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arXiv:2112.10586 · Scientific Reports

Improved polar-code-based efficient post-processing algorithm for quantum key distribution

Junbin Fang, Zhengzhong Yi, Jin Li, Zhipeng Liang, Yulin Wu, Wen Lei, Zoe L. Jiang, Xuan Wang

Published Jun 16, 2022• 9 citations
arXivHTMLPDF

Abstract

Combined with one-time pad encryption scheme, quantum key distribution guarantees the unconditional security of communication in theory. However, error correction and privacy amplification in the post-processing phase of quantum key distribution result in high time delay, which limits the final secret key generation rate and the practicability of quantum key distribution systems. To alleviate this limitation, this paper proposes an efficient post-processing algorithm based on polar codes for quantum key distribution. In this algorithm, by analyzing the channel capacity of the main channel and the wiretap channel respectively under the Wyner's wiretap channel model, we design a codeword structure of polar codes, so that the error correction and privacy amplification could be completed synchronously in a single step. Through combining error correction and privacy amplification into one single step, this efficient post-processing algorithm reduces complexity of the system and lower the post-processing delay. Besides, the reliable and secure communicaiton conditions for this algorithm has been given in this paper. Simulation results show that this post-processing algorithm satisfies the reliable and secure communication conditions well.

DOI
10.1038/s41598-022-14145-6

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Combined with one-time pad encryption scheme, quantum key distribution guarantees the unconditional security of communication in theory. However, error correction and privacy amplification in the post-processing phase of quantum key distribution result in high time delay, which limits the final secret key generation rate and the practicability of quantum key distribution systems. To alleviate this limitation, this paper proposes an efficient post-processing algorithm based on polar codes for quantum key distribution. In this algorithm, by analyzing the channel capacity of the main channel and the wiretap channel respectively under the Wyner's wiretap channel model, we design a codeword structure of polar codes, so that the error correction and privacy amplification could be completed synchronously in a single step. Through combining error correction and privacy amplification into one single step, this efficient post-processing algorithm reduces complexity of the system and lower the post-processing delay. Besides, the reliable and secure communicaiton conditions for this algorithm has been given in this paper. Simulation results show that this post-processing algorithm satisfies the reliable and secure communication conditions well.
Quantum key distribution (QKD), based on quantum mechanics, enables unconditionally secure key exchange even against adversaries with unlimited computing power. As the core of QKD post-processing, information reconciliation (IR) and privacy amplification (PA) ensure key consistency and security by correcting errors and removing leaked information. With the trend toward miniaturized and chip-based QKD systems, post-processing modules require highly integrated designs. FPGAs offer an ideal solution due to their low cost, power efficiency, and flexibility. This paper presents an FPGA-based QKD post-processing architecture using a polar codes-based appending IR algorithm, achieving reconciliation efficiency better than 1.1 under Eµ≥ 0.06 and Rm= 4. A convolution-structured Toeplitz hash module is developed for PA, supporting 53.13 Mbps data rate and 26.45 Mbps key rate with RPA= 0.5. The complete system is implemented on a Xilinx XCKU040 FPGA. Experimental results show support for 176.58 Mbps input, 36.59 Mbps real-time processing, and 17.56 Mbps key output, demonstrating strong performance and engineering suitability. The design features high integration and portability, offering a practical hardware solution for efficient QKD post-processing.
This paper presents the design and development of practical post-processing software for a general quantum key distribution system. The proposed algorithms consist of three main contributions: 1) channel parameter estimation for quantum bit error rates by a random key sampling method, 2) information reconciliation using rate-adaptive LDPC codes, that collaborate with identical key confirmation by employing a polynomial-based hash function, and 3) privacy amplification performed by a universal hash function, where the binary information is randomly chosen to construct the Toeplitz matrix corresponding to the condition of a secure secret key rate. The proposed post-processing algorithms were implemented and tested in an entangled quantum key distribution experiment based on the BBM92 protocol over a 11-meter free-space quantum channel link. The experiment was conducted over 100 cycles and was able to generate the average sifted key rate of 1,109.08 bits per second. The efficiency of the proposed algorithms enabled two legitimate parties to generate the identical secret key according to the information-theoretic security principles, where the average estimated quantum bit error rate was 2.0127%, the average efficiency of information reconciliation was 1.1919, and the average final secret key rate was 428.42 bits per second. The proposed algorithms could be used in the industrial quantum key distribution systems based on a discrete-variable protocol by optimizing the input parameters of the post-processing procedure, especially for high-speed applications.
The post-processing of quantum key distribution mainly includes error correction and privacy amplification. The error correction algorithms and privacy amplification methods used in the existing quantum key distribution are completely unrelated. Based on the principle of correspondence between error-correcting codes and hash function families, we proposed the idea of time-division multiplexing for error correction and privacy amplification for the first time. That is to say, through the common error correction algorithms and their corresponding hash function families or the common hash function families and their corresponding error-correcting codes, error correction and privacy amplification can be realized by time-division multiplexing with the same set of devices. In addition, we tested the idea from the perspective of error correction and privacy amplification, respectively. The analysis results show that the existing error correction algorithms and their corresponding hash function families or the common privacy amplification methods and their corresponding error-correcting codes cannot realize time-division multiplexing for error correction and privacy amplification temporarily. However, according to the principle of correspondence between error-correcting codes and hash function families, the idea of time-division multiplexing is possible. Moreover, the research on time-division multiplexing for error correction and privacy amplification has some practical significance. Once the idea of time-division multiplexing is realized, it will further reduce the calculation and storage cost of the post-processing process, reduce the deployment cost of quantum key distribution, and help to remote the practical engineering of quantum key distribution.
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.
Key reconciliation is important for practical Quantum key distribution (QKD) systems since it corrects the error bits in a key string by sacrificing some key bits. Therefore, its performance directly affects the secret key rate of a practical QKD system. Although key reconciliation scheme based on polar codes can achieve a high coding efficiency, the high frame error rate causes discarding key strings and decreases the secret key rate. In this paper, we fist analyze the limitation of successive cancellation decoding of polar codes, and then we propose an improved key reconciliation scheme using polar codes with successive cancellation list decoding and optimized coding structures, which can decrease the frame error probability, resulting in a higher secret key rate. Numerical results show that the proposed scheme can achieve a 12.8% higher secret key rate than the previous polar codes-based scheme with a code length of 216 bits and a quantum bit error rate of 2%. Besides, the proposed scheme is robust and it can extract secret key bits even when the quantum bit error rate reaches 10.2% with a code length of 220 bits and a coding efficiency of 90.6%.
Although the quantum technology introduces an unprecedented threat to the classical encryption field, the combination of Quantum Key Distribution (QKD) and one-time pad makes the absolutely secure encryption possible. However the key distribution rate of most QKD systems still cannot meet the requirements of practical applications. The complex QKD post-processing is one of the largest obstacles to improving the key distribution rate. In this paper, the design and implementation of a multi-thread QKD post-processing software is introduced, including the motivation, architecture and communication protocol. The QKD post processing software is flexible, efficient and easy to implement.