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Enhancing entropy in quantum random number generator

Xiaomin Guo, Ripeng Liu, Pu Li, Cheng Chen, Ming-Chuan Wu, Yanqiang Guo

Published May 26, 2018• 0 citations
OpenAlex

Abstract

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.

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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.
Information-theoretically provable unique true random numbers, which cannot be correlated or controlled by an attacker, can be generated based on quantum measurement of vacuum state and universal-hashing randomness extraction. Quantum entropy in the measurements decides the quality and security of the random number generator (RNG). At the same time, it directly determines the extraction ratio of true randomness from the raw data, in other words, it obviously affects quantum random bits generating rate. In this work, we commit to enhancing quantum entropy content in the vacuum noise based quantum RNG. We have taken into account main factors in this proposal to establish the theoretical model of quantum entropy content, including the effects of classical noise, the optimum dynamical analog-digital convertor (ADC) range, the local gain and the electronic gain of the homodyne system. We demonstrate that by amplifying the vacuum quantum noise, abundant quantum entropy is extractable in the step of post-processing even classical noise excursion, which may be deliberately induced by an eavesdropper, is large. Based on the discussion and the fact that the bandwidth of quantum vacuum noise is infinite, we propose large dynamical range and moderate TIA gain to pursue higher local oscillator (LO) amplification of vacuum quadrature and broader detection bandwidth in homodyne system. High true randomness extraction ratio together with high sampling rate is attainable. Experimentally, an extraction ratio of true randomness of 85.3% is achieved by finite enhancement of the laser power of the LO when classical noise excursions of the raw data is obvious.
A quantum random number generator (QRNG) provides a reliable means for the generation of true random numbers. The inherent randomness of the vacuum fluctuations makes the quantum vacuum state a superior source of entropy. However, in practice, the raw sequences of QRNG are inevitably contaminated by classical technical noise, which compromises the security of the QRNG. Min-entropy conditioned on the classical noise is a useful method that can quantify the side-information independent randomness. To improve the extractable randomness from the raw sequences arising from the quantum vacuum-based QRNG, we propose and experimentally demonstrate two approaches, discarding-boundary-bin measurement and multi-interval sampling. The first one increases the conditional min-entropy at a low quantum-to-classical-noise ratio. The latter exploits parallel sampling using multiple analog-to-digital converters (ADCs) and effectively overcomes the finite resolution limit and uniform sampling of a single ADC. The maximum average conditional min-entropy can reach 9.2 per sample when combining these two approaches together in contrast to 6.93 with a single 8-bit ADC.
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) harness the intrinsic randomness in measurement processes: the measurement outputs are truly random, given the input state is a superposition of the eigenstates of the measurement operators. In the case of trusted devices, true randomness could be generated from a mixed state ρ so long as the system entangled with ρ is well protected. We propose a random number generation scheme based on measuring the quadrature fluctuations of a single mode thermal state using an optical homodyne detector. By mixing the output of a broadband amplified spontaneous emission (ASE) source with a single mode local oscillator (LO) at a beam splitter and performing differential photo-detection, we can selectively detect the quadrature fluctuation of a single mode output of the ASE source, thanks to the filtering function of the LO. Experimentally, a quadrature variance about three orders of magnitude larger than the vacuum noise has been observed, suggesting this scheme can tolerate much higher detector noise in comparison with QRNGs based on measuring the vacuum noise. The high quality of this entropy source is evidenced by the small correlation coefficients of the acquired data. A Toeplitz-hashing extractor is applied to generate unbiased random bits from the Gaussian distributed raw data, achieving an efficiency of 5.12 bits per sample. The output of the Toeplitz extractor successfully passes all the NIST statistical tests for random numbers.
Quantum random number generators (QRNGs) are currently in high demand across a large number of cryptographic applications as secure sources of true randomness. In this work, we characterize the conditions from which randomness can be extracted in a QRNG based on homodyne measurements of vacuum fluctuations by assessing the impact of experimental limitations, such as the digitizer resolution or the presence of excess local oscillator (LO) noise due to an unbalanced detection. Moreover, we propose an estimation method to quantify the excess entropy contribution introduced by an unbalanced detection and analyze the implementation of the post-processing algorithm. Finally, we submitted the generated numbers to a set of statistical tests to assess the quality of its output randomness and verified that it passes the standard libraries.
Abstract We present a quantum random number generator (QRNG) based on vacuum fluctuations that meets the statistical and structural entropy source validation criteria defined in NIST standards. We measured how optical imbalance in a balanced homodyne detector affects the dominance of vacuum fluctuations over the quadrature-phase noise of the local oscillator. Based on this analysis, we developed a simple and direct method to quantify the relative strength of vacuum noise, enabling precise balancing of the detector to maximize the vacuum fluctuation contribution. Our approach ensures that the raw entropy exhibits negligible auto-correlation and that the output samples are independent and identically distributed (i.i.d.), without relying on external post-processing beyond standard NIST-approved conditioning. Following a symbol-space reduction strategy guided by NIST SP 800-90B, we extract high-quality 8-bit entropy samples from 16-bit raw data. To produce full-entropy outputs, the samples are processed using the 384-bit version of the Secure Hash algorithm 3 (SHA3-384). The resulting quantum random numbers successfully pass all tests in the NIST statistical test suite (NIST SP 800-22) and achieve a generation rate of approximately 4 Gbps. This work demonstrates a practical and fully standards-aligned QRNG implementation using only vacuum fluctuations and vetted conditioning.