Enhancing colour image encryption through parameters optimization of memristive hyperchaotic system with CPSO algorithm and LSAIM
Abstract
Particle Swarm Optimization (PSO) is a simple and effective algorithm for optimization. However, it often converges too early and depends heavily on proper parameter settings for good results, especially in complex or high-dimensional search spaces. Therefore, this algorithm is inappropriate for parameter optimization of hyperchaotic systems and may not provide sufficient robustness and security of colour images. This study presents a new colour image encryption based on optimizing a four-dimensional Memristor-based hyperchaotic system, in which the fourteen parameters of the hyperchaotic system are optimized by the Chaotic Particle Swarm Optimization (CPSO) method, in combination with DNA code and a new logistic sine adjusted integrated map (LSAIM). Simulation results have shown that the algorithm achieved a key space of up to 21116, providing sufficient protection against brute-force attacks, with entropy values close to the ideal (7.9994), NPCR of 99.6178%, and UACI of 33.965%, indicating robust security.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
The proposed method achieves an entropy value of 7.9973, which is very close to the theoretical ideal of 8 and comparable to the best results reported in the literature.
“As summarized in Table 9, the proposed method achieves an entropy value of 7.9973, which is very close to the theoretical ideal of 8 and comparable to the best results reported in the literature (e.g.,20,29).”
From A novel memristor-based hyperchaotic hybrid encryption system with DNA for image encryption on the Jetson TX2 (2025) · cites this paper as [29]
Cites
Particle Swarm Optimization: A Comprehensive Survey
Shami, T. M., El-Saleh, A. A., Alswaitti, M., Al-Tashi, Q., Summakieh, M. A., & Mirjalili, S. (2022) · IEEE Access · doi:10.1109/access.2022.3142859 · Cited by 1,433 · see citing works
Gao, X., Mou, J., Xiong, L., Sha, Y., Yan, H., & Cao, Y. (2022) · Nonlinear Dynamics · doi:10.1007/s11071-021-07192-7 · Cited by 311 · see citing works
Coexisting Hidden Attractors in a 4-D Simplified Lorenz System
Li, C., & Sprott, J. C. (2014) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127414500345 · Cited by 281 · see citing works
Color Image Encryption Through Chaos and KAA Map
Alexan, W., Elkandoz, M. T., Mashaly, M. E., Azab, E., & Aboshousha, A. (2023) · IEEE Access · doi:10.1109/access.2023.3242311 · Cited by 248 · see citing works
Zia, U., McCartney, M., Scotney, B. W., Carracedo, J. M., Abu-Tair, M., Memon, J., & Sajjad, A. (2022) · International Journal of Information Security · doi:10.1007/s10207-022-00588-5 · Cited by 228 · see citing works
Cryptanalysis of a DNA-based image encryption scheme
Chen, J., Chen, L., & Zhou, Y. (2020) · Information Sciences · doi:10.1016/j.ins.2020.02.024 · Cited by 195 · see citing works
Colour image encryption algorithm combining Arnold map, DNA sequence operation, and a Mandelbrot set
Jithin, K. C., & Sankar, S. (2019) · Journal of Information Security and Applications · doi:10.1016/j.jisa.2019.102428 · Cited by 193 · see citing works
Image encryption based on a combination of multiple chaotic maps
Elkandoz, M. T., & Alexan, W. (2022) · Multimedia Tools and Applications · doi:10.1007/s11042-022-12595-8 · Cited by 172 · see citing works
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 · see citing works
Adaptive chaotic maps and their application to pseudo-random numbers generation
Вадимовна, Т. А., Nepomuceno, E. G., Karimov, A. I., Andreev, V. S., & Бутусов, Д. (2020) · Chaos Solitons & Fractals · doi:10.1016/j.chaos.2020.109615 · Cited by 164 · see citing works
Hyperchaotic image encryption algorithm based on bit-level permutation and DNA encoding
Wang, T., & Wang, M. (2020) · Optics & Laser Technology · doi:10.1016/j.optlastec.2020.106355 · Cited by 151 · see citing works
Constructing dynamic strong S-Box using 3D chaotic map and application to image encryption
Liu, H., Liu, J., & Ma, C. (2022) · Multimedia Tools and Applications · doi:10.1007/s11042-022-12069-x · Cited by 144 · see citing works
Liu, H., Kadir, A., & Sun, X. (2017) · IET Image Processing · doi:10.1049/iet-ipr.2016.0040 · Cited by 117 · see citing works
Alexan, W., Gabr, M., Mamdouh, E., Elias, R., & Aboshousha, A. (2023) · IEEE Access · doi:10.1109/access.2023.3282160 · Cited by 108 · see citing works
A Color Image Encryption Using Dynamic DNA and 4-D Memristive Hyper-Chaos
Liu, Z., Wu, C., Wang, J., & Hu, Y. H. (2019) · IEEE Access · doi:10.1109/access.2019.2922376 · Cited by 102 · see citing works
A color image encryption algorithm based on hyperchaotic map and Rubik’s Cube scrambling
Qiu, H., Xu, X., Jiang, Z., Sun, K., & Xiao, C. (2022) · Nonlinear Dynamics · doi:10.1007/s11071-022-07756-1 · Cited by 100 · see citing works
Heltberg, M. L., Krishna, S., & Jensen, M. H. (2019) · Nature Communications · doi:10.1038/s41467-018-07932-1 · Cited by 99 · see citing works
Hyperchaotic Maps and the Single Neuron Model: A Novel Framework for Chaos-Based Image Encryption
Alexan, W., Chen, Y., Por, L. Y., & Gabr, M. (2023) · Symmetry · doi:10.3390/sym15051081 · Cited by 97 · see citing works
Dynamical analysis and image encryption application of a novel memristive hyperchaotic system
Yang, Y., Wang, L., Duan, S., & Luo, L. (2020) · Optics & Laser Technology · doi:10.1016/j.optlastec.2020.106553 · Cited by 92 · see citing works
Color Image Encryption with Cipher Feedback and Coupling Chaotic Map
Liu, H., Kadir, A., & Xu, C. (2020) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127420501734 · Cited by 91 · see citing works
Wei, M., Du, Y., Wu, X., Su, Q., Zhu, J., Zheng, L., Lv, G., & Zhuang, J. (2020) · Computational and Mathematical Methods in Medicine · doi:10.1155/2020/5894010 · Cited by 91 · see citing works
A memristor-based chaotic system and its application in image encryption
Wang, B., Zou, F. C., & Cheng, J. S. (2017) · Optik · doi:10.1016/j.ijleo.2017.10.080 · Cited by 89 · see citing works
A new image encryption based on bit replacing, chaos and DNA coding techniques
Yousif, S. F., Abboud, A. J., & Alhumaima, R. S. (2022) · Multimedia Tools and Applications · doi:10.1007/s11042-022-12762-x · Cited by 86 · see citing works
A New Image Encryption Algorithm Based on Composite Chaos and Hyperchaos Combined with DNA Coding
Wan, Y., Gu, S., & Du, B. (2020) · Entropy · doi:10.3390/e22020171 · Cited by 82 · see citing works
Gabr, M., Korayem, Y., Chen, Y.-L., Yee, P. L., Ku, C. S., & Alexan, W. (2023) · IEEE Access · doi:10.1109/access.2023.3326848 · Cited by 79 · see citing works
Hameed, M. A., Abdel-Aleem, O. A., & Hassaballah, M. (2022) · Journal of Ambient Intelligence and Humanized Computing · doi:10.1007/s12652-022-04366-y · Cited by 75 · see citing works
A fast color image encryption technique based on three dimensional chaotic map
Valandar, M. Y., Barani, M. J., & Ayubi, P. (2019) · Optik · doi:10.1016/j.ijleo.2019.06.021 · Cited by 73 · see citing works
Qian, K., Yang, X., Wei, Y., Liu, D., Wang, Q., & Feng, W. (2023) · Micromachines · doi:10.3390/mi14112090 · Cited by 73 · see citing works
Symmetric keys image encryption and decryption using 3D chaotic maps with DNA encoding technique
Patel, S., Bharath, K. P., & Rajesh Kumar, M. (2020) · Multimedia Tools and Applications · doi:10.1007/s11042-020-09551-9 · Cited by 65 · see citing works
A synchronous intertwining logistic map-DNA approach for color image encryption
Dua, S., & Vijay, R. (2018) · Journal of Ambient Intelligence and Humanized Computing · doi:10.1007/s12652-018-0825-0 · Cited by 62 · see citing works
DNA encoding for RGB image encryption with memristor based neuron model and chaos phenomenon
Yıldırım, M. (2020) · Microelectronics Journal · doi:10.1016/j.mejo.2020.104878 · Cited by 57 · see citing works
Image encryption algorithm based on dynamic DNA coding operations and 3D chaotic systems
Telem, A. N. K., Fotsin, H. B., & Kengne, J. (2021) · Multimedia Tools and Applications · doi:10.1007/s11042-021-10549-0 · Cited by 56 · see citing works
Encryption scheme for RGB images using chaos and affine hill cipher technique
Lone, M. A., & Qureshi, S. (2022) · Nonlinear Dynamics · doi:10.1007/s11071-022-07995-2 · Cited by 56 · see citing works
A New Fractional Chaotic System and Its Application in Image Encryption With DNA Mutation
Jin, H., Li, H., Yan, H., & Mou, J. (2021) · IEEE Access · doi:10.1109/access.2021.3069977 · Cited by 55 · see citing works
Image encryption based on 2DNA encoding and chaotic 2D logistic map
Alrubaie, A. H., Khodher, M. A. A., & Abdulameer, A. T. (2023) · Journal of Engineering and Applied Science · doi:10.1186/s44147-023-00228-2 · Cited by 52 · see citing works
Image encryption using DNA coding and three-dimensional chaotic systems
Lone, P. N., Singh, D., & Mir, U. H. (2021) · Multimedia Tools and Applications · doi:10.1007/s11042-021-11802-2 · Cited by 51 · see citing works
Khan, L. S., Hazzazi, M. M., Khan, M., & Jamal, S. S. (2021) · Chinese Journal of Physics · doi:10.1016/j.cjph.2021.03.029 · Cited by 50 · see citing works
Design of a hyperchaotic memristive circuit based on wien bridge oscillator
Şahin, M. E., Demirkol, A. Ş., Güler, H., & Hamamcı, S. E. (2020) · Computers & Electrical Engineering · doi:10.1016/j.compeleceng.2020.106826 · Cited by 44 · see citing works
Block Image Encryption Algorithm Based on Novel Chaos and DNA Encoding
Zhao, J., Wang, S., & Zhang, L. (2023) · Information · doi:10.3390/info14030150 · Cited by 43 · see citing works
New Chaotic System: M-Map and Its Application in Chaos-Based Cryptography
Lawnik, M., & Berezowski, M. (2022) · Symmetry · doi:10.3390/sym14050895 · Cited by 42 · see citing works
Data Security Utilizing a Memristive Coupled Neural Network in 3D Models
Gabr, M., Diab, A., Elshoush, H. T. I., Chen, Y., Por, L. Y., Ku, C. S., & Alexan, W. (2024) · IEEE Access · doi:10.1109/access.2024.3447075 · Cited by 42 · see citing works
Secure DNA-Coding Image Optical Communication Using Non-Degenerate Hyperchaos and Dynamic Secret-Key
Wen, H., Liu, Z., Lai, H., Zhang, C., Liu, L., Yang, J., Lin, Y., Li, Y., Liao, Y., Ma, L., et al. (2022) · Mathematics · doi:10.3390/math10173180 · Cited by 40 · see citing works
An image encryption approach based on a novel two-dimensional chaotic system
Zhao, M., Li, L., & Yuan, Z. (2024) · Nonlinear Dynamics · doi:10.1007/s11071-024-10053-8 · Cited by 39 · see citing works
Dharminder, D., Kumar, U., & Gupta, P. (2021) · Complex & Intelligent Systems · doi:10.1007/s40747-021-00441-7 · Cited by 36 · see citing works
Chaotic image encryption method based on improved zigzag permutation and DNA rules
Wang, X., & Du, X. (2022) · Multimedia Tools and Applications · doi:10.1007/s11042-022-13012-w · Cited by 35 · see citing works
Zhang, S., Zhang, H., & Wang, C. (2023) · Nonlinear Dynamics · doi:10.1007/s11071-023-08652-y · Cited by 34 · see citing works
Advanced approach for encryption using advanced encryption standard with chaotic map
Alemami, Y., Mohamed, M. A., & Atiewi, S. (2022) · International Journal of Power Electronics and Drive Systems/International Journal of Electrical and Computer Engineering · doi:10.11591/ijece.v13i2.pp1708-1723 · Cited by 32 · see citing works
A new DNA coding and hyperchaotic system based asymmetric image encryption algorithm
Liu, M., & Ye, G. (2021) · Mathematical Biosciences & Engineering · doi:10.3934/mbe.2021194 · Cited by 31 · see citing works
Single-Objective Particle Swarm Optimization-Based Chaotic Image Encryption Scheme
Wang, J., Song, X., & El‐Latif, A. A. A. (2022) · Electronics · doi:10.3390/electronics11162628 · Cited by 30 · see citing works
Secure and Fast Image Encryption Algorithm Based on Modified Logistic Map
Riaz, M., Dilpazir, H., Naseer, S., Mahmood, H., Anwar, A., Khan, J. A., Benitez, I. B., & Ahmad, T. (2024) · Information · doi:10.3390/info15030172 · Cited by 27 · see citing works
Image encryption algorithm based on the density and 6D logistic map
Rashid, A. A., & Hussein, K. A. (2022) · International Journal of Power Electronics and Drive Systems/International Journal of Electrical and Computer Engineering · doi:10.11591/ijece.v13i2.pp1903-1913 · Cited by 27 · see citing works
An image encryption scheme based on particle swarm optimization algorithm and hyperchaotic system
Luo, Y.-L., Ouyang, X., Liu, J.-X., Cao, L., & Zou, Y. (2022) · Soft Computing - A Fusion of Foundations, Methodologies and Applications · doi:10.1007/s00500-021-06554-y · Cited by 26 · see citing works
A novel colour image encryption scheme using dynamic DNA coding, chaotic maps, and SHA-2
Paul, L. S. J., Gracias, C., Desai, A., Thanikaiselvan, V., Shanthini, S. S., & Amirtharajan, R. (2022) · Multimedia Tools and Applications · doi:10.1007/s11042-022-13095-5 · Cited by 26 · see citing works
Image Security Based on Three-Dimensional Chaotic System and Random Dynamic Selection
Ran, B., Zhang, T., Wang, L., Liu, S., & Zhou, X. (2022) · Entropy · doi:10.3390/e24070958 · Cited by 23 · see citing works
A Novel Color Image Encryption Algorithm Based on 5-D Hyperchaotic System and DNA Sequence
Li, X., Zeng, J., Ding, Q., & Fan, C. (2022) · Entropy · doi:10.3390/e24091270 · Cited by 23 · see citing works
Liang, Z., Qin, Q., Zhou, C., & Xu, S. (2022) · Journal of Electrical Engineering and Technology · doi:10.1007/s42835-022-01157-5 · Cited by 23 · see citing works
Comparative analysis of image encryption based on 1D maps and their integrated chaotic maps
Gebereselassie, S. A., & Roy, B. K. (2024) · Multimedia Tools and Applications · doi:10.1007/s11042-024-18319-4 · Cited by 22 · see citing works
Chaotic particle swarm optimization
Sun, Y., Qi, G., Wang, Z., van Wyk, B. J., & Hamam, Y. (2009) · ACM/SIGEVO Summit on Genetic and Evolutionary Computation (GEC) · doi:10.1145/1543834.1543902 · Cited by 20 · see citing works
Chaos in synthetic microbial communities
Karkaria, B. D., Manhart, A., Fedorec, A. J. H., & Barnes, C. P. (2022) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1010548 · Cited by 18 · see citing works
El‐Shorbagy, M. A., Eldesoky, I. M., Basyouni, M. M., Nassar, I., & El-Refaey, A. M. (2022) · Mathematics · doi:10.3390/math10091368 · Cited by 16 · see citing works
Particle Swarm Optimization Combined with Inertia-Free Velocity and Direction Search
Miao, K., Feng, Q., & Kuang, W. H. (2021) · Electronics · doi:10.3390/electronics10050597 · Cited by 16 · see citing works
Tong, X., Liu, X., Pan, T., Zhang, M., & Wang, Z. (2024) · Multimedia Systems · doi:10.1007/s00530-024-01370-4 · Cited by 14 · see citing works
Secure speech communication based on the combination of chaotic oscillator and logistic map
Gebereselassie, S. A., & Roy, B. K. (2022) · Multimedia Tools and Applications · doi:10.1007/s11042-022-12803-5 · Cited by 13 · see citing works
Secure digital image watermarking using memristor-based hyperchaotic circuit
Sonam, S., Sehra, K., Singh, R. P., Singh, S., Wadhera, S., Kasturi, P., Saxena, G. J., & Saxena, M. K. (2022) · The Visual Computer · doi:10.1007/s00371-022-02601-3 · Cited by 13 · see citing works
Self-citationImage encryption algorithm based on a memcapacitor‐based hyperchaotic system and DNA coding
Belete, B. A., Gelmecha, D. J., & Singh, R. S. (2024) · Security and Privacy · doi:10.1002/spy2.432 · Cited by 12 · see citing works
Self-citationAbd-El-Atty, B., & El‐Latif, A. A. A. (2023) · Neural Computing and Applications · doi:10.1007/s00521-023-08643-5 · Cited by 10 · see citing works
Ramli, K., Suryanto, Y., Magfirawaty, M., & Hayati, N. Q. (2020) · IEEE Access · doi:10.1109/access.2020.3001949 · Cited by 9 · see citing works
Dynamic analysis of a novel hyperchaotic system based on STM32 and application in image encryption
Cheng, X., Zhu, H., Liu, L., Mao, K., & Liu, J. (2024) · Scientific Reports · doi:10.1038/s41598-024-71338-x · Cited by 8 · see citing works
An, X., Jiang, M., Deng, W., & Fang, J. (2020) · International Journal of Numerical Modelling Electronic Networks Devices and Fields · doi:10.1002/jnm.2825 · Cited by 8 · see citing works
A new RGB image encryption algorithm based on hyper-chaotic-discrete-wavelet-packet-transform
Kumar, M. (2023) · Multimedia Tools and Applications · doi:10.1007/s11042-023-17812-6 · Cited by 6 · see citing works
Sahoo, S., Gebereselassie, S. A., Nathasarma, R., & Roy, B. K. (2024) · IFAC-PapersOnLine · doi:10.1016/j.ifacol.2024.05.038 · Cited by 4 · see citing works
Impact of Perturbation Schemes on the Ensemble Prediction in a Coupled Lorenz Model
Zou, Q., Zhong, Q., Mao, J., Ding, R., Lu, D., Li, J., & Li, X. (2023) · Advances in Atmospheric Sciences · doi:10.1007/s00376-022-1376-z · Cited by 2 · see citing works
Flagged first, then by citations
Cited by
Sorted by citations
Ulutas, H. (2025) · Scientific Reports · doi:10.1038/s41598-025-21604-3 · Cited by 17 · see citing works
“As summarized in Table 9, the proposed method achieves an entropy value of 7.9973, which is very close to the theoretical ideal of 8 and comparable to the best results reported in the literature (e.g., 20,29 ).”
InfluentialOnline sequential Extreme learning Machine (OSELM) based denoising of encrypted image
Belete, B. A., Gelmecha, D. J., & Singh, R. S. (2025) · Expert Systems with Applications · doi:10.1016/j.eswa.2025.126999 · Cited by 11 · see citing works
Self-citationA first-order memristor-based Rulkov neuron for image encryption and LSB steganography
Xu, Y., Xu, X., Zhang, M., Banerjee, S., Cao, Y., Gao, S., & Mou, J. (2026) · Nonlinear Dynamics · doi:10.1007/s11071-026-12264-7 · Cited by 4 · see citing works
Belete, B. A., Gelmecha, D. J., & Singh, R. S. (2025) · Iran Journal of Computer Science · doi:10.1007/s42044-025-00328-7 · Cited by 3 · see citing works
Self-citationÖZDEMİR, B., & Doğan, N. (2026) · Fractal and Fractional · doi:10.3390/fractalfract10070484 · Cited by 1 · see citing works
Sakthi Kumar, B., & Revathi, R. (2025) · Journal of Machine and Computing · doi:10.53759/7669/jmc202505092
Optimized K-means algorithm for image segmentation based on improved dung beetle algorithm
Li, N., Luo, Y., Feng, Z., Qu, H., & Liu, Z. (2026) · Scientific Reports · doi:10.1038/s41598-026-38438-2
Feistel-inspired and novel hybrid chaotic maps based robust encryption scheme for satellite imagery
Dua, M., Kumar, A., Chakravarty, N., & Dua, S. (2026) · Earth Science Informatics · doi:10.1007/s12145-026-02136-4
Sakthi Kumar, B., & Revathi, R. (2026) · Systems and Soft Computing · doi:10.1016/j.sasc.2026.200524
Allaoua, O., Djellab, H., Maamri, F., Belhocine, Y., Meraoumia, A., Alawad, M. A., Salem, A. M., & Alkhrijah, Y. M. (2026) · Telecommunication Systems · doi:10.1007/s11235-026-01527-8
- Authors
- Belete, B. A., Gelmecha, D. J., & Singh, R. S.
- Affiliations
- Adama Science and Technology University (ET)
- Corresponding author
- Gelmecha, Demissie Jobir
- Venue
- The Imaging Science Journal
- Publisher
- Informa UK Limited
- Published
- 2025-01-21
- Volume
- 73
- Issue
- 6
- Pages
- 681-701
- ISSN
- 1368-2199 (ISSN-L)
- 1743-131X
- OpenAlex
- W4406662105
- Cited by
- 9
- References
- 72
- Citations by year
- 2026: 5 · 2025: 4
- FWCI
- 3.18
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- The Imaging Science Journal (publishedVersion)
- Topics
- Physical Sciences › Computer Science › Computer Vision and Pattern Recognition › Chaos-based Image/Signal Encryption
- Physical Sciences › Computer Science › Artificial Intelligence › Metaheuristic Optimization Algorithms Research
- Physical Sciences › Computer Science › Artificial Intelligence › Computer Science and Engineering
- Keywords
- color image encryption, chaotic particle swarm optimization, DNA codes, key space, brute-force attack resistance, NPCR, UACI
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
