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

Abstract

The speed at which two remote parties can exchange secret keys over a fixed-length fiber-optic cable in continuousvariable quantum key distribution (CV-QKD) is currently limited by the computational complexity of post-processing algorithms for key reconciliation. Multi-edge low-density paritycheck (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 4.10×10 −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 1.07× and 8.03× higher decoded information throughput over the upper bound on the secret key rate for a lossy channel. For distances beyond 130km, the GPU decoder delivers an information throughput between 1868× and 18790× higher than the achievable secret key rates with a 1MHz light source. The GPU-based QC-LDPC decoder achieves a 1.29× 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, and that the secret key rate remains limited only by the physical parameters of the quantum channel and the latency of privacy amplification.

The Road to Near-Capacity CV-QKD Reconciliation: An FEC-Agnostic Design

“…3 9 Even though System C is not a balanced-complexity system, there are practical scenarios, where having a balanced complexity is not imperative, such as in ground station to unmanned aerial vehicle (UVA) quantum communication [95], [96], etc. 10 As for handling decoding failures, it is assumed to be identical to that in the conventional LDPC-based reconciliation scheme of [66], which is based on the classic cyclic redundancy check. Specifically, the system opts for discarding the sifted keys, if decoding failure occurs.…”

Continuous-variable measurement-device-independent quantum key distribution: Composable security against coherent attacks

“…where the mutual informations are bounded by the results of parameter estimation. In our example we choose the conservative value β = 0.95 [34][35][36][37]. (Notice that in principle the factor β is a function of n and ǫ EC , but for the sake of illustration we assume it to be constant.…”

Finite-size analysis of measurement-device-independent quantum cryptography with continuous variables

“…where ξ ≤ 1 quantifies the inefficiency of error correction and privacy amplification protocols [69][70][71] and I AB is Alice-Bob mutual information. This is given by…”