Semiconductor superlattice secure key distribution (SSL-SKD) has been experimentally demonstrated to be a novel scheme to generate and agree on the identical key in unconditional security just by public channel. The error correction in the information reconciliation procedure is introduced to eliminate the inevitable differences of analog systems in SSL-SKD. Nevertheless, the error correction has been proved to be the performance bottleneck of information reconciliation for high computational complexity. Hence, it determines the final secure key throughput of SSL-SKD. In this paper, different frequently-used error correction codes, including BCH codes, LDPC codes, and Polar codes, are optimized separately to raise the performance, making them usable in practice. Firstly, we perform multi-threading to support multi-codeword decoding for BCH codes and Polar codes and updated value calculation for LDPC codes. Additionally, we construct lookup tables to reduce redundant calculations, such as logarithmic table and antilogarithmic table for finite field computation. Our experimental results reveal that our proposed optimization methods can significantly promote the efficiency of SSL-SKD, and three error correction codes can reach the throughput of Mbps and provide a minimum secure key rate of 99%.
Semiconductor superlattice secure key distribution (SSL-SKD) has been experimentally demonstrated to be a novel scheme to generate and agree on the identical key in unconditional security just by public channel. The error correction in the information reconciliation procedure is introduced to eliminate the inevitable differences of analog systems in SSL-SKD. Nevertheless, the error correction has been proved to be the performance bottleneck of information reconciliation for high computational complexity. Hence, it determines the final secure key throughput of SSL-SKD. In this paper, different frequently-used error correction codes, including BCH codes, LDPC codes, and Polar codes, are optimized separately to raise the performance, making them usable in practice. Firstly, we perform multi-threading to support multi-codeword decoding for BCH codes and Polar codes and updated value calculation for LDPC codes. Additionally, we construct lookup tables to reduce redundant calculations, such as logarithmic table and antilogarithmic table for finite field computation. Our experimental results reveal that our proposed optimization methods can significantly promote the efficiency of SSL-SKD, and three error correction codes can reach the throughput of Mbps and provide a minimum secure key rate of 99%.
For high-speed quantum key distribution (QKD) post processing, information reconciliation is the most computational step, which usually acts as the system speed bottleneck. Reconciliation efficiency and operation throughput are the two most important performance parameters, but they are often compromised to each other in actual realization due to the available hardware resources. Another characteristic of the information reconciliation is that its channel is time-varying, and in order to guarantee high efficiency, some rate-compatible error correction scheme should be adopted. To cope with the above problems, this paper proposes a rate-compatible high-efficiency reconciliation algorithm based on quasi-cyclic (QC) low-density parity-check (LDPC) codes and puncturing algorithms. On the other hand, in order to obtain high throughput while maintaining low implementation complexity, the normalized min-sum algorithm (NMSA) is realized and optimized by using the fast prototyping tool of high-level synthesis (HLS). The proposed information reconciliation module was implemented on the Xilinx Zynq Ultrascale+ ZCU102 development board. Experimental results show that the maximum throughput rate of the implemented reconciliation module in this paper can reach 136 Mbps, while the efficiency factor is kept lower than 1.32 across the error rate range of 1.7%∼10.6% under the remaining frame error rate level of 10−3. The comprehensive good performance obtained by our design can strongly support the development of modern high-speed QKD systems.
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.
Quantum telecommunication has received a lot of attention today by providing unconditional security because of the inherent nature of quantum channels based on the no-cloning theorem. In this mode of communication, first, the key is sent through a quantum channel that is resistant to eavesdropping, and then secure communication is established using the exchanged key. Due to the inevitability of noise, the received key needs to be distilled. One of the vital steps in key distillation is named key reconciliation which corrects the occurred errors in the key. Different solutions have been presented for this issue, with different efficiency and success rate. One of the most notable works is LDPC decoding which has higher efficiency compared to the others, but unfortunately, this method does not work well in the codes with a high rate. In this paper, we present an approach to correct the errors in the high rate LDPC code-based reconciliation algorithm. The proposed algorithm utilizes Integer Linear Programming to model the error correction problem to an optimization problem and solve it. Testing the proposed approach through simulation, we show it has high efficiency in high rate LDPC codes as well as a higher success rate compared with the LDPC decoding method - belief propagation – in a reasonable time.
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.
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
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.