reconciliation. Subsequently, the FER improvement results in significant influence on reconciliation efficiency and secret key rate of the CVQKD system.