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arXiv:2402.14607 · IET Quantum Communication

Real‐time seedless post‐processing for quantum random number generators

Qian Li, Hongyi Zhou

Published Dec 1, 2024• 0 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1049/qtc2.12118

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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.
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.
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.
We study the problem of constructing multi-source extractors in the quantum setting, which extract almost uniform random bits against quantum side information collected from several initially independent classical random sources. This is a natural generalization of seeded randomness extraction against quantum side information and classical independent source extraction. With new challenges such as potential entanglement in the side information, it is not a prior clear under what conditions do quantum multi-source extractors exist; the only previous work is [KK12], where the classical inner-product two-source extractors of [CG88] and [DEOR04] are shown to be quantum secure in the restricted Independent Adversary (IA) Model and entangled Bounded Storage (BS) Model. In this paper we propose a new model called General Entangled (GE) Adversary Model, which allows arbitrary entanglement in the side information and subsumes both the IA model and the BS model. We proceed to show how to construct GE-secure quantum multi-source extractors. To that end, we propose another model called One-sided Adversary (OA) Model, which is weaker than all the above models. Somewhat surprisingly, we establish equivalence between strong OA-security and strong GE-security. As a result, all classical multi-source extractors can either directly work, or be modified to work in the GE model at the cost of one extra random source. Thus, our constructions essentially match the best known constructions of classical multi-source extractors. We also apply our techniques to two important problems in cryptography and distributed computing --- privacy amplification and network extractor. We show that as long as the sources have certain amounts of conditional min-entropy in our GE model (even with entangled quantum side information), we can design very efficient privacy amplification protocols and network extractors.
Randomness extractors, widely used in classical and quantum cryptography and other fields of computer science, e.g., derandomization, are functions which generate almost uniform randomness from weak sources of randomness. In the quantum setting one must take into account the quantum side information held by an adversary which might be used to break the security of the extractor. In the case of seeded extractors the presence of quantum side information has been extensively studied. For multi-source extractors one can easily see that high conditional min-entropy is not sufficient to guarantee security against arbitrary side information, even in the classical case. Hence, the interesting question is under which models of (both quantum and classical) side information multi-source extractors remain secure. In this work we suggest a natural model of side information, which we call the Markov model, and prove that any multi-source extractor remains secure in the presence of quantum side information of this type (albeit with weaker parameters). This improves on previous results in which more restricted models were considered or the security of only some types of extractors was shown.
Randomness extractors, widely used in classical and quantum cryptography and other fields of computer science, e.g., derandomization, are functions which generate almost uniform randomness from weak sources of randomness. In the quantum setting one must take into account the quantum side information held by an adversary which might be used to break the security of the extractor. In the case of seeded extractors the presence of quantum side information has been extensively studied. For multi-source extractors one can easily see that high conditional min-entropy is not sufficient to guarantee security against arbitrary side information, even in the classical case. Hence, the interesting question is under which models of (both quantum and classical) side information multi-source extractors remain secure. In this work we suggest a natural model of side information, which we call the Markov model, and prove that any multi-source extractor remains secure in the presence of quantum side information of this type (albeit with weaker parameters). This improves on previous results in which more restricted models were considered and the security of only some types of extractors was shown.
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.