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<p>This paper unveils the theoretical probing, microcontroller realization, and image encryption of a quadratically damped Josephson junction (JJ) circuit with 4π-periodic superconducting current (QDJJC4PSC). The differential equation representing the model is established based on the fundamental Kirchhoff’s laws and steady state analysis results in two steady states: the stable and saddle nodes, distinguished by the Routh-Hurwitz criteria. Numerical simulations demonstrate a range of dynamic behaviours, including bursting oscillations, periodic, chaotic, coexisting, hidden, periodic bubbles and chaotic bubbles attractors, and antimonotonicity phenomenon. The experimental validation of the simulated results using microcontroller implementation shows qualitative agreement. Offset boosting control unveils the perfect transition of complex signals in the voltage and current state QDJJC4PSC variables. The NIST-800.22 tests validate the ability of the chaotic attractor uncovered in the QDJJC4PSC to be used for generating random numbers. The key generation, the steps of the proposed encryption and decryption algorithms based on zigzag permutation and XOR diffusion are presented, as well as the results of the various analyses conducted to evaluate the security and robustness of the proposed encryption scheme. The chaotic characteristic uncovered in the QDJJC4PSC has successfully demonstrated its use for medical images encryption applications based on zigzag permutation and XOR diffusion. The results underscore the practical impact and methodological rigor of our findings.</p>

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Theoretical probing, microcontroller implementation, and medical image encryption of a quadratically damped Josephson junction circuit oscillating with strictly the \(4\pi\)-periodic superconducting current

  • 期刊论文

  • 发表日期：

    2026年1月9日

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  • Vijeesh Vijayan,
  • Finalise Komofor Ngopuh,
  • Ahamat Mahamat Hassane,
  • Hubert Boudoue Malwe,
  • Gaetan Fautso Kuiate,
  • Karthikeyan Rajagopal

摘要

This paper unveils the theoretical probing, microcontroller realization, and image encryption of a quadratically damped Josephson junction (JJ) circuit with 4π-periodic superconducting current (QDJJC4PSC). The differential equation representing the model is established based on the fundamental Kirchhoff’s laws and steady state analysis results in two steady states: the stable and saddle nodes, distinguished by the Routh-Hurwitz criteria. Numerical simulations demonstrate a range of dynamic behaviours, including bursting oscillations, periodic, chaotic, coexisting, hidden, periodic bubbles and chaotic bubbles attractors, and antimonotonicity phenomenon. The experimental validation of the simulated results using microcontroller implementation shows qualitative agreement. Offset boosting control unveils the perfect transition of complex signals in the voltage and current state QDJJC4PSC variables. The NIST-800.22 tests validate the ability of the chaotic attractor uncovered in the QDJJC4PSC to be used for generating random numbers. The key generation, the steps of the proposed encryption and decryption algorithms based on zigzag permutation and XOR diffusion are presented, as well as the results of the various analyses conducted to evaluate the security and robustness of the proposed encryption scheme. The chaotic characteristic uncovered in the QDJJC4PSC has successfully demonstrated its use for medical images encryption applications based on zigzag permutation and XOR diffusion. The results underscore the practical impact and methodological rigor of our findings.