Journal of Machine and Computing


Enhancing Image Security with Memristor Driven Fractional Chaotic Systems and Secretary Bird Optimization



Journal of Machine and Computing

Received On : 26 March 2024

Revised On : 15 September 2024

Accepted On : 16 March 2025

Published On : 05 April 2025

Volume 05, Issue 02

Pages : 1160-1173


Abstract


The extensive utilization of information and communication technologies nowadays enhances information accessibility and underscores the importance of information and data security. Image encryption is a prevalent technique for safeguarding medical data on public networks, serving a vital function in the healthcare sector. Due to their intricate dynamics, memristors are frequently employed in the creation of innovative chaotic systems that enhance the efficacy of chaos-based encryption techniques. In recent years, chaos-based encryption methods have surfaced as a viable method for safeguarding the confidentiality of transmitted images. Memristor-based Fractional-order chaotic systems (MFOCS) have garnered considerable interest because to their resilience and intricacy. Fractional-order chaotic systems (FOCS) exhibit more intricate dynamics than integer-order chaotic systems. Consequently, the exploration of fractional chaotic systems for the development of picture cryptosystems has gained popularity recently. This research introduces an innovative image encryption framework utilizing a memristor-based fractional chaotic map in conjunction with the Secretary Bird Optimization Algorithm (SBOA) to improve security and resilience against cryptographic threats. The suggested method utilizes the distinctive memory properties and high-dimensional chaotic dynamics of the memristor-based fractional system to produce unpredictable encryption keys. The SBOA is utilized to enhance essential encryption parameters, guaranteeing superior randomness and resilience against statistical and differential assaults. The encryption method comprises a confusion phase, in which pixel positions are randomized using chaotic sequences, succeeded by a diffusion phase, where pixel intensities are altered utilizing optimal key sequences. Performance evaluation is executed by entropy analysis, correlation coefficient tests, NPCR, UACI, and studies of computational complexity. The findings indicate that the suggested method attains elevated entropy, minimal correlation, and robust key sensitivity, rendering it exceptionally resilient against brute-force and differential assaults. Notwithstanding its computing burden from fractional-order chaotic dynamics, the suggested model offers a secure and efficient encryption method appropriate for real-time image protection applications.


Keywords


Memristor-Based Fractional-Order Chaotic Systems (FOCS), Fractional-Order Chaotic Systems (FOCS), Secretary Bird Optimization Algorithm (SBOA).


  1. M. Vijayakumar and A. Ahilan, “An optimized chaotic S-box for real-time image encryption scheme based on 4-dimensional memristive hyperchaotic map,” Ain Shams Engineering Journal, vol. 15, no. 4, p. 102620, Apr. 2024, doi: 10.1016/j.asej.2023.102620.
  2. B. S. Kumar and R. Revathi, “An efficient image encryption algorithm using a discrete memory-based logistic map with deep neural network,” Journal of Engineering and Applied Science, vol. 71, no. 1, Feb. 2024, doi: 10.1186/s44147-023-00349-8.
  3. B. A. Belete, D. J. Gelmecha, and R. S. Singh, “Image encryption algorithm based on a memcapacitor‐based hyperchaotic system and DNA coding,” Security and Privacy, vol. 7, no. 6, Jun. 2024, doi: 10.1002/spy2.432.
  4. K. Qian, Y. Xiao, Y. Wei, D. Liu, Q. Wang, and W. Feng, “A Robust Memristor-Enhanced Polynomial Hyper-Chaotic Map and Its Multi-Channel Image Encryption Application,” Micromachines, vol. 14, no. 11, p. 2090, Nov. 2023, doi: 10.3390/mi14112090.
  5. S. Gao, “A 3D Memristive Cubic Map with Dual Discrete Memristors: Design, Implementation, and Application in Image Encryption,” IEEE Transactions on Circuits and Systems for Video Technology, pp. 1–1, 2025, doi: 10.1109/tcsvt.2025.3545868.
  6. Z.-A. S. A. Rahman, B. H. Jasim, Y. I. A. Al-Yasir, and R. A. Abd-Alhameed, “High-Security Image Encryption Based on a Novel Simple Fractional-Order Memristive Chaotic System with a Single Unstable Equilibrium Point,” Electronics, vol. 10, no. 24, p. 3130, Dec. 2021, doi: 10.3390/electronics10243130.
  7. Q. K. Abed and W. A. M. Al-Jawher, “An Image Encryption Method Based on Lorenz Chaotic Map and Hunter-Prey Optimization,” Journal Port Science Research, vol. 6, no. 4, pp. 332–343, Nov. 2023, doi: 10.36371/port.2023.4.3.
  8. B. A. Belete, D. J. Gelmecha, and R. S. Singh, “Enhancing colour image encryption through parameters optimization of memristive hyperchaotic system with CPSO algorithm and LSAIM,” The Imaging Science Journal, pp. 1–21, Jan. 2025, doi: 10.1080/13682199.2025.2454055.
  9. O. Elnoamy, M. Gabr, Y. Korayem, W. Alexan, and M. El-Aasser, “Enhancing Image Security Using Legacy-Based Encryption With Chaotic Tent Map and Memristor,” 2023 Signal Processing: Algorithms, Architectures, Arrangements, and Applications (SPA), pp. 124–129, Sep. 2023, doi: 10.23919/spa59660.2023.10274006.
  10. Y.-G. Yang, F.-E. Cheng, D.-H. Jiang, Y.-H. Zhou, W.-M. Shi, and X. Liao, “A visually meaningful image encryption algorithm based on P-tensor product compressive sensing and newly-designed 2D memristive chaotic map,” Physica Scripta, vol. 98, no. 10, p. 105211, Sep. 2023, doi: 10.1088/1402-4896/acf52d.
  11. Sonam et al., “Secure digital image watermarking using memristor-based hyperchaotic circuit,” The Visual Computer, vol. 39, no. 10, pp. 4459–4485, Jul. 2022, doi: 10.1007/s00371-022-02601-3.
  12. Q. K. Abed and W. A. M. Al-Jawher, “Optimized Color Image Encryption Using Arnold Transform, URUK Chaotic Map and GWO Algorithm,” Journal Port Science Research, vol. 7, no. 3, Jul. 2024, doi: 10.36371/port.2024.3.3.
  13. Y. Zhang, J. Zeng, W. Yan, and Q. Ding, “RBFNN-PSO Intelligent Synchronisation Method for Sprott B Chaotic Systems with External Noise and Its Application in an Image Encryption System,” Entropy, vol. 26, no. 10, p. 855, Oct. 2024, doi: 10.3390/e26100855.
  14. Y. Deng, X. Tian, Z. Chen, Y. Xiao, and Y. Xiao, “An image encryption algorithm based on a novel two-dimensional hyperchaotic map and difference algorithm,” Nonlinear Dynamics, vol. 113, no. 4, pp. 3801–3828, Oct. 2024, doi: 10.1007/s11071-024-10415-2.
  15. Q. Lai, C.-K. Zhu, and X.-W. Zhao, “Design and hardware implementation of 4D memristive hyperchaotic map with rich initial-relied and parameter-relied dynamics,” Integration, vol. 99, p. 102252, Nov. 2024, doi: 10.1016/j.vlsi.2024.102252.
  16. Y. Dong, S. Zhang, H. Zhang, X. Zhou, and J. Jiang, “Chaotic evolution optimization: A novel metaheuristic algorithm inspired by chaotic dynamics,” Chaos, Solitons & Fractals, vol. 192, p. 116049, Mar. 2025, doi: 10.1016/j.chaos.2025.116049.
  17. P. Li, X. Feng, S. Zhou, P. Yan, and H. Zhang, “Compression and encryption for remote sensing image based on PSO-BP and 2D-MCCM,” Physica Scripta, vol. 99, no. 8, p. 085268, Jul. 2024, doi: 10.1088/1402-4896/ad6487.
  18. X. Leng, X. Wang, B. Du, F. Ren, and Z. Zeng, “Real-time dynamic medical image encryption based on extended multi-scroll memristive Hopfield neural network,” Nonlinear Dynamics, Jan. 2025, doi: 10.1007/s11071-025-10884-z.
  19. W. Yao et al., “Dynamics analysis and image encryption application of Hopfield neural network with a novel multistable and highly tunable memristor,” Nonlinear Dynamics, vol. 112, no. 1, pp. 693–708, Nov. 2023, doi: 10.1007/s11071-023-09041-1.
  20. F. Yu, X. Kong, A. A. M. Mokbel, W. Yao, and S. Cai, “Complex Dynamics, Hardware Implementation and Image Encryption Application of Multiscroll Memeristive Hopfield Neural Network With a Novel Local Active Memeristor,” IEEE Transactions on Circuits and Systems II: Express Briefs, vol. 70, no. 1, pp. 326–330, Jan. 2023, doi: 10.1109/tcsii.2022.3218468.
  21. J. Cui, Y. Cao, H. Jahanshahi, J. Mou, and B. Sun, “Secure transmission cryptographic approach for remote-sensing image based on discrete memristor-coupled Rulkov neuron map and TIMG,” Multimedia Tools and Applications, Jun. 2024, doi: 10.1007/s11042-024-19651-5.
  22. H. Guler, “Real-time fuzzy-pid synchronization of memristor-based chaotic circuit using graphical coded algorithm in secure communication applications,” Physica Scripta, vol. 97, no. 5, p. 055212, Apr. 2022, doi: 10.1088/1402-4896/ac6707.
  23. A. Toktas, U. Erkan, and D. Ustun, “An image encryption scheme based on an optimal chaotic map derived by multi-objective optimization using ABC algorithm,” Nonlinear Dynamics, vol. 105, no. 2, pp. 1885–1909, Jul. 2021, doi: 10.1007/s11071-021-06675-x.
  24. M. A. Tahiri, “New color image encryption using hybrid optimization algorithm and Krawtchouk fractional transformations,” The Visual Computer, vol. 39, no. 12, pp. 6395–6420, Dec. 2022, doi: 10.1007/s00371-022-02736-3.
  25. X. Wang and Y. Li, “Chaotic image encryption algorithm based on hybrid multi-objective particle swarm optimization and DNA sequence,” Optics and Lasers in Engineering, vol. 137, p. 106393, Feb. 2021, doi: 10.1016/j.optlaseng.2020.106393.
  26. J. Zeng and C. Wang, “A Novel Hyperchaotic Image Encryption System Based on Particle Swarm Optimization Algorithm and Cellular Automata,” Security and Communication Networks, vol. 2021, pp. 1–15, Feb. 2021, doi: 10.1155/2021/6675565.
  27. Y. Zhu, C. Wang, J. Sun, and F. Yu, “A Chaotic Image Encryption Method Based on the Artificial Fish Swarms Algorithm and the DNA Coding,” Mathematics, vol. 11, no. 3, p. 767, Feb. 2023, doi: 10.3390/math11030767.

CRediT Author Statement


The authors confirm contribution to the paper as follows:

Conceptualization: Sakthi Kumar B and Revathi R; Methodology: Revathi R; Data Curation: Revathi R; Writing- Original Draft Preparation: Sakthi Kumar B and Revathi R; Visualization: Sakthi Kumar B; Investigation: Revathi R; Supervision: Sakthi Kumar B; Validation: Sakthi Kumar B and Revathi R; Writing- Reviewing and Editing: Sakthi Kumar B and Revathi R; All authors reviewed the results and approved the final version of the manuscript.


Acknowledgements


Author(s) thanks to Dr. Revathi R for this research completion and support.


Funding


No funding was received to assist with the preparation of this manuscript.


Ethics declarations


Conflict of interest

The authors have no conflicts of interest to declare that are relevant to the content of this article.


Availability of data and materials


Data sharing is not applicable to this article as no new data were created or analysed in this study.


Author information


Contributions

All authors have equal contribution in the paper and all authors have read and agreed to the published version of the manuscript.


Corresponding author


Rights and permissions


Open Access This article is licensed under a Creative Commons Attribution NoDerivs is a more restrictive license. It allows you to redistribute the material commercially or non-commercially but the user cannot make any changes whatsoever to the original, i.e. no derivatives of the original work. To view a copy of this license, visit https://creativecommons.org/licenses/by-nc-nd/4.0/


Cite this article


Sakthi Kumar B and Revathi R, “Enhancing Image Security with Memristor Driven Fractional Chaotic Systems and Secretary Bird Optimization”, Journal of Machine and Computing, pp. 1160-1173, April 2025, doi: 10.53759/7669/jmc202505092.


Copyright


© 2025 Sakthi Kumar B and Revathi R. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.