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IEEE Transactions on Applied Superconductivity

Random-Number Generation Using Chaos in RF-Irradiated Stacked Intrinsic Josephson Junction

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

Published Jan 14, 2026• 1 citation
Publisher

Abstract

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 Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+\delta }$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.

DOI
10.1109/tasc.2025.3650523

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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.
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.
We propose a new method for fabricating resistively shunted intrinsic Josephson junctions (RS-IJJs). Two mesas, measuring 6 × 6μm 2 and 100 × 100 μm 2 respectively in the a - b plane, have been fabricated in a Bi 2 Sr 2 CaCu 2 O 8+ x single crystal with a SiO layer evaporated in-between as an insulator. A gold stripe was sputtered onto the insulator to connect the mesas, thus effectively shunting the smaller one. The current–voltage ( I – V ) curves of such RS-IJJs have shown the typical behaviour of a resistively shunted junction with greatly reduced hysteresis and voltage jump. Under microwave irradiation at a 3 mm waveband, we have registered three types of Shapiro steps: conventional, sub-harmonic and zero-crossing. In this rapid communication, we discuss the fabrication details, as well as the observations of the Shapiro steps.
SUMMARY In this paper, we review the progress in BiSrCaCuO-2212 Intrinsic Josephson junctions (IJJs) bysummarizing our recent results in fabrication and high frequencyexperiments. Using a double-side fabrication process, a well defined number of intrinsic Josephson junctions in a well defined geometrycan be fabricated. The junctions in the stack are quite homogeneous, and the power distribution of external irradiation among the junctions is even. Shapiro steps are clearlyobserved up to 2.5 THz, and the general condition for the occurrence of Shapiro steps at frequency f is that it should be much greater than the plasma frequency fpl. Under certain conditions the Shapiro steps are zero-crossing, making some applications possible, such as quantum voltage standard etc.
Studies on intrinsic Josephson junctions (IJJs) of cuprate superconductors are reviewed. A system consisting of a few IJJs provides phenomena to test the Josephson phase dynamics and its interaction between adjacent IJJs within a nanometer scale, which is unique to cuprate superconductors. Quasiparticle density of states, which provides direct information on the Cooper-pair formation, is also revealed in the system. In contrast, Josephson plasma emission, which is an electromagnetic wave radiation in the sub-terahertz frequency range from an IJJ stack, arises from the synchronous phase dynamics of hundreds of IJJs coupled globally. This review summarizes a wide range of physical phenomena in IJJ systems having capacitive and inductive couplings with different nanometer and micrometer length scales, respectively.
With a thin gold layer, we fabricated mesa-like shunted intrinsic Josephson junction stacks on Bi2Sr2CaCu2O8+x single crystals. Instead of the multibranch structure and large voltage jumps often observed in conventional intrinsic junctions, current–voltage characteristics typical of resistively shunted junctions were obtained. Individual Shapiro steps were clearly visible with irradiation at frequencies from a few to 20 GHz. The experiments demonstrated not only the ac Josephson effects directly but also the possibility of employing intrinsic Josephson junctions in high-frequency applications.