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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July 2025
Research Article|
July 01 2025
A three-dimensional memristor-based hyperchaotic map for pseudorandom number generation and multi-image encryption Available to Purchase
Suo Gao
;
Suo Gao
(Conceptualization, Data curation, Writing – original draft)
1
School of Information Science and Engineering, Dalian Polytechnic University
, Dalian 116034, China
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Siqi Ding
;
Siqi Ding
a)
(Writing – original draft)
2
School of Mathematical Sciences, Dalian University of Technology
, Dalian 116024, China
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Herbert Ho-Ching Iu
;
Herbert Ho-Ching Iu
(Data curation, Formal analysis)
3
School of Electrical, Electronic and Computer Engineering, The University of Western Australia
, Perth 6009, Australia
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Uğur Erkan
;
Uğur Erkan
(Methodology)
4
Department of Artificial Intelligence and Data Engineering, Engineering Faculty, Ankara University
, 06830 Ankara, Turkiye
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Abdurrahim Toktas
;
Abdurrahim Toktas
(Resources)
4
Department of Artificial Intelligence and Data Engineering, Engineering Faculty, Ankara University
, 06830 Ankara, Turkiye
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Cemaleddin Simsek
;
Cemaleddin Simsek
(Software)
5
Electrical Electronics Engineering, Karamanoglu Mehmetbey University
, Karaman, Turkey 70200, Karaman, Turkiye
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Rui Wu
;
Rui Wu
(Investigation, Methodology)
6
School of Computer Science and Technology, Harbin Institute of Technology
, 150001 Harbin, China
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Xianying Xu
;
Xianying Xu
(Validation, Visualization)
1
School of Information Science and Engineering, Dalian Polytechnic University
, Dalian 116034, China
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Yinghong Cao
;
Yinghong Cao
(Project administration, Resources, Software)
1
School of Information Science and Engineering, Dalian Polytechnic University
, Dalian 116034, China
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Suo Gao
1
Siqi Ding
2,a)
Herbert Ho-Ching Iu
3
Uğur Erkan
4
Abdurrahim Toktas
4
Cemaleddin Simsek
5
Xianying Xu
1
Yinghong Cao
1
Jun Mou
1,a)
1
School of Information Science and Engineering, Dalian Polytechnic University
, Dalian 116034, China
2
School of Mathematical Sciences, Dalian University of Technology
, Dalian 116024, China
3
School of Electrical, Electronic and Computer Engineering, The University of Western Australia
, Perth 6009, Australia
4
Department of Artificial Intelligence and Data Engineering, Engineering Faculty, Ankara University
, 06830 Ankara, Turkiye
5
Electrical Electronics Engineering, Karamanoglu Mehmetbey University
, Karaman, Turkey 70200, Karaman, Turkiye
6
School of Computer Science and Technology, Harbin Institute of Technology
, 150001 Harbin, China
Chaos 35, 073105 (2025)
Article history
Received:
March 10 2025
Accepted:
June 11 2025
Citation
Suo Gao, Siqi Ding, Herbert Ho-Ching Iu, Uğur Erkan, Abdurrahim Toktas, Cemaleddin Simsek, Rui Wu, Xianying Xu, Yinghong Cao, Jun Mou; A three-dimensional memristor-based hyperchaotic map for pseudorandom number generation and multi-image encryption. Chaos 1 July 2025; 35 (7): 073105. https://doi.org/10.1063/5.0270220
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