Search Results (104)

We show that Out-of-Time-Ordered Correlator (OTOC) growth in the Quantum Kicked Rotor (QKR) quantifies information scrambling rather than entropy production. Numerical simulations reproduce the quadratic OTOC scaling at resonance (${\hslash }_{\mathrm{eff}}=4\pi$) and its suppression under detuning. Bitstreams derived from the evolving wavefunction reveal a nonmonotonic relationship between chaos and entropy: the resonant (maximally chaotic) regime exhibits lower measured entropy due to coherent phase correlations, whereas slight detuning enhances statistical uniformity. While Out-of-Time-Ordered Correlators quantify information scrambling rather than entropy production, we show that the strength of scrambling strongly constrains the amount of classical entropy that can be extracted after measurement. Full article

Quantum watermarking is a technique that embeds specific information into a quantum carrier for the purpose of digital copyright protection. In this paper, we propose a novel color image watermarking algorithm that integrates quantum discrete wavelet transform with Sinusoidal–Tent mapping and baker mapping. Initially, chaotic sequences are generated using Sinusoidal–Tent mapping to determine the channels suitable for watermark embedding. Subsequently, a one-level quantum Haar wavelet transform is applied to the selected channel to decompose the image. The watermarked image is then scrambled via discrete baker mapping, and the scrambled image is embedded into the High-High subbands. The invisibility of the watermark is evaluated by calculating the peak signal-to-noise ratio, Structural similarity index measure, and Learned Perceptual Image Patch Similarity, with comparisons made against the color histogram. The robustness of the proposed algorithm is assessed through the calculation of Normalized Cross-Correlation. In the simulation results, PSNR is close to 63, SSIM is close to 1, LPIPS is close to 0.001, and NCC is close to 0.97. This indicates that the proposed watermarking algorithm exhibits excellent visual quality and a robust capability to withstand various attacks. Additionally, through ablation study, the contribution of each technique to overall performance was systematically evaluated. Full article

Amid growing threats of image data leakage and misuse, image encryption has become a critical safeguard for protecting visual information. However, many recent image encryption algorithms remain constrained by trade-offs between security, efficiency, and practicability. To address these challenges, this paper first proposes a novel two-dimensional variable fractional-order coupled quadratic hyperchaotic map (2D-VFCQHM), which incorporates a state-dependent dynamic memory effect, wherein the fractional-order is adaptively determined at each iteration by the mean of the system’s current state. This mechanism substantially enhances the complexity and unpredictability of the underlying chaotic dynamics. Building upon the superior hyperchaotic properties of the 2D-VFCQHM, we further develop a high-performance image encryption algorithm that integrates a novel fusion strategy within a dynamic vector-level diffusion-scrambling framework (IEA-VMFD). Comprehensive security analyses and experimental results demonstrate that the proposed algorithm achieves robust cryptographic performance, including a key space of $2^{298}$, inter-pixel correlation coefficients below 0.0018, ciphertext entropy greater than 7.999, and near-ideal plaintext sensitivity. Crucially, the algorithm attains an encryption speed of up to 126.2963 Mbps. The exceptional balance between security strength and computational efficiency underscores the practical viability of our algorithm, rendering it well-suited for modern applications such as telemedicine, instant messaging, and cloud computing. Full article

To address the security of digital images, this paper proposes a novel image encryption algorithm based on a six-dimensional memristive chaotic system. First, the algorithm uses the Secure Hash Algorithm 256 (SHA-256) to generate a hash value, from which the initial dynamic key is derived. Next, it integrates Zigzag scrambling, chaotic index scrambling, and diffusion operations to form an encryption scheme with multiple rounds of scrambling and diffusion. In this framework, after each encryption operation, a part of the dynamic key is changed according to the input parameters, and the six-dimensional memristive chaotic system continues iterating to generate the pseudo-random sequence for the next operation. Finally, the proposed algorithm is evaluated using indicators including information entropy, histograms, the Number of Pixels Change Rate (NPCR) and Unified Average Changing Intensity (UACI), encryption time, and so on. The results show that the information entropy of the encrypted image reaches 7.9979; its Chi-square statistic is 186.6875; the average NPCR and UACI are 99.6111% and 33.4643%, respectively; and the encryption time is 0.342 s for the 256 × 256 Cameraman image. These indicate that image encryption is not only effective in encrypting images but also resistant to many conventional attacks. Full article

With the rapid advancement of hyperspectral remote sensing technology, the security of hyperspectral images (HSIs) has become a critical concern. However, traditional image encryption methods—designed primarily for grayscale or RGB images—fail to address the high dimensionality, large data volume, and spectral-domain characteristics inherent to HSIs. Existing chaotic encryption schemes often suffer from limited chaotic performance, narrow parameter ranges, and inadequate spectral protection, leaving HSIs vulnerable to spectral feature extraction and statistical attacks. To overcome these limitations, this paper proposes a novel hyperspectral image encryption algorithm based on a newly designed two-dimensional cross-coupled hyperchaotic map (2D-CSCM), which synergistically integrates Cubic, Sinusoidal, and Chebyshev maps. The 2D-CSCM exhibits superior hyperchaotic behavior, including a wider hyperchaotic parameter range, enhanced randomness, and higher complexity, as validated by Lyapunov exponents, sample entropy, and NIST tests. Building on this, a layered encryption framework is introduced: spectral-band scrambling to conceal spectral curves while preserving spatial structure, spatial pixel permutation to disrupt correlation, and a bit-level diffusion mechanism based on dynamic DNA encoding, specifically designed to secure high bit-depth digital number (DN) values (typically >8 bits). Experimental results on multiple HSI datasets demonstrate that the proposed algorithm achieves near-ideal information entropy (up to 15.8107 for 16-bit data), negligible adjacent-pixel correlation (below 0.01), and strong resistance to statistical, cropping, and differential attacks (NPCR ≈ 99.998%, UACI ≈ 33.30%). The algorithm not only ensures comprehensive encryption of both spectral and spatial information but also supports lossless decryption, offering a robust and practical solution for secure storage and transmission of hyperspectral remote sensing imagery. Full article

In the digital era where images are easily accessible, concerns about image authenticity and integrity are increasing. To address this, we propose a deep learning-based fragile watermarking method for secure image authentication and content recovery. The method utilizes bottleneck features extracted by the convolutional encoder to carry both authentication and recovery information and employs deconvolution at the decoder to reconstruct image content. Additionally, the Arnold Transform is applied to scramble feature information, effectively enhancing resistance to collage attacks. At the detection stage, block voting and morphological closing operations improve tamper localization accuracy and robustness. Experiments tested various tampering ratios, with performance evaluated by PSNR, SSIM, precision, recall, and F1-score. Experiments under varying tampering ratios demonstrate that the proposed method maintains high visual quality and achieves reliable tamper detection and recovery, even at 75% tampering. Evaluation metrics including PSNR, SSIM, precision, recall, and F1-score confirm the effectiveness and practical applicability of the method. Full article

In complex electromagnetic environments, especially those with pulsed interference sources, long-period pulsed interference can repeatedly disrupt the real-time data within navigation messages, preventing receivers from obtaining complete message information and significantly extending the time to first fix (TTFF). To address this problem, the interference mechanism is modeled and analyzed from the perspective of navigation message structure. An anti-interference strategy based on navigation message scrambling is proposed, including two key techniques: random scrambling of subframe order and message interleaving encoding. Simulation and experimental results demonstrate that various pulsed interference patterns, with different periods and duty cycles, can significantly impact TTFF. The subframe scrambling method is effective against interference whose period exceeds the subframe duration but is limited when the period is equal to or shorter than the subframe. In contrast, the interleaving method provides more universal resistance across interference patterns. When both techniques are combined, the overall anti-interference performance is further enhanced. Specifically, for interference patterns with periods longer than the subframe duration, the probability that the receiver fails to achieve positioning across multiple consecutive frames is reduced by at least 50% compared to the case without interference mitigation. Full article

With the rapid advancement of information technology, as critical information carriers, images are confronted with significant security risks. To ensure the image security, this paper proposes an image encryption algorithm based on a dynamic rhombus transformation and digital tube model. Firstly, a two-dimensional hyper-chaotic system is constructed by combining the Sine map, Cubic map and May map. The analysis results demonstrate that the constructed hybrid chaotic map exhibits superior chaotic characteristics in terms of bifurcation diagrams, Lyapunov exponents, sample entropy, etc. Secondly, a dynamic rhombus transformation is proposed to scramble pixel positions, and chaotic sequences are used to dynamically select transformation centers and traversal orders. Finally, a digital tube model is designed to diffuse pixel values, which utilizes chaotic sequences to dynamically control the bit reversal and circular shift operations, and the exclusive OR operation to diffuse pixel values. The performance analyses show that the information entropy of the cipher image is 7.9993, and the correlation coefficients in horizontal, vertical, and diagonal directions are 0.0008, 0.0001, and 0.0005, respectively. Moreover, the proposed algorithm has strong resistance against noise attacks, cropping attacks, and exhaustive attacks, effectively ensuring the security of images during storage and transmission. Full article

The rapid development of Internet technology, while providing convenient services for users, has also aroused deep concern among the public about the issue of privacy leakage during image data transmission. To address this situation, this article proposes a color image encryption algorithm based on RNA extended dynamic coding and quantum chaos (CIEA-RQ). This algorithm significantly improves the ability of the system to withstand cryptographic attacks by introducing RNA extended dynamic encoding with 384 encoding rules. The employed quantum chaotic map improves the randomness of chaotic sequences and increases the key space. First, the algorithm decomposes the plaintext image into bit planes and obtains two parts, high 4-bit and low 4-bit planes, based on different weights of information. Then, the high 4-bit planes are partitioned into blocks and scrambled, and the scrambled planes are confused using RNA extended coding rules. Meanwhile, the low 4-bit planes employ a lightweight XOR operation to improve encryption efficiency. Finally, the algorithm performs cross-iterative diffusion on the processed high 4-bit and low 4-bit planes and then synthesizes a color ciphertext image. Experimental simulations and security assessments demonstrate the superior numerical statistical outcomes of the CIEA-RQ. According to the criteria of cryptanalysis, it can effectively resist known-plaintext attacks and chosen-plaintext attacks. Therefore, the CIEA-RQ presented in this article serves as an efficient digital image privacy safeguard technique, promising extensive applications in image secure transmission for the upcoming generation of networks. Full article

The rapid development of network communication technology has led to an increased focus on the security of image storage and transmission in multimedia information. This paper proposes an enhanced image security communication scheme based on Fibonacci interleaved diffusion and non-degenerate chaotic system to address the inadequacy of current image encryption technology. The scheme utilizes a hash function to extract the hash characteristic values of the plaintext image, generating initial perturbation keys to drive the chaotic system to generate initial pseudo-random sequences. Subsequently, the input image is subjected to a light scrambling process at the bit level. The Q matrix generated by the Fibonacci sequence is then employed to diffuse the obtained intermediate cipher image. The final ciphertext image is then generated by random direction confusion. Throughout the encryption process, plaintext correlation mechanisms are employed. Consequently, due to the feedback loop of the plaintext, this algorithm is capable of resisting known-plaintext attacks and chosen-plaintext attacks. Theoretical analysis and empirical results demonstrate that the algorithm fulfils the cryptographic requirements of confusion, diffusion, and avalanche effects, while also exhibiting a robust password space and excellent numerical statistical properties. Consequently, the security enhancement mechanism based on Fibonacci interleaved diffusion and non-degenerate chaotic system proposed in this paper effectively enhances the algorithm’s resistance to cryptographic attacks. Full article

In the digital information age, although digital images are widely used, the security issues associated with them have become increasingly severe. Consequently, ensuring secure image transmission has become a critical challenge in contemporary information security research. Chaotic systems are characterized by non-periodic behavior, strong dependence on initial conditions, and other favorable characteristics, and have been widely employed in the scrambling and diffusion processes of image encryption. Compared to classical chaotic maps, a quantum Logistic map exhibits better randomness and stronger sensitivity to initial values, effectively overcoming the attractor problem inherent in classical Logistic maps, thereby significantly enhancing the robustness of encryption methodologies. This article focuses on a innovative integration of a quantum Logistic map, hyper-chaotic Lorenz map, and DNA dynamic encoding technology, to design and implement a highly secure and efficient image encryption scheme. First, high-quality random number sequences are produced utilizing the quantum Logistic map, which is then employed to perform a scrambling operation on the image. Next, by integrating the chaotic sequences yielded from the hyper-chaotic Lorenz map with DNA dynamic encoding and operation rules, we implement a diffusion process, thereby increasing the strength of the image encryption. Experimental simulation results and multiple security analyses demonstrated that our encryption methodology achieved excellent encryption performance, effectively resisting a variety of attack strategies, and it holds significant potential for research on protecting image information through encryption. Full article

Images serve as significant conduits of information and are extensively utilized in several facets of life. As chaotic encryption evolves, current chaotic key generators have grown increasingly prevalent and susceptible to compromise. We present an advanced chaos architecture that integrates numerous nonlinear functions and incorporates common chaotic maps as perturbation factors. The produced two-dimensional QWT chaotic map exhibits a more stable chaotic state and a broader chaotic range in comparison to existing maps. Simultaneously, we developed a novel roulette scrambling technique that shifts the conventional in-plane scrambling to cross-plane scrambling. Upon evaluation, the encrypted image demonstrates commendable performance regarding information entropy, correlation, and other parameters, while its encryption algorithm exhibits robust security. Full article

Many important practical problems connected to energy efficiency in buildings, ecology, metallurgy, the development of wireless communication systems, the optimization of radar technology, quantum computing, pharmacology, and seismology are described by large-scale mathematical models that are typically represented by systems of partial differential equations. Such systems often involve numerous input parameters. It is crucial to understand how susceptible the solutions are to uncontrolled variations or uncertainties within these input parameters. This knowledge helps in identifying critical factors that significantly influence the model’s outcomes and can guide efforts to improve the accuracy and reliability of predictions. Sensitivity analysis (SA) is a method used efficiently to assess the sensitivity of the output results from large-scale mathematical models to uncertainties in their input data. By performing SA, we can better manage risks associated with uncertain inputs and make more informed decisions based on the model’s outputs. In recent years, researchers have developed advanced algorithms based on the analysis of variance (ANOVA) technique for computing numerical sensitivity indicators. These methods have also incorporated computationally efficient Monte Carlo integration techniques. This paper presents a comprehensive theoretical and experimental investigation of Monte Carlo algorithms based on “symmetrized shaking” of Sobol’s quasi-random sequences. The theoretical proof demonstrates that these algorithms exhibit an optimal rate of convergence for functions with continuous and bounded first derivatives and for functions with continuous and bounded second derivatives, respectively, both in terms of probability and mean square error. For the purposes of numerical study, these approaches were successfully applied to a particular problem. A specialized software tool for the global sensitivity analysis of an air pollution mathematical model was developed. Sensitivity analyses were conducted regarding some important air pollutant levels, calculated using a large-scale mathematical model describing the long-distance transport of air pollutants—the Unified Danish Eulerian Model (UNI-DEM). The sensitivity of the model was explored focusing on two distinct categories of key input parameters: chemical reaction rates and input emissions. To validate the theoretical findings and study the applicability of the algorithms across diverse problem classes, extensive numerical experiments were conducted to calculate the main sensitivity indicators—Sobol’ global sensitivity indices. Various numerical integration algorithms were employed to meet this goal—Monte Carlo, quasi-Monte Carlo (QMC), scrambled quasi-Monte Carlo methods based on Sobol’s sequences, and a sensitivity analysis approach implemented in the SIMLAB software for sensitivity analysis. During the study, an essential task arose that is small in value sensitivity measures. It required numerical integration approaches with higher accuracy to ensure reliable predictions based on a specific mathematical model, defining a vital role for small sensitivity measures. Both the analysis and numerical results highlight the advantages of one of the proposed approaches in terms of accuracy and efficiency, particularly for relatively small sensitivity indices. Full article

With the development of society and the Internet, images have become an important medium for information exchange. To improve the security of image encryption and transmission, a new image encryption algorithm based on bit-plane decomposition, DNA encoding and the 5D Hamiltonian conservative chaotic system is proposed. This encryption scheme is different from the traditional scrambling and diffusion methods at the level of image spatial pixels but encodes images into DNA strands and completely scrambles and diffuses operations on the DNA strands to ensure the security of images and improve the efficiency of image encryption. Firstly, the initial value sequence and convolution kernel of the five-dimensional Hamiltonian conservative chaotic system are obtained using SHA-256. Secondly, the bit-plane decomposition is used to decompose the image into high-bit and low-bit-planes, combine with DNA encoding to generate DNA strands, hide the large amount of valid information contained in the high-bit-planes, and preliminarily complete the hiding of the image information. In order to further ensure the effect of image encryption, seven DNA operation index tables controlling the diffusion process of the DNA strands are constructed based on the DNA operation rules. Finally, the scrambled and diffused DNA strand is decomposed into multiple bit-planes to reconstruct an encrypted image. The experimental results and security analysis show that this algorithm has a large enough key space, strong key sensitivity, high image encryption quality, strong robustness and high encryption efficiency. In addition, it can resist statistical attacks, differential attacks, and common attacks such as cropping attack, noise attack and classical attack. Full article

This paper skillfully incorporates the memristor model into a chaotic system, creating a two-dimensional (2D) hyperchaotic map. The system’s exceptional chaotic performance is verified through methods such as phase diagrams, bifurcation diagrams, and Lyapunov exponential spectrum. Additionally, a universal framework corresponding to the chaotic system is proposed. To enhance encryption security, the pixel values of the image are preprocessed, and a hash function is used to generate a hash value, which is then incorporated into the secret keys generation process. Existing algorithms typically encrypt the three channels of a color image separately or perform encryption only at the pixel level, resulting in certain limitations in encryption effectiveness. To address this, this paper proposes a novel encryption algorithm based on 2D hyperchaotic maps that extends from single-channel encryption to multi-channel encryption (SEME-TDHM). The SEME-TDHM algorithm combines single-channel and multi-channel random scrambling, followed by local cross-diffusion of pixel values across different planes. By integrating both pixel-level and bit-level diffusion, the randomness of the image information distribution is significantly increased. Finally, the diffusion matrix is decomposed and restored to generate the encrypted color image. Simulation results and comparative analyses demonstrate that the SEME-TDHM algorithm outperforms existing algorithms in terms of encryption effectiveness. The encrypted image maintains a stable information entropy around 7.999, with average NPCR and UACI values close to the ideal benchmarks of 99.6169% and 33.4623%, respectively, further affirming its outstanding encryption effectiveness. Additionally, the histogram of the encrypted image shows a uniform distribution, and the correlation coefficient is nearly zero. These findings indicate that the SEME-TDHM algorithm successfully encrypts color images, providing strong security and practical utility. Full article