The speed at which two remote parties can exchange secret keys in continuous-variable quantum key distribution (CV-QKD) is currently limited by the computational complexity of key reconciliation. Multi-dimensional reconciliation using multi-edge low-density parity-check (LDPC) codes with low code rates and long block lengths has been shown to improve error-correction performance and extend the maximum reconciliation distance. We introduce a quasi-cyclic code construction for multi-edge codes that is highly suitable for hardware-accelerated decoding on a graphics processing unit (GPU). When combined with an 8-dimensional reconciliation scheme, our LDPC decoder achieves an information throughput of 7.16 Kbit/s on a single NVIDIA GeForce GTX 1080 GPU, at a maximum distance of 142 km with a secret key rate of 6.64 × 10−8 bits/pulse for a rate 0.02 code with block length of 106 bits. The LDPC codes presented in this work can be used to extend the previous maximum CV-QKD distance of 100 km to 142 km, while delivering up to 3.50× higher information throughput over the tight upper bound on secret key rate for a lossy channel. Improvements in the post-processing algorithms for quantum cryptography can extend the secure transmission distance by over 40%. Quantum key distribution protocols rely on the transmission of quantum states, but also on classical post-processing to eliminate errors introduced by imperfect equipment or the interference of an attacker. Over long distances, the requirements of this classical 'reconciliation' processing can become the bottleneck for key exchange. Mario Milicevic and colleagues from the University of Toronto and the University of British Columbia in Canada have developed a high-throughput error correction scheme that increases the potential operating range for quantum key distribution from 100 to 143 km. Their method is fast enough that the rate of key distribution is instead limited by the physical properties of the communication channel.

/pdf/quasi-cyclic-multi-edge-ldpc-codes-for-long-distance-quantum-2cy1b2xz1w.pdf

Quasi-cyclic multi-edge LDPC codes for long-distance quantum cryptography

The speed at which two remote parties can exchange secret keys over a fixed-length fiber-optic cable in continuous-variable quantum key distribution (CV-QKD) is currently limited by the computational complexity of post-processing algorithms for key reconciliation. Multi-edge low-density parity-check (LDPC) codes with low code rates and long block lengths were proposed for CV-QKD, in order to extend the maximum reconciliation distance between the two remote parties. Key reconciliation over multiple dimensions has been shown to further improve the error-correction performance of multi-edge LDPC codes in CV-QKD, thereby increasing both the secret key rate and distance. However, the computational complexity of LDPC decoding for long block lengths on the order of 10^6 bits remains a challenge. This work introduces a quasi-cyclic (QC) code construction for multi-edge LDPC codes that is highly suitable for hardware-accelerated decoding on a modern graphics processing unit (GPU). When combined with an 8-dimensional reconciliation scheme, the LDPC decoder achieves a raw decoding throughput of 1.72Mbit/s and an information throughput of 7.16Kbit/s using an NVIDIA GeForce GTX 1080 GPU at a maximum distance of 160km with a secret key rate of 4.10x10^{-7} bits/pulse for a rate 0.02 multi-edge code with block length of 10^6 bits when finite-size effects are considered. This work extends the previous maximum CV-QKD distance of 100km to 160km, while delivering between 1.07x and 8.03x higher decoded information throughput over the upper bound on the secret key rate for a lossy channel. The GPU-based QC-LDPC decoder achieves a 1.29x improvement in throughput over the best existing GPU decoder implementation for a rate 1/10 multi-edge LDPC code with block length of 2^{20} bits. These results show that LDPC decoding is no longer the computational bottleneck in long-distance CV-QKD.

/pdf/key-reconciliation-with-low-density-parity-check-codes-for-4mdb7vvd1n.pdf

Key Reconciliation with Low-Density Parity-Check Codes for Long-Distance Quantum Cryptography

In the system of quantum key distribution (QKD), errors may occur in the initial keys due to system noise or eavesdropping during the transmission on quantum channel. The goal of information reconciliation is to remove these errors by exchanging messages on an authenticated public channel. In this paper, we discuss the problem of secrete key reconciliation (SKR) in QKD, analyze the cascade protocol used for SKR, then modify it according to our conclusion. Experiments have shown that the modified protocol is of much higher efficiency.

Information Reconciliation Protocol in Quantum Key Distribution System

Around forty years have passed since the first pioneering works have introduced the possibility of using quantum physics to strongly enhance communications safety. Nowadays Quantum Cryptography, and in particular, Quantum Key Distribution (QKD) exited the physics laboratories to become commercial technologies that increasingly trigger the attention of States, military forces, banks, and private corporations. This work takes on the challenge of bringing QKD closer to a consumer technology: optical fibers deployed and used by telecommunication companies of different States have been used to realize a quantum network, the first-ever connecting three different countries. This pushes towards the necessary coexistence of QKD and classical communications on the same infrastructure, which currently represents a main limit of this technology. Our network connects Trieste to Rijeka and Ljubljana via a trusted node in Postojna; a key rate of over 3 kbps has been achieved in the shortest link, and a 7-hour long measurement has demonstrated the system stability and reliability. Finally, the network has been used for a public demonstration of QKD at the G20 Digital Ministers' Meeting in Trieste. The reported experimental results, together with the significant interest that one of the most important events of international politics has attracted, showcase the maturity of the QKD technology bundle, placing it in the spotlight for consumer applications in the near term. 

Deploying an Inter‐European Quantum Network

Quantum Key Distribution (QKD) protocols allow the establishment of symmetric cryptographic keys up to a limited distance at limited rates. Due to optical misalignment, noise in quantum detectors, disturbance of the quantum channel or eavesdropping, an error key reconciliation technique is required to eliminate errors. This chapter analyses different key reconciliation techniques with a focus on communication and computing performance. We also briefly describe a new approach to key reconciliation techniques based on artificial neural networks.

/pdf/error-reconciliation-in-quantum-key-distribution-protocols-9d7kvy8glk.pdf

Error Reconciliation in Quantum Key Distribution Protocols

Post-processing is an important part of Quantum Key Distribution (QKD) system. This paper discusses the motivation for designing a multi-thread QKD post processing software, its architecture, communication protocol specification, and synchronization issues. It is shown that efficiency is gained from multi-thread programming. Future work to improve the software is also discussed.

An Implementation of Post-Processing Software in Quantum Key Distribution

Secret key reconciliation is an important step in the process of quantum key distribution. In the protocols used for reconciliation, Winnow has been proved a fast and efficient one. In this paper, we analyze the efficiency of Winnow in terms of amount of leaked information in details. We give the optimal block size in Winnow theoretically and experimentally for different error rate.

Efficiency of Winnow Protocol in Secret Key Reconciliation

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Information Reconciliation Protocol in Quantum Key Distribution System

An Implementation of Post-Processing Software in Quantum Key Distribution

Efficiency of Winnow Protocol in Secret Key Reconciliation