Ensuring copyright protection against illegal attacks and image processing operations while maintaining blind detection capabilities presents a significant challenge in color image watermarking. To address this issue, in this article, we propose a blind watermarking approach that integrates the Arnold transformation with watermark embedding in the transformed domain. Modified forms of Hahn discrete moments are introduced to effectively extract the key image features within this domain. The watermark is encrypted before being embedded into the magnitudes of the Hahn moments for each block using dither modulation, ensuring robustness against different types of attacks. Additionally, a reconstruction algorithm for color images based on Hahn moments is developed and employed during the watermark extraction phase. Experimental results confirm that the proposed scheme achieves high efficiency in terms of both imperceptibility and robustness. Extensive evaluations demonstrate its superior performance, with its PSNR and SSIM values reaching 64.693 dB and 0.9998, respectively. In the no-attack scenario, a perfect-quality watermark is extracted with BER = 0 and NCC = 1. Under various attacks, including filtering, noise, geometric, and robustness attacks, the proposed scheme continues to extract high-quality watermarks, achieving an average BER of 0.00001 and NCC of 0.9998, thereby outperforming the existing image watermarking techniques.

Light field (LF) images capture both spatial and angular data, providing enhanced detail in multi-view and 3D scenes, which makes them highly applicable across various domains. Thus, compared to traditional images, LF images not only contain more complex data and are more susceptible to unauthorized tampering or malicious uses during transmission due to their unique structure, thereby increasing the need for verification. Existing dual watermarking techniques are designed for single-view images and lack adaptability to the multi-view structure and geometric consistency of LF images, making it difficult to simultaneously address integrity verification and ownership verification for LF images. Given the multi-view characteristics and geometric consistency of LF images, there is an urgent need for a highly robust and adaptable dual watermarking method. Therefore, we propose a dual verification framework with customizable watermarking, called DeVIL, which specifically designed for LF images and enables both ownership and integrity verification. By embedding reversible ownership watermarks into the sub-aperture images (SAIs), affiliation can be verified after transmission. Among them, the embedding technique can flexibly choose either a reversible robust watermarking technique or a robust zero-watermarking technique based on different application scenarios. Subsequently, we perform Arnold transformation on key SAIs and embed them into non-key SAIs to create stego images, effectively reducing the risk of information leakage. Furthermore, integrity watermarks are embedded in the stego images, forming stego images with integrity watermarks to detect subtle tampering during transmission. Experimental results show that DeVIL can successfully recover SAIs and demonstrates strong robustness and adaptability against various attacks. Compared to state-of-the-art methods, DeVIL reduces the average bit error rate by 9.32% under different attacks, with average normalized cross-correlation improvement of 0.17, significantly enhancing the robustness of ownership protection in different datasets.

Securing digital images captured by unmanned aerial vehicles (UAVs) is important for maintaining data confidentiality and integrity during transmission over insecure networks. This study surveys and evaluates existing encryption schemes such as Arnold transformation, chaos-based, bit-plane extraction, quantum, and permutation-based algorithms. The existing image encryption algorithms are implemented and tested in MATLAB 2015 using standard benchmark images (Quantum, Baboon, and Cameraman), selected for their frequent use and benchmark relevance in recent image security literature. For algorithms whose statistical indices are already documented in prior research, those published values are adopted for reference. In cases where such data were unavailable, the corresponding schemes were re-implemented and experimentally evaluated in MATLAB 2015 to produce consistent and reproducible performance results. The comparative statistical analysis across these datasets demonstrates that hybrid quantum–chaotic and permutation–diffusion methods achieve near-ideal entropy values ( $$\approx $$ 7.999), high NPCR ( $$\approx $$ 99.6%), and UACI ( $$\approx $$ 33.4%). This indicates strong resistance to statistical and differential attacks. These schemes also exhibit low correlation coefficients (< 0.002) and large key spaces (> $$2^{100}$$ ).

Digital image watermarking faces significant challenges in balancing imperceptibility and robustness under diverse distortions. With the growing prevalence of deepfake and image manipulation technologies, preserving the authenticity and integrity of digital images has become increasingly critical. This paper presents a novel hybrid optimization-based framework for digital image watermarking, integrating the Arnold Transform (AT), Discrete Wavelet Transform (DWT), Singular Value Decomposition (SVD), and the Artificial Protozoa Optimizer (APO). The watermark, such as a QR code, is first encrypted using the Arnold Transform and embedded into the low-frequency sub-band via SVD, while the APO determines the optimal scaling factor α through an objective function combining the Structural Similarity Index Measure (SSIM) and Normalized Cross-Correlation (NCC) ensuring an optimal balance between imperceptibility and robustness. Experiments on a diverse set of images, including medical (e.g., MRI and chest X-ray) and standard benchmark images (e.g., Baboon, Peppers), demonstrate that the proposed framework achieves high SSIM and NCC, along with low Learned Perceptual Image Patch Similarity (LPIPS) and Bit Error Rate (BER). These metrics ensure accurate watermark extraction under attacks such as JPEG compression, noise, and rotation, while supporting ownership protection and multimedia authentication.

In this proposed study, a new hybrid approach is employed, which ensures the safe embedding as well as retrieval of digital data by using modern cryptography techniques along with steganographic techniques. By combining NTRU encryption, which provides quantum-resistant security, with the Arnold Transform, which improves data scrambling, the method significantly increases the stability of encrypted data. The transmission and storage of data are enhanced using Generative Adversarial Networks (GAN)-based compression without carrier file integrity being compromised. Efficient embedding and robust resistance to steganalysis attacks are promised by the Convolutional Neural Networks (CNN)-based data hiding method.

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.

Abstract Chaos-based cryptography requires robust, dynamically controllable systems for secure communication; however, existing hyperchaotic systems frequently lack precise signal characteristic control and adequate hardware validation for practical deployment. Addressing these limitations, we validate the practical feasibility of a newly developed 4-D hyperchaotic system with amplitude control and offset boosting capabilities through FPGA implementation. Our key contributions include: (1) hardware-validated controllable hyperchaotic dynamics with image-dependent adaptation, (2) quantum-inspired operations integration with verified chaotic sequences, and (3) comprehensive medical image encryption security evaluation. The cryptosystem encompasses five operational stages: image-dependent key generation, position scrambling via Generalized Quantum Arnold Transform, chaotic sequence generation, pixel value diffusion through quantum XOR operations, and controlled qubit-level scrambling. Experimental results demonstrate favorable security metrics, including high entropy values, near-zero correlation coefficients, strong resistance to differential attacks, along with notable resilience against data loss and noise interference, making it particularly suitable for telemedicine applications. This work adds a leaf to the branch of chaos-based cryptography by combining hyperchaotic dynamics with quantum-inspired principles, offering a promising and practical approach to secure data transmission.

Most image encryption methods based on Rubik’s cube scrambling adopt the idea of cyclic shift or map the image pixels to the cube surface, not fully considering the cube’s three-dimensional (3D) properties. In response to this defect, we propose a mixed chaotic color image encryption method based on parallel rotation scrambling in 3D Rubik’s cube space. First, a seven-dimensional hyperchaotic system is introduced to generate chaotic pseudo-random integer sequences. Then, a proven lemma is applied to preprocess the red (R), green (G), and blue (B) channels of the plain image to realize the first diffusion. Next, the chaotic integer sequence is employed to control Arnold transformation, and the scrambled two-dimensional (2D) pixel matrix is converted into a 3D matrix. Then, the 3D cube is scrambled by dynamically selecting the rotating axis, layer number, and angle through the chaotic integer sequence. The scrambled 3D matrix is converted into a 2D matrix, realizing the second diffusion via exclusive OR with the chaotic matrix generated by logistic mapping. Finally, the matrices of the R, G, and B channels are combined into an encrypted image. By performing the encryption algorithm in reverse, the encrypted image can be decrypted into the plain image. A simulation analysis shows that the proposed method has a larger key space and exhibits stronger key sensitivity than some existing methods.

Digital watermarking is considered a trustworthy strategy for proving ownership of valuable digital files such as audio, image, and video documents. Most of the prevailing image watermarking systems embed grayscale or binary image watermarks, while only a few use color images as watermarks. In this paper, we develop a secure, imperceptible, and robust optimized semi-blind color image watermarking technique that uses color images as watermarks. It is based on Hessenberg Decomposition (HD) and Singular Value Decomposition (SVD) in the Discrete Wavelet Transform (DWT) domain. First, the color host image and color watermark image in RGB space are converted to YCbCr space, and then the watermark data are embedded into the luminance component (Y) of the host image. In this work, the principal component of the watermark's luminance (Y) is implanted into the associated singular value of the host image with an appropriate scaling factor that optimizes the robustness-imperceptibility tradeoff. The Artificial Bee Colony (ABC) algorithm is used to find the appropriate scaling factors. To further enhance the security, the Arnold transformation is used to scramble the Y channel of the watermark before it is injected into the host image. As demonstrated by the Peak Signal to Noise Ratio (PSNR) and Normalized Correlation (NC) metrics, the proposed scheme exhibits high invisibility and is robust to most image processing manipulations, geometric operations, and combinational attacks. Compared to various existing color image watermarking schemes that use color images as watermarks, it shows higher imperceptibility and robustness.

Purpose: This research proposes an improvised version of the image encryption technique by incorporating Quantum Random Phase Encoding with the Arnold Transform to help enhance the strength and non-predictability of the encryption process. In this research work, some ideas gained from quantum-based methods have been brought to use with conventional approaches in image encryption techniques for enhancing their security. Methods: This model represents the basic methodology that underlies the Arnold Transform for scrambling the arrangement of image pixels to mask recognizable structures within quantum random phase encoding to introduce complexity through quantum-generated random phases. Result: The experimental results show much improvement in encryption efficiency. For example, in the case of "Cameraman" and "Lena", MSE parameters are 98.134 and 104.76, respectively; these now go up to 832.01 and 888.78. This implies that the higher decrement of these values 21.17 dB and 23.98 dB to 13.41 dB and 13.33 dB translates into higher distortion with higher security. Meanwhile, UACI and NPCR are also very steady and the mean value is about 0.3356 to 0.3358 and 99.60 to 99.61, which proves that this method has been effective in changing the pixel's value, and sensitive input changes. Novelty: This work is novel due to the introduction of quantum technologies in the classical methodology of image encryption. While classical techniques make use of conventional transforms for scrambling, like the Arnold Transform, this work embeds quantum randomness and intricacy in the process as a means of encoding namely, Quantum Random Phase Encoding.

Abstract In the era of big data, vast amounts of digital images are transmitted over the Internet. To safeguard the confidentiality of these images, this paper proposes a multiple image encryption algorithm (MIEA) based on 3D non-equilateral Arnold transformation (3D-NEAT) and a chaotic system, capable of encrypting any number of images simultaneously. First, the K plaintext images are superimposed to form a plaintext cube image. Next, 3D-NEAT is applied to scramble the 3D cube plaintext image at the bit level. Finally, chaotic sequences generated by Chen’s hyper-chaotic system (CHCS) are used to further confuse and diffuse the scrambled 3D cube image, resulting in a 3D cube encrypted image. Experimental simulations and security analyses demonstrate that the 3D ciphertext image produced by the proposed algorithm can withstand various security and statistical analyses and shows strong robustness against occlusion and noise attacks. These results indicate that the algorithm is both secure and efficient, making it suitable for practical applications. Mathematics Subject Classi cation (2020) MSC code1 · MSC code2 · more

With the acceleration of information technology development, the protection of information security becomes increasingly critical. Images, as extensively used multimedia tools, encounter serious challenges in safeguarding sensitive data, including personal privacy and business confidentiality. This research presents a novel algorithm for color image encryption, that combines a meminductor chaotic system and DNA encoding cross-coupling operations to enhance image security and effectively prevent unauthorized access and decryption. Initially, this paper designs an equivalent circuit model for the Meminductor and constructs the corresponding chaotic system, followed by an in-depth analysis of its nonlinear dynamic characteristics. Then, artificial neuron is employed to perturb the original chaotic sequence generated by the system, resulting in a highly random mixed sequence. The original image is then subjected to rearrangement and encoding through Arnold transformation and dynamic DNA encoding techniques. Additionally, this research introduces a DNA encoding cross-coupling operation method that operates at the block level of pixels to diffuse and confuse image data, enhancing the complexity of the image encryption algorithm. Finally, a dynamic decoding technique is employed to decode the encoded image, yielding the encrypted result. Experimental results show that the algorithm is capable of providing larger key space and higher complexity in image encryption applications, and is able to withstand various types of attacks.

A new image encryption algorithm based on the Arnold transform and URUK chaotic maps is proposed to deal with the issues of inadequate security and low encryption efficiency. Colored images consist of three linked channels used in the scheme. This method uses different keys to break the correlations between adjacent pixels in each channel. First, the plain image is split into RGB channels to encrypt each channel separately. Second, the Arnold transform performs pixel permutation, resulting in scrambled channels. third, the URUK chaotic maps generate three key vectors to perform pixel diffusion, resulting in diffused channels used as input for the following step. Finally, the GWO shuffles each channel independently, to get the minimum correlation between image pixels, which are then merged to obtain a cipher image. This method generates the cipher image with great unpredictability and security. The security is evaluated using various measures. The results demonstrated a high level of security attained by successfully encrypting colored images. Recent encryption algorithms are compared in terms of entropy, correlation coefficients, and attack robustness. The proposed method provided outstanding security and outperformed existing image encryption algorithms.

In order to protect the copyright of the digital contents, the robust watermarking techniques are employed based on frequency domains or combined frequency domains. Another techniques, called zero-watermarking which does not modify the original image to embed the watermark but create a watermark from its robust features, is a useful technique for resolving the tension between robustness and invisibility. In this paper, we propose a new zero-watermarking algorithm based on discrete wavelet transform and discrete cosine transform domain with significant feature points matching for improving the robustness. In our proposed method, the original image is firstly separated into three components (Y, Cr, Cb), then its Y-component is performed with discrete wavelet transform, afterwards its LL3 is transformed with discrete cosine transform. To generate the master share of the original image, the DCT-based image is binarized. After performing the Arnold transformation on the watermark, the owner share is generated by taking the XOR operation on the scrambled watermark and master share. The robustness of the our proposed algorithm for imaging processes is analyzed, and the results show that the proposed algorithm is robust to common signal processing such as noise, filtering, JPEG compression, geometric attacks such as rotation, scaling, translation and so on.

In recent years, extensive research has focused on encryption algorithms for square images, with relatively little attention given to nonsquare images. This paper introduces a novel encryption algorithm tailored for nonequal length images, integrating bit-plane chaotic mapping and Arnold transformation. To effectively implement the algorithm, the plain image is initially transformed into two equal-sized binary sequences. A new diffusion strategy is then introduced to mutually diffuse these sequences, followed by the use of a chaotic map to control the swapping of binary elements between them, enabling permutation of bits across different bitplanes. Finally, the positional information of the image is scrambled using the Arnold transform, resulting in the generation of the encrypted image. By utilizing nonequal Arnold transformation parameters and the initial value of the Lorenz chaotic map as keys, the transmission of keys is simplified, and the cryptosystem gains infinite key space to resist brute force attacks. Experimental results and security analysis confirm the effectiveness of the proposed quantum image encryption algorithm in encrypting nonsquare images, demonstrating good performance in terms of nonstatistical properties, key sensitivity, and robustness. Furthermore, simulation experiments based on Qiskit successfully validate the correctness and feasibility of the quantum image encryption algorithm.

Background: Quantum image processing is rapidly developing in the field of quantum computing, and it can be successfully implemented on the Noisy Intermediate-Scale Quantum (NISQ) device. Quantum image encryption holds a pivotal position in this domain. However, the encryption process often encounters security vulnerabilities and entails complex computational complexities, thereby consuming substantial quantum resources. To address this, the present study proposes a quantum image encryption algorithm based on four-dimensional chaos.Methods: The classical image is first encoded into quantum information using the Generalized Quantum Image Representation (GQIR) method. Subsequently, the trajectory of the four-dimensional chaotic system is randomized, and multi-dimensional chaotic keys are generated to initially encrypt the pixel values of the image. Then, the Arnold transformation is applied to randomly encrypt the pixel positions, resulting in the encrypted image. During the decryption process, the inverse process of encryption is employed to restore the original image.Results: We simulated this process in the Python environment, and the information entropy analysis experiment showed that the information entropy of the three encrypted images reached above 7.999, so the system has good encryption. At the same time, the correlation of the pixel distribution after the encryption algorithm is weak, which proves that the control parameters of the chaotic system can effectively reduce the correlation between pixels in the image. In the final key space analysis, the key space issued by our encryption can reach $10140\gg 2128$.Conclusion: Our method is resistant to destructive attacks and can produce scrambled images with higher encryption and usability. This algorithm solves the problems of general encryption algorithms such as periodicity, small key space, and vulnerability to statistical analysis, and proposes a reliable and effective encryption scheme. By making full use of the characteristics of Arnold transformation permutation, ergodicity and the randomness of the four-dimensional chaotic system, the encryption algorithm uses the larger key space provided by the four-dimensional Lorenz system.

As the most commonly used information transmission method, digital images often store a large amount of personal information. To prevent information leakage, encrypting images is essential. Common image encryption techniques suffer from certain limitations, such as overly simple encryption methods and long encryption times. In response to the above issues, this study proposes the Frobenius canonical form image encryption scheme. It calculates the fractal code through the fractal compression algorithm and to encrypt the image, it adjusts the brightness coefficient in the fractal code. To address unsatisfactory correlation coefficients in encrypted images, the Frobenius canonical form image encryption is improved by introducing the Arnold transformation encryption, which combines the two methods to reduce correlation coefficients. Finally, the knight tour algorithm is put forward. In response to the long image scrambling time in the knight tour algorithm, the Tetragonal theorem is combined with the scheme to encrypt the image. It is then re-encrypted using the Frobenius canonical form. The experimental findings illustrate that when using Frobenius canonical form, Arnold transformation combined with Frobenius canonical form, and the tetragonal algorithm combined with knight tour algorithm to encrypt Lena images, the three decryption methods correspond to image similarity of over 70%, over 80%, and over 90%, respectively. Combining the tetragonal algorithm and the knight tour algorithm can significantly increase the security of image encryption.

Steganography refers to hiding a secret message from various sources, such as images, videos, audio and so on. The advantage of steganography is to avoid data hacking in transmission medium during the transmission of information sources. Video steganography is superior to image steganography since the videos can hide a substantial quantity of secret messages more than the image. Hence, this research introduced the video stereography technique, Arnold Transform with SqueezeNet-based Pelican Whale Optimization Algorithm (AT[Formula: see text]SqueezeNet_PWOA), for concealing the secret image on the video. To hide the secret image on the video, the proposed method follows three steps: key frame and feature extraction, pixel prediction and embedding. The extraction of the key frame process is carried out by the Structural Similarity Index Measure (SSIM), and then the neighborhood features and convolutional neural network (CNN) features are extracted from the frame to improve the robustness of the embedding process. Moreover, the pixel prediction is completed by the SqueezeNet model, wherein the learning factors are tuned by the PWOA. In addition, the embedding process is completed by applying the Arnold transform on the predicted pixel, and the transformed regions are combined with the secret image using the embedding function. Likewise, the extraction process extracts the secret image from the embedded video by substituting the predicted pixel and Arnold transform on the embedded video. The proposed method is used to hide chunks of secret data in the form of video sequences and it improves the performance. The Arnold transform used in this work provides security by encrypting the data. The use of SqueezeNet makes the proposed model a simple design and this reduces the computational time. Thus, the AT[Formula: see text]SqeezeNet_PWOA attained better correlation coefficient (CC), peak signal-to-noise ratio (PSNR) and mean square error (MSE) of 0.908, 48.66 and 0.001 dB with the Gaussian noise.

This study introduces an optimized image encryption algorithm that integrates Henon mapping and Arnold transformation to enhance the security and randomness of digital image encryption. The algorithm is designed to address the vulnerabilities of open network environments where data theft or corruption can compromise image quality during encryption. Initially, images are processed through grayscale conversion to reduce dimensionality, followed by Henon mapping to induce a chaotic sequence that scrambles the pixel matrix. Subsequently, Arnold transformation is applied, iterating 100 times to further disrupt the image structure, ensuring a high level of diffusion and complexity. The proposed method demonstrates superior performance with an average pixel change rate (NPCR) of 0.9982 and a normalized average change intensity (NACI) of 0.3654, significantly increasing resistance to differential attacks. The encrypted images exhibit higher information entropy and effectively mask the original data, although at the cost of extended encryption time due to the dual scrambling process. The study concludes that the combined use of Henon mapping and Arnold transformation not only strengthens encryption against various attacks but also introduces a novel approach to image encryption, with potential for further optimization to enhance efficiency in handling larger images. This advancement is crucial for protecting privacy and ensuring data integrity in the transmission and storage of images, particularly in the face of evolving cyber threats.

To clarify the copyrights of 3D models of oblique photography (3DMOP) and guarantee their security, a novel security protection scheme of 3DMOP was proposed in this study by synergistically applying digital watermarking and data encryption. In the proposed scheme, point clouds were clustered first, and then the centroid and feature points of each cluster were calculated and extracted, respectively. Afterward, the watermarks were embedded into the point clouds cluster-by-cluster, taking distances between feature points and centroids as the embedding positions. In addition, the watermarks were also embedded using texture coordinates of 3DMOP to further enhance the robustness of the watermarking algorithm. Furthermore, Arnold transformation was performed on texture images of 3DMOP for security protection of classified or sensitive information. Experimental results have verified the strong imperceptibility and robustness of the proposed watermarking algorithm, as well as the high security of the designed data encryption algorithm. The outcomes of this work can refine the current security protection methods of 3DMOP and thus further expand their application scope.