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Electronics

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

Enjian Bai, Xueqin Jiang, Yun Ping Wu

Published Jan 27, 2022• 16 citations
Publisher

Abstract

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.

DOI
10.3390/electronics11030377

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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.
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 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 (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.
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 (PA) is an essential part in a quantum key distribution (QKD) system, distilling a highly secure key from a partially secure string by public negotiation between two parties. The optimization objectives of privacy amplification for QKD are large block size, high throughput and low cost. For the global optimization of these objectives, a novel privacy amplification algorithm is proposed in this paper by combining multilinear-modular-hashing and modular arithmetic hashing. This paper proves the security of this hybrid hashing PA algorithm within the framework of both information theory and composition security theory. A scheme based on this algorithm is implemented and evaluated on a CPU platform. The results on a typical CV-QKD system indicate that the throughput of this scheme (261Mbps@2.6*10^8 input block size) is twice higher than the best existing scheme (140Mbps@1*10^8 input block size). Moreover, This scheme is implemented on a mobile CPU platform instead of a desktop CPU or a server CPU, which means that this algorithm has a better performance with a much lower cost and power consumption.
In this paper, a high-performance field-programmable gate array (FPGA) based privacy amplification (PA) scheme for both continuous variable and discrete variable - quantum key distribution (QKD) is presented, which can provide more than 1.5 Gbps throughput at the input block size close to10810^{8}108. Besides, the resource consumption is so economical that there is no need of any external storage. To the best of our knowledge, our scheme outperforms existing FPGA based PA schemes by over an order of magnitude in terms of throughput and input block size. To achieve this feature, we design a novel FPGA-based hybrid hash PA algorithm combining multilinear modular hash and modular arithmetic hash (MMH-MH) based on number theoretical transform (NTT). Based on the hybrid hash algorithm, many optimization strategies are designed in our FPGA based PA scheme, such as an NTT-based optimization unit, an NTT-reusable architecture, a memory-saving modular accumulation unit for multilinear modular hash and a pipelined binary modulo unit for modular arithmetic hash. Plentiful experiment results demonstrate the high performance and reliability of our scheme. It can be embedded in most standalone QKD devices conveniently. What's more, it is also a good candidate for a chip-based QKD system.