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National Conference on Communications

Quantum Random Number Generator with One and Two Entropy Sources

Gautam Kumar Shaw, S.R. Sivaram, Anil Prabhakar

Published Feb 1, 2019• 8 citations
Publisher

Abstract

Quantum random number generators (QRNGs) are an integral part of quantum key distribution (QKD) systems. To better understand the inherent physical processes, we compare the random numbers generated by two separate schemes, one is based on entropy (arrival time of photons) and another with an additional source of entropy (space) i.e, path superposition of arrival time of photons from a weak coherent source on a gated InGaAs single photon detector. Both experiments yield bits that appear random. However, they satisfy different criteria of randomness. The weak coherent source has a Poissonian distribution and extracting the variation about the arrival time of photons on gated SPD yields a source of random numbers that pass most of the Dieharder Tests. With the inclusion of superposition, we obtain random numbers that pass all the Dieharder tests. The physical origins of the random numbers in the two experiments is different, one is single entropy source based and other one is two entropy source based, and this is reflected in the outcomes of the different tests for randomness.

DOI
10.1109/ncc.2019.8732222

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Quantum random number generators (QRNGs) are an integral part of quantum key distribution (QKD) systems. To better understand the inherent physical processes, we compare the random numbers generated by two separate schemes, one is based on entropy (arrival time of photons) and another with an additional source of entropy (space) i.e, path superposition of arrival time of photons from a weak coherent source on a gated InGaAs single photon detector. Both experiments yield bits that appear random. However, they satisfy different criteria of randomness. The weak coherent source has a Poissonian distribution and extracting the variation about the arrival time of photons on gated SPD yields a source of random numbers that pass most of the Dieharder Tests. With the inclusion of superposition, we obtain random numbers that pass all the Dieharder tests. The physical origins of the random numbers in the two experiments is different, one is single entropy source based and other one is two entropy source based, and this is reflected in the outcomes of the different tests for randomness.
Abstract This work presents two significant contributions from the perspectives of quantum random number generator (QRNG) manufacturers and users. For manufacturers, the conventional method of assessing the quantumness of single-photon-based QRNGs through mean and variance comparisons of photon counts is statistically unreliable due to finite sample sizes. Given the sub-Poissonian statistics of single photons, confirming the underlying distribution is crucial for validating a QRNG’s quantumness. We propose a more efficient two-fold statistical approach to ensure the quantumness of optical sources with the desired confidence level. Additionally, we demonstrate that the output of QRNGs from exponential and uniform distributions exhibits similarity under device noise, deriving corresponding photon statistics and conditions for ε-randomness. From the user’s perspective, the fundamental parameters of a QRNG are quantumness, efficiency (entropy and random number generation rate), and cost. Our analysis reveals that these parameters depend on three factors, namely, expected photon count per unit time, external reference cycle duration, and detection efficiency. A lower expected photon count enhances entropy but increases cost and decreases the generation rate. A shorter external reference cycle boosts entropy but must exceed a minimum threshold to minimize timing errors, with minor impacts on cost and rate. Lower detection efficiency enhances entropy and lowers cost but reduces the generation rate. Finally, to validate our results, we perform statistical tests like NIST, Dieharder, AIS-31, ENT etc over the data simulated with different values of the above parameters. Our findings can empower manufacturers to customize QRNGs to meet user needs effectively.
Quantum random number generators are becoming mandatory in a demanding technological world of high-performing learning algorithms and security guidelines. Our implementation, based on the principles of quantum mechanics, enables us to achieve the required randomness. We have generated high-quality quantum random numbers from a weak coherent source at the telecommunication wavelength. The entropy is based on the time of arrival of quantum states within a predefined time interval. The detection of photons by the InGaAs single-photon detectors and high-precision time measurement of 5 ps enables us to generate 16 random bits per arrival time, which is the highest reported to date. We have presented the theoretical analysis and experimental verification of the random number generation methodology. The method eliminates the requirement of any randomness extractor, thereby leveraging the principles of quantum physics to generate random numbers. The output data rate averages 2.4 Mbps. The generated raw quantum random numbers are compared with the NIST-prescribed Blum-Blum-Shub pseudo-random number generator and an in-house-built hardware random number generator from FPGA, on the ENT and NIST platform.
Quantum random number generators are becoming mandatory in a demanding technology world of high performing learning algorithms and security guidelines. Our implementation based on principles of quantum mechanics enable us to achieve the required randomness. We have generated high-quality quantum random numbers from a weak coherent source at telecommunication wavelength. The entropy is based on time of arrival of quantum states within a predefined time interval. The detection of photons by the InGaAs single-photon detectors and high precision time measurement of 5 ps enables us to generate 16 random bits per arrival time which is the highest reported to date. We have presented the theoretical analysis and experimental verification of the random number generation methodology. The method eliminates the requirement of any randomness extractor to be applied thereby, leveraging the principles of quantum physics to generate random numbers. The output data rate is on an average of 2.4 Mbps. The raw quantum random numbers are compared with NIST prescribed Blum-Blum-Shub pseudo random number generator and an in-house built hardware random number generator from FPGA, on the ENT and NIST Platform.
We report a demonstration of a high-entropy optical quantum random number generator (QRNG) based on photon arrival time. We have implemented the scheme with high-speed and high-precision electronics with a time resolution of 1 ps generating 115 Mbps raw data. The random bit generation efficiency is 8 bits per detection. The experimental data is quite consistent with theoretical estimation showing minimum bias. We apply a real-time information-theoretic randomness extractor to generate a final data rate of 109 Mbps. The randomness is rigorously evaluated against well-known statistical test suites of NIST, ENT, Diehard, TU-01 and Dieharder.
Abstract The speed of quantum random number generators (QRNGs) is a major concern for practical applications. In this work, we introduce scattering as a method to enhance the randomness characteristics of the entropy source. This method allows optical bit extraction with a faster sampling rate without compromising the randomness quality compared to the coherent source based balanced homodyne detection. Scattering is a probabilistic phenomenon which increases the chaotic behaviour of coherent sources. It broadens the distribution of photon statistics and makes it super-Poissonian. We show that a signal with super-Poissonian distribution has better randomness compared to a Poissonian one, indicated by their autocorrelation characteristics and the randomness test results. The use of scattering mechanisms as an entropy source eases the miniaturization of QRNGs, it also makes them compatible and adaptable to existing technologies.
Quantum random number generators (QRNGs) leverage the inherent unpredictability of quantum mechanical phenomena to produce random numbers. However, the performance of many QRNGs is hindered by limitations such as low generation rates and the bulkiness of systems utilizing single-photon detectors (SPDs). In this study, we present a QRNG that addresses these challenges by using a micro-LED as an entropy source, utilizing the intensity fluctuations of spontaneous emissions. By applying post-processing techniques, our 5 × 5 µm 2 micro-LED-based system achieves a PD bandwidth-limited generation rate of 9.375 Gbit/s while successfully passing the required randomness tests outlined by the National Institute of Standards and Technology (NIST). Importantly, systematic testing across micro-LEDs of varying sizes demonstrates consistently high performance, highlighting the robustness of this approach. The compact, small footprint, scalable design, and surface emission characteristics of micro-LEDs pave the way for the development of parallel QRNG-integrated chips, which hold the potential to deliver ultra-high random number generation rates in practical, miniaturized platforms.