A novel visually meaningful image encryption scheme based on authentication, RSA cryptosystem, and multidimensional chaotic maps

Real-time fire localization in urban environments remains a significant challenge due to sparse IoT sensor deployments, measurement uncertainties, and the computational uses of AI-based estimation techniques. To address these limitations, this paper proposes a Chaotic Interval-Based Multi-Objective Honey Badger Algorithm (CI-MOHBA) designed to improve the accuracy and reliability of fire source localization under uncertain and limited sensor data. The approach formulates localization as a multi-objective optimization problem that simultaneously minimizes source estimation error, false alarm rates, and computation time. CI-MOHBA integrates a new chaotic map to improve global search capability and interval arithmetic to effectively manage sensor uncertainty within sparse measurement environments. Experimental evaluation of the proposed chaotic map, supported by entropy convergence analysis and Lyapunov exponent verification, demonstrates the stability and robustness of the proposed technique. Results indicate that CI-MOHBA achieves an average localization error of 0.73 m and a false alarm rate of 8.2%, while maintaining high computational efficiency. Results show that the proposed algorithm is well-suited for real-time fire localization in urban IoT-based monitoring systems.

Due to their complexity and nonlinearity, metaheuristic algorithms have become the standard in problem solving for problems that cannot be solved by standard computational solutions. However, the global performance of these algorithms is strongly linked to the population structuring and the mechanism of replacing the worst solutions within the population. In this paper, an Adaptive Artificial Hummingbird Algorithm (AAHA), a new version of the basic AHA, is introduced and designed to enhance performance by studying the impacts of different population initialization methods within a broad and continual migration form. For the initialization phase, four methods—the Gaussian chaotic map, the Sinus chaotic map, opposite-based learning (OBL), and diagonal uniform distribution (DUD)—are proposed as an alternative to the random population initialization method. A new strategy is proposed as a replacement for the worst solution in the migration phase. The new strategy uses the best solution as an alternative to the worst solution with simple and effective local search. The proposed strategy stimulates exploitation and exploration when using the best solution and local search, respectively. The proposed AAHA is tested through various benchmark functions with different characteristics under many statistical indices and tests. Additionally, the AAHA results are benchmarked against those of other optimization algorithms to assess their effectiveness. The proposed AAHA outperformed alternatives in terms of both speed and reliability. DUD-based initialization enabled the fastest convergence and optimal solutions. These findings underscore the significance of initialization in metaheuristics and highlight the efficacy of the AAHA for complex continuous optimization problems.

A novel two-dimensional Logistic–Chebyshev–Sine hybrid chaotic map for secure color image encryption

Inference of hidden common driver dynamics by anisotropic self-organizing neural networks.

In the service-oriented modern society, logistics enterprises focusing solely on cost minimization can no longer meet market demands, as customers place greater emphasis on timely delivery and service satisfaction. Therefore, this paper constructs a multi-objective optimization model that simultaneously minimizes distribution costs and hierarchical customer delivery duration. From the perspective of symmetry, the two objectives form a symmetric complementary system, which reflects the mutually restrictive and trade-off relationship between the two objectives, thereby facilitating the achievement of a balance between enterprise benefits and customer satisfaction. An improved multi-objective grey wolf optimizer (IMOGWO) is proposed to solve the model, incorporating a chaotic mapping initialization mechanism, a cosine nonlinear convergence factor, and a learning factor-based hunting mechanism to enhance global optimization capability. The algorithm’s effectiveness is validated through comparisons on benchmark cases. Applied to a Zhengzhou food company, the solution improved distribution efficiency while prioritizing key clients, thereby enhancing service levels and stabilizing important customer relationships, providing a practical reference for logistics enterprises to increase revenue and undergo digital transformation.

HighlightsIn lithium battery charge-discharge cycle experiments, four sets of indirect health factors were extracted as predictive features: constant current charging time (CCCT), constant voltage rise time, and time integral of the current curve during the constant voltage (CV) charging phase; and constant voltage decay time during the discharging phase.This paper proposes an improved ALA optimization algorithm that enhances population diversity by incorporating the Tent chaotic map. Combined with the mutation and crossover operations from the differential evolution (DE) algorithm, it improves local search accuracy and convergence speed to prevent getting stuck in local optima.This paper proposes a hybrid CNN-LSTM neural network model that combines the strengths of both architectures: CNNs extract spatial features from data and uncover deep relationships, while LSTMs capture long-term dependencies in time series. By connecting them in series, the model enhances predictive performance.Through comparative experiments on publicly available datasets from NASA and CALCE, this study demonstrates that the proposed method achieves a root mean square error (RMSE) of less than 1.8% in lithium-ion battery remaining useful life (RUL) prediction, indicating high predictive accuracy.

In this paper, we first prove (Theorem 1) that any two inputs producing the same output in a symmetric pair of discrete skew tent maps always have the same parity, meaning that they are either both even or both odd. Building on this property, we then propose (Definition 1) a new discrete chaotic map and prove that (Theorem 2) the proposed map is a bijection for all control parameters. We further prove that (Theorem 3) the discrete Lyapunov exponent (dLE) of the proposed map is not only positive but also approaches the maximum value among all permutation maps over the integers as m gets larger. In other words, (Corollary 1) the proposed map asymptotically achieves the highest possible chaotic divergence among the permutation maps over the integers . To provide some further evidence that the proposed map is highly chaotic, we present at the end some results from the numerical experiments. We calculate the approximation and permutation entropy of the output integer sequences. We also show the NIST SP800-22 tests results and correlation properties of some derived binary sequences.

To overcome the limitations of single models in addressing complex, nonlinear problems in predicting rock shear strength parameters and the hyperparameter random selection problem, this study constructed a novel prediction framework for rock shear strength parameters. First, the light gradient boosting machine (LightGBM), extreme gradient boosting (XGBoost), categorical boosting (CatBoost), and random forest (RF) algorithms are employed as the base-learners for the ensemble model, with XGBoost serving as the meta-learner to build a stacking ensemble model. On the basis of the sparrow search algorithm (SSA), tent chaotic mapping is used to initialize the sparrow population, the Cauchy‒Gaussian hybrid mutation mechanism is used to dynamically select the probability control mutation type, the dynamic adaptive weight is used to adjust the balance between global exploration and local development, and Levy flight is used to help the sparrow population individuals jump out of the local optimum to construct the chaos-improved sparrow search algorithm (CISSA) to optimize the hyperparameters of the stacking model. Second, based on the 199 datasets of different rock types, the model was trained via fivefold cross-validation and evaluated based on the coefficient of determination (R²), root mean square error (RMSE) and mean absolute error (MAE). Concurrently, the Shapley additive explanations (SHAP) method was employed to analyse the degree of contribution of each predictive index. The results demonstrate that the CISSA-Stacking model achieves R² values of 0.9936 and 0.9744 for c and φ, respectively, with corresponding RMSE of 0.4303 and 0.7635 and MAE of 0.2161 and 0.5867, indicating significantly superior overall performance compared with benchmark models. SHAP interpretability analysis revealed that the importance rankings for c are Vp, UCS, BTS, and ρ, whereas those for φ are ρ, UCS, Vp, and BTS. Finally, intelligent prediction software based on the CISSA-Stacking model was developed. The software is simple in operation, intuitive in results and excellent in performance, enables rapid and accurate prediction of c and φ through manual input of the Vp, ρ, UCS, and BTS indices or by importing tabular data containing these four indices. The engineering application further confirmed the accuracy and practical utility of both the model and the software, providing a new efficient method for engineers to quickly and accurately estimate rock shear strength parameters.Supplementary InformationThe online version contains supplementary material available at 10.1038/s41598-025-32687-3.

Abstract In the era of intelligent healthcare, medical images play a crucial role in remote diagnosis, disease detection, cloud storage, and data sharing. However, they are vulnerable to security threats such as data tampering, copyright disputes, and privacy breaches. Traditional digital watermarking algorithms struggle to balance imperceptibility and robustness, making them insufficient to meet the security requirements of medical image protection. Motivated by these challenges, this paper proposes an efficient, robust, secure digital watermarking scheme for medical images. The proposed method integrates Dual-Tree Complex Wavelet Transform (DTCWT), Discrete Cosine Transform (DCT), and Singular Value Decomposition (SVD) to extract image features. Particle Swarm Optimization (PSO) is then employed to adaptively adjust the watermark embedding parameters, enhancing imperceptibility and robustness. Moreover, Henon chaotic mapping is introduced to generate pseudo-random sequences for watermark encryption, further enhancing security. Experimental results show that the proposed method achieves a PSNR of 34.59 dB, ensuring good imperceptibility. Under various attacks, the extracted watermark maintains high robustness, with an average NC of 0.99 under Gaussian low-pass filtering (5 $$\times $$ × 5), 0.99 under JPEG compression (QF = 10), 0.97 under Gaussian noise, and 0.98 under rotation attacks (15 $$^{\circ }$$ ∘ ). Research shows that this method can effectively improve the secure storage and transmission capabilities of medical images, providing strong support for the security of medical image data in intelligent medical environments.

To address the path-planning challenge for unmanned aerial vehicles (UAVs) in complex environments, this study presents an improved pelican optimization algorithm enhanced with multiple strategies (MIPOA). The proposed method introduces four main improvements: (1) using chaotic mapping to spread the initial search points more evenly, thereby increasing population variety; (2) incorporating a random Lévy-flight strategy to improve the exploration of the search space; (3) integrating a differential evolution approach based on Cauchy mutation to strengthen individual diversity and overall optimization ability; and (4) adopting an adaptive disturbance factor to speed up convergence and fine-tune solutions. To evaluate MIPOA, comparative tests were carried out against classical and modern intelligent algorithms using the CEC2017 and CEC2022 benchmark sets, along with a custom UAV environmental model. Results show that MIPOA converges faster and achieves more accurate solutions than the original pelican optimization algorithm (POA). On CEC2017 in 30-, 50-, and 100-dimensional cases, MIPOA attained the best average ranks of 1.57, 2.37, and 2.90, respectively, and achieved the top results on 26, 21, and 19 test functions, outperforming both POA and other advanced algorithms. For CEC2022 (20 dimensions), MIPOA obtained the highest Friedman average rank of 1.42, demonstrating its effectiveness in complex UAV path-planning tasks. The method enables the generation of faster, shorter, safer, and collision-free flight paths for UAVs, underscoring the robustness and wide applicability of MIPOA in real-world UAV path-planning scenarios.

IntroductionGinseng, as a precious medicinal plant, requires precise classification of its seeds, which directly impacts production processes and the stability of herbal quality. Furthermore, this classification plays a critical role in advancing ginseng breeding and the modernization of the industry. Current research indicates that systematic automated precision classification technologies for ginseng seeds remain underdeveloped, necessitating breakthroughs in technical bottlenecks.MethodsThis study innovatively proposes a smart classification method based on multimodal data fusion. It employs recursive feature elimination (RFE) to select morphological features from images, followed by competitive adaptive reweighted sampling (CARS) to extract spectral bands from hyperspectral data within the 350~2500 nm range. Morphological and spectral features are then integrated to construct a random forest (RF) classification model optimized using an enhanced, red-billed blue magpie optimization (RBMO) algorithm. To address the RBMO algorithm’s tendency to converge to local optima, the hybrid optimization framework is constructed by integrating three mechanisms: the improved Circle chaotic map, the golden sine search strategy, and the adaptive simulated annealing perturbation mechanism.ResultsExperimental results demonstrate that the proposed model outperforms the baseline model RF, achieving 4.69%、4.79%、4.69 and 4.74% improvements in classification accuracy, precision, recall, and F1-score on test datasets, respectively.DiscussionThe established multimodal data fusion classification system not only provides theoretical and technical foundations for industrial-scale ginseng seed classification but also offers a transferable intelligent decision-making paradigm for non-destructive testing in traditional Chinese medicine.

In today’s technological age, ensuring the security of data transmitted across unsecured and open channels from one destination to another is an important issue. Strong techniques to protect images during transmission and storage are becoming more and more critical as the digital age advances. The main focus of the presented work is to enhance the protection of digital image data from unapproved sources over these open networks. It is possible that conventional encryption methods may not provide enough protection against contemporary cryptographic attacks. Thus, this study proposes an encryption method that combines the cryptographic properties of S-boxes and Baker’s map together with the chaotic dynamics of the discrete compound chaotic (DCC) map. During encryption, the level of confusion and diffusion is well maintained. The confusion is achieved by employing the chaotic sequence obtained from the DCC map and through the use of Baker’s map. The S-box and a DCC map are utilized for diffusion purposes. Further, to achieve a better scrambling effect, Baker’s map is implemented multiple times (n_b k times). The innovation of the proposed scheme lies in its novel integration of the discrete compound chaotic map (DCC map) with the cryptographic properties of S-boxes and Baker’s map, achieving an enhanced level of diffusion and confusion in encrypted images. Further, the hashSHA−256 utilized to derive initial conditions ensures the dependency of the proposed scheme on the original image, offering a robust defence against differential attacks and providing a more secure framework than traditional encryption techniques. The strong proposed scheme’s capability was demonstrated via the following key results: average entropy value of 7.9971, low correlation coefficients in the encrypted images, high MSE values, average encryption time of 0.2599 seconds, UACI of 33.4765, NPCR of 99.6113, successful decryption without data loss. These statistical and simulation analysis results confirm the scheme’s efficiency, high security, and robustness.

To address the limited defect-detection capability of existing performance testing methods for switching power supplies under varying operating conditions, this paper proposes a defect identification approach based on an enhanced Dung Beetle Optimizer. The algorithm integrates multi-strategy improvements—including piecewise chaotic mapping, Lévy flight perturbation, hybrid sine–cosine updating, and an alert sparrow mechanism—to refine the initial population generation, position update rules, and late-stage exploration. These enhancements strengthen its spatial search ability and computational performance. The experimental results show that the method accurately identifies the predefined defect intervals with a precision of 94.79%, covering 91.3% of the operating conditions. Comparisons with existing mainstream methods confirm the superior performance, effectiveness, and feasibility of the proposed method.

In view of the complex flight scenarios existing in UAV path planning, it is necessary to model the UAV flight trajectory. When constructing the model, cost factors such as the minimum flight path of the UAV, obstacle avoidance, flight altitude, and trajectory smoothness are fully taken into account. To reduce the overall flight cost, a novel secretary bird optimization algorithm (NSBOA) is proposed in this paper, which effectively addresses the limitations of traditional algorithms in handling UAV path planning tasks. First of all, the Singer chaotic map is adopted to initialize the population instead of the conventional random initialization method. This improvement increases population diversity, enables the initial population to be more evenly distributed in the search space, and further accelerates the algorithm’s convergence speed in the subsequent optimization process. Second, an adaptive adjustment mechanism is integrated with the Levy flight mechanism to optimize the core logic of the algorithm, with a specific focus on improving the exploitation stage. By introducing appropriate perturbations near the current optimal solution, the algorithm is guided to jump out of local optimal traps, thereby enhancing its global optimization capability and avoiding premature convergence caused by insufficient population diversity. By comparing and analyzing NSBOA with SBOA, WOA, PSO, POA, NGO, and HHO algorithms in 12 common evaluation functions and CEC 2017 test functions, and applying NSBOA to the UAV path optimization problem, the simulation results show the effectiveness and superiority of the proposed scheme.

Wind energy's stochasticity and volatility challenge grid stability and dispatch reliability. To overcome limitations of existing decomposition-based forecasting methods, this paper proposes an Improved Escape Algorithm (IESC) incorporating chaotic mapping to optimize the hyperparameters of Time-Varying Filter Empirical Mode Decomposition (TVF-EMD), effectively mitigating mode mixing and enhancing non-stationary wind signal separation. Departing from uniform modeling, we employ a frequency-adaptive strategy: XLSTM captures high-frequency volatility, LSTM models medium-frequency transitions, and ELM rapidly processes low-frequency trends. Evaluated on a large-scale dataset, IESC outperforms standard ESC, GWO, and DE by 6.2%, 11.3%, and 8.4%, respectively. The proposed hybrid model demonstrates superior robustness, achieving a 29.8% lower 1-step MAE (0.5109) and a 65.6% higher 15-step R² (0.7685) compared to XLSTM alone. Crucially, error growth (1-15 steps) is contained within 12% and R² degradation is 35% slower. These results confirm that the method significantly enhances forecasting precision and effectively bridges multi-step accuracy with real-time dispatch needs, ensuring dynamic grid-demand matching and improved operational stability.

Image security is vital in sectors such as healthcare, defence, finance, and personal data exchange, where breaches of image integrity can result in severe consequences. To address this challenge, we propose a novel image encryption framework. It combines a Fractal-Fibonacci diffusion process based on the Hilbert curve, recursive scrambling guided by chaotic sequences, and a new chaotic map entitled the Two Dimensional Cosine Power Sine Coupled Map (2D-CPSCM). These components enhance randomness and ensure maximum efficiency, resistance against cryptographic attacks. The proposed two-dimensional chaotic system exhibits positive Lyapunov exponents and superior statistical properties compared to traditional systems, as demonstrated by high sample entropy, permutation entropy, and Kolmogorov entropy, confirming its hyperchaotic behaviour. The encryption system has been evaluated using extensive simulations on benchmark images. The findings demonstrate strong key sensitivity, with an entropy of 7.9994, Number of Pixel Change Rate (NPCR) of 99.6%, Unified Average Changing Intensity (UACI) of 33.47%, and Number of Bit Change Rate (NBCR) of 50%. Additionally, Structural Similarity Index Metric (SSIM) and Visual Information Fidelity (VIF) values of 1 between input and decrypted images guarantee successful decryption, whereas low Peak Signal to Noise Ratio (PSNR), SSIM, and VIF between input and encrypted images reduce information leakage. The superior security, resilience, and robustness of the 2D-CPSCM based approach against statistical, noise, and cropping attacks highlights its potential for safe multimedia transmission and useful cryptographic applications.

Lightweight three-factor authentication protocol for 6G-enabled healthcare systems using Chebyshev chaotic maps and BioHashing

This paper presents the Circle-Mapping Transition and Weighted Red-Billed Blue Magpie Optimizer (CTWRBMO), designed to address significant challenges in 3D path planning for drones. Although the original Red-Billed Blue Magpie Optimizer (RBMO) algorithm features a simple structure, few parameters, and strong local search capability, making it well-suited for UAV path optimization, it suffers from insufficient population diversity, limited global search ability, and a tendency to fall into local optima in complex high-dimensional scenarios. To overcome these limitations, four enhancement strategies are introduced. Firstly, the Circle chaotic mapping strategy leverages the randomness and ergodicity of chaotic sequences to generate an initial population that is uniformly distributed. This enhancement improves population diversity from the beginning and provides a solid foundation for global optimization. Secondly, the ε parameter is dynamically adjusted to prioritize local refinement during the early stages of optimization. This adjustment enables rapid convergence toward potentially optimal areas. This parameter increases to enhance global search capabilities as the algorithm progresses, thereby broadening the optimization space and achieving a dynamic equilibrium. Additionally, a nonlinear dynamic weighting factor (wd) is incorporated into the position update formula. The algorithm’s ability to escape local optima is significantly improved by dynamically altering the weight ratio between historical optimal positions and the current position. Furthermore, an elite perturbation mechanism based on individual neighborhoods is implemented to generate candidate solutions using local information. This mechanism enhances the algorithm’s local exploration capabilities and improves the stability of preserving optimal solutions, supported by a greedy criterion for optimal retention. Experimental results show that the CTWRBMO algorithm significantly outperforms comparison algorithms in terms of optimization accuracy and convergence speed, demonstrating exceptional global optimization capabilities. Additional applications in UAV 3D path planning simulations evaluated paths based on length, threat avoidance efficiency, and smoothness. The results indicate that paths planned using CTWRBMO are shorter, safer, and smoother compared to those generated by the Harrier Hawks Optimization (HHO), African Vulture Optimization Algorithm (AVOA), Artificial Bee Colony (ABC) Algorithm, and the traditional Magpie Algorithm, effectively meeting practical engineering requirements for UAV 3D path planning.

To address the limitations of the standard Sparrow Search Algorithm (SSA) in complex optimization problems—such as insufficient convergence accuracy and susceptibility to local optima—this paper proposes a Composite Strategy Sparrow Search Algorithm (CSSA) for multidimensional optimization. The algorithm first employs chaotic mapping during initialization to enhance population diversity; second, it integrates coordinate axis pattern search to strengthen local exploitation capabilities; third, it applies intelligent crossover operations to promote effective information exchange among individuals; and finally, it introduces an adaptive vigilance mechanism to dynamically balance exploration and exploitation throughout the optimization process. Compared with seven state-of-the-art algorithms, CSSA demonstrates superior performance in both 30-dimensional low-dimensional and 100-dimensional high-dimensional test scenarios. It achieves optimal solutions in three real-world engineering applications: thermal management of electric vehicle battery packs, photovoltaic power system configuration, and data center cooling systems. Wilcoxon rank-sum tests further confirm the statistical significance of these improvements. Experimental results show that CSSA significantly outperforms mainstream optimization methods in terms of convergence accuracy and speed, demonstrating substantial theoretical value and practical engineering significance.