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IEEE Transactions on Applied Superconductivity

Superconductive Random Number Generator Using Thermal Noises in SFQ Circuits

Yuki Yamanashi, Nobuyuki Yoshikawa

Published Jun 1, 2009• 43 citations
Publisher

Abstract

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.

DOI
10.1109/tasc.2009.2019294

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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.
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.
True random number generators, which output truly random numbers by extracting entropy from physical phenomena such as thermal and electronic noises, are widely used in the field of the cryptographic communication systems. We have been developing a superconductive true random number generator that can generate truly random number sequences, impossible to be predicted, by utilizing the high-speed operation and high-sensitivity of superconductive integrated circuits. In this study, we have calculated the dependences of correlation of output random bits on the generation rate. Statistical tests have been performed on the basis of the NIST statistical test suite in order to evaluate the quality of the randomness of sequences generated by the superconductive true random number generator at high generation rate. We have generated a random number sequence consisting of 3.2 M-bit at the generation rate of 30 Gbit/s using the superconductive true random number generator, fabricated by the ISTEC-SRL 2.5 kA/cm2Nb standard process. The generated random number sequences passed 13 kinds of the statistical tests in the NIST statistical test suit, although the 3 tests were not performed because of the shortage of the generated random numbers. The result sufficiently proves that a superconductive true random number generator can generate a high quality of random numbers that can be used for practical cryptographic applications, at a generation rate of up to 30 Gbit/s.
A physical random number generator, which generates truly random number trains by using the randomness of physical phenomena, is widely used in the field of cryptographic applications. We have developed an ultra high-speed superconductive physical random number generator that can generate random numbers at a frequency of more than 10GHz by utilizing the high-speed operation and high-sensitivity of superconductive integrated circuits. In this study, we have statistically evaluated the quality of the random number trains generated by the superconductive physical random number generator. The performances of the statistical tests were based on a test method provided by National Institute of Standards and Technology (NIST). These statistical tests comprised several fundamental tests that were performed to evaluate the random number trains for their utilization in practical cryptographic applications. We have generated 230 random number trains consisting of 20, 000-bits by using the superconductive physical random number generator fabricated by the SRL 2.5kA/cm2 Nb standard process. The generated random number trains passed all the fundamental statistical tests. This result indicates that the superconductive random number generator can be sufficiently utilized in practical applications.
Abstract Superconducting single flux quantum (SFQ) circuits can operate at ultrafast speeds, and their superconducting random number generators (SRNGs) produce high-quality stochastic bit sequences at several tens GHz, with an arbitrary probability of outputting ‘1’, making them ideal for stochastic computing. The conventional superconducting stochastic adder uses a multiplexer (MUX) controlled by a random bit sequence generated by the SRNG. However, the SFQ-based MUX occupies a large circuit area, and any deviation in the probability of the control signal directly degrades the accuracy of stochastic addition. To overcome these limitations, we propose a deterministic stochastic adder comprising only an AND gate, an XOR gate, and a toggle flip-flop. Our design outputs one ‘1’ for every two input ‘1’s, achieving stochastic addition without the random control signal. Compared to the MUX-based stochastic adder, the proposed adder reduces the root-mean-square error by a factor of 32 when adding 1024-bit random sequences, reduces circuit area by 49.0%, and Josephson junction count by 28.1%, while supporting operating frequencies of about 120 GHz in simulation. We fabricated the proposed adder with two SRNGs for generating input sequences using a 10 kA cm −2 Nb four-layer superconducting process. High-speed operation was verified up to approximately 35.4 GHz with a constant bias margin by measuring the average voltage at the input and outputs. To the best of our knowledge, this is the first demonstration of ultrafast stochastic arithmetic operations above 30 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.
Abstract Stochastic computing (SC) is a form of probabilistic computation that encodes information in the probability of a ‘1’ occurring within a finite-length binary sequence. SC has been investigated for applications in various fields that do not require deterministic and precise computation. A superconducting single-flux-quantum (SFQ) circuit is considered a promising candidate for implementing SC hardware due to its high-speed operation and probabilistic behavior. In this study, we propose a novel large fan-out signal splitter to enable large-scale SFQ-based stochastic arithmetic circuits, addressing the issue of computation accuracy degradation caused by correlations between binary sequences. The proposed signal splitter generates uncorrelated output binary sequences by utilizing superconductor random number generators frequency-synchronized to the input binary sequence. The fan-out can be easily increased by simply adding more superconductor random number generators. We implemented a four-output stochastic number signal splitter using the 10 kA cm−2 Nb four-layer superconducting circuit fabrication process. Its operation was successfully demonstrated by measuring the average voltage at the input and outputs under continuous high-speed binary sequence input. High-speed operation up to 33.2 GHz was confirmed. The proposed signal splitter uniquely leverages the properties of superconducting circuits, where flux quanta determined by fundamental physical constants serve as the information carrier. We believe this development will significantly advance the realization of practical SFQ-based SC systems.