Search Results (124)

This study presents a novel two-dimensional hyperchaotic map, referred to as the 2D exponent-logarithm-sine chaotic map (2D-ELSCM), which is intricately designed through the interplay of exponential, logarithmic, and sine functions. To comprehensively evaluate the chaotic performance of the 2D-ELSCM, several critical metrics are employed, including the largest Lyapunov exponent (LLE), permutation entropy (PE), sample entropy (SE), Kolmogorov entropy (KE), and the results of the 0–1 test, which yield values of 8.3175, 0.9998, 1.9826, 2.1117, and 0.9970, respectively. Furthermore, the 2D-ELSCM successfully passes the NIST randomness tests, collectively confirming its exceptional randomness and complexity. Building upon this robust chaotic map, we develop a distinctive chaotic image encryption scheme that employs an improved Knuth-Durstenfeld shuffle (IKDS) to rearrange pixel positions, effectively disrupting the correlation between adjacent pixels. Complementing this, we introduce a dynamic diffusion mechanism that integrates DNA encoding with the Zigzag transform, thereby promoting global pixel diffusion and enhancing encryption security. The initial conditions of the chaotic map are generated from the SHA-512 hash of the plaintext image in conjunction with an external key, which not only expands the key space but also significantly improves key sensitivity. Simulation results demonstrate that the proposed encryption scheme achieves correlation coefficients approaching 0 in the encrypted test images, with an average NPCR of 99.6090% and UACI of 33.4707%. These findings indicate a strong resistance to various attacks and showcase excellent encryption quality, thereby underscoring the scheme’s potential for secure image transmission and storage. Full article

Continuous advancements in digital image transmission technology within network environments have heightened the necessity for secure, convenient, and well-suited image encryption systems. Base64 encoding possesses the ability to convert raw data into printable ASCII characters, facilitating excellent stability transmission across various communication protocols. In this paper, base64 encoding is first used in image encryption to pursue high application value in network transmission. First, a novel one-dimensional discrete chaotic system (1D-LSCM) with complex chaotic behavior is introduced and extensively tested. Second, a new multi-image encryption algorithm based on the proposed 1D-LSCM and base64 encoding is presented. Technically, three original grayscale images are constructed as a color image and encoded in base64 characters. To purse high plaintext sensitivity, the original image is input to the SHA-256 hash function and its output is used to influence the generated keystream employed in the permutation and diffusion process. After scramble and diffusion operations, the base64 ciphertext is obtained. Finally, test results derived from comprehensive tests prove that our proposed algorithm has remarkable security and encryption efficiency. Full article

Accurate short-term power load forecasting (STPLF) is critical for balancing electricity supply–demand and ensuring grid reliability. To address the challenges of fluctuating power loads and inaccurate predictions by conventional methods, this paper presents a novel hybrid framework combining Variational Mode Decomposition (VMD), Long Short-Term Memory (LSTM), and the Improved Sparrow Search Algorithm (ISSA). First, the power load series is decomposed into intrinsic mode functions (IMFs) via VMD, where the optimal decomposition order K is determined using permutation entropy (PE). Next, the decomposed IMFs and meteorological covariates are reconstructed into feature vectors, which are then input into the LSTM network for component-wise forecasting, and, finally, the prediction results of each component are reconstructed to obtain the final power load prediction result. The Improved Sparrow Search Algorithm (ISSA), which integrates piecewise chaotic mapping into population initialization to augment the global exploration capability, is employed to fine-tune LSTM hyperparameters, thereby enhancing the prediction precision. Finally, two case studies are conducted using Australian regional load data and Detu’an City historical load records. The experimental results indicate that the proposed model achieves reductions of 73.03% and 82.97% compared with the VMD-LSTM baseline, validating its superior predictive accuracy and cross-domain generalization capability. Full article

We prove a conjecture on the second minimal odd periodic orbits with respect to Sharkovski ordering for the continuous endomorphisms on the real line. A $(2k+1)$-periodic orbit $\{{\beta }_1<{\beta }_2<\cdots <{\beta }_{2k+1}\}$, ($k\ge 3$) is called second minimal for the map f, if $2k-1$ is a minimal period of ${f|}_{[{\beta }_1,{\beta }_{2k+1}]}$ in the Sharkovski ordering. Full classification of second minimal orbits is presented in terms of cyclic permutations and directed graphs of transitions. It is proved that second minimal odd orbits either have a Stefan-type structure like minimal odd orbits or one of the $4k-3$ types, each characterized with unique cyclic permutations and directed graphs of transitions with an accuracy up to the inverses. The new concept of second minimal orbits and its classification have an important application towards an understanding of the universal structure of the distribution of the periodic windows in the bifurcation diagram generated by the chaotic dynamics of nonlinear maps on the interval. Full article

The accurate prediction of incipient cavitation is of great significance for ensuring the stable operation of hydraulic turbines. Hydroacoustic signals contain essential information about the turbine’s operating state. Considering that traditional entropy methods are easily affected by environmental noise when the state pattern is chaotic, leading to the extracted cavitation features not being obvious, a Symbol Conditional Entropy (SCE) feature extraction method is proposed to classify the original variables according to different state patterns. The uncertainty is reduced, and the ability to extract fault information is improved, so more effective cavitation features can be extracted to describe the evolving trend of cavitation. The extracted cavitation features are used as indicators to predict incipient cavitation. In order to avoid missing critical information in the prediction process, an interval mean (IM) algorithm is proposed to determine the initial prediction point. The effectiveness of the proposed method is validated with hydroacoustic signals collected at the Harbin Institute of Large Electric Machinery. The root mean square error (RMSE), mean absolute error (MAE), and mean absolute percentage error (MAPE) of incipient cavitation prediction results decreased to 0.0018, 0.0015, and 1.59%, respectively. The RMSE, MAE, and MAPE of the proposed SCE decreased by 84.62%, 85.29%, and 87% compared with the Permutation Entropy (PE) method. The comparison results with different prediction algorithms show that the proposed SCE has excellent trend prediction performance and high precision. Full article

We propose using the ordinal pattern transition (OPT) entropy measured at sentinel central nodes as a potential predictor of explosive transitions to synchronization in networks of various dynamical systems with increasing complexity. Our results demonstrate that the OPT entropic measure surpasses traditional early warning signal (EWS) measures and could be valuable to the tools available for predicting critical transitions. In particular, we investigate networks of diffusively coupled phase oscillators and chaotic Rössler systems. As maps, we consider a neural network of Chialvo maps coupled in star and scale-free configurations. Furthermore, we apply this measure to time series data obtained from a network of electronic circuits operating in the chaotic regime. Full article

This study implements the permutation Jensen–Shannon distance as a metric for discerning ordinal patterns and similarities across multiple temporal scales in time series data. Initially, we present a numerically controlled analysis to validate the multiscale capabilities of this method. Subsequently, we apply our methodology to a complex photonic system, showcasing its practical utility in a real-world scenario. Our findings suggest that this approach is a powerful tool for identifying the precise temporal scales at which two distinct time series exhibit ordinal similarity. Given its robustness, we anticipate that this method could be widely applicable across various scientific disciplines, offering a new lens through which to analyze time series data. Full article

To enhance the performance of entropy algorithms in analyzing complex time series, generalized Gaussian distribution improved permutation entropy (GGDIPE) and its multiscale variant (MGGDIPE) are proposed in this paper. First, the generalized Gaussian distribution cumulative distribution function is employed for data normalization to enhance the algorithm’s applicability across time series with diverse distributions. The algorithm further processes the normalized data using improved permutation entropy, which maintains both the absolute magnitude and temporal correlations of the signals, overcoming the equal value issue found in traditional permutation entropy (PE). Simulation results indicate that GGDIPE is less sensitive to parameter variations, exhibits strong noise resistance, accurately reveals the dynamic behavior of chaotic systems, and operates significantly faster than PE. Real-world data analysis shows that MGGDIPE provides markedly better separability for RR interval signals, EEG signals, bearing fault signals, and underwater acoustic signals compared to multiscale PE (MPE) and multiscale dispersion entropy (MDE). Notably, in underwater target recognition tasks, MGGDIPE achieves a classification accuracy of 97.5% across four types of acoustic signals, substantially surpassing the performance of MDE (70.5%) and MPE (62.5%). Thus, the proposed method demonstrates exceptional capability in processing complex time series. Full article

The computer network has fundamentally transformed modern interactions, enabling the effortless transmission of multimedia data. However, the openness of these networks necessitates heightened attention to the security and confidentiality of multimedia content. Digital images, being a crucial component of multimedia communications, require robust protection measures, as their security has become a global concern. Traditional color image encryption/decryption algorithms, such as DES, IDEA, and AES, are unsuitable for image encryption due to the diverse storage formats of images, highlighting the urgent need for innovative encryption techniques. Chaos-based cryptosystems have emerged as a prominent research focus due to their properties of randomness, high sensitivity to initial conditions, and unpredictability. These algorithms typically operate in two phases: shuffling and replacement. During the shuffling phase, the positions of the pixels are altered using chaotic sequences or matrix transformations, which are simple to implement and enhance encryption. However, since only the pixel positions are modified and not the pixel values, the encrypted image’s histogram remains identical to the original, making it vulnerable to statistical attacks. In the replacement phase, chaotic sequences alter the pixel values. This research introduces a novel encryption technique for color images (RGB type) based on DNA subsequence operations to secure these images, which often contain critical information, from potential cyber-attacks. The suggested method includes two main components: a high-speed permutation process and adaptive diffusion. When implemented in the MATLAB software environment, the approach yielded promising results, such as NPCR values exceeding 98.9% and UACI values at around 32.9%, demonstrating its effectiveness in key cryptographic parameters. Security analyses, including histograms and Chi-square tests, were initially conducted, with passing Chi-square test outcomes for all channels; the correlation coefficient between adjacent pixels was also calculated. Additionally, entropy values were computed, achieving a minimum entropy of 7.0, indicating a high level of randomness. The method was tested on specific images, such as all-black and all-white images, and evaluated for resistance to noise and occlusion attacks. Finally, a comparison of the proposed algorithm’s NPCR and UAC values with those of existing methods demonstrated its superior performance and suitability. Full article

This paper presents a hardware-based audio encryption system using a 2D chaotic map and dynamic S-box design implemented on an Artix-7 FPGA platform. Three distinct chaotic maps—logistic–fraction (2D-LF), logistic–sine (2D-LS), and fraction–sine (2D-FS)—were investigated and implemented on an FPGA. The 2D-LF map was employed in the encryption system for its throughput and power efficiency performance. The proposed encryption system benefits from the randomness of chaotic sequences for block permutation and S-box substitution to enhance the diffusion and confusion properties of the encrypted speech signal. The system’s encryption strength is validated through performance evaluations, using the mean squared error (MSE), signal-to-noise ratio (SNR), correlation coefficients, and NIST randomness tests, which confirm the unpredictability of the encrypted speech signal. The hardware implementation results show a throughput of 2880 Mbps and power consumption of 0.13 W. Full article

As information systems become more widespread, data security becomes increasingly important. While traditional encryption methods provide effective protection against unauthorized access, they often struggle with multimedia data like images and videos. This necessitates specialized image encryption approaches. With the rise of mobile and Internet of Things (IoT) devices, lightweight image encryption algorithms are crucial for resource-constrained environments. These algorithms have applications in various domains, including medical imaging and surveillance systems. However, the biggest challenge of lightweight algorithms is balancing strong security with limited hardware resources. This work introduces a novel nonlinear matrix permutation approach applicable to both confusion and diffusion phases in lightweight image encryption. The proposed method utilizes three different chaotic maps in harmony, namely a 2D Zaslavsky map, 1D Chebyshev map, and 1D logistic map, to generate number sequences for permutation and diffusion. Evaluation using various metrics confirms the method’s efficiency and its potential as a robust encryption framework. The proposed scheme was tested with 14 color images in the SIPI dataset. This approach achieves high performance by processing each image in just one iteration. The developed scheme offers a significant advantage over its alternatives, with an average NPCR of 99.6122, UACI of 33.4690, and information entropy of 7.9993 for 14 test images, with an average correlation value as low as 0.0006 and a vast key space of $2^{800}$. The evaluation results demonstrated that the proposed approach is a viable and effective alternative for lightweight image encryption. Full article

At present, there is a growing emphasis on safeguarding image data, yet conventional encryption methods are full of numerous limitations. In order to tackle the limitations of conventional color image encryption methodologies, such as inefficiency and insufficient security, this paper designs an expedited encryption method for color images that uses DNA coding in conjunction with multiple chaotic systems. The encryption algorithm proposed in this paper is based on three-dimensional permutation, global scrambling, one-dimensional diffusion and DNA coding. First of all, the encryption algorithm uses three-dimensional permutation algorithms to scramble the image, which disrupts the high correlation among the image pixels. Second, the RSA algorithm and the SHA-256 hashing algorithm are utilized to derive the starting value necessary for the chaotic system to produce the key. Third, the image is encrypted by using global scrambling and one-dimensional diffusion. Finally, DNA coding rules are used to perform DNA computing. The experimental results indicate that the encryption scheme exhibits a relatively weak inter-pixel correlation, uniform histogram distribution, and an information entropy value approaching eight. This shows that the proposed algorithm is able to protect the image safely and efficiently. Full article

Data security and privacy have become essential due to the increasingly advanced interconnectivity in today’s world, hence the reliance on cryptography. This paper introduces a new algorithm that uses a novel hybrid Tent–May chaotic map to generate pseudo-random numbers, as well as block encryption. We design a robust S-box by combining the Tent and May Maps, which yields a chaotic system with improved cryptographic properties. This S-box is a critical cryptographic primitive that significantly improves encryption security and leverages the strengths of both maps. The encryption process involves two key steps: block-wise substitution and permutation. First, we divide the image into $16\times 16$ blocks, then substitute each pixel with the $8-byte$ key and S-box. Next, we convert the encrypted image back into vector form, reorganize it using the permutation vector based on the subgroups of $S_{16}$, and finally return it to its original form. This approach greatly improves block cipher security when used, especially to protect medical images by guaranteeing their confidentiality and noninterference. Performance measures like PSNR, UACI, MSE, NCC, AD, SC, MD, and NAE prove how immune our method is to various cryptographic and statistical attacks, making it more accurate and more secure than the existing techniques. Full article

In digital image security, the Josephus permutation is widely used in cryptography to enhance randomness. However, its application in steganography is underexplored. This study introduces a novel method integrating the Josephus permutation into the LSB 3-3-2 embedding technique for image steganography. This approach improves the randomness of the keystream generated by the chaotic logistic map, addressing vulnerabilities in basic logistic maps susceptible to steganalysis. Our algorithm is tested on RGB images as secret data, presenting higher complexity compared to grayscale images used in previous studies. Comparative analysis shows that the proposed algorithm offers higher payload capacity while maintaining image quality, outperforming traditional LSB techniques. This research advances the field of image steganography by demonstrating the effectiveness of the Josephus permutation in creating more secure and robust steganographic images. Full article

To analyze the security of encryption, an effectual encryption scheme based on colored images utilizing the hybrid pseudo-random binary sequence (HPRBS) and substitution boxes, known as S-boxes, is proposed. The presented work aims to design S-boxes using pseudo-random binary numbers acquired by Linear Feedback Shift Registers (LFSRs) in combination with a modified quadratic chaotic map. Firstly, cryptographically robust S-boxes are constructed by using binary pseudo-random number sequences, and then the cryptographic properties of the presented S-boxes are tested. The suggested S-boxes showed good results. Secondly, an RGB image encryption algorithm utilizing sequences generated by modified quadratic chaotic maps and S-boxes is offered. The new color image encryption techniques comprise two steps, including a permutation and a substitution step. The key association with the content of the image is also addressed. This strategy can result in a “one-time pad” effect and make the algorithm resistant to chosen-plaintext attack (CPA). The proposed scheme has been confirmed to be more valuable than most of the existing schemes. S-boxes are analyzed by the nonlinearity test, bit independence criterion (BIC), linear and differential approximation probabilities (LPs; DPs), and Strict-Avalanche Criterion (SAC) tests. A comparison with different S-boxes presented in the literature is also carried out. The comparison shows encouraging results about the quality of the proposed box. From security and experimental outcomes, the effectiveness of the presented color image encryption technique is verified. The proposed scheme has evident efficiency benefits, which implies that the proposed colored encryption of the image scheme has better potential for application in encryption schemes in real-time. Full article