Dynamic analysis and image encryption using a novel 4D map for secure transmission using WDM 4*20 Gbps techniques

Authors

J. Fotsing, R. Kengne, A. Tiedeu, E. Tonye

Abstract

This study presents a detailed examination of the design, dynamic analysis, and applications of a novel four-dimensional hyperchaotic system, which has not been explored in previous literature. We propose a new 4D autonomous hyperjerk system, characterized by its distinctive nonlinearity, specifically the Van der Pol nonlinearity. To validate our theoretical findings, we implemented the system both in PSpice software and through a real analog circuit built in the laboratory. This setup successfully reproduced the chaotic attractor phase portrait observed in numerical simulations, confirming the accuracy of the theoretical analysis. Notably, this system is the first to incorporate an adaptive backstepping controller in a PSpice environment, validating both theoretical and numerical synchronization results. Furthermore, we applied this system to image encryption, introducing a novel encryption method based on the proposed 4D hyperjerk system. Based on the NIST SP800–22 standard, the hyperjerk key sequence generated by the algorithm passed all 15 test metrics, proving its excellent randomness. The encrypted images and sequences were subjected to various tests, including statistical and differential attacks, key sensitivity, correlation, and key space analysis. These tests demonstrated the effectiveness and reliability of the proposed system. Notably, when the key was altered by even a tiny value (10−15 difference from the correct key), the data could not be decoded, ensuring secure transmission. The cryptosystem also showed robustness against known attacks, such as chosen plaintext attacks (CPA) and chosen ciphertext attacks (CCA), proving its resilience in real-world scenarios. The optical communication system utilizing 4 × 20 Gbps WDM technology was also evaluated. Simulations showed that the system provided reliable, secure transmission over long distances. Performance metrics, including Quality Factor (Q-factor), Bit Error Rate (BER), and eye diagram analysis, were assessed. By varying input power from -15 dBm to 15 dBm in 5 dBm increments, we observed that the lowest BER and highest Q-factor occurred at 5 dBm input power. At this power level, the maximum Q-factor reached 5.43, and the minimum BER of 0.209 × 10–08 was achieved for an optical fiber length of 140 km.

Keywords

4D hyperjerk system; Vand der Pol nonlinearity; Image encryption; WDM 4*20 Gbps; Security

Citation

• Journal: Franklin Open
• Year: 2025
• Volume: 10
• Issue:
• Pages: 100242
• Publisher: Elsevier BV
• DOI: 10.1016/j.fraope.2025.100242

BibTeX

@article{Fotsing_2025,
  title={{Dynamic analysis and image encryption using a novel 4D map for secure transmission using WDM 4*20 Gbps techniques}},
  volume={10},
  ISSN={2773-1863},
  DOI={10.1016/j.fraope.2025.100242},
  journal={Franklin Open},
  publisher={Elsevier BV},
  author={Fotsing, J. and Kengne, R. and Tiedeu, A. and Tonye, E.},
  year={2025},
  pages={100242}
}

Download the bib file

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