The DOI matches its Crossref record; 48 of the 48 references it cites were found in a registry or an index.
A 3D Memristive Cubic Map With Dual Discrete Memristors: Design, Implementation, and Application in Image Encryption
Abstract
Discrete chaotic systems based on memristors exhibit excellent dynamical properties and are more straightforward to implement in hardware, making them highly suitable for generating cryptographic keystreams. However, most existing memristor-based chaotic systems rely on a single memristor. This paper introduces a novel discrete chaotic system employing dual memristors, named the 3D memristive cubic map with dual discrete memristors (3D-MCM). The 3D-MCM system demonstrates richer and more intricate dynamical behaviors compared to its single-memristor counterparts, as verified through bifurcation diagrams, Lyapunov exponent spectra, and complexity analyses. Notably, the system exhibits coexisting attractors, substantially enhancing its dynamical complexity. Hardware implementation of the 3D-MCM attractors confirms its feasibility for industrial applications. To illustrate the system’s potential in encryption tasks, this study integrates the quaternary-based permutation and dynamic emanating diffusion (QPDED-IE) scheme with the 3D-MCM for image encryption. Experimental results demonstrate that the QPDED-IE scheme based on the 3D-MCM exhibits strong diffusion and confusion properties, effectively resisting cryptanalytic attacks.
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“Chaotic systems are highly sensitive to initial conditions and exhibit pseudo-random behavior, making them well-suited for creating confusion and diffusion in image data.”
From Hyperchaotic fractional-order image encryption with Knight’s tour scrambling for satellite imagery (2026) · cites this paper as [5]
Citations
Cites
If it's pinched it's a memristor
Chua, L. (2014) · Semiconductor Science and Technology · doi:10.1088/0268-1242/29/10/104001 · Cited by 685 · cited 1×
“According to Chua’s definition of memristors [29], a generic charge-controlled memristor can be characterized as where, the variable i ( t ) signifies the current, v( t ) denotes the voltage, and q represents an internal charge variable.”
Kong, X., Yu, F., Yao, W., Cai, S., Zhang, J., & Lin, H. (2023) · Neural Networks · doi:10.1016/j.neunet.2023.12.008 · Cited by 292
Discrete Memristor Hyperchaotic Maps
Bao, H., Hua, Z., Li, H., Chen, M., & Bao, B. (2021) · IEEE Transactions on Circuits and Systems I Regular Papers · doi:10.1109/tcsi.2021.3082895 · Cited by 256
A novel pixel-split image encryption scheme based on 2D Salomon map
Lai, Q., Hu, G., Erkan, U., & Toktaş, A. (2022) · Expert Systems with Applications · doi:10.1016/j.eswa.2022.118845 · Cited by 254
Self-citationPSO-based image encryption scheme using modular integrated logistic exponential map
Kocak, O., Erkan, U., Toktaş, A., & Gao, S. (2023) · Expert Systems with Applications · doi:10.1016/j.eswa.2023.121452 · Cited by 212
Self-citationFeng, W., Zhang, J., Chen, Y., Qin, Z., Zhang, Y., Ahmad, M., & Woźniak, M. (2024) · Expert Systems with Applications · doi:10.1016/j.eswa.2024.123190 · Cited by 210
Lai, Q., Yang, L., Hu, G., Guan, Z., & Iu, H. H. (2024) · IEEE Transactions on Cybernetics · doi:10.1109/tcyb.2024.3377011 · Cited by 195
Feng, W., Wang, Q., Liu, H., Ren, Y., Zhang, J., Zhang, S., Qian, K., & Wen, H. (2023) · Fractal and Fractional · doi:10.3390/fractalfract7120887 · Cited by 174
A chaotic based image encryption scheme using elliptic curve cryptography and genetic algorithm
Kumar, S., & Sharma, D. (2024) · Artificial Intelligence Review · doi:10.1007/s10462-024-10719-0 · Cited by 170
Lai, Q., Wan, Z., Zhang, H., & Chen, G. (2022) · IEEE Transactions on Neural Networks and Learning Systems · doi:10.1109/tnnls.2022.3146570 · Cited by 146
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Sorted by citations
Gao, S., Zhang, Z., Li, Q., Ding, S., Iu, H. H., Cao, Y., Xu, X., Wang, C., & Mou, J. (2025) · IEEE Transactions on Dependable and Secure Computing · doi:10.1109/tdsc.2025.3603570 · Cited by 192
Self-citationChaos-based video encryption techniques: A review
Gao, S., Wu, R., Iu, H. H., Erkan, U., Cao, Y., Li, Q., Toktaş, A., & Mou, J. (2025) · Computer Science Review · doi:10.1016/j.cosrev.2025.100816 · Cited by 121
Self-citationGao, S., Ding, S., Ho-Ching Iu, H., Erkan, U., Toktas, A., Simsek, C., Wu, R., Xu, X., Cao, Y., & Mou, J. (2025) · Chaos: An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/5.0270220 · Cited by 100
Self-citationAlexan, W., Shabasy, N. H. E., Ehab, N., & Maher, E. A. (2025) · Scientific Reports · doi:10.1038/s41598-025-15794-z · Cited by 78
3D Non-Degenerate Hyperchaos: Design, Analysis, and Application in Image Encryption
Lin, Y., Liao, Y., Zeng, W., Wei, Y., Chen, D., Yuan, X., Li, Y., Erkan, U., Toktaş, A., Zhang, C., et al. (2026) · IEEE Transactions on Consumer Electronics · doi:10.1109/tce.2026.3672135 · Cited by 77
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Metadata
- Authors
- Gao, S., Ho-Ching Iu, H., Erkan, U., Simsek, C., Toktas, A., Cao, Y., Wu, R., Mou, J., Li, Q., & Wang, C.
- Affiliations
- Dalian Polytechnic University (CN)
- School of Electrical, Electronic and Computer Engineering, The University of Western Australia, Perth, WA, Australia
- Karamanoğlu Mehmetbey University (TR)
- Department of Electrical Electronics Engineering, Karamanoglu Mehmetbey University, Karaman, Turkiye
- Department of Artificial Intelligence and Data Engineering, Engineering Faculty, Ankara University, Ankara, Türkiye
- Harbin Institute of Technology (CN)
- Qilu University of Technology (CN)
- ORCID
- Venue
- IEEE Transactions on Circuits and Systems for Video Technology
- Published
- 2025-08
- Volume
- 35
- Issue
- 8
- Pages
- 7706-7718
- ISSN
- 1051-8215 (ISSN-L)
- 1558-2205
- OpenAlex
- W4407948341
- Semantic Scholar
- f042f07247a3fa8fb0b49202b08488dd33b3b7da
- Cited by
- 250
- References
- 48
- Citations by year
- 2026: 132 · 2025: 118
- FWCI
- 87.28
- Type
- journal article
- Language
- en
- Open access
- closed
- Licence
- Locations
- IEEE Transactions on Circuits and Systems for Video Technology (publishedVersion)
- UWA Profiles and Research Repository (UWA) (submittedVersion)
- Funders
- Basic Scientific Research Projects in the Department of Education of Liaoning Province (LJ212410152049)
- Technological Innovation Projects in the field of artificial intelligence in Liaoning (2023JH26/10300011)
- Topics
- Physical Sciences › Computer Science › Computer Vision and Pattern Recognition › Chaos-based Image/Signal Encryption
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Chaos control and synchronization
- Physical Sciences › Mathematics › Mathematical Physics › Mathematical Dynamics and Fractals
- Keywords
- discrete-time chaotic systems, image encryption, coexisting attractors, hardware implementation, confusion and diffusion, cryptanalysis resistance
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