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IEICE Transactions on Electronics

Statistical Evaluation of a Superconductive Physical Random Number Generator

Tatsuro Sugiura, Yuki Yamanashi, Nobuyuki Yoshikawa

Published Jan 1, 2010• 6 citations
Publisher

Abstract

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.

DOI
10.1587/transele.e93.c.453

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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.
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 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.
Generation of random numbers is a central problem for many applications in the field of information processing, including, e.g., cryptography, in classical and quantum regime, but also mathematical modeling, Monte Carlo methods, gambling and many others. Both, the quality of the randomness and efficiency of the random numbers generation process are crucial for the most of these applications. Software produced pseudorandom bit sequences, though sufficiently quick, do not fulfill required randomness quality demands. Hence, the physical hardware methods are intensively developed to generate truly random number sequences for information processing and electronic security application. In the present paper we discuss the idea of the quantum random number generators. We also present a variety of tests utilized to assess the quality of randomness of generated bit sequences. In the experimental part we apply such tests to assess and compare two quantum random number generators, PQ4000KSI (of company ComScire US) and JUR01 (constructed in Wroclaw University of Science and Technology upon the project of The National Center for Research and Development) as well as a pseudorandom generator from the Mathematica Wolfram package. Finally, we present our new prototype of fully operative miniaturized quantum random generator JUR02 producing a random bit sequence with velocity of 1 Mb/s, which successfully passed standard tests of randomness quality (like NIST and Dieharder tests). We also shortly discuss our former concept of an entanglement-based quantum random number generator protocol with unconditionally secure public randomness verification.
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.
True random number generators are essential for many applications including security and statistical simulations. A novel superconductive true random number generator is proposed based on inductor-less bistable Josephson junction circuits. The recently proposed design methodology, based on all-Josephson junctions, promises higher area efficiency and simpler circuit design. In this brief, this methodology is extended to a superconductive circuit design that extracts randomness from thermal noise present in electronic circuits. A high throughput of 16 GHz is achieved using the proposed design, with no bias or correlation in the output sequence. The quality of the generated randomness is assessed using NIST SP 800-22 statistical tests. A 100 Mb binary sequence is demonstrated to pass all 15 statistical tests using recommended parameters as per NIST guidelines. The simulation methodology, described in detail, is based on the MIT-LL SFQ5EE 10 kA/cm2 Nb standard process and open source Verilog-A model.
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.