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arXiv:2301.08621 · Advanced Quantum Technologies

Improved Real‐Time Post‐Processing for Quantum Random Number Generators

Li Qian, Xiaoming Sun, Xingjian Zhang, Hongyi Zhou

Published Apr 29, 2024• 4 citations
arXivHTMLPDF

Abstract

Abstract Randomness extraction is a key problem in cryptography and theoretical computer science. With the recent rapid development of quantum cryptography, quantum‐proof randomness extraction has also been widely studied, addressing the security issues in the presence of a quantum adversary. In contrast with conventional quantum‐proof randomness extractors characterizing the input raw data as min‐entropy sources, it is found that the input raw data generated by a large class of trusted‐device quantum random number generators can be characterized as the so‐called reverse block source. This fact enables us to design improved extractors. Two novel quantum‐proof randomness extractors for reverse block sources that realize real‐time block‐wise extraction are proposed specifically. In comparison with the general min‐entropy randomness extractors, the designs achieve a significantly higher extraction speed and a longer output data length with the same seed length. In addition, they enjoy the property of online algorithms, which process the raw data on the fly without waiting for the entire input raw data to be available. These features make the design an adequate choice for the real‐time post‐processing of practical quantum random number generators. Applying the extractors to the raw data generated by a widely used quantum random number generator, a simulated extraction speed as high as 300 Gbps is achieved.

DOI
10.1002/qute.202400025

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Abstract Randomness extraction is a key problem in cryptography and theoretical computer science. With the recent rapid development of quantum cryptography, quantum‐proof randomness extraction has also been widely studied, addressing the security issues in the presence of a quantum adversary. In contrast with conventional quantum‐proof randomness extractors characterizing the input raw data as min‐entropy sources, it is found that the input raw data generated by a large class of trusted‐device quantum random number generators can be characterized as the so‐called reverse block source. This fact enables us to design improved extractors. Two novel quantum‐proof randomness extractors for reverse block sources that realize real‐time block‐wise extraction are proposed specifically. In comparison with the general min‐entropy randomness extractors, the designs achieve a significantly higher extraction speed and a longer output data length with the same seed length. In addition, they enjoy the property of online algorithms, which process the raw data on the fly without waiting for the entire input raw data to be available. These features make the design an adequate choice for the real‐time post‐processing of practical quantum random number generators. Applying the extractors to the raw data generated by a widely used quantum random number generator, a simulated extraction speed as high as 300 Gbps is achieved.
Abstract Quantum‐proof randomness extraction is essential for handling quantum side information possessed by a quantum adversary, which is widely applied in various quantum cryptography tasks. In this study, the authors introduce a real‐time two‐source quantum randomness extractor against quantum side information. The authors’ extractor is tailored for forward block sources, a novel category of min‐entropy sources introduced in this work. These sources retain the flexibility to accommodate a broad range of quantum random number generators. The authors’ online algorithms demonstrate the extraction of a constant fraction of min‐entropy from two infinitely long independent forward block sources. Moreover, the authors’ extractor is inherently block‐wise parallelisable, presenting a practical and efficient solution for the timely extraction of high‐quality randomness. Applying the authors’ extractors to the raw data of one of the most commonly used quantum random number generators, a simulated extraction speed as high as 64 Gbps is achieved.
Randomness extraction is indispensable for quantum random number generators, serving to eliminate bias and potential information leakage from raw measurement data. Conventional extractors operate in a block-wise fashion, requiring the complete accumulation of raw data before processing. To circumvent the latency and buffering overheads that hinder real-time random number generation, recent work introduced a stream-cipher implementation for the randomness extractor based on the Toeplitz matrix hashing. In this work, we generalize this stream-processing paradigm to the broader family of randomness extractors based on (almost dual) universal2_22​ random hashing. Specifically, we shift the computational burden from a time-consuming block-wise post-processing stage into an offline pre-processing stage that generates a pseudo-random mask. This allows the raw data to be processed by the mask on the fly using a simple bitwise exclusive-OR operation. Crucially, we prove that this stream implementation strictly preserves the security guarantees of the original block-wise protocols. We detail the transformation of three typical constructions -- based on standard Toeplitz, circulant, and modified Toeplitz matrices -- from block to stream implementations, and benchmark their practical performance using realistic quantum experimental data. We anticipate our framework will enhance the efficiency of real-time quantum cryptographic systems.
Randomness is widely used in various fields, including encryption, statistical analysis, and numerical simulations. Randomness is also a fundamental resource in science and engineering. For such applications, we usually need to provide unbiased and independent random bits. This raises the issue of where to get these supposed random bits. Quantum random number generators (QRNGs) generate real random numbers based on the inherent randomness of quantum measurements. In practice, unfortunately, quantum randomness is inevitably mixed with classical randomness due to classical noise. Also, randomness is often correlated and biased. It is necessary to process the resulting raw bits sequence and convert them to good-quality output values that are as close to uniform distribution as possible. Random extractors are required for this. We analyze the randomness obtained by quantum random number generators as well as various examples of post-processing. We discuss the types of randomness extractors. Also, we use information-theoretically secure extractors and present improved novel randomness extraction.
Quantum random number generation is a technique to generate random numbers by extracting randomness from specific quantum processes. As for practical random number generators, they are required not only to have no information leakage but also have a high speed at generating random sequences. In this paper, we consider the generators based on laser phase noise and propose a method to modify the estimation of min-entropy, which can guarantee no information leakage to the eavesdropper. We also accelerate post processing based on Toeplitz matrix with Fast Fourier Transformation, reducing its time complexity to O(nlogn). Furthermore, we discuss the influence on post processing speed by block length and find a proper block length to process a fixed-length raw sequence.
Quantum random-number generators (QRNGs) can offer a means to generate information-theoretically provable random numbers, in principle. In practice, unfortunately, the quantum randomness is inevitably mixed with classical randomness due to classical noises. To distill this quantum randomness, one needs to quantify the randomness of the source and apply a randomness extractor. Here, we propose a generic framework for evaluating quantum randomness of real-life QRNGs by min-entropy, and apply it to two different existing quantum random-number systems in the literature. Moreover, we provide a guideline of QRNG data postprocessing for which we implement two information-theoretically provable randomness extractors: Toeplitz-hashing extractor and Trevisan's extractor.
Quantum random number generators (QRNG) based on continuous variable (CV) quantum fluctuations offer great potential for their advantages in measurement bandwidth, stability and integrability. More importantly, it provides an efficient and extensible path for significant promotion of QRNG generation rate. During this process, real-time randomness extraction using information theoretically secure randomness extractors is vital, because it plays critical role in the limit of throughput rate and implementation cost of QRNGs. In this work, we investigate parallel and real-time realization of several Toeplitz-hashing extractors within one field-programmable gate array (FPGA) for parallel QRNG. Elaborate layout of Toeplitz matrixes and efficient utilization of hardware computing resource in the FPGA are emphatically studied. Logic source occupation for different scale and quantity of Toeplitz matrices is analyzed and two-layer parallel pipeline algorithm is delicately designed to fully exploit the parallel algorithm advantage and hardware source of the FPGA. This work finally achieves a real-time post-processing rate of QRNG above 8 Gbps. Matching up with integrated circuit for parallel extraction of multiple quantum sideband modes of vacuum state, our demonstration shows an important step towards chip-based parallel QRNG, which could effectively improve the practicality of CV QRNGs, including device trusted, device-independent, and semi-device-independent schemes.