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Nanosystems Physics Chemistry Mathematics

Unpredictable and uniform random number generation based on time of arrival using InGaAs detectors

Deepika Aggarwal, A. Banerjee, Ankush Kumar Sharma, G. Yadav

Published Nov 5, 2025• 0 citations
Publisher

Abstract

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.

DOI
10.17586/2220-8054-2025-16-5-597-605

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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.
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.
This paper presents the design and theoretical framework for a quantum random number generator (QRNG) rooted in the principles of quantum mechanics. The core innovation lies in leveraging the inherent randomness associated with quantum measurement, specifically the uncertainty principle, to generate truly random numbers, a significant departure from the limitations of classical random number generators. The proposed system utilizes a measurement process involving a quantum system, such as a photon polarization or a quantum bit, to produce a sequence of random bits. The generated bits are then processed to eliminate bias and ensure high uniformity. The theoretical analysis focuses on quantifying the randomness inherent in the measurement process and demonstrating the potential for generating high-quality random numbers. This work addresses the growing demand for secure communication, cryptography, and simulation applications that require truly random numbers, offering a fundamentally different approach compared to traditional methods.
We present a practical high-speed quantum random number generator, where the timing of single-photon detection relative to an external time reference is measured as the raw data. The bias of the raw data can be substantially reduced compared with the previous realizations. The raw random bit rate of our generator can reach 109 Mbps. We develop a model for the generator and evaluate the min-entropy of the raw data. Toeplitz matrix hashing is applied for randomness extraction, after which the final random bits are able to pass the standard randomness tests.
Random numbers are a fundamental resource in science and engineering, and are also widely used in many fields, such as simulation, cryptography, lotteries, fundamental science. There are algorithmically generated numbers that look like random numbers but are not truly random. These pseudo random numbers are generated from a computer, using deterministic algorithms. Because, we cannot use pseudo random generators in situations, where true randomness is necessary, we use true random number generators. In this case, we use unpredictable random events as a random source. Quantum random number generators (QRNG) output true random numbers based on inherent randomness in quantum measurements. Our goal is to generate fast random numbers at a lower cost. At the same time, a high level of randomness is essential. We present the improved novel quantum random number generator, which is based the on time of arrival QRNG. It is rather efficient, as it uses the simple version of the detectors with rather few requirements. The novel QRNG produces more than one random bit per each photon detection.