Search Results (153)

This survey provides a comprehensive overview of the solutions to the matrix equation $AXB=C$ over real numbers, complex numbers, quaternions, dual quaternions, dual split quaternions, and dual generalized commutative quaternions, including various special solutions. Additionally, we summarize the numerical algorithms for these special solutions. This matrix equation plays an important role in solving linear systems and control theory. We specifically explore the application of this matrix equation in color image processing, highlighting its unique value in this field. Taking the dual quaternion matrix equation $AXB=C$ as an example, we design a scheme for simultaneously encrypting and decrypting two color images. The experimental results demonstrate that this scheme is highly feasible. Full article

Outsourcing storage to the cloud can save storage costs and is commonly used in businesses. It should fulfill two major goals: storage efficiency and data confidentiality. Encrypted deduplication can achieve both goals via performing deduplication to eliminate the duplicate data within encrypted data. Traditional encrypted deduplication generates the encryption key on the client side, which poses a risk of offline brute-force cracking of the outsourced data. Server-aided encryption schemes have been proposed to strengthen the confidentiality of encrypted deduplication by distributing the encryption process to dedicated servers. Existing schemes rely on expensive cryptographic primitives to provide a decentralized setting on the dedicated servers for scalability. However, this incurs substantial performance slowdown and can not be applied in practical encrypted deduplication storage systems. In this paper, we propose a new decentralized server-aided encrypted deduplication approach for outsourced storage, called ECDedup, which leverages secret sharing to achieve secure and efficient key management. We are the first to use the coding matrix as the encryption key to couple the encryption and encoding processes in encrypted deduplication. We also propose a acceleration scheme to speed up the encryption process of our ECDedup. We prototype ECDedup in cloud environments, and our experimental results based on the real-world backup datasets show that ECDedup can improve the client throughput by up to 51.9% compared to the state-of-the-art encrypted deduplication schemes. 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

This work is devoted to the hyperbolic sine function (HSF) control-based finite-time bipartite synchronization of fractional-order spatiotemporal networks and its application in image encryption. Initially, the addressed networks adequately take into account the nature of anisotropic diffusion, i.e., the diffusion matrix can be not only non-diagonal but also non-square, without the conservative requirements in plenty of the existing literature. Next, an equation transformation and an inequality estimate for the anisotropic diffusion term are established, which are fundamental for analyzing the diffusion phenomenon in network dynamics. Subsequently, three control laws are devised to offer a detailed discussion for HSF control law’s outstanding performances, including the swifter convergence rate, the tighter bound of the settling time and the suppression of chattering. Following this, by a designed chaotic system with multi-scroll chaotic attractors tested with bifurcation diagrams, Poincaré map, and Turing pattern, several simulations are pvorided to attest the correctness of our developed findings. Finally, a formulated image encryption algorithm, which is evaluated through imperative security tests, reveals the effectiveness and superiority of the obtained results. Full article

Cryptography is one of the most important branches of information security. Cryptography ensures secure communication and data privacy, and it has been increasingly applied in healthcare and related areas. As a significant cryptographic method, the Hill cipher has attracted significant attention from experts and scholars. To enhance the security of the traditional Hill cipher (THC) and expand its application in medical image encryption, a novel dynamic Hill cipher with Arnold scrambling technique (DHCAST) is proposed in this work. Unlike the THC, the proposed DHCAST uses a time-varying matrix as its secret key, which greatly increases the security of the THC, and the new DHCAST is successfully applied in medical images encryption. In addition, the new DHCAST method employs the Zeroing Neural Network (ZNN) in its decryption to find the time-varying inversion key matrix (TVIKM). In order to enhance the efficiency of the ZNN for solving the TVIKM, a new fuzzy zeroing neural network (NFZNN) model is constructed, and the convergence and robustness of the NFZNN model are validated by both theoretical analysis and experiment results. Simulation experiments show that the convergence time of the NFZNN model is about 0.05 s, while the convergence time of the traditional Zeroing Neural Network (TZNN) model is about 2 s, which means that the convergence speed of the NFZNN model is about 400 times that of the TZNN model. Moreover, the Peak Signal to Noise Ratio (PSNR) and Number of Pixel Change Rate (NPCR) of the proposed DHCAST algorithm reach 9.51 and 99.74%, respectively, which effectively validates its excellent encryption quality and attack prevention ability. Full article

This paper introduces a novel approach based on matrix multiplication in ${\mathbb{F}}_p^{n\times n}$, which enables methods for public key exchange, user authentication, digital signatures, blockchain integration, and homomorphic encryption. Unlike traditional algorithms that rely on integer factorization or discrete logarithms, our approach utilizes matrix factorization, rendering it resistant to current quantum cryptanalysis techniques. This method enhances confidentiality by ensuring secure communication and facilitating user authentication through public key validation. We have incorporated a method that allows a Certification Authority to certify the public keys. Furthermore, the incorporation of digital signatures ensures nonrepudiation, while the system functions as a blockchain technology to enhance transaction security. A key innovation of this approach is its capability to perform homomorphic encryption. Our approach has practical applications in artificial intelligence, robotics, and image processing. Full article

Chaos-based encryption is promising for safeguarding digital images. Nonetheless, existing chaos-based encryption algorithms still exhibit certain shortcomings. Given this, we propose a novel multi-channel image encryption algorithm that leverages pixel reorganization and hyperchaotic maps (MIEA-PRHM). Our MIEA-PRHM algorithm employs two hyperchaotic maps to jointly generate chaotic sequences, ensuring a larger key space and better randomness. During the encryption process, we first convert input images into two fused matrices through pixel reorganization. Then, we apply two rounds of scrambling and diffusion operations, coupled with one round of substitution operations, to the high 4-bit matrix. For the low 4-bit matrix, we conduct one round of substitution and diffusion operations. Extensive experiments and comparisons demonstrate that MIEA-PRHM outperforms many recent encryption algorithms in various aspects, especially in encryption efficiency. Full article

To address the vulnerability of existing hiding algorithms to differential attacks and the limitations of single chaotic systems, such as small key space and low security, a novel algorithm combining audio encryption with information hiding is proposed. First, the original audio is divided into blocks to enhance efficiency. A “one-time pad” mechanism is achieved by associating the key with the plaintext, and a new multidimensional sine-coupled chaotic map is designed, which, in conjunction with multiple chaotic systems, generates the key stream. Next, the block-processed audio signals are matrix-converted and then encrypted using cyclic remainder scrambling, an improved Josephus scrambling, XOR diffusion, and bit diffusion. This results in an encrypted audio information matrix. Finally, the GHM multiwavelet transform is used to select embedding channels, and the least significant bit (LSB) method is employed to hide the information within the carrier image. The algorithm is symmetric, and decryption involves simply reversing the encryption process on the stego image. Experimental results demonstrate that the Structural Similarity Index (SSIM) between the carrier image and the stego image is 0.992540, the Peak Signal-to-Noise Ratio (PSNR) is 49.659404 dB, and the Mean Squared Error (MSE) is 0.708044. These metrics indicate high statistical similarity and indistinguishability in visual appearance. The key space of the encryption algorithm is approximately 2⁸⁵⁰, which effectively resists brute-force attacks. The energy distribution of the encrypted audio approximates noise, with information entropy close to 8, uniform histograms, high scrambling degree, strong resistance to differential attacks, and robustness against noise and cropping attacks. Full article

The integration of smart contracts (SCs) within blockchain technology represents a pivotal direction in the evolution of the Internet of Things (IoT), enabling decentralization and enhancing user trust in the system. However, ensuring data privacy is a fundamental challenge that must be addressed during the deployment of these SCs. Many scholars have adopted data aggregation to protect privacy, but these methods are difficult to achieve fine-grained data collection. To this end, this paper proposes an efficient anonymous data collection (EADC) scheme suitable for the IoT environment. The scheme combines matrix algorithms with homomorphic encryption (HE) technology to effectively cut off the connection between users and data during data upload. In addition, the EADC scheme introduces a sophisticated data grouping protocol to improve the overall efficiency of the system. Analysis shows that the scheme can achieve efficient data collection without compromising user privacy. Full article

In this paper, we describe the concept of a new data-hiding technique for steganography in RGB images where a secret message is embedded in the blue layer of specific bytes. For increasing security, bytes are chosen randomly using a random square Hermitian positive definite matrix, which is a stego-key. The proposed solution represents a very strong key since the number of variants of positive definite matrices of order 8 is huge. Implementing the proposed steganographic method consists of splitting a color image into its R, G, and B channels and implementing two segments, which take place in several phases. The first segment refers to embedding a secret message in the carrier (image or text) based on the unique absolute elements values of the Hermitian positive definite matrix. The second segment refers to extracting a hidden message based on a stego-key generated based on the Hermitian positive definite matrix elements. The objective of the data-hiding technique using a Hermitian positive definite matrix is to embed confidential or sensitive data within cover media (such as images, audio, or video) securely and imperceptibly; by doing so, the hidden data remain confidential and tamper-resistant while the cover media’s visual or auditory quality is maintained. 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

With the rapid advancement of information technology, digital images such as medical images, grayscale images, and color images are widely used, stored, and transmitted. Therefore, protecting this type of information is a critical challenge. Meanwhile, quaternions enable image encryption algorithm (IEA) to be more secure by providing a higher-dimensional mathematical system. Therefore, considering the importance of IEA and quaternions, this paper explores the global exponential synchronization (GES) problem for a class of quaternion-valued neural networks (QVNNs) with discrete time-varying delays. By using Hamilton’s multiplication rules, we first decompose the original QVNNs into equivalent four real-valued neural networks (RVNNs), which avoids non-commutativity difficulties of quaternions. This decomposition method allows the original QVNNs to be studied using their equivalent RVNNs. Then, by utilizing Lyapunov functions and the matrix measure method (MMM), some new sufficient conditions for GES of QVNNs under designed control are derived. In addition, the original QVNNs are examined using the non-decomposition method, and corresponding GES criteria are derived. Furthermore, this paper presents novel results and new insights into GES of QVNNs. Finally, two numerical verifications with simulation results are given to verify the feasibility of the obtained criteria. Based on the considered master–slave QVNNs, a new IEA for color images Mandrill (256 × 256), Lion (512 × 512), Peppers (1024 × 1024) is proposed. In addition, the effectiveness of the proposed IEA is verified by various experimental analysis. The experiment results show that the algorithm has good correlation coefficients (CCs), information entropy (IE) with an average of 7.9988, number of pixels change rate (NPCR) with average of 99.6080%, and unified averaged changed intensity (UACI) with average of 33.4589%; this indicates the efficacy of the proposed IEAs. 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

This paper proposes a highly secure image encryption technique based on chaotic synchronization. Firstly, through the design of a synchronization controller, we ensure that the master–slave chaotic extremum-coded random number generators (ECRNGs) embedded in separated transmitters and receivers are fully synchronized to provide synchronized dynamic random sequences for image encryption applications. Next, combining these synchronized chaotic sequences with the AES encryption algorithm, we propose an image segmentation and multi-encryption method to enhance the security of encrypted images and realize a secure image transmission system. Notably, in the design of the synchronization controller, the transient time before complete synchronization between the master and slave ECRNGs is effectively controlled by specifying the eigenvalues of the matrix in the synchronization error dynamics. Research results in this paper also show that complete synchronization of ECRNGs can be achieved within a single sampling time, which significantly contributes to the time efficiency of the image transmission system. As for the image encryption technique, we propose the method of image segmentation and use the synchronized dynamic random sequences generated by the ECRNGs to produce the keys and initialization vectors (IVs) required for AES-CBC image encryption, greatly enhancing the security of the encrypted images. To highlight the contribution of the proposed segmented image encryption, statistical analyses are conducted on the encrypted images, including histogram analysis (HA), information entropy (IE), correlation coefficient analysis (CCA), number of pixels change rate (NPCR), and unified average changing intensity (UACI), and compared with existing literature. The comparative results fully demonstrate that the proposed encryption method significantly enhances image encryption performance. Finally, under the network transmission control protocol (TCP), the synchronization of ECRNGs, dynamic keys, and IVs is implemented as well as segmented image encryption and transmission, and a highly secure image transmission system is realized to validate the practicality and feasibility of our design. Full article

This paper proposes an asymmetric scanning holography cryptosystem based on the Elgamal algorithm. The method encodes images with sine and cosine holograms. Subsequently, each hologram is divided into a signed bit matrix and an unsigned hologram matrix, both encrypted using the sender’s private key and the receiver’s public key. The resulting ciphertext matrices are then transmitted to the receiver. Upon receipt, the receiver decrypts the ciphertext matrices using their private key and the sender’s public key. We employ an asymmetric single-image encryption method for key management and dispatch for securing imaging and transmission. Furthermore, we conducted a sensitivity analysis of the encryption system. The image encryption metrics, including histograms of holograms, adjacent pixel correlation, image correlation, the peak signal-to-noise ratio, and the structural similarity index, were also examined. The results demonstrate the security and stability of the proposed method. Full article