{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,30]],"date-time":"2026-07-30T17:10:14Z","timestamp":1785431414450,"version":"3.56.0"},"reference-count":66,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2025,12,6]],"date-time":"2025-12-06T00:00:00Z","timestamp":1764979200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100021171","name":"Guangdong Basic and Applied Basic Research Foundation","doi-asserted-by":"crossref","award":["2023A1515011717"],"award-info":[{"award-number":["2023A1515011717"]}],"id":[{"id":"10.13039\/501100021171","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Special Projects for Key Fields of the Education Department of Guangdong Province","award":["2024ZDZX1048"],"award-info":[{"award-number":["2024ZDZX1048"]}]},{"DOI":"10.13039\/100014472","name":"Scientific Research Foundation of Hunan Provincial Education Department","doi-asserted-by":"publisher","award":["23B0638"],"award-info":[{"award-number":["23B0638"]}],"id":[{"id":"10.13039\/100014472","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Key Project of the Panzhihua Municipal Key Laboratory of \u201cInternet+\u201d Big Data and Artificial Intelligence","award":["25HLW0003"],"award-info":[{"award-number":["25HLW0003"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>As digital images proliferate across open networks, securing them against unauthorized access has become imperative. However, many recent image encryption algorithms are limited by weak chaotic dynamics and inadequate cryptographic design. To overcome these, we propose a new 2D coupling-enhanced cubic hyperchaotic map with exponential parameters (2D-CCHM-EP). By incorporating exponential terms and strengthening interdependence among state variables, the 2D-CCHM-EP exhibits strict local expansiveness, effectively suppresses periodic windows, and achieves robust hyperchaotic behavior, validated both theoretically and numerically. It outperforms several recent chaotic maps in key metrics, yielding significantly higher Lyapunov exponents and Kolmogorov\u2013Sinai entropy, and passes all NIST SP 800-22 randomness tests. Leveraging the 2D-CCHM-EP, we further develop a hierarchical significance-aware multi-image encryption algorithm (MIEA-CPHS). The core of MIEA-CPHS is a hierarchical significance-aware encryption strategy that decomposes input images into high-, medium-, and low-significance layers, which undergo three, two, and one round of vector-level adaptive encryption operations. An SHA-384-based hash of the fused data dynamically generates a 48-bit adaptive control parameter, enhancing plaintext sensitivity and enabling integrity verification. Comprehensive security analyses confirm the exceptional performance of MIEA-CPHS: near-zero inter-pixel correlation (&lt;0.0016), near-ideal Shannon entropy (&gt;7.999), and superior plaintext sensitivity (NPCR \u224899.61%, UACI \u224833.46%). Remarkably, the hierarchical design and vectorized operations achieve an average encryption throughput of 87.6152 Mbps, striking an outstanding balance between high security and computational efficiency. This makes MIEA-CPHS highly suitable for modern high-throughput applications such as secure cloud storage and real-time media transmission.<\/jats:p>","DOI":"10.3390\/axioms14120901","type":"journal-article","created":{"date-parts":[[2025,12,8]],"date-time":"2025-12-08T16:41:41Z","timestamp":1765212101000},"page":"901","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":29,"title":["Two-Dimensional Coupling-Enhanced Cubic Hyperchaotic Map with Exponential Parameters: Construction, Analysis, and Application in Hierarchical Significance-Aware Multi-Image Encryption"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3023-5225","authenticated-orcid":false,"given":"Wei","family":"Feng","sequence":"first","affiliation":[{"name":"School of Mathematics and Computer Science, Panzhihua University, Panzhihua 617000, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0007-7224-6279","authenticated-orcid":false,"given":"Zixian","family":"Tang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Computer Science, Panzhihua University, Panzhihua 617000, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2538-8657","authenticated-orcid":false,"given":"Xiangyu","family":"Zhao","sequence":"additional","affiliation":[{"name":"School of Electrical and Information Engineering, Panzhihua University, Panzhihua 617000, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0009-7458-978X","authenticated-orcid":false,"given":"Zhentao","family":"Qin","sequence":"additional","affiliation":[{"name":"School of Mathematics and Computer Science, Panzhihua University, Panzhihua 617000, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0000-3916-3390","authenticated-orcid":false,"given":"Yao","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Mathematics and Computer Science, Panzhihua University, Panzhihua 617000, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0006-1505-6164","authenticated-orcid":false,"given":"Bo","family":"Cai","sequence":"additional","affiliation":[{"name":"School of Mathematics and Computer Science, Panzhihua University, Panzhihua 617000, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhengguo","family":"Zhu","sequence":"additional","affiliation":[{"name":"School of Mathematics and Computer Science, Panzhihua University, Panzhihua 617000, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1495-8303","authenticated-orcid":false,"given":"Kun","family":"Qian","sequence":"additional","affiliation":[{"name":"College of Physics and Electronics, Hunan Institute of Science and Technology, Yueyang 414006, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1178-4598","authenticated-orcid":false,"given":"Heping","family":"Wen","sequence":"additional","affiliation":[{"name":"School of Electronic Information, University of Electronic Science and Technology of China, Zhongshan Institute, Zhongshan 528402, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2025,12,6]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"123583","DOI":"10.1016\/j.eswa.2024.123583","article-title":"Cross-channel color image encryption through 2D hyperchaotic hybrid map of optimization test functions","volume":"249","author":"Toktas","year":"2024","journal-title":"Expert Syst. Appl."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Zhou, A., Yang, C., Yi, C., and Fan, H. (2025). New \u03bc-Synchronization Criteria for Nonlinear Drive\u2013Response Complex Networks with Uncertain Inner Couplings and Variable Delays of Unknown Bounds. Axioms, 14.","DOI":"10.3390\/axioms14030161"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Feng, W., Zhang, K., Zhang, J., Zhao, X., Chen, Y., Cai, B., Zhu, Z., Wen, H., and Ye, C. (2025). Integrating Fractional-Order Hopfield Neural Network with Differentiated Encryption: Achieving High-Performance Privacy Protection for Medical Images. Fractal Fract., 9.","DOI":"10.3390\/fractalfract9070426"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Rasouli, M., Zare, A., Yaghoubi, H., and Alizadehsani, R. (2023). Designing a Secure Mechanism for Image Transferring System Based on Uncertain Fractional Order Chaotic Systems and NLFPID Sliding Mode Controller. Axioms, 12.","DOI":"10.3390\/axioms12090828"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"125854","DOI":"10.1016\/j.eswa.2024.125854","article-title":"Secure medical image encryption scheme for Healthcare IoT using novel hyperchaotic map and DNA cubes","volume":"264","author":"Lai","year":"2025","journal-title":"Expert Syst. Appl."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Romero-Arellano, A., Moya-Albor, E., Brieva, J., Cruz-Aceves, I., Avina-Cervantes, J.G., Hernandez-Gonzalez, M.A., and Lopez-Montero, L.M. (2021). Image Encryption and Decryption System through a Hybrid Approach Using the Jigsaw Transform and Langton\u2019s Ant Applied to Retinal Fundus Images. Axioms, 10.","DOI":"10.3390\/axioms10030215"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Yu, F., Zhang, S., Su, D., Wu, Y., Gracia, Y.M., and Yin, H. (2025). Dynamic analysis and implementation of FPGA for a new 4D fractional-order memristive Hopfield neural network. Fractal Fract., 9.","DOI":"10.3390\/fractalfract9020115"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"114800","DOI":"10.1016\/j.chaos.2024.114800","article-title":"A joint image encryption based on a memristive Rulkov neuron with controllable multistability and compressive sensing","volume":"182","author":"Li","year":"2024","journal-title":"Chaos Solitons Fractals"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Yu, F., Gracia, Y.M., Guo, R., Ying, Z., Xu, J., Yao, W., Jin, J., and Lin, H. (2025). Dynamic Analysis and Application of 6D Multistable Memristive Chaotic System with Wide Range of Hyperchaotic States. Axioms, 14.","DOI":"10.3390\/axioms14080638"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1016\/j.matcom.2022.07.030","article-title":"A cluster of 1D quadratic chaotic map and its applications in image encryption","volume":"204","author":"Liu","year":"2023","journal-title":"Math. Comput. Simul."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"115135","DOI":"10.1016\/j.chaos.2024.115135","article-title":"A variable-order fractional memristor neural network: Secure image encryption and synchronization via a smooth and robust control approach","volume":"186","author":"Mesdoui","year":"2024","journal-title":"Chaos Solitons Fractals"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"7277","DOI":"10.1007\/s11071-024-10480-7","article-title":"A robust image encryption technique based on an improved fractional order chaotic map","volume":"113","author":"Jackson","year":"2025","journal-title":"Nonlinear Dyn."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"120931","DOI":"10.1016\/j.eswa.2023.120931","article-title":"Visually semantic-preserving and people-oriented color image encryption based on cross-plane thumbnail preservation","volume":"233","author":"An","year":"2023","journal-title":"Expert Syst. Appl."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"25559","DOI":"10.1109\/JIOT.2025.3558963","article-title":"Discrete Memristive Delay Feedback Rulkov Neuron Model: Chaotic Dynamics, Hardware Implementation, and Application in Secure Communication","volume":"12","author":"Deng","year":"2025","journal-title":"IEEE Internet Things J."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"2450170","DOI":"10.1142\/S0218127424501700","article-title":"An image encryption algorithm based on tabu search and hyperchaos","volume":"34","author":"Ma","year":"2024","journal-title":"Int. J. Bifurc. Chaos"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"300","DOI":"10.1109\/TCSI.2024.3439869","article-title":"Memristive Tabu Learning Neuron Generated Multi-Wing Attractor with FPGA Implementation and Application in Encryption","volume":"72","author":"Deng","year":"2025","journal-title":"IEEE Trans. Circuits Syst. I Regul. Pap."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"110717","DOI":"10.1016\/j.isci.2024.110717","article-title":"Image encryption hiding algorithm based on digital time-varying delay chaos model and compression sensing technique","volume":"27","author":"Jin","year":"2024","journal-title":"iScience"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"3926","DOI":"10.1109\/TCYB.2025.3565333","article-title":"Discrete Memristive Conservative Chaotic Map: Dynamics, Hardware Implementation, and Application in Secure Communication","volume":"55","author":"Deng","year":"2025","journal-title":"IEEE Trans. Cybern."},{"key":"ref_19","first-page":"2479","article-title":"Two-Dimensional Cosine\u2013Sine Interleaved Chaotic System for Secure Communication","volume":"71","author":"Tang","year":"2024","journal-title":"IEEE Trans. Circuits Syst. II Express Briefs"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1320401","DOI":"10.1007\/s11431-024-2678-7","article-title":"A family of image encryption schemes based on hyperchaotic system and cellular automata neighborhood","volume":"68","author":"Lai","year":"2025","journal-title":"Sci. China Technol. Sci."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Sajid, M., Chaudhary, H., and Kaushik, S. (2023). Chaos Controllability in Non-Identical Complex Fractional Order Chaotic Systems via Active Complex Synchronization Technique. Axioms, 12.","DOI":"10.3390\/axioms12060530"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Li, Y.M., Deng, Y., Jiang, M., and Wei, D. (2024). Fast Encryption Algorithm Based on Chaotic System and Cyclic Shift in Integer Wavelet Domain. Fractal Fract., 8.","DOI":"10.3390\/fractalfract8020075"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"10485","DOI":"10.1007\/s11071-024-09580-1","article-title":"A novel adaptive image privacy protection method based on Latin square","volume":"112","author":"Chen","year":"2024","journal-title":"Nonlinear Dyn."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"31","DOI":"10.51537\/chaos.1500547","article-title":"Chaotic Encryption Algorithm Based on Gingerbreadman Map with Adaptive Symmetry","volume":"7","author":"Fedoseev","year":"2024","journal-title":"Chaos Theory Appl."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"50","DOI":"10.69882\/adba.cs.2025074","article-title":"True random number generator design with a fractional order sprott b chaotic system","volume":"2","author":"Hosbas","year":"2025","journal-title":"ADBA Comput. Sci."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"53","DOI":"10.69882\/adba.cem.2025074","article-title":"A Chaos-Based Encryption Scheme for Secure Medical X-ray Images","volume":"2","author":"Kaya","year":"2025","journal-title":"Comput. Electron. Med."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"14719","DOI":"10.1007\/s11071-024-09816-0","article-title":"Cryptanalysis of substitution-permutation network based image encryption schemes: A systematic review","volume":"112","author":"Dhall","year":"2024","journal-title":"Nonlinear Dyn."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Zhang, C., Chen, J., and Chen, D. (2022). Cryptanalysis of an Image Encryption Algorithm Based on a 2D Hyperchaotic Map. Entropy, 24.","DOI":"10.3390\/e24111551"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1109\/MMUL.2024.3484414","article-title":"Cryptanalyzing an Image Encryption Algorithm Underpinned by 3D-BCNN","volume":"31","author":"You","year":"2024","journal-title":"IEEE Multimed."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"103424","DOI":"10.1016\/j.jvcir.2021.103424","article-title":"Security Measurement of a Medical Image Communication Scheme based on Chaos and DNA","volume":"83","author":"Chen","year":"2022","journal-title":"J. Vis. Commun. Image Represent."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"145459","DOI":"10.1109\/ACCESS.2021.3123571","article-title":"Cryptanalysis and Improvement of the Image Encryption Scheme Based on Feistel Network and Dynamic DNA Encoding","volume":"9","author":"Feng","year":"2021","journal-title":"IEEE Access"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"12584","DOI":"10.1109\/ACCESS.2019.2893760","article-title":"Cryptanalysis and improvement of the image encryption scheme based on 2D logistic-adjusted-sine map","volume":"7","author":"Feng","year":"2019","journal-title":"IEEE Access"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"112628","DOI":"10.1016\/j.chaos.2022.112628","article-title":"PixAdapt: A novel approach to adaptive image encryption","volume":"164","author":"Tuli","year":"2022","journal-title":"Chaos Solitons Fractals"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"112586","DOI":"10.1016\/j.chaos.2022.112586","article-title":"Cross-plane multi-image encryption using chaos and blurred pixels","volume":"164","author":"Wang","year":"2022","journal-title":"Chaos Solitons Fractals"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"59313","DOI":"10.1109\/ACCESS.2021.3070350","article-title":"2D-SCMCI Hyperchaotic Map for Image Encryption Algorithm","volume":"9","author":"Sun","year":"2021","journal-title":"IEEE Access"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"2705","DOI":"10.1007\/s11071-022-07335-4","article-title":"Remote sensing image compression and encryption based on block compressive sensing and 2D-LCCCM","volume":"108","author":"Nan","year":"2022","journal-title":"Nonlinear Dyn."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"108489","DOI":"10.1016\/j.sigpro.2022.108489","article-title":"A stable meaningful image encryption scheme using the newly-designed 2D discrete fractional-order chaotic map and Bayesian compressive sensing","volume":"195","author":"Zhu","year":"2022","journal-title":"Signal Process."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"4402","DOI":"10.1109\/TSMC.2021.3096967","article-title":"Two-Dimensional Parametric Polynomial Chaotic System","volume":"52","author":"Hua","year":"2022","journal-title":"IEEE Trans. Syst. Man, Cybern. Syst."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"118845","DOI":"10.1016\/j.eswa.2022.118845","article-title":"A novel pixel-split image encryption scheme based on 2D Salomon map","volume":"213","author":"Lai","year":"2023","journal-title":"Expert Syst. Appl."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"1063","DOI":"10.1016\/j.ins.2020.09.032","article-title":"Cross-plane colour image encryption using a two-dimensional logistic tent modular map","volume":"546","author":"Hua","year":"2021","journal-title":"Inf. Sci."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"9603","DOI":"10.1007\/s11071-024-09530-x","article-title":"An internal perturbation method to counteract the dynamical degradation of digital chaotic maps and its application","volume":"112","author":"Li","year":"2024","journal-title":"Nonlinear Dyn."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"176057","DOI":"10.1109\/ACCESS.2024.3462807","article-title":"Leveraging Finite-Precision Errors in Chaotic Systems for Enhanced Image Encryption","volume":"12","author":"Aldosary","year":"2024","journal-title":"IEEE Access"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1016\/j.chaos.2019.03.026","article-title":"Image encryption using finite-precision error","volume":"123","author":"Nardo","year":"2019","journal-title":"Chaos Solitons Fractals"},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"Dinu, A., and Frunzete, M. (2021, January 15\u201316). The Lorenz chaotic system, statistical independence and sampling frequency. Proceedings of the 2021 International Symposium on Signals, Circuits and Systems (ISSCS), Iasi, Romania.","DOI":"10.1109\/ISSCS52333.2021.9497431"},{"key":"ref_45","doi-asserted-by":"crossref","unstructured":"Macovei, C., Vaduva, A., Vlad, A., and Zamfir, M. (2019, January 11\u201312). A mean test on the autocorrelation function of a chaotic signal aiming to support the statistical independence sampling distance. Proceedings of the 2019 International Symposium on Signals, Circuits and Systems (ISSCS), Iasi, Romania.","DOI":"10.1109\/ISSCS.2019.8801778"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"28","DOI":"10.69882\/adba.chf.2025071","article-title":"Attack-Resistant Chaotic Communication System in Non-ideal Physical Channel","volume":"2","author":"Karimov","year":"2025","journal-title":"Chaos Fractals"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1007\/s11071-018-4056-x","article-title":"Brief review on application of nonlinear dynamics in image encryption","volume":"92","year":"2018","journal-title":"Nonlinear Dyn."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"121090","DOI":"10.1016\/j.eswa.2023.121090","article-title":"Mutil-medical image encryption by a new spatiotemporal chaos model and DNA new computing for information security","volume":"235","author":"Liu","year":"2024","journal-title":"Expert Systems with Applications"},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"113032","DOI":"10.1016\/j.chaos.2022.113032","article-title":"Design of two dimensional hyperchaotic system through optimization benchmark function","volume":"167","author":"Erkan","year":"2023","journal-title":"Chaos Solitons Fractals"},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"2591","DOI":"10.1103\/PhysRevA.28.2591","article-title":"Estimation of the Kolmogorov entropy from a chaotic signal","volume":"28","author":"Grassberger","year":"1983","journal-title":"Phys. Rev. A"},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"114361","DOI":"10.1016\/j.chaos.2023.114361","article-title":"A comprehensive survey on image encryption: Taxonomy, challenges, and future directions","volume":"178","author":"SaberiKamarposhti","year":"2024","journal-title":"Chaos Solitons Fractals"},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"4564","DOI":"10.1109\/TCAD.2025.3567878","article-title":"Bursting Firings in Memristive Hopfield Neural Network with Image Encryption and Hardware Implementation","volume":"44","author":"Yu","year":"2025","journal-title":"IEEE Trans. -Comput.-Aided Des. Integr. Circuits Syst."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"3829","DOI":"10.1007\/s11071-024-10403-6","article-title":"Quantum image encryption algorithm based on 3D-BNM chaotic map","volume":"113","author":"Verma","year":"2025","journal-title":"Nonlinear Dyn."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"2129","DOI":"10.1142\/S0218127406015970","article-title":"Some basic cryptographic requirements for chaos-based cryptosystems","volume":"16","author":"Alvarez","year":"2006","journal-title":"Int. J. Bifurc. Chaos"},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"102475","DOI":"10.1016\/j.vlsi.2025.102475","article-title":"Dynamical analysis, hardware implementation, and image encryption application of new 4D discrete hyperchaotic maps based on parallel and cascade memristors","volume":"104","author":"Yu","year":"2025","journal-title":"Integration"},{"key":"ref_56","first-page":"102844","article-title":"A novel image encryption scheme based on non-adjacent parallelable permutation and dynamic DNA-level two-way diffusion","volume":"61","author":"Li","year":"2021","journal-title":"J. Inf. Secur. Appl."},{"key":"ref_57","doi-asserted-by":"crossref","unstructured":"Zhang, B., and Liu, L. (2023). Chaos-Based Image Encryption: Review, Application, and Challenges. Mathematics, 11.","DOI":"10.3390\/math11112585"},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"2550146","DOI":"10.1142\/S0218127425501469","article-title":"Influence of Memristive Activated Gradient on Chaotic Dynamics in Discrete Neural Networks","volume":"35","author":"Yu","year":"2025","journal-title":"Int. J. Bifurc. Chaos"},{"key":"ref_59","doi-asserted-by":"crossref","unstructured":"He, S., Yu, F., Guo, R., Zheng, M., Tang, T., Jin, J., and Wang, C. (2025). Dynamic Analysis and FPGA Implementation of a Fractional-Order Memristive Hopfield Neural Network with Hidden Chaotic Dual-Wing Attractors. Fractal Fract., 9.","DOI":"10.3390\/fractalfract9090561"},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"114440","DOI":"10.1016\/j.chaos.2023.114440","article-title":"Dynamics analysis, synchronization and FPGA implementation of multiscroll Hopfield neural networks with non-polynomial memristor","volume":"179","author":"Yu","year":"2024","journal-title":"Chaos Solitons Fractals"},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1109\/MMUL.2024.3356494","article-title":"Cryptanalyzing an Image Encryption Algorithm Underpinned by 2-D Lag-Complex Logistic Map","volume":"31","author":"Li","year":"2024","journal-title":"IEEE Multimed."},{"key":"ref_62","first-page":"31","article-title":"NPCR and UACI randomness tests for image encryption","volume":"1","author":"Wu","year":"2011","journal-title":"Cyber J. Multidiscip. J. Sci. Technol. J. Sel. Areas Telecommun. (JSAT)"},{"key":"ref_63","first-page":"103785","article-title":"PSDCLS: Parallel simultaneous diffusion\u2013confusion image cryptosystem based on Latin square","volume":"83","year":"2024","journal-title":"J. Inf. Secur. Appl."},{"key":"ref_64","doi-asserted-by":"crossref","unstructured":"Qian, K., Xiao, Y., Wei, Y., Liu, D., Wang, Q., and Feng, W. (2023). A robust memristor-enhanced polynomial hyper-chaotic map and its multi-channel image encryption application. Micromachines, 14.","DOI":"10.3390\/mi14112090"},{"key":"ref_65","doi-asserted-by":"crossref","unstructured":"Li, H., Yu, S., Feng, W., Chen, Y., Zhang, J., Qin, Z., Zhu, Z., and Wozniak, M. (2023). Exploiting Dynamic Vector-Level Operations and a 2D-Enhanced Logistic Modular Map for Efficient Chaotic Image Encryption. Entropy, 25.","DOI":"10.3390\/e25081147"},{"key":"ref_66","doi-asserted-by":"crossref","unstructured":"Feng, W., Zhao, X., Zhang, J., Qin, Z., Zhang, J., and He, Y. (2022). Image Encryption Algorithm Based on Plane-Level Image Filtering and Discrete Logarithmic Transform. Mathematics, 10.","DOI":"10.3390\/math10152751"}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/14\/12\/901\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,12,10]],"date-time":"2025-12-10T05:22:57Z","timestamp":1765344177000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/14\/12\/901"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,12,6]]},"references-count":66,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2025,12]]}},"alternative-id":["axioms14120901"],"URL":"https:\/\/doi.org\/10.3390\/axioms14120901","relation":{},"ISSN":["2075-1680"],"issn-type":[{"value":"2075-1680","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,12,6]]}}}