A three-dimensional memristor-based hyperchaotic map for pseudorandom number generation and multi-image encryption
Abstract
The resistance state of a memristor can be influenced by external stimuli, and these variations can be converted into a pseudorandom sequence through appropriate circuitry and control mechanisms. By leveraging this property, a reliable and complex pseudorandom number generator suitable for encryption can be designed. To enhance the chaotic complexity of memristor-based discrete systems, this paper introduces a three-dimensional hyperchaotic map based on a memristor (3D-HMBM), which integrates a sine-function nonlinearity with a discrete memristor model. Analyzing its dynamical properties via Lyapunov exponents, the 3D-HMBM exhibits evolution from periodicity to chaos and hyperchaos. The complexity of its iterated sequences is verified through metrics such as Spectral Entropy and C0 complexity. Furthermore, the 3D-HMBM displays a unique phenomenon of infinite coexisting attractors. As initial values vary, the system generates attractors at different positions, suggesting that—in theory—an infinite number of attractors exist. Finally, the simulation results are validated via digital-circuit implementation. Building on this foundation, we propose a multi-image encryption algorithm based on the 3D-HMBM, offering a more secure solution for encrypting large volumes of data. Through statistical testing and cryptographic analysis, we confirm the significant potential of the keystream generated by the 3D-HMBM for cryptographic applications.
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FPGA-based data possess strong characteristics in terms of complexity measures, comparable to systems based on chaotic maps reported in the literature.
“These findings indicate that FPGA-based data possess strong characteristics in terms of complexity measures, comparable to systems based on chaotic maps reported in the literature (Gao et al. 2025b(Gao et al. , 2025c)).”
From A novel deep learning-based statistical randomness evaluation test methodology for cryptographic applications (2025) · cites this paper as Gao et al. 2025b
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Non-regular thumbnail-preserving encryption based on cross-coupled chaotic model
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A novel 2D hyperchaotic map with high complexity and its application in DCSK
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- Authors
- Gao, S., Ding, S., Ho-Ching Iu, H., Erkan, U., Toktas, A., Simsek, C., Wu, R., Xu, X., Cao, Y., & Mou, J.
- Affiliations
- Dalian Polytechnic University (CN)
- Dalian University of Technology (CN)
- School of Electrical, Electronic and Computer Engineering, The University of Western Australia 3 , Perth 6009,
- Ankara University (TR)
- Department of Artificial Intelligence and Data Engineering, Engineering Faculty, Ankara University 4 , 06830 Ankara,
- Electrical Electronics Engineering, Karamanoglu Mehmetbey University 5 , Karaman, Turkey 70200, Karaman,
- Harbin Institute of Technology (CN)
- Corresponding author
- Ding, Siqi
- Mou, Jun
- ORCID
- Venue
- Chaos: An Interdisciplinary Journal of Nonlinear Science
- Publisher
- AIP Publishing
- Published
- 2025-07-01
- Volume
- 35
- Issue
- 7
- ISSN
- 1054-1500 (ISSN-L)
- 1089-7682
- OpenAlex
- W4411865836
- Cited by
- 100
- References
- 49
- Citations by year
- 2026: 30 · 2025: 70
- FWCI
- 35.11
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Chaos An Interdisciplinary Journal of Nonlinear Science (publishedVersion)
- PubMed (publishedVersion)
- UWA Profiles and Research Repository (UWA) (submittedVersion)
- Funders
- Institution: Liaoning Provincial Science and Technology Plan Joint Project (2024-MSLH-033)
- Institution: Technological innovation projects in the field of artificial intelligence in Liaoning province (2023JH26/10300011)
- Institution: Basic scientific research projects in department of education of Liaoning Province (LJ212410152049)
- 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
- memristors, hyperchaotic map, pseudorandom number generation, multi-image encryption, chaotic dynamics, Lyapunov exponents, spectral entropy, C0 complexity, keystream, digital circuit implementation
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