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Cybersecurity

One-way information reconciliation schemes of quantum key distribution

Li Yang, Hua Dong, Li Zhao

Published May 22, 2019• 10 citations
Publisher

Abstract

With the rapid improvement of quantum computing technology, quantum key distribution(QKD) is a hot technology. Information reconciliation is a key step of QKD which is useful for correcting key error. Classical message interaction is necessary in a practical information reconciliation scheme, which makes the efficiency of these protocols decreased. Therefore, some one-way information reconciliation schemes based on low-density parity-check(LDPC) codes and polar codes are proposed. Here we propose a concatenated method of IR schemes which can achieve any given error rate level without the need of interactions. Compared with the one-way IR schems based on LDPC codes and polar codes, the IR schemes based on the proposed concatenated method can get lower bit error rates after error correction, which can also reduce the communication delay and system complexity of QKD, improve the final key generation rate and enhance the practicability of QKD system.

DOI
10.1186/s42400-019-0033-z

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With the rapid improvement of quantum computing technology, quantum key distribution(QKD) is a hot technology. Information reconciliation is a key step of QKD which is useful for correcting key error. Classical message interaction is necessary in a practical information reconciliation scheme, which makes the efficiency of these protocols decreased. Therefore, some one-way information reconciliation schemes based on low-density parity-check(LDPC) codes and polar codes are proposed. Here we propose a concatenated method of IR schemes which can achieve any given error rate level without the need of interactions. Compared with the one-way IR schems based on LDPC codes and polar codes, the IR schemes based on the proposed concatenated method can get lower bit error rates after error correction, which can also reduce the communication delay and system complexity of QKD, improve the final key generation rate and enhance the practicability of QKD system.
Information reconciliation (IR) is an important step in quantum key distribution (QKD). The error correcting codes are widely used in IR, which can also be seen as error correction. But it proved that this approach contains deleting the leaked information in practical applications. Error coding is not always a guarantee of the reconciliation. It only require of the data's consistency and security. In this paper, Author proposed an improvement scheme of LDPC code on the property of reconciliation and performed some number simulations to evaluate that method. It's shown that this method would achieve a higher efficiency than the original algorithm. Therefore, this algorithm has special important meaning to the key generation.
We study the information reconciliation (IR) scheme for quantum key distribution (QKD) protocols. The IR for the QKD can be seen as the asymmetric Slepian-Wolf problem, which low-density parity-check (LDPC) codes can solve with efficient algorithms, i.e., the belief propagation. However, the LDPC codes are needed to be chosen properly from a collection of codes optimized for multiple key rates, which leads to complex decoder devices and performance degradation for unoptimized key rates. Therefore, it is desired that establish an IR scheme with a single LDPC code which supports multiple rates. To this end, in this paper, we propose an IR scheme with a rate-compatible non-binary LDPC code. Numerical results show the proposed scheme achieves IR efficiency comparable to the best know conventional IR scheme with lower decoding error rates.
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.
Quantum Key Distribution (QKD) provides unconditional security, but requires a robust information reconciliation step to eliminate errors introduced by the quantum channel. The efficiency of this step directly determines the net secret key generation rate. The paper presents a detailed comparative analysis of three major reconciliation techniques: CASCADE, LDPC (Low-Density Parity-Check), and Polar Codes. The analysis focuses on seven essential metrics, including reconciliation efficiency (f), maximum error tolerance (QBERmax,), final secure key rate (R), frame error rate (FER), and computational complexity. Simulations are performed on a realistic QKD channel model (BB84 with depolarization), with QBER varying between 0.1% and 16%, covering experimental conditions. Keywords: QKD, Information Reconciliation, LDPC, CASCADE, Polar Codes, Secret Key Rate
Abstract 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 block checked successive cancellation list decoder of polar codes. Afterward, only the failure corrected sub-blocks perform the additional acknowledgment reconciliation phase, which decreases the frame error rate of the SLA IR scheme. The experimental results show that the overall failure probability of SLA IR scheme is decreased to 10−810^{-8}10−8 10 - 8 and the efficiency is improved to 1.091 with the IR block length of 128 Mb. Furthermore, the efficiency of the proposed SLA IR scheme is 1.055, approached to Shannon limit, when the quantum bit error rate is 0.02 and the input scale of 1 Gb, which is hundred times larger than the state-of-the-art implemented polar codes-based IR schemes.