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Electronics

High-Speed Privacy Amplification Algorithm Using Cellular Automate in Quantum Key Distribution

Yekai Lu, Enjian Bai, Xueqin Jiang, Yun Ping Wu

Published Aug 3, 2022• 4 citations
Publisher

Abstract

Privacy amplification is an important step in the post-processing of quantum communication, which plays an indispensable role in the security of quantum key distribution systems. In this paper, we propose a Cellular Automata-based privacy amplification algorithm, which improves the speed of key distribution. The proposed algorithm is characterized by block iteration to generate secure key of arbitrary length. The core of the algorithm in this paper is to use the property that Cellular Automata can generate multiple new associated random sequences at the same time to carry out bit operations for multiple negotiation keys in the meantime and calculate in turn, so as to quickly realize the compression of negotiation keys. By analyzing the final key, the proposed algorithm has the advantages of fast key generation speed and high real-time performance. At the same time, the results of the NIST randomness test and avalanche test show that the algorithm has good randomness performance.

DOI
10.3390/electronics11152426

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Privacy amplification is an important step in the post-processing of quantum communication, which plays an indispensable role in the security of quantum key distribution systems. In this paper, we propose a Cellular Automata-based privacy amplification algorithm, which improves the speed of key distribution. The proposed algorithm is characterized by block iteration to generate secure key of arbitrary length. The core of the algorithm in this paper is to use the property that Cellular Automata can generate multiple new associated random sequences at the same time to carry out bit operations for multiple negotiation keys in the meantime and calculate in turn, so as to quickly realize the compression of negotiation keys. By analyzing the final key, the proposed algorithm has the advantages of fast key generation speed and high real-time performance. At the same time, the results of the NIST randomness test and avalanche test show that the algorithm has good randomness performance.
Privacy amplification is a critical component in quantum key distribution (QKD) to eliminate eavesdropper information and distill unconditionally secure keys. While conventional Toeplitz hash privacy amplification algorithms face challenges in computational complexity and hardware resource demands, existing one-dimensional cellular automata (1D CAs) algorithm lacks sufficient parallelism and exhibits limited diffusion under finite-size constraints. To overcome these limitations, a privacy amplification algorithm using two-dimensional cellular automata (2D CAs) for QKD is presented in this paper. The proposed algorithm decreases the computation complexity and increases the processing speed. Unlike conventional Toeplitz hash algorithms, the proposed algorithm utilizes the inherent parallelism of 2D CAs to enable simultaneous multi-bit confusion through cyclic row shifts and XOR operations. Furthermore, we prove that the 2D CAs-based algorithm is a universal hash family and satisfies the principle of privacy amplification. The randomness of the proposed algorithm was evaluated through the NIST test suite and an avalanche test, both of which indicated great performance. Finally, we implement the proposed algorithm in field-programmable gate array (FPGA). The experimental results on a Xilinx Artix-7 FPGA demonstrate that our scheme achieves high throughput and significantly reduces hardware resource consumption.
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.
Post-processing is indispensable in quantum key distribution (QKD), which is aimed at sharing secret keys between two distant parties. It mainly consists of key reconciliation and privacy amplification, which is used for sharing the same keys and for distilling unconditional secret keys. In this paper, we focus on speeding up the privacy amplification process by choosing a simple multiplicative universal class of hash functions. By constructing an optimal multiplication algorithm based on four basic multiplication algorithms, we give a fast software implementation of length-adaptive privacy amplification. "Length-adaptive" indicates that the implementation of privacy amplification automatically adapts to different lengths of input blocks. When the lengths of the input blocks are 1 Mbit and 10 Mbit, the speed of privacy amplification can be as fast as 14.86 Mbps and 10.88 Mbps, respectively. Thus, it is practical for GHz or even higher repetition frequency QKD systems.
State-of-art quantum key distribution (QKD) systems are performed with several GHz pulse rates, meanwhile privacy amplification (PA) with large scale inputs has to be performed to generate the final secure keys with quantified security. In this paper, we propose a fast Fourier transform (FFT) enhanced high-speed and large-scale (HiLS) PA scheme on commercial CPU platform without increasing dedicated computational devices. The long input weak secure key is divided into many blocks and the random seed for constructing Toeplitz matrix is shuffled to multiple sub-sequences respectively, then PA procedures are parallel implemented for all sub-key blocks with correlated sub-sequences, afterwards, the outcomes are merged as the final secure key. When the input scale is 128 Mb, our proposed HiLS PA scheme reaches 71.16 Mbps, 54.08 Mbps and 39.15 Mbps with the compression ratio equals to 0.125, 0.25 and 0.375 respectively, resulting achievable secure key generation rates close to the asymptotic limit. HiLS PA scheme can be applied to 10 GHz QKD systems with even larger input scales and the evaluated throughput is around 32.49 Mbps with the compression ratio equals to 0.125 and the input scale of 1 Gb, which is ten times larger than the previous works for QKD systems. Furthermore, with the limited computational resources, the achieved throughput of HiLS PA scheme is 0.44 Mbps with the compression ratio equals to 0.125, when the input scale equals up to 128 Gb. In theory, the PA of the randomness extraction in quantum random number generation (QRNG) is same as the PA procedure in QKD, and our work can also be efficiently performed in high-speed QRNG.
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.
In a quantum key distribution (QKD) system, privacy amplification (PA) is an essential procedure that can effectively eliminate the leaked information to an eavesdropper and distill a secret key. The processing speed of the PA algorithm inevitably affects the final key rate of the QKD system. We propose a high-speed PA algorithm based on field-programmable gate array (FPGA), where the matrix multiplications are divided into a number of rhomboid-block operations. The implementation of the PA reduces significantly the required number of FPGA Block RAMs. Meanwhile, it automatically adapts to different lengths of input and output blocks. Finally, we verified the correctness and high-speed of the algorithm when implemented in a Xilinx Virtex-7 FPGA.