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IET Quantum Communication

Certification of the efficient random number generation technique based on single‐photon detector arrays and time‐to‐digital converters

Andrea Stanco, Davide G. Marangon, Giuseppe Vallone, Samuel Burri, Edoardo Charbon A, Paolo Villoresi

Published Aug 27, 2021• 2 citations
Publisher

Abstract

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.

DOI
10.1049/qtc2.12018

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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.
SPAD-Based Quantum Random Number Generator With an NthN^{\rm{th}}Nth -Order Rank Algorithm on FPGA
We present a compact, all-solid-state, low-cost quantum random number generator (QRNG) based on a single-photon avalanche diode (SPAD) and a field programmable gate array (FPGA). A new algorithm for random bit generation is described, ranking the inter-arrival times of a group of M photons detected by the SPAD device, and processed directly on the FPGA. The proposed approach improves the efficiency of generated random bits per detected photon, spanning from 0.5 bits/photon in case of 0 order rank, up to 0.875 bits/photon for second order rank. By extending the algorithm to higher orders, the proposed system approaches the maximum theoretical value of 1.0 bit/photon. The rate of generation of random numbers is limited by the SPAD minimum deadtime, achieving an experimentally proven bit rate of 7.3 Mbps. The standard randomness statistical tests are passed for a wide range of photon fluxes and for all the implemented rank orders with no additional post-processing on the generated sequence.
For globally connected devices like smart phones, personal computers and Internet-of-things devices, the ability to generate random numbers is essential for execution of cryptographic protocols responsible for information security. Generally, a random number generator should be small, robust, utilize as few hardware and energy resources as possible, yet provide excellent randomness at a high enough speed (bitrate) for a given purpose. In this work we present a quantum random number generator (QRNG) which makes use of a photoelectric effect in single-photon avalanche diodes (SPADs) as a source of randomness and is scalable to any desired bitrate. We use the random flip-flop method in which random bits are obtained by periodic sampling of a randomly toggling flip-flop. For the first time we investigate this method in detail and find that, out of two main imperfections, bias is due only to hardware imperfections while autocorrelation predominantly resides with the method itself. SPADs are integrated on a silicon chip together with passive quenching and digital pulse-shaping circuitry, using a standard 180 nm CMOS process. A separate FPGA chip derives random numbers from the detection signals. The basic QRNG cell, made of only two SPADs and a few logic circuits, can generate up to 20 Mbit/s that pass NIST statistical tests without any further postprocessing. This technology allows integration of a QRNG on a single silicon chip using readily available industrial processes.
Optical quantum random number generators (QRNGs) are a special class of physical random data sources, whose randomness is established on elementary quantum optics processes. We present a QRNG based on a CMOS chip which overcomes the limitations of the commonly used optical QRNG and which achieves a random bit generation rate up to 200 Mb/s. The CMOS chip is based on an array of single-photon avalanche diodes (SPADs) and digital counters. We prove the absolute randomness of the generated random data through statistical test suites and even more stringent correlation and bias tests applied to 32 Gbit streams. The QRNG passes all tests; hence, it proves to be one of the fastest and more reliable CMOS optical QRNGs currently available.
Quantum random number generators (QRNGs) can generate true random numbers and have significant applications in quantum communication, numerical computation, and model simulation. However, the rate of random number generation based on photon detection is constrained by the maximum count rate of a single-photon detector. Therefore, improving the efficiency of random number generation for individual photon detection events becomes an optional way to increase the rate of random number generation. In this paper, multidimensional photon detection is implemented to enhance single-photon detection events, thereby providing a new, to the best of our knowledge, technical development strategy for high-speed random number generators. The temporal and spatial coherence of coherent-state photons is utilized as a valuable quantum resource, enabling us to achieve the simultaneous extraction of time-space measurement collapsed randomness for single-photon detection events using a chip-scale CMOS-integrated single-photon avalanche diode array. The efficiency of random number generation for single-photon detection events is effectively improved. In our experiments, up to 20 bits can be extracted from an individual photon detection event, and the rate of random number generation reaches up to 2.067 Gbps.
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.
A random number generation approach comprising a silicon nanocrystals LED (Si-NCs LED), silicon single photon avalanche photodiode (Si SPAD) and a field-programmable gate array (FPGA) is introduced. The Si-NCs LED is the source of entropy with photon emission in the visible range detectable by silicon detectors allowing the fabrication of an all-silicon-based device. The proposed quantum random number generator (QRNG) is robust against variations of the internal and external parameters such as aging of the components, changing temperature, the ambient interferences and the silicon detector artifacts. The raw data show high quality of randomness and passed all the statistical tests in National Institute of Standards and Technology (NIST) tests suite without the application of a post-processing algorithm. The efficiency of random number generation is 4-bits per detected photon.