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Telecoms Conference (ConfTELE)

Secret key extraction in direct reconciliation CV-QKD systems

Margarida Almeida, M. Facão, Nelson Jesus Muga, Armando N. Pinto, Nuno A. Silva

Published Feb 11, 2021• 2 citations
Publisher

Abstract

Quantum Key Distribution (QKD) is, nowadays, the dominant practical application in the quantum technologies field. Nevertheless, extracting secure keys from a physical implementation of a QKD system remains a complicated procedure. In this paper, post-processing algorithms were implemented to extract secret keys from a Continuous-Variable QKD (CV-QKD) system. The Discrete Modulated Four State CV-QKD protocol was considered due to lower complexity in the reconciliation procedure. The secret keys were extracted considering Maximum-Likelihood Estimators (MLEs) for parameter estimation, Iterative Low-Density Parity Check (LDPC) codes complemented with the Sum-Product Algorithm and error groups iterative reconciliation for information reconciliation, and the Toeplitz matrix as the universal hash function for privacy amplification. The post-processing algorithms were applied to extract secret keys from a simulated implementation of the Discrete Modulated Four State CV-QKD protocol, with double homodyne detection.

DOI
10.1109/conftele50222.2021.9435567

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Quantum Key Distribution (QKD) is, nowadays, the dominant practical application in the quantum technologies field. Nevertheless, extracting secure keys from a physical implementation of a QKD system remains a complicated procedure. In this paper, post-processing algorithms were implemented to extract secret keys from a Continuous-Variable QKD (CV-QKD) system. The Discrete Modulated Four State CV-QKD protocol was considered due to lower complexity in the reconciliation procedure. The secret keys were extracted considering Maximum-Likelihood Estimators (MLEs) for parameter estimation, Iterative Low-Density Parity Check (LDPC) codes complemented with the Sum-Product Algorithm and error groups iterative reconciliation for information reconciliation, and the Toeplitz matrix as the universal hash function for privacy amplification. The post-processing algorithms were applied to extract secret keys from a simulated implementation of the Discrete Modulated Four State CV-QKD protocol, with double homodyne detection.
Information reconciliation is a significant step for a continuous-variable quantum key distribution (CV-QKD) system. We propose a reconciliation method that allows two authorized parties to extract a consistent and secure binary key in a CV-QKD protocol, which is based on Gaussian-modulated coherent states and homodyne detection. This method named spherical reconciliation is based on spherical quantization and non-binary low-density parity-check (LDPC) codes. With the suitable signal-to-noise ratio (SNR) and code rate of non-binary LDPC codes, spherical reconciliation algorithm has a high efficiency and can extend the transmission distance of CV-QKD.
Continuous-variable (CV) quantum key distribution (QKD) employs the quadratures of a bosonic mode to establish a secret key between two remote parties, and this is usually achieved via a Gaussian modulation of coherent states. The resulting secret key rate depends not only on the loss and noise in the communication channel, but also on a series of data processing steps that are needed for transforming shared correlations into a final string of secret bits. Here we consider a Gaussian-modulated coherent-state protocol with homodyne detection in the general setting of composable finite-size security. After simulating the process of quantum communication, the output classical data are postprocessed via procedures of parameter estimation, error correction, and privacy amplification. In particular, we analyze the high signal-to-noise regime, which requires the use of high-rate (nonbinary) low-density parity check codes. We implement all these steps in a python-based library that allows one to investigate and optimize the protocol parameters to be used in practical experimental implementations of short-range CV-QKD.
In a continuous-variable quantum key distribution (CV-QKD) system, the computation speed of the post-processing procedure, including information reconciliation (IR) and privacy amplification (PA), inevitably affects the practical secret key rate. IR and PA can be implemented in parallel using low-density parity-check (LDPC) codes and hash functions, respectively. We achieve high-speed hardware-accelerated post-processing procedure for Gaussian symbols on a field-programmable gate array (FPGA) by taking advantage of its superior parallel processing ability. To this end, the sum-product algorithm decoders and a modified LDPC codes construction algorithm adapted to FPGA's characteristics are developed and employed. Two different structures including multiplexing and non-multiplexing are designed to achieve the trade-off between the speed and area of FPGAs, so that an optimal scheme can be adopted according to the requirement of a practical system. Simulation results show that the maximum throughput can reach 100 M symbols/s. We verified the correctness of the post-processing procedures when implemented on the Xilinx VC709 evaluation board, which is populated with the Virtex-7 XC7VX690T FPGA and provided some possible solutions to obtain better performance when more advanced FPGAs are available. The scheme can be applied readily for real-time key extraction and effectively reduce power consumption of the CV-QKD system.
Continuous-variable quantum key distribution (CV-QKD) can extract secret keys in an efficient and practical manner using off-the-shelf telecommunication equipment. This sets CV-QKD as a key technology for implementation in optical fiber networks already deployed in the field. Notwithstanding, the extraction of secret keys in CV-QKD requires the exchange of information, not only on a quantum channel, but also on an authenticated and public classical channel. The classical channel is required to exchange part of the coherent states to aid with the parameter estimation step to conclude on the secrecy of the extracted key, and to exchange side information essential to the reconciliation step. Here, we study the bandwidth demand of the information exchanged in the classical channel and how it can impact the extraction key rate of a CV-QKD system. The post-processing step consuming the highest bandwidth of the classical channel is the reconciliation step, due to the exchange of the side information. We consider different dimensions for the multidimensional reconciliation demanding different bandwidths on the classical channel and compute the allowed extraction key rate depending on the performance of the method, in terms of frame error rate.
We have developed a continuous-variable quantum key distribution (CV-QKD) system that employs discrete quadrature-amplitude modulation and homodyne detection of coherent states of light. We experimentally demonstrated automated secure key generation with a rate of 50 kbps when a quantum channel is a 10 km optical fibre. The CV-QKD system utilises a four-state and post-selection protocol and generates a secure key against the entangling cloner attack. We used a pulsed light source of 1550 nm wavelength with a repetition rate of 10 MHz. A commercially available balanced receiver is used to realise shot-noise-limited pulsed homodyne detection. We used a non-binary LDPC code for error correction (reverse reconciliation) and the Toeplitz matrix multiplication for privacy amplification. A graphical processing unit card is used to accelerate the software-based post-processing.
We report on the development of continuous-variable quantum key distribution (CV-QKD) system that are based on discrete quadrature amplitude modulation (QAM) and homodyne detection of coherent states of light. We use a pulsed light source whose wavelength is 1550 nm and repetition rate is 10 MHz. The CV-QKD system can continuously generate secret key which is secure against entangling cloner attack. Key generation rate is 50 kbps when the quantum channel is a 10 km optical fiber. The CV-QKD system we have developed utilizes the four-state and post-selection protocol [T. Hirano, et al., Phys. Rev. A 68, 042331 (2003).]; Alice randomly sends one of four states {|±α⟩,|±𝑖α⟩}, and Bob randomly performs x- or p- measurement by homodyne detection. A commercially available balanced receiver is used to realize shot-noise-limited pulsed homodyne detection. GPU cards are used to accelerate the software-based post-processing. We use a non-binary LDPC code for error correction (reverse reconciliation) and the Toeplitz matrix multiplication for privacy amplification.