Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

IEEE photonics journal

Memory-Saving Implementation of High-Speed Privacy Amplification Algorithm for Continuous-Variable Quantum Key Distribution

Dengwen Li, Peng Huang, Yingming Zhou, Yuan Li, Guihua Zeng

Published Aug 14, 2018• 19 citations
Publisher

Abstract

Privacy amplification is an indispensable procedure to share secure secret key between legitimate parties in quantum key distribution (QKD) because a portion of bits are still leaked to eavesdropper Eve after the secret reconciliation. Here, we propose a novel privacy amplification scheme with an optimal hash function. In particular, by utilizing the linear feedback shift register (LFSR) technique, we optimize and simplify the construction of the Toeplitz matrix. In this way, the LFSR-based Toeplitz matrix is used to execute the privacy amplification algorithm. The hardware storage resources can then be drastically saved, and the time consuming will be only about half of that without using the LFSR-based Toeplitz matrix. This work breaks the bottleneck of privacy amplification in high-speed continuous-variable QKD (CVQKD), and thus contributes to the real-time performance of the whole CVQKD system.

DOI
10.1109/jphot.2018.2865486

Related papers

Memory-Saving and High-Speed Privacy Amplification Algorithm Using LFSR-Based Hash Function for Key Generation

Enjian Bai, Xueqin Jiang, Yun Ping Wu

Privacy amplification is an indispensable procedure for key generation in the quantum key distribution system and the physical layer key distribution system. In this paper, we propose a high-speed privacy amplification algorithm that saves hardware memory and improves the key randomness performance. Based on optimizing the structure of the Toeplitz matrix generated by a linear feedback shift register, the core of our algorithm is a block-iterative structure hash function that is used to generate a secure key of arbitrary length. The proposed algorithm adopts multiple small Toeplitz matrices to compress the negotiation key for convenient implementation. The negotiated key is equally divided into multiple small blocks, and the multiplication operation of the negotiated key with the Toeplitz matrix is converted into a modular addition operation through an accumulator. The analysis results demonstrate that the algorithm has the advantages of saving memory and running quickly. In addition, the NIST randomness test and avalanche effect test on the key sequences indicate that the proposed algorithm has a favorable performance.

Electronics•Jan 27, 2022•16 citations

High-speed implementation of privacy amplification for continuous-variable quantum-key distribution with Toeplitz matrix based on FPGA

Yujie Luo, Yang Li, Li Ma +6 more

For a high-speed and secure continuous-variable quantum key distribution (CV-QKD) system, privacy amplification (PA) plays an important role. To reduce the finite size effect, the input length of PA should be at least on the order of 10^8, 10^9, 10^10 when the transmission distance is about 50km, 80km, 100km, respectively. This leads to high computation complexity and large storage demand of the data, which is unfriendly to field programmable gate array (FPGA) implementation for its limited resource. In addition, the limited IO speed of Double Data Rate Synchronous Dynamic Random Access Memory (DDR SDRAM) restricts the implementation performance of PA. In this paper, we propose an effective way to access data based on DDR to improve the performance of PA. As a result, the reading time from DDR can be reduced, and it can eliminate the effect of the limited IO speed of DDR, so that PA can perform with multiple code-words. This can make full use of the resource of FPGA and increase the execution speed of PA. Besides, combining with the proposed method, an easier algorithm is used to decrease the complexity of calculations. Based on these methods, we realize PA with Toeplitz matrix based on FPGA and the experimental throughput is about 288Mbps when the input length is about 100Mbits.

SPIE Conference on Quantum and Nonlinear Optics•Oct 12, 2023•2 citations

High-speed Implementation of FFT-based Privacy Amplification on FPGA in Quantum Key Distribution

Qiong Li, Bingze Yan, Haokun Mao +1 more

Privacy amplification (PA) is a vital procedure in quantum key distribution (QKD) to generate the secret key that the eavesdropper has only negligible information from the identical correcting key for the communicating parties. With the increase of repeat frequency of discrete-variable QKD (DV-QKD) system, the processing speed of PA has become the bottle neck restricting DV-QKD's secure key rate. The PA using Toeplitz-based Hash function is adopted widely because of its simplicity and parallel feature. Because this algorithm can be accelerated with Fast Fourier Transform (FFT), an improved scheme PA for Field-programmable Gate Array (FPGA) based on this is proposed. This paper improves the custom FFT-based algorithm by reducing the number of computations and read/write memory operations significantly. The correctness is verified when implemented in a Xilinx Virtex-6 FPGA. Meanwhile, the processing speed of improved scheme can nearly double the classical Toeplitz Hashing scheme on FPGA through the actual experiment.

arXiv:1809.07592•Sep 20, 2018•2 citations

High-Speed Implementation of Length-Compatible Privacy Amplification in Continuous-Variable Quantum Key Distribution

Xiangyu Wang, Yichen Zhang, Song Yu +1 more

Privacy amplification is an indispensable step in postprocessing of continuous-variable quantum key distribution (CV-QKD), which is used to distill unconditional secure keys from identical corrected keys between two distant legal parties. The processing speed of privacy amplification has a significant effect on the secret key rate of a CV-QKD system. We report the high-speed parallel implementation of the length-compatible privacy amplification algorithm based on a graphic processing unit. The length-compatible algorithm is used to satisfy the security requirements of privacy amplification at different transmission distances when considering finite-size effect. We achieve the speed of privacy amplification over 1 Gb/s at arbitrary input length and the speed is one to two orders of magnitude faster than previous demonstrations, which supports the high-speed real-time CV-QKD system and ensures the security of privacy amplification.

arXiv:1805.02372•IEEE photonics journal•Apr 9, 2018•233 citations

High-speed implementation of privacy amplification for continuous-variable quantum key distribution

Yujie Luo, Yang Li, Jie Yang +3 more

Privacy amplification (PA) is an essential process for high-speed and real-time implementation of a continuous-variable quantum key distribution (CV-QKD) system. This work focuses on the improvement of the performance of PA, and we realize PA with Toeplitz matrix and accelerate it using fast Fourier transform (FFT) on graphic processing unit (GPU). Based on the architectural feature of FFT, we adjust its form of input length and obtained an average speed of PA about 2Gbps with input length ranges from 1Mbits to 128Mbits, which is length-adaptable to satisfy various requirements of CV-QKD systems at different transmission distances. Furthermore, we test this work with different compress ratios of PA, which can also achieve a high implementation speed around 2Gbps. With the method used in this paper, the requirements of PA for the high-speed and real-time CV-QKD system can be entirely satisfied.

SPIE Conference on Quantum and Nonlinear Optics•Oct 9, 2020•3 citations

High-Speed and Adaptive FPGA-Based Privacy Amplification in Quantum Key Distribution

Qiong Li, Bingze Yan, Haokun Mao +3 more

Privacy amplification (PA) is a vital procedure in quantum key distribution (QKD) to shrink the eavesdropper's information about the final key almost to zero. With the increase of repeat frequency of discrete variable QKD (DV-QKD) system, PA processing speed has become the bottleneck in many high-speed DV-QKD systems. In this paper, a high-speed adaptive field-programmable gate array (FPGA)-based PA scheme using a fast Fourier transform (FFT) is presented. To decrease the computation complexity, a modified 2-D FFT-based Toeplitz PA scheme is designed. To increase the processing speed of the scheme on the constraint of limited resources, a real-value oriented FFT acceleration method and a fast read/write balanced matrix transposition method are designed and implemented in our scheme. The experimental results on a Xilinx Virtex-6 FPGA demonstrate that the throughput is nearly double of the latest FPGA based Toeplitz PA scheme according to the literature. Besides, this scheme owns not only the good adaptivity to compression ratio but also the compression ratio independent resource consumption. Therefore, this scheme can fit many high-speed QKD applications.

IEEE Access•Jan 1, 2019•30 citations
Privacy amplification is an indispensable procedure to share secure secret key between legitimate parties in quantum key distribution (QKD) because a portion of bits are still leaked to eavesdropper Eve after the secret reconciliation. Here, we propose a novel privacy amplification scheme with an optimal hash function. In particular, by utilizing the linear feedback shift register (LFSR) technique, we optimize and simplify the construction of the Toeplitz matrix. In this way, the LFSR-based Toeplitz matrix is used to execute the privacy amplification algorithm. The hardware storage resources can then be drastically saved, and the time consuming will be only about half of that without using the LFSR-based Toeplitz matrix. This work breaks the bottleneck of privacy amplification in high-speed continuous-variable QKD (CVQKD), and thus contributes to the real-time performance of the whole CVQKD system.
Privacy amplification is an indispensable procedure for key generation in the quantum key distribution system and the physical layer key distribution system. In this paper, we propose a high-speed privacy amplification algorithm that saves hardware memory and improves the key randomness performance. Based on optimizing the structure of the Toeplitz matrix generated by a linear feedback shift register, the core of our algorithm is a block-iterative structure hash function that is used to generate a secure key of arbitrary length. The proposed algorithm adopts multiple small Toeplitz matrices to compress the negotiation key for convenient implementation. The negotiated key is equally divided into multiple small blocks, and the multiplication operation of the negotiated key with the Toeplitz matrix is converted into a modular addition operation through an accumulator. The analysis results demonstrate that the algorithm has the advantages of saving memory and running quickly. In addition, the NIST randomness test and avalanche effect test on the key sequences indicate that the proposed algorithm has a favorable performance.
For a high-speed and secure continuous-variable quantum key distribution (CV-QKD) system, privacy amplification (PA) plays an important role. To reduce the finite size effect, the input length of PA should be at least on the order of 10^8, 10^9, 10^10 when the transmission distance is about 50km, 80km, 100km, respectively. This leads to high computation complexity and large storage demand of the data, which is unfriendly to field programmable gate array (FPGA) implementation for its limited resource. In addition, the limited IO speed of Double Data Rate Synchronous Dynamic Random Access Memory (DDR SDRAM) restricts the implementation performance of PA. In this paper, we propose an effective way to access data based on DDR to improve the performance of PA. As a result, the reading time from DDR can be reduced, and it can eliminate the effect of the limited IO speed of DDR, so that PA can perform with multiple code-words. This can make full use of the resource of FPGA and increase the execution speed of PA. Besides, combining with the proposed method, an easier algorithm is used to decrease the complexity of calculations. Based on these methods, we realize PA with Toeplitz matrix based on FPGA and the experimental throughput is about 288Mbps when the input length is about 100Mbits.
Privacy amplification (PA) is a vital procedure in quantum key distribution (QKD) to generate the secret key that the eavesdropper has only negligible information from the identical correcting key for the communicating parties. With the increase of repeat frequency of discrete-variable QKD (DV-QKD) system, the processing speed of PA has become the bottle neck restricting DV-QKD's secure key rate. The PA using Toeplitz-based Hash function is adopted widely because of its simplicity and parallel feature. Because this algorithm can be accelerated with Fast Fourier Transform (FFT), an improved scheme PA for Field-programmable Gate Array (FPGA) based on this is proposed. This paper improves the custom FFT-based algorithm by reducing the number of computations and read/write memory operations significantly. The correctness is verified when implemented in a Xilinx Virtex-6 FPGA. Meanwhile, the processing speed of improved scheme can nearly double the classical Toeplitz Hashing scheme on FPGA through the actual experiment.
Privacy amplification is an indispensable step in postprocessing of continuous-variable quantum key distribution (CV-QKD), which is used to distill unconditional secure keys from identical corrected keys between two distant legal parties. The processing speed of privacy amplification has a significant effect on the secret key rate of a CV-QKD system. We report the high-speed parallel implementation of the length-compatible privacy amplification algorithm based on a graphic processing unit. The length-compatible algorithm is used to satisfy the security requirements of privacy amplification at different transmission distances when considering finite-size effect. We achieve the speed of privacy amplification over 1 Gb/s at arbitrary input length and the speed is one to two orders of magnitude faster than previous demonstrations, which supports the high-speed real-time CV-QKD system and ensures the security of privacy amplification.
Privacy amplification (PA) is an essential process for high-speed and real-time implementation of a continuous-variable quantum key distribution (CV-QKD) system. This work focuses on the improvement of the performance of PA, and we realize PA with Toeplitz matrix and accelerate it using fast Fourier transform (FFT) on graphic processing unit (GPU). Based on the architectural feature of FFT, we adjust its form of input length and obtained an average speed of PA about 2Gbps with input length ranges from 1Mbits to 128Mbits, which is length-adaptable to satisfy various requirements of CV-QKD systems at different transmission distances. Furthermore, we test this work with different compress ratios of PA, which can also achieve a high implementation speed around 2Gbps. With the method used in this paper, the requirements of PA for the high-speed and real-time CV-QKD system can be entirely satisfied.
Privacy amplification (PA) is a vital procedure in quantum key distribution (QKD) to shrink the eavesdropper's information about the final key almost to zero. With the increase of repeat frequency of discrete variable QKD (DV-QKD) system, PA processing speed has become the bottleneck in many high-speed DV-QKD systems. In this paper, a high-speed adaptive field-programmable gate array (FPGA)-based PA scheme using a fast Fourier transform (FFT) is presented. To decrease the computation complexity, a modified 2-D FFT-based Toeplitz PA scheme is designed. To increase the processing speed of the scheme on the constraint of limited resources, a real-value oriented FFT acceleration method and a fast read/write balanced matrix transposition method are designed and implemented in our scheme. The experimental results on a Xilinx Virtex-6 FPGA demonstrate that the throughput is nearly double of the latest FPGA based Toeplitz PA scheme according to the literature. Besides, this scheme owns not only the good adaptivity to compression ratio but also the compression ratio independent resource consumption. Therefore, this scheme can fit many high-speed QKD applications.