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IEEE Transactions on Circuits & Systems II Express Briefs

True Random Number Generation Using Dark Noise Modulation of a Single-Photon Avalanche Diode

Md Sajal, Marc P. Dandin

Published Dec 28, 2023• 11 citations
Publisher

Abstract

This brief presents the application of perimeter-gated single-photon avalanche diodes (pg-SPADs) as true random number generators (TRNGs). Typical SPADs have been used as random number generators (RNGs) in photon-based or dark event-based configurations, and they utilize complex debiasing algorithms to increase their random bit efficiency (RBE). In contrast, we propose leveraging the dark count rate modulation property of pg-SPADs to enable true random number generation using simpler debiasing algorithms. Further, we demonstrate that perimeter gating may be used to maintain a constant dark count rate across a wide temperature range, conferring stability to the RNG in that range. A set of debiased random bits from a tested prototype chip was benchmarked against the National Institute of Standards and Technology (NIST) Statistical Test Suite (STS) with a success rate of 99.375%.

DOI
10.1109/tcsii.2023.3347735

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IEEE Transactions on Circuits and Systems I Regular Papers•Apr 16, 2026•0 citations
This brief presents the application of perimeter-gated single-photon avalanche diodes (pg-SPADs) as true random number generators (TRNGs). Typical SPADs have been used as random number generators (RNGs) in photon-based or dark event-based configurations, and they utilize complex debiasing algorithms to increase their random bit efficiency (RBE). In contrast, we propose leveraging the dark count rate modulation property of pg-SPADs to enable true random number generation using simpler debiasing algorithms. Further, we demonstrate that perimeter gating may be used to maintain a constant dark count rate across a wide temperature range, conferring stability to the RNG in that range. A set of debiased random bits from a tested prototype chip was benchmarked against the National Institute of Standards and Technology (NIST) Statistical Test Suite (STS) with a success rate of 99.375%.
The objective of this study is to generate random numbers using Single Photon Avalanche Diode (SPAD) native noise, specifically the Dark Count Rate (DCR). This is achieved by counting events over a fixed acquisition time window and creating a sequence of random bits using the least significant bits of the counter. A simple model was developed to evaluate the concept, which was then implemented on noisy SPADs integrated in CMOS Fully Depleted Silicon-On-Insulator (FD-SOI) technology, resulting in a compact 3D cell. The study tested the randomness quality of the measured bit sequences under various operating conditions, including voltage and temperature. The results indicate that the measured bit sequences pass successfully the NIST randomness quality tests under specific operating conditions. It is recommended to use the least significant bit and work with a sufficiently high excess voltage.
Random number generators that utilize arrays of entropy source elements suffer from bias variation (BV). Despite the availability of efficient debiasing algorithms, optimized implementations of hardware friendly options depend on the bit bias in the raw bit streams and cannot accommodate a wide BV. In this work, we present a64×6464 \times 6464×64array of perimeter gated single photon avalanche diodes (pgSPADs), fabricated in a0.35μ m0.35 \mu ~\mathrm{m}0.35μ mstandard CMOS technology, as a source of entropy to generate random binary strings with a BV compensation technique. By applying proper gate voltages based on the devices' native dark count rates, we demonstrate less than 1 % BV for a raw-bit generation rate of2kHz/2 \text{kHz} /2kHz/pixel at room temperature. The raw bits were debiased using the classical iterative Von Neumann's algorithm and the debiased bits were found to pass all of the 16 tests from NIST's Statistical Test Suite.
A robust true random number generator (TRNG), able to assure high quality output at different working conditions, is an attractive solution in secure communication application, because it increases resilience against possible external attacks. Among different TRNGs, quantum RNGs (QRNG) represent a good candidate for such systems, because of their compactness, low cost and performance [1–6]. They typically consist of a source of photons, such as an attenuated LED, coupled to a detector with single photon capability (SPAD). Many works in the literature have used a single detector [1–4] for random bit extraction. These devices are characterized by a limited bit rate [1], which can be increased by exploiting the arrival time of photons at the cost of circuit and system complexity [2–4]. Recent works [5–6] proposed to implement an array of detectors based on SPAD working in parallel thus extending the speed of QRNG up to 5 Gb/s [5]. Despite the high bit rate, the main drawback of [5] is the strong dependence of each pixel bias on the impinging light intensity which forces the system to work only for a narrow range of photon flux that poses several constraints on the design of the final QRNG system, e.g. the need of a feedback control loop to maintain a constant flux of photons, and of a uniform distribution of light over the entire sensor. Moreover, it is impractical to implement algorithms for bit extraction to all detectors of the array because of different responses and mismatches among SPADs.
Abstract True random number generators (TRNGs) allow the generation of true random bit sequences, guaranteeing the unpredictability and perfect balancing of the generated values. TRNGs can be realised from the sampling of quantum phenomena, for instance, the detection of single photons. Here, a recently proposed technique, which implements a quantum random number generator (QRNG) out of a device that was realised for a different scope, is further analysed and certified [1]. The combination of a CMOS single‐photon avalanche diode (SPAD) array, a high‐resolution time‐to‐digital converter (TDC) implemented on a field programmable gate array (FPGA), the exploitation of a single‐photon temporal degree of freedom, and an unbiased procedure provided by H. Zhou and J. Bruck [2, 3] allows the generation of true random bits with a high bitrate in a compact and easy‐to‐calibrate device. Indeed, the use of the ‘Zhou–Bruck’ method allows the removal of any correlation from the binary representation of decimal data. This perfectly fits with the usage of a device with non‐idealities like SPAD's afterpulses, pixel cross‐correlation, and time‐to‐digital converter non‐uniform conversion. In this work, an in‐depth analysis and certification of the technique presented in [1] is provided by processing the data with the NIST suite tests in order to prove the effectiveness and validity of this approach.
Experimental demonstration of a quantum random number generator based on one single-photon avalanche diode (SPAD) detector, a T / ( T − t ) pulse-shaped laser, and an field-programmable gate array (FPGA) acquisition module is presented. An integrated laser driver drives an external laser diode at 670 nm wavelength, whereas the SPAD with a photon detection probability of 18.5% is integrated together with an active quenching-resetting circuit. The SPAD detector generates counts for the interarrival time (IAT) measurement system implemented in an FPGA, where the change of the IATs between consecutive pulses is used to derive a random bit stream. It is shown how the application of a pulse-shaped laser driver can increase the performance of the system as compared to the continuous-wave operation of the laser diode to achieve the maximum generation rate of 5 Mbps while using a single SPAD. The generated numbers pass all randomness tests of the National Institute of Standards and Technology (NIST), Dieharder, and ENT test (pseudorandom number sequence test) suits.
A compact quantum random number generator (QRNG) based on an array of Single Photon Avalanche Diodes (SPADs) is presented here. The main feature of the proposed chip is the capability to generate random numbers without the use of any external source of light. In this view, SPADs are configured to be used in two ways: 1) as a controlled light emitter and 2) as a detector. An embedded logic is able to distinguish dark events against detected emitted photon in such a way to make the system sensitive only to the presence of light. The extracted random bits show a uniform distribution and the QRNG, thanks to an integrated conditioning block maximizing the output entropy, eventually passes all AIS31 tests. The average raw bit rate in the default device configuration (one enabled column) is measured equal to 800 kbps.