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arXiv:2011.04130

Performance Optimization on Practical Quantum Random Number Generators: Modification on Min-entropy Evaluation and Acceleration on Post Processing

Zehao Zhao, Xiongfeng Ma, Hongyi Zhou

Published Jan 1, 2017• 2 citations
arXivHTMLPDF

Abstract

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.

DOI
10.13140/rg.2.2.10007.88480

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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.
Unique true random numbers with information-theoretically provable randomness can be generated based on homodyne detection of quantum vacuum state and universal-hashing randomness extraction. To increase the min-entropy in the raw data and enhance the generation rate of true random number, the influence of classical noise excursion, which may be intrinsic to a system or deliberately induced by an eavesdropper, on the min-entropy of the raw data is discussed in the optimum dynamical ADC range scenario. We propose enhancing local oscillator intensity rather than electrical gain for noise-independent amplification of quadrature fluctuation of vacuum state. Abundant min-entropy is extractable from the raw data even when classical noise excursion is large. The quality and generation speed of the quantum random number generator are guaranteed. Experimentally, when classical noise excursions of the raw data is about 17.2 times of the classical noise standard deviation. An extraction ratio of true randomness of 85.3% is achieved by finite enhancement of the local oscillator power.
Random numbers generated via quantum process is indeterministic, which are of essential to the cryptographic communication and the large-scale computer modeling. However, in realistic scenarios, classical noises can inevitably contaminate the raw sequences of a quantum randomness number generator (QRNG), and then compromise the security of the QRNG. Min-entropy is a useful approach that can quantify the randomness independent of side-information. To enhance the extractable randomness of the raw sequences arising from the QRNG, we propose a new method which exploits non-uniform quantization methods instead of uniform sampling methods and effectively enhances the extractable randomness from the QRNG at a high quantum-to-classical-noise ratio (QCNR). Given a QCNR as 50 dB and a 16-bit analog-to-digital converter (ADC), the worst-case conditional min-entropy of the non-uniform quantization scheme is improved by nearly 11% compared with that of the uniform sampling scheme.
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.
The efficient generation of high-quality random numbers is essential in the operation of cryptographic modules. The quality of a random number generator is evaluated by the min-entropy of its entropy source. The typical method used to achieve high min-entropy of the output sequence is an entropy accumulation based on a hash function. This is grounded in the famous Leftover Hash Lemma, which guarantees a lower bound on the min-entropy of the output sequence. However, the hash function-based entropy accumulation has slow speed in general. For a practical perspective, we need a new efficient entropy accumulation with the theoretical background for the min-entropy of the output sequence. In this work, we obtain the theoretical bound for the min-entropy of the output random sequence through the very efficient entropy accumulation using only bitwise XOR operations, where the input sequences from the entropy source are independent. Moreover, we examine our theoretical results by applying them to the quantum random number generator that uses dark shot noise arising from image sensor pixels as its entropy source.
The quantum random number generation based on laser phase noise, which is featured with high random number generation rate and ease for photonic integration, has been extensively investigated and demonstrated. Despite these advancements, a theoretical model to achieve optimal performance in terms of maximizing the random number generation rate is still incomplete. In this work, a comprehensive physical model for this scheme is introduced to accurately predict the power spectrum of entropy source and probability distribution of raw data, based on which the entropy source bandwidth and extractable randomness can be accordingly estimated and thus the system performance can be quantitatively evaluated and optimized. The model is sufficiently validated through both simulation and experiment with significant agreement under various typical setups. Furthermore, our proposal enables the proactive design of experimental parameters to achieve optimal system performance, which is crucial for the design and practical implementation of photonics integrated quantum random number generations.
The speed of a quantum random number generator is essential for practical applications, such as high-speed quantum key distribution systems. Here, we push the speed of a quantum random number generator to 68 Gbps by operating a laser around its threshold level. To achieve the rate, not only high-speed photodetector and high sampling rate are needed but also a very stable interferometer is required. A practical interferometer with active feedback instead of common temperature control is developed to meet the requirement of stability. Phase fluctuations of the laser are measured by the interferometer with a photodetector and then digitalized to raw random numbers with a rate of 80 Gbps. The min-entropy of the raw data is evaluated by modeling the system and is used to quantify the quantum randomness of the raw data. The bias of the raw data caused by other signals, such as classical and detection noises, can be removed by Toeplitz-matrix hashing randomness extraction. The final random numbers can pass through the standard randomness tests. Our demonstration shows that high-speed quantum random number generators are ready for practical usage.