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Photonics & Electromagnetics Research Symposium (PIERS)

Random Number Generation Utilizing Timing Jitters of Single-Flux-Quantum Propagation

Yoshinao Mizugaki, Kenta Sato, Hiroshi Shimada, Takeshi Onomi

Published Jul 3, 2023• 0 citations
Publisher

Abstract

We present superconducting hardware random number generators comprising single-flux-quantum (SFQ) digital circuits. We refer to them as SFQ oscillator-based hardware random number generators, or SO-HRNGs in short. The source of randomness in SO-HRNGs is timing jitters induced by thermal noises in integrated circuits. Test circuits were fabricated using a 10 kA/cm2Nb/AlOx/Nb integration process, and measured in a liquid helium bath. The NIST FIPS 140-2 test suite was used for evaluation of the randomness of generated random numbers. For a single-output SO-HRNG, pass rates of 100% were confirmed. For a triple-output SO- HRNG, on the other hand, pass rates for two outputs reached 100%, whereas those for the rest were not as high as 100%, 76% at the highest.

DOI
10.1109/piers59004.2023.10221525

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We present superconducting hardware random number generators comprising single-flux-quantum (SFQ) digital circuits. We refer to them as SFQ oscillator-based hardware random number generators, or SO-HRNGs in short. The source of randomness in SO-HRNGs is timing jitters induced by thermal noises in integrated circuits. Test circuits were fabricated using a 10 kA/cm2Nb/AlOx/Nb integration process, and measured in a liquid helium bath. The NIST FIPS 140-2 test suite was used for evaluation of the randomness of generated random numbers. For a single-output SO-HRNG, pass rates of 100% were confirmed. For a triple-output SO- HRNG, on the other hand, pass rates for two outputs reached 100%, whereas those for the rest were not as high as 100%, 76% at the highest.
We experimentally evaluated random number sequences generated by a superconducting hardware random number generator composed of a Josephson-junction oscillator, a rapid-single-flux-quantum (RSFQ) toggle flip-flop (TFF), and an RSFQ AND gate. Test circuits were fabricated using a 10 kA/cm2 Nb/AlOx/Nb integration process. Measurements were conducted in a liquid helium bath. The random numbers were generated for a trigger frequency of 500 kHz under the oscillating Josephson-junction at 29 GHz. 26 random number sequences of 20 kb length were evaluated for bias voltages between 2.0 and 2.7 mV. The NIST FIPS PUBS 140-2 tests were used for the evaluation. 100% pass rates were confirmed at the bias voltages of 2.5 and 2.6 mV. We found that the Monobit test limited the pass rates. As numerical simulations suggested, a detailed evaluation for the probability of obtaining “1” demonstrated the monotonical dependence on the bias voltage.
Abstract A Hardware Random Number Generator (HRNG), which generates true random number sequences, is studied. In superconducting Single Flux Quantum (SFQ) circuitry, HRNGs that utilized timing jitters in trigger signals have been demonstrated. In this paper, we propose an HRNG with two oscillators to enhance stability against variation of oscillator frequencies. We investigate the characteristics of random numbers generated with the proposed HRNG not only by numerical simulation but also by experiments using Nb test circuits. In the numerical simulation, the probability of “1” in random number sequences has a local minimum of “1” output probability at conditions where fclk (the clock oscillator frequency) and fgate (the gate oscillator frequency) are approximately equal (fclk ≈ fgate ) for fclk ≤ 60 GHz. It is also found that pass rates for the FIPS140-2 random number tests are little affected by variations of fclk at fgate = 69.2 GHz. The random number generation rate for fclk = 60 GHz and fgate = 43 GHz reaches 3.98 GHz. In experimental measurements, random numbers of 1 Mbits generated by a test circuit pass the SP800-22 random number tests at fclk = 48.79 GHz and fgate = 19.81 GHz.
We describe the operation of a rapid-single-flux-quantum (RSFQ) hardware random number generator comprising two Josephson oscillators, an XOR gate, and a non-destructive read-out (NDRO) cell. Single-flux-quantum (SFQ) pulse trains fed to the input terminals of the XOR gate contain timing jitters due to thermal noises. Then, the output of the XOR gate becomes random, which is stored in the NDRO cell and fetched by the trigger signal. We experimentally evaluated the output randomness of a test circuit fabricated using a 10 kA/cm2 Nb/AlOx/Nb integration process. For evaluation, the NIST FIPS 140-2 test suite was used. 24 random number sequences of 20 kb length were acquired with the trigger signal of 1 MHz, and evaluated for each operation condition. Relationships between the output randomness and operation conditions were obtained. In addition, numerical simulation demonstrated true random number generation at 20 GHz.
A hardware random number generator using Josephson oscillation and a few single flux quantum (SFQ) logic gates is presented. The logic circuit of the random number generator consists of one toggle flip flop and one and gate. A prototype random number generator is designed by logic cells based on a 2.5-kA/cm2Nb/AlOx/Nb integration process. The fundamental operation at a few hundred megahertz of the random number sampling frequency is confirmed by numerical simulation when a DC/SFQ converter is used for generating trigger signals. An additional delay line using an overdamped Josephson transmission line is used for increasing the timing jitter to get random numbers. The delay line makes it possible for the random number generator to operate over 1 GHz. To confirm the fundamental operation of the circuit, a primitive SFQ random number generator is fabricated using the AIST standard process with 2.5-kA/cm2Nb/AlOx/Nb junctions and the standard logic cell library. A random number generation based on a low-speed functional test is successfully confirmed.
A novel high-speed physical random number generator using the superconductive single-flux-quantum (SFQ) circuits and thermal noises in the circuit has been proposed. The proposed physical random number generator is similar to an SFQ balanced comparator. Thermal noises in shunt resisters are used to obtain random outputs. Because of the high-sensitivity of SFQ circuits, the true random numbers can be generated without amplification of the noises at high clock frequency. Generation of the true random numbers at the frequency of several tens GHz can be realized by using the proposed circuit. Moreover, the circuit scale of the proposed circuit is very small and the generation frequency of the random number generator can be easily enhanced by parallelizing the circuits. We have designed and tested the superconductive physical random number generator using the 2.5 kA/cm2Nb standard process and evaluated the quality of the generated random number train. We have examined a 220-bit random number train generated at a low frequency and no periodicity is observed. We believe that the superconductive physical random number generator can be applied to cryptographic applications for more secure information processing.
Maximum-length sequences (M-sequences) are known as pseudo-random numbers generated with relatively simple digital circuits. In this paper, we present a single-flux-quantum digital circuit that generated three output bits of a 4-bit M-sequence in one clock operation. The circuit comprised three clocked exclusive-or gates, one delay flip-flop, three dc/SFQ converters (for set, reset, and low-frequency clock signals), and three SFQ/dc converters (for three parallel outputs), all of which were integrated on a superconducting Nb chip. A 10-GHz clock generator was also implemented for high-speed testing. The total number of Nb/AlOx/Nb Josephson junctions was 568. Verilog simulation demonstrated correct circuit operation with a 20-GHz clock, which corresponded to the generation rate of 60 Gb/s. The measurement was carried out in a liquid helium bath. Low-speed testing with a 1-kHz clock demonstrated periodic signals of three parallelized 4-bit M-sequence. We also confirmed that the outputs were correctly shifted when 13 clock signals of 10 GHz were fed between two 1-kHz clock signals.