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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]
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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
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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
Jahanshahi, H., Yousefpour, A., Munoz-Pacheco, J. M., Kaçar, S., Pham, V., & Alsaadi, F. E. (2020) · Applied Mathematics and Computation · doi:10.1016/j.amc.2020.125310 · Cited by 122
Ren, L., Mou, J., Banerjee, S., & Zhang, Y. (2022) · Chaos Solitons & Fractals · doi:10.1016/j.chaos.2022.113024 · Cited by 118
Self-citationSine-Transform-Based Memristive Hyperchaotic Model With Hardware Implementation
Bao, H., Li, H., Hua, Z., Xu, Q., & Bao, B. (2022) · IEEE Transactions on Industrial Informatics · doi:10.1109/tii.2022.3157296 · Cited by 117
EFR-CSTP: Encryption for face recognition based on the chaos and semi-tensor product theory
Gao, S., Wu, R., Wang, X., Liu, J., Li, Q., & Tang, X. (2022) · Information Sciences · doi:10.1016/j.ins.2022.11.121 · Cited by 116
Self-citationFeng, W., Yang, J., Zhao, X., Qin, Z., Zhang, J., Zhu, Z., Wen, H., & Qian, K. (2024) · Mathematics · doi:10.3390/math12243917 · Cited by 105
Zhang, Z., Tang, J., Zhang, F., Huang, T., & Lü, M. (2024) · IEEE Transactions on Circuits and Systems for Video Technology · doi:10.1109/tcsvt.2024.3394951 · Cited by 93
Lai, Q., Liu, Y., & Fortuna, L. (2024) · IEEE Transactions on Circuits and Systems I Regular Papers · doi:10.1109/tcsi.2024.3434551 · Cited by 90
Rogers, T. D., & Whitley, D. C. (1983) · Mathematical Modelling · doi:10.1016/0270-0255(83)90030-1 · Cited by 90
Wang, M., Fu, X., Teng, L., Yan, X., Xia, Z., & Liu, P. (2024) · Chaos, Solitons & Fractals · doi:10.1016/j.chaos.2024.114959 · Cited by 87
Yu, F., Lin, Y., Yao, W., Cai, S., Lin, H., & Li, Y. (2024) · Neural Networks · doi:10.1016/j.neunet.2024.106904 · Cited by 86
Cryptanalysis of an image encryption scheme using variant Hill cipher and chaos
Wen, H., Lin, Y., Yang, L., & Chen, R. (2024) · Expert Systems with Applications · doi:10.1016/j.eswa.2024.123748 · Cited by 86
Lai, Q., & Hu, G. (2024) · IEEE Transactions on Industrial Informatics · doi:10.1109/tii.2024.3403266 · Cited by 84
Image Encryption via Complementary Embedding Algorithm and New Spatiotemporal Chaotic System
Liu, P., Wang, X., & Su, Y. (2022) · IEEE Transactions on Circuits and Systems for Video Technology · doi:10.1109/tcsvt.2022.3222559 · Cited by 80
Memristive effects on an improved discrete Rulkov neuron model
Bao, H., Li, K., Ma, J., Hua, Z., Xu, Q., & Bao, B. (2023) · Science China Technological Sciences · doi:10.1007/s11431-023-2432-1 · Cited by 79
Ding, D., Wang, W., Yang, Z., Hu, Y., Wang, J., Wang, M., Niu, Y., & Zhu, H. (2023) · Chaos Solitons & Fractals · doi:10.1016/j.chaos.2023.113841 · Cited by 79
Gao, S., Liu, J., Iu, H. H., Erkan, U., Zhou, S., Wu, R., & Tang, X. (2024) · Applied Mathematical Modelling · doi:10.1016/j.apm.2024.06.016 · Cited by 78
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Gao, S., Iu, H. H., Mou, J., Erkan, U., Liu, J., Wu, R., & Tang, X. (2024) · Chaos Solitons & Fractals · doi:10.1016/j.chaos.2024.114958 · Cited by 69
Self-citationLiu, P., Wang, X., Su, Y., Liu, H., & Unar, S. (2023) · IEEE Transactions on Circuits and Systems I Regular Papers · doi:10.1109/tcsi.2023.3250713 · Cited by 69
Multiobjective Design of 2D Hyperchaotic System Using Leader Pareto Grey Wolf Optimizer
Toktaş, A., Erkan, U., Üstün, D., & Lai, Q. (2024) · IEEE Transactions on Systems Man and Cybernetics Systems · doi:10.1109/tsmc.2024.3401412 · Cited by 69
Self-citationAn image encryption method based on improved Lorenz chaotic system and Galois field
Zhang, X., Liu, G., & Zou, C. (2024) · Applied Mathematical Modelling · doi:10.1016/j.apm.2024.04.023 · Cited by 66
Memristive Hénon map with hidden Neimark–Sacker bifurcations
Rong, K., Bao, H., Li, H., Hua, Z., & Bao, B. (2022) · Nonlinear Dynamics · doi:10.1007/s11071-022-07380-z · Cited by 59
Erkan, U., Toktaş, A., Memiş, S., Toktas, F., Lai, Q., Wen, H., & Gao, S. (2024) · IEEE Internet of Things Journal · doi:10.1109/jiot.2024.3432494 · Cited by 58
Self-citationReLU Function-Based Locally Active Memristor and its Application in Generating Spiking Behaviors
Xu, Q., Chen, X., Wu, H., Iu, H. H., Parastesh, F., & Wang, N. (2024) · IEEE Transactions on Circuits & Systems II Express Briefs · doi:10.1109/tcsii.2024.3401860 · Cited by 51
Low power and high-speed FPGA implementation for 4D memristor chaotic system for image encryption
Hagras, E. A. A., & Saber, M. (2020) · Multimedia Tools and Applications · doi:10.1007/s11042-019-08517-w · Cited by 43
A novel fractional nonautonomous chaotic circuit model and its application to image encryption
Kamal, F., Elsonbaty, A., & Elsaid, A. (2021) · Chaos Solitons & Fractals · doi:10.1016/j.chaos.2021.110686 · Cited by 40
Image encryption algorithm based on Hilbert sorting vector and new spatiotemporal chaotic system
Zhang, H., Hu, H., & Ding, W. (2023) · Optics & Laser Technology · doi:10.1016/j.optlastec.2023.109655 · Cited by 36
Image encryption algorithm based on the Matryoshka transform and modular-inverse matrix
Zhang, X., & Zhang, X. (2023) · Nonlinear Dynamics · doi:10.1007/s11071-023-09010-8 · Cited by 34
Gao, S., Iu, H. H., Erkan, U., Şimşek, C., Mou, J., Toktaş, A., Wu, R., & Tang, X. (2024) · IEEE Internet of Things Journal · doi:10.1109/jiot.2024.3411623 · Cited by 34
Self-citationCFB-Then-ECB Mode-Based Image Encryption for an Efficient Correction of Noisy Encrypted Images
Puteaux, P., & Puech, W. (2020) · IEEE Transactions on Circuits and Systems for Video Technology · doi:10.1109/tcsvt.2020.3039112 · Cited by 31
Al-Barakati, A. A., Mesdoui, F., Bekiros, S. D., Kaçar, S., & Jahanshahi, H. (2024) · Chaos Solitons & Fractals · doi:10.1016/j.chaos.2024.115135 · Cited by 30
Wang, M., An, M., He, S., Zhang, X., Iu, H. H., & Li, Z. (2023) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/5.0154516 · Cited by 30
A physical memristor-based chaotic system and its application in colour image encryption scheme
Das, P., & Mandal, S. (2023) · Physica Scripta · doi:10.1088/1402-4896/ad033f · Cited by 30
Tamba, V. K., Biamou, A. L. M., Pham, V., & Grassi, G. (2024) · Electronics · doi:10.3390/electronics13122414 · Cited by 18
Guler, H. (2022) · Physica Scripta · doi:10.1088/1402-4896/ac6707 · Cited by 13
Energy Efficient Memristive Transiently Chaotic Neural Network for Combinatorial Optimization
Bao, H., Ren, P., Xu, K., Yang, L., Zhou, H., Li, J., Li, Y., & Miao, X. (2024) · IEEE Transactions on Circuits and Systems I Regular Papers · doi:10.1109/tcsi.2024.3406167 · Cited by 7
Use of memristor-based chaotic circuits in AM-DCSK and FM-DCSK modulation
Şahin, M. E., Kolumbán, G., Hamamcı, S. E., & Güler, H. (2023) · Physica Scripta · doi:10.1088/1402-4896/acf7ff · Cited by 7
Richard, T. B. F., Alain, K. S. T., Vaidyanathan, S. V., Clemente-López, D., Munoz-Pacheco, J. M., & Martin, S. S. (2024) · Analog Integrated Circuits and Signal Processing · doi:10.1007/s10470-023-02199-z · Cited by 6
Hidden dynamics in a fractional-order memristive Hindmarsh–Rose model
Yu, Y., Shi, M., Kang, H.-Y., Chen, M., & Bao, B. (2020) · Nonlinear dynamics · doi:10.1007/s11071-020-05495-9 · Cited by 2
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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
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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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