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Journal of Applied Physics

White-noise quality evaluation in chaotic oscillation of Josephson junction for random-number generation

Dai Oikawa, Hirokazu Komatsu, K. Tsuzuki, Hiroya Andoh

Published Oct 14, 2025• 0 citations
Publisher

Abstract

Recently, a high-quality random-number generator has been highly expected. In obtaining high-quality random-numbers, the use of random physical phenomena is necessary. Among random-number generation methods, we focused on the chaos in a Josephson junction (JJ) under irradiation with a radio frequency (RF). In this study, the chaos in the intrinsic JJ for random-number generation was numerically investigated using the equivalent circuit of the RF-irradiated JJ. In particular, it is important for the random-number generation to obtain a high-quality white-noise output signal. We proposed that the quality of the white noise is quantitatively evaluated using the half-width of the autocorrelation peak. Furthermore, random-numbers were generated from the chaos in the RF-irradiated JJ at high-speed operation than the previous study. The high-quality random-numbers were successfully generated from this chaos, and their quality was verified through statistical verification.

DOI
10.1063/5.0283866

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Recently, a high-quality random-number generator has been highly expected. In obtaining high-quality random-numbers, the use of random physical phenomena is necessary. Among random-number generation methods, we focused on the chaos in a Josephson junction (JJ) under irradiation with a radio frequency (RF). In this study, the chaos in the intrinsic JJ for random-number generation was numerically investigated using the equivalent circuit of the RF-irradiated JJ. In particular, it is important for the random-number generation to obtain a high-quality white-noise output signal. We proposed that the quality of the white noise is quantitatively evaluated using the half-width of the autocorrelation peak. Furthermore, random-numbers were generated from the chaos in the RF-irradiated JJ at high-speed operation than the previous study. The high-quality random-numbers were successfully generated from this chaos, and their quality was verified through statistical verification.
The configuration of a robust, high-security system has become increasingly important because, as computer processing speeds continue to improve, the vulnerabilities of cryptographic systems that rely on conventional pseudo-random-numbers have raised concerns regarding potential leaks of confidential information. To establish such a secure system, high-quality and high-speed random numbers are essential. Here, high-quality random-numbers are defined as statistically unbiased, non-reproducible, and unpredictable values. One approach to generating such numbers is to exploit physical random phenomena, such as chaos. In particular, chaos in Josephson junctions (JJs) under radio-frequency (RF) irradiation has been identified as a suitable mechanism for random-number generation. In this study, we considered RF-biased intrinsic Josephson junctions (IJJs) in a mesa-type Bi2_{2}2​Sr2_{2}2​CaCu2_{2}2​O8+δ_{8+\delta }8+δ​single crystal. Since the interactions among stacked IJJs must be considered, it is insufficient to evaluate their properties using the conventional resistively and capacitively shunted junction (RCSJ) circuit model. Instead, we numerically investigated the chaotic voltage of an IJJ stack irradiated with higher frequencies than those typically used in conventional RF systems, employing the capacitively coupled JJ model with diffusion current, which incorporates interlayer interactions. Based on the time-series output voltage of the IJJ, we then generated random-numbers and evaluated their quality using statistical tests.
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.
Random numbers have great application value in the fields of secure communications, which are commonly used as secret keys to encrypt the information. To guarantee that the information is absolutely secure in the current high-speed communication, the applied random keys should possess a generation speed not less than the encrypted data rate, according to one-time pad theory found by Shannon (Shannon C E 1949 Bell.Syst.Tech.J. 28 656) Pseudo-random numbers generated by algorithm may easily reach a fast speed, but a certain periodicity makes them difficult to meet the aforementioned demand of information security. Utilizing physical stochastic phenomena can provide reliable random numbers, called physical random number generators (RNGs). However, limited by the bandwidth of the conventional physical sources such as electronic noise, frequency jitter of oscillator and quantum randomness, the traditional physical RNG has a generation speed at a level of Mb/s typically. Therefore, real-time and ultrafast physical random number generation is urgently required from the view of absolute security for high-speed communication today. With the advent of wideband photonic entropy sources, in recent years lots of schemes for high-speed random number generation are proposed. Among them, chaotic laser has received great attention due to its ultra-wide bandwidth and large random fluctuation of intensity. The real-time speed of physical RNG based on chaotic laser is now limited under 5 Gb/s, although the reported RNG claims that an ultrafast speed of Tb/s is possible in theory. The main issues that restrict the real-time speed of RNG based on chaotic laser are from two aspects. The first aspect is electrical jitter bottleneck confronted by the electrical analog-to-digital converter (ADC). Specifically, most of the methods of extracting random numbers are first to convert the chaotic laser into an electrical signal by a photo-detector, then use an electrical ADC driven by radio frequency (RF) clock to sample and quantify the chaotic signal in electronic domain. Unfortunately, the response rate of ADC is below Gb/s restricted by the aperture jitter (several picoseconds) of RF clock in the sample and hold circuit. The second aspect comes from the complex post-processes, which are fundamental in current RNG techniques to realize a good randomness. The strict synchronization among post-processing components (e.g., XOR gates, memory buffers, high-order difference) is controlled by an RF clock. Similarly, it is also an insurmountable obstacle to achieve an accurate synchronization due to the electronic jitter of the RF clock. In this paper, we propose a method of ultrafast multi-bit physical RNG based on chaotic laser without any post-process. In this method, a train of optical pulses generated by a GHz mode-locked laser with low temporal jitter at a level of fs is used as an optical sampling clock. The chaotic laser is sampled in the optical domain through a low switching energy and high-linearity terahertz optical asymmetric demultiplexer (TOAD) sampler, which is a fiber loop with an asymmetrical nonlinear semiconductor optical amplifier. Then, the peak amplitude of each sampled chaotic pulse is digitized by a multi-bit comparator (i.e., a multi-bit ADC without sample and hold circuit) and converted into random numbers directly. Specifically, a proof-of-principle experiment is executed to demonstrate the aforementioned proposed method. In this experiment, an optical feedback chaotic laser is used, which has a bandwidth of 6 GHz. Through setting a sampling rate to be 5 GSa/s and selecting 4 LSBs outputs of the 8-bit comparator, 20 Gb/s (=5 GSa/s4 LSBs) physical random number sequences are obtained. Considering the ultrafast response rate of TOAD sampler, the speed of random numbers generated by this method has the potential to reach several hundreds of Gb/s as long as the used chaotic laser has a sufficient bandwidth.
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.
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.