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IEEE International Symposium on Applied Computational Intelligence and Informatics (SACI)

Efficiency improvement of photon arrival time based quantum random number generator with hashing

Balázs Solymos, László Bacsárdi

Published May 23, 2023• 1 citation
Publisher

Abstract

Quantum random number generators can deliver entropy based on inherently non-deterministic physical phenomena, which is essential for applications where quality randomness is needed (e.g. in cryptography). Our generator based on photon time-of-arrival exploits the randomness of light emission in semiconductors. To measure the time between detections we use a continuous (non-restartable) clock for time tagging, which permits simpler hardware but produces slightly different output from the optimal exponential distribution. To handle this and produce quality output, we use Toeplitz hashing based bit generation after modeling and calculating a lower bound of extractable min-entropy for the general case of this generation scheme with a continuous clock. We produced uniformly distributed output bits with our setup, while also reaching a generation efficiency of 9.75 output bits per 16-bit input record, which is an improvement to our previously used method. Our generator has also been statistically tested using four of the popular statistical test suites.

DOI
10.1109/saci58269.2023.10158613

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Quantum random number generators can deliver entropy based on inherently non-deterministic physical phenomena, which is essential for applications where quality randomness is needed (e.g. in cryptography). Our generator based on photon time-of-arrival exploits the randomness of light emission in semiconductors. To measure the time between detections we use a continuous (non-restartable) clock for time tagging, which permits simpler hardware but produces slightly different output from the optimal exponential distribution. To handle this and produce quality output, we use Toeplitz hashing based bit generation after modeling and calculating a lower bound of extractable min-entropy for the general case of this generation scheme with a continuous clock. We produced uniformly distributed output bits with our setup, while also reaching a generation efficiency of 9.75 output bits per 16-bit input record, which is an improvement to our previously used method. Our generator has also been statistically tested using four of the popular statistical test suites.
Utilizing the inherently unpredictable nature of quantum mechanics, quantum random number generators (QRNGs) can provide randomness for applications where quality entropy (like in the case of cryptography) is essential. We present a post-processing scheme utilizing min-entropy estimation and hashing for optical QRNGs based on measuring individual photon arrival times. Our method allows for the handling of possible errors due to non-ideal components or even a potential attacker, given some basic assumptions to reliably produce a safe, good quality, uniformly distributed bitstream as output. We validate our results with an intentionally non-ideal measurement setup to show robustness, while also statistically testing our final output with four popular statistical test suites.
We demonstrate a novel high speed and multi-bit optical quantum random number generator by continuously measuring arrival time of photons with a common starting point. To obtain the unbiased and post-processing free random bits, the measured photon arrival time is converted into the sum of integral multiple of a fixed period and a phase time. Theoretical and experimental results show that the phase time is an independent and uniform random variable. A random bit extraction method by encoding the phase time is proposed. An experimental setup has been built and the unbiased random bit generation rate could reach 128 Mb/s, with random bit generation efficiency of 8 bits per detected photon. The random numbers passed all tests in the statistical test suite.
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.
Quantum random number generators offer various ways of generating entropy based on inherently nondeterministic physical processes, thus guaranteeing the quality and security of their output. While the expected output of random number generators is a uniformly distributed stream of bits, actual physical measurement statistics typically follow some other distribution, mandating additional post-processing steps. We present a post-processing scheme inspired by the continuous probability integral transform that can be used with the typically discrete distributions of physical measurement statistics to produce a close to uniformly distributed output bitstream. We give bounds on the maximum bias of the output and also show a way to produce output that is arbitrarily close statistically to the expected uniform distribution in an ideal scenario. While the scheme can be used with any input distribution, we utilized a photonic time-of-arrival based architecture to give a practical example of usage and acquire experimental results, which we statistically tested with the NIST Statistical Test Suite.
The bit generation algorithm of a quantum random number generator based on photon arrival time differences is improved in terms of the bit generation efficiency and bit generation rate. The method is analyzed mathematically, proving that, in theory, the improved generator still produces random numbers of high quality without the need of resorting to postprocessing algorithms. The effects of nonidealities are quantitatively analyzed to provide bounds for the maximum tolerable deviations from uniformity. Experimental investigations are conducted on a prototype, showing that the method is capable of increasing the rate of bit generation by more than 47% on the same physical architecture.