Hybrid chaotic image encryption in spatial-frequency domain integrated with bit-level dynamic diffusion

Yizhe Lu; Jianhua Song; Xinrong Fu; Xinying Huang; Yizhe Lu; Jianhua Song; Xinrong Fu; Xinying Huang

doi:10.3934/era.2025222

Electronic Research Archive

2025, Volume 33, Issue 8: 4933-4963. doi: 10.3934/era.2025222

Previous Article Next Article

Research article

Hybrid chaotic image encryption in spatial-frequency domain integrated with bit-level dynamic diffusion

1.
Key Laboratory of Light Field Manipulation and System Integration Applications in Fujian Province, Minnan Normal University, Zhangzhou 363000, China
2.
College of Physics and Information Engineering, Minnan Normal University, Zhangzhou 363000, China

Received: 15 July 2025 Revised: 13 August 2025 Accepted: 19 August 2025 Published: 25 August 2025

We aimed to address the issues of low encryption complexity and insufficient resistance to statistical attacks in chaotic image encryption algorithms. This paper proposes a novel method that combines hash scrambling, and bit-level transformation, leveraging the synergy between chaotic mapping and spatial-frequency transformation. Firstly, a specific hash function is constructed using the cubic chaotic system to achieve efficient scrambling of the image. Subsequently, the frequency domain data is generated by the Fourier transform and represented in the form of an optimized complementary code. Finally, the encryption is completed by DNA primary diffusion, secondary diffusion based on adjacent blocks, and the neighbor bit deprivation operation, and the entire process is jointly regulated by the Chen chaotic system and the Sin-Tent-Cos chaotic system. The experiment demonstrates that this scheme exhibits excellent robustness and security, with all indicators surpassing those of traditional methods. In particular, its resistance to differential attacks is close to the theoretical optimal value, demonstrating the important application potential of spatial-frequency joint encryption.
- image encryption,
- chaotic system,
- hash scrambling,
- DRPE (double random-phase encoding),
- bit-level transformation,
- security analysis
Citation: Yizhe Lu, Jianhua Song, Xinrong Fu, Xinying Huang. Hybrid chaotic image encryption in spatial-frequency domain integrated with bit-level dynamic diffusion[J]. Electronic Research Archive, 2025, 33(8): 4933-4963. doi: 10.3934/era.2025222

Related Papers:

Abstract

We aimed to address the issues of low encryption complexity and insufficient resistance to statistical attacks in chaotic image encryption algorithms. This paper proposes a novel method that combines hash scrambling, and bit-level transformation, leveraging the synergy between chaotic mapping and spatial-frequency transformation. Firstly, a specific hash function is constructed using the cubic chaotic system to achieve efficient scrambling of the image. Subsequently, the frequency domain data is generated by the Fourier transform and represented in the form of an optimized complementary code. Finally, the encryption is completed by DNA primary diffusion, secondary diffusion based on adjacent blocks, and the neighbor bit deprivation operation, and the entire process is jointly regulated by the Chen chaotic system and the Sin-Tent-Cos chaotic system. The experiment demonstrates that this scheme exhibits excellent robustness and security, with all indicators surpassing those of traditional methods. In particular, its resistance to differential attacks is close to the theoretical optimal value, demonstrating the important application potential of spatial-frequency joint encryption.

References

[1]	K. U. Shahna, A. Mohamed, A novel image encryption scheme using both pixel level and bit level permutation with chaotic map, Appl. Soft Comput., 90 (2020), 106162. https://doi.org/10.1016/j.asoc.2020.106162 doi: 10.1016/j.asoc.2020.106162
[2]	W. Feng, K. Zhang, J. Zhang, X. Zhao, Y. Chen, B. Cai, et al., Integrating fractional-order hopfield neural network with differentiated encryption: Achieving high-performance privacy protection for medical images, Fractal Fract., 9 (2025), 426. https://doi.org/10.3390/fractalfract9070426 doi: 10.3390/fractalfract9070426
[3]	C. Ye, S. Tan, J. Wang, L. Shi, Q. Zuo, W. Feng, Social image security with encryption and watermarking in hybrid domains, Entropy, 27 (2025), 276. https://doi.org/10.3390/e27030276 doi: 10.3390/e27030276
[4]	W. Feng, J. Zhang, Y. Chen, Z. Qin, Y. Zhang, M. Ahmad, et al., Exploiting robust quadratic polynomial hyperchaotic map and pixel fusion strategy for efficient image encryption, Expert Syst. Appl., 246 (2024), 123190. https://doi.org/10.1016/j.eswa.2024.123190 doi: 10.1016/j.eswa.2024.123190
[5]	H. Li, S. Yu, W. Feng, Y. Chen, J. Zhang, Z. Qin, et al., Exploiting dynamic vector-level operations and a 2D-enhanced logistic modular map for efficient chaotic image encryption, Entropy, 25 (2023), 1147. https://doi.org/10.3390/e25081147 doi: 10.3390/e25081147
[6]	Z. Hua, J. Yao, Y. Zhang, H. Bao, S. Yi, Two-dimensional coupled complex chaotic map, IEEE Trans. Ind. Inf., 21 (2025), 85–95. https://doi.org/10.1109/TII.2024.3431085 doi: 10.1109/TII.2024.3431085
[7]	B. Abd-El-Atty, Efficient S-box construction based on quantum-inspired quantum walks with PSO algorithm and its application to image cryptosystem, Complex Intell. Syst., 9 (2023), 4817–4835. https://doi.org/10.1007/s40747-023-00988-7 doi: 10.1007/s40747-023-00988-7
[8]	C. Wang, Y. Zhang, A novel image encryption algorithm with deep neural network, Signal Process., 196 (2022), 108536. https://doi.org/10.1016/j.sigpro.2022.108536 doi: 10.1016/j.sigpro.2022.108536
[9]	H. Liu, Y. Xu, C. Ma, Chaos-based image hybrid encryption algorithm using key stretching and hash feedback, Optik, 216 (2020), 164925. https://doi.org/10.1016/j.ijleo.2020.164925 doi: 10.1016/j.ijleo.2020.164925
[10]	L. Li, A novel chaotic map application in image encryption algorithm, Expert Syst. Appl., 35 (2024), 124316. https://doi.org/10.1016/j.eswa.2024.124316 doi: 10.1016/j.eswa.2024.124316
[11]	W. Dai, B. Li, Q. Du, Z. Zhu, A. Liu, Chaos-based index-of-min hashing scheme for cancellable biometrics security, IEEE Trans. Inf. Forensics Secur., 19 (2024), 8982–8997. https://doi.org/10.1109/TIFS.2024.3455109 doi: 10.1109/TIFS.2024.3455109
[12]	C. Xue, H. Wan, P. Gu, N. Jiang, Y. Hong, Z. Zhang, Ultrafast secure key distribution based on random dna coding and electro-optic chaos synchronization, IEEE J. Quantum Electron., 58 (2022). https://doi.org/10.1109/JQE.2021.3139711
[13]	A. K. Singh, K. Chatterjee, A. Singh, An image security model based on chaos and DNA cryptography for IIoT images, IEEE Trans. Ind. Inf., 19 (2023), 1957–1964. https://doi.org/10.1109/TII.2022.3176054 doi: 10.1109/TII.2022.3176054
[14]	X. Wang, H. Zhao, Y. Hou, C. Luo, Y. Zhang, C. Wang, Chaotic image encryption algorithm based on pseudo-random bit sequence and DNA plane, Mod. Phys. Lett. B, 33 (2019), 1950263. https://doi.org/10.1142/S0217984919502634 doi: 10.1142/S0217984919502634
[15]	H. Nematzadeh, R. Enayatifar, M. Yadollahi, M. Lee, G. Jeong, Binary search tree image encryption with DNA, Optik, 202 (2020), 163505. https://doi.org/10.1016/j.ijleo.2019.163505 doi: 10.1016/j.ijleo.2019.163505
[16]	S. Zhang, L. Liu, A novel image encryption algorithm based on SPWLCM and DNA coding, Math. Comput. Simul., 190 (2021), 723–744. https://doi.org/10.1016/j.matcom.2021.06.012 doi: 10.1016/j.matcom.2021.06.012
[17]	Z. Yang, Y. Cao, Y. Ji, Z. Liu, H. Chen, Securing color image by using bit-level modified integer nonlinear coupled chaos model in Fresnel diffraction domains, Opt. Lasers Eng., 152 (2022), 106969. https://doi.org/10.1016/j.optlaseng.2022.106969 doi: 10.1016/j.optlaseng.2022.106969
[18]	K. Qian, W. Feng, Z. Qin, J. Zhang, X. Luo, Z. Zhu, A novel image encryption scheme based on memristive chaotic system and combining bidirectional bit-level cyclic shift and dynamic DNA-level diffusion, Front. Phys., 10 (2022), 963795. https://doi.org/10.3389/fphy.2022.963795 doi: 10.3389/fphy.2022.963795
[19]	J. Gao, Y. Wang, Z. Song, S. Wang, Quantum image encryption based on quantum DNA codec and pixel-level scrambling, Entropy, 25 (2023), 865. https://doi.org/10.3390/e25060865 doi: 10.3390/e25060865
[20]	A. A. A. El-Latif, B. Abd-El-Atty, Adaptive particle swarm optimization with quantum-inspired quantum walks for robust image security, IEEE Access, 11 (2023), 71143–71153. https://doi.org/10.1109/ACCESS.2023.3286347 doi: 10.1109/ACCESS.2023.3286347
[21]	Y. Su, X. Wang, H. Gao, Chaotic image encryption algorithm based on bit-level feedback adjustment, Inf. Sci., 679 (2024), 121088. https://doi.org/10.1016/j.ins.2024.121088 doi: 10.1016/j.ins.2024.121088
[22]	X. Jiang, Y. Xiao, Y. Xie, B. Liu, Y. Ye, T. Song, et al., Exploiting optical chaos for double images encryption with compressive sensing and double random phase encoding, Opt. Commun., 484 (2021), 126683. https://doi.org/10.1016/j.optcom.2020.126683 doi: 10.1016/j.optcom.2020.126683
[23]	T. Zeng, Y. Zhu, E.Y. Lam, Deep learning for digital holography: a review, Opt. Express, 29 (2021), 40572. https://doi.org/10.1364/OE.443367 doi: 10.1364/OE.443367
[24]	Y. Hualong, G. Daidou, Research on double encryption of ghost imaging by SegNet deep neural network, IEEE Photonics Technol. Lett., 36 (2024), 669–672. https://doi.org/10.1109/LPT.2024.3379554 doi: 10.1109/LPT.2024.3379554
[25]	Y. Wang, Y. Su, X. Sun, X. Hao, Y. Liu, X. Zhao, et al., Principle and implementation of stokes vector polarization imaging technology, Appl. Sci., 12 (2022), 6613. https://doi.org/10.3390/app12136613 doi: 10.3390/app12136613
[26]	L. Wang, T. Wang, R. Yan, X. Yue, H. Wang, Y. Wang, et al., Color printing and encryption with polarization-switchable structural colors on all-dielectric metasurfaces, Nano Lett., 23 (2023), 5581–5587. https://doi.org/10.1021/acs.nanolett.3c01007 doi: 10.1021/acs.nanolett.3c01007
[27]	J. Zhang, Z. Huang, X. Li, M. Wu, X. Wang, Y. Dong, Quantum image encryption based on quantum image decomposition, Int. J. Theor. Phys., 60 (2021), 2930–2942. https://doi.org/10.1007/s10773-021-04862-5 doi: 10.1007/s10773-021-04862-5
[28]	K. Benyahia, A. Khobzaoui, S. Benbakreti, Hybrid image encryption: leveraging DNA sequencing and Lorenz chaotic dynamics for enhanced security, Cluster Comput., 28 (2025), 218. https://doi.org/10.1007/s10586-024-04948-9 doi: 10.1007/s10586-024-04948-9
[29]	C. Zhang, J. Cheng, D. Chen, Cryptanalysis of an image encryption algorithm based on a 2D hyperchaotic map, Entropy, 24 (2022), 1551. https://doi.org/10.3390/e24111551 doi: 10.3390/e24111551
[30]	J. Tang, Z. Zhang, T. Huang, Two-dimensional cosine–sine interleaved chaotic system for secure communication, IEEE Trans. Circuits Syst. II Express Briefs, 71 (2024), 2479–2483. https://doi.org/10.1109/TCSII.2023.3337145 doi: 10.1109/TCSII.2023.3337145
[31]	A. Yahi, B. Tewfik, M. E. H. Daachi, N. Diffellah, A color image encryption scheme based on 1D cubic map, Optik, 249 (2022), 168290. https://doi.org/10.1016/j.ijleo.2021.168290 doi: 10.1016/j.ijleo.2021.168290
[32]	S. M. Basha, P. Mathivanan, A. B. Ganesh, Bit level color image encryption using Logistic-Sine-Tent-Chebyshev (LSTC) map, Optik, 259 (2022), 168956. https://doi.org/10.1016/j.ijleo.2022.168956 doi: 10.1016/j.ijleo.2022.168956
[33]	M. T. Yassen, Chaos control of Chen chaotic dynamical system, Chaos, Solitons Fractals, 15 (2003), 271–283. https://doi.org/10.1016/s0960-0779(01)00251-x doi: 10.1016/s0960-0779(01)00251-x
[34]	F. Pengfei, L. Miaomiao, L. Min, L. Han, Image encryption algorithm based on hyperchaotic system and DNA coding, in 2021 International Conference on Computer Communication and Artificial Intelligence (CCAI), IEEE, (2021), 41–46. https://doi.org/10.1109/CCAI50917.2021.9447470
[35]	H. Wen, S. Kang, Z. Wu, Y. Lin, Y. Huang, Dynamic RNA coding color image cipher based on chain feedback structure, Mathematics, 11 (2023), 3133. https://doi.org/10.3390/math11143133 doi: 10.3390/math11143133
[36]	Y. Huang, Q. Zhang, Y. Zhao, Color image encryption algorithm based on hybrid chaos and layered strategies, J. Inf. Secur. Appl., 89 (2025), 103921. https://doi.org/10.1016/j.jisa.2024.103921 doi: 10.1016/j.jisa.2024.103921
[37]	M. Wang, X. Song, S. Liu, X. Zhao, N. Zhou, A novel 2D Log-Logistic–Sine chaotic map for image encryption, Nonlinear Dyn., 113 (2025), 2867–2896. https://doi.org/10.1007/s11071-024-10331-5 doi: 10.1007/s11071-024-10331-5
[38]	R. Zhang, R. Zhou, J. Luo, Nonequal-length image encryption based on bitplane chaotic mapping, Sci. Rep., 14 (2024), 9075. https://doi.org/10.1038/s41598-024-58612-8 doi: 10.1038/s41598-024-58612-8
[39]	X. Wang, S. Chen, Y. Zhang, A chaotic image encryption algorithm based on random dynamic mixing, Opt. Laser Techol., 138 (2021), 106837. https://doi.org/10.1016/j.optlastec.2020.106837 doi: 10.1016/j.optlastec.2020.106837
[40]	X. An, S. Liu, L. Xiong, J. Zhang, X. Li, Mixed gray-color images encryption algorithm based on a memristor chaotic system and 2D compression sensing, Expert Syst. Appl., 243 (2024), 122899. https://doi.org/10.1016/j.eswa.2023.122899 doi: 10.1016/j.eswa.2023.122899
[41]	Y. Xian, X. Wang, Fractal sorting matrix and its application on chaotic image encryption, Inf. Sci., 547 (2021), 1154–1169. https://doi.org/10.1016/j.ins.2020.09.055 doi: 10.1016/j.ins.2020.09.055
[42]	Q. Cun, X. Tong, Z. Wang, M. Zhang, A new chaotic image encryption algorithm based on dynamic DNA coding and RNA computing, Visual Comput., 39 (2023), 6589–6608. https://doi.org/10.1007/s00371-022-02750-5 doi: 10.1007/s00371-022-02750-5
[43]	K. M. Hosny, S. T. Kamal, M. M. Darwish, A novel color image encryption based on fractional shifted Gegenbauer moments and 2D logistic-sine map, Visual Comput., 39 (2023), 1027–1044. https://doi.org/10.1007/s00371-021-02382-1 doi: 10.1007/s00371-021-02382-1
[44]	Q. Lai, Y. Liu, L. Yang, Remote sensing image encryption algorithm utilizing 2D Logistic memristive hyperchaotic map and SHA-512, Sci. China Technol. Sci., 67 (2024), 1553–1566. https://doi.org/10.1007/s11431-023-2584-y doi: 10.1007/s11431-023-2584-y
[45]	X. Liu, X. Tong, M. Zhang, Z. Wang, A highly secure image encryption algorithm based on conservative hyperchaotic system and dynamic biogenetic gene algorithms, Chaos, Solitons Fractals, 171 (2023), 113450. https://doi.org/10.1016/j.chaos.2023.113450 doi: 10.1016/j.chaos.2023.113450
[46]	A. Moatsum, S. Azman, S. T. Je, S. A. Rami, A new hybrid digital chaotic system with applications in image encryption, Signal Process., 160 (2019), 45–58. https://doi.org/10.1016/j.sigpro.2019.02.016 doi: 10.1016/j.sigpro.2019.02.016
[47]	Y. Zhou, L. Bao, C. L. P. Chen, Image encryption using a new parametric switching chaotic system, Signal Process., 93 (2013), 3039–3052. https://doi.org/10.1016/j.sigpro.2013.04.021 doi: 10.1016/j.sigpro.2013.04.021
[48]	T. Hu, Y. Liu, L. H. Gong, C. J. Ouyang, An image encryption scheme combining chaos with cycle operation for DNA sequences, Nonlinear Dyn., 87 (2017), 51–66. https://doi.org/10.1007/s11071-016-3024-6 doi: 10.1007/s11071-016-3024-6
[49]	S. Kumar, D. Sharma, A chaotic based image encryption scheme using elliptic curve cryptography and genetic algorithm, Artif. Intell. Rev., 57(2024), 87. https://doi.org/10.1007/s10462-024-10719-0 doi: 10.1007/s10462-024-10719-0
[50]	S. Kumar, D. Sharma, Image scrambling encryption using chaotic map and genetic algorithm: a hybrid approach for enhanced security, Nonlinear Dyn., 112 (2024), 12537–12564. https://doi.org/10.1007/s11071-024-09670-0 doi: 10.1007/s11071-024-09670-0
[51]	W. Alexan, M. Elkandoz, M. Mashaly, E. Azab, A. Aboshousha, Color image encryption through chaos and KAA map, IEEE Access, 11 (2023), 11541–11554. https://doi.org/10.1109/access.2023.3242311 doi: 10.1109/access.2023.3242311
[52]	H. Wen, Y. Lin, S. Kang, X. Zhang, K. Zou, Secure image encryption algorithm using chaos-based block permutation and weighted bit planes chain diffusion, IScience, 27 (2024), 108610. https://doi.org/10.1016/j.isci.2023.108610 doi: 10.1016/j.isci.2023.108610
[53]	W. Alexan, M. ElBeltagy, A. Aboshousha, Rgb image encryption through cellular automata, s-box and the lorenz system, Symmetry, 14 (2022), 443. https://doi.org/10.3390/sym14030443
[54]	M. A. B. Farah, A. Farah, T. Farah, An image encryption scheme based on a new hybrid chaotic map and optimized substitution box, Nonlinear Dyn., 99 (2020), 3041–3064. https://doi.org/10.1007/s11071-019-05413-8 doi: 10.1007/s11071-019-05413-8

Reader Comments

Your name:*

Email:*
© 2025 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)