Arnold Map Research Articles

A fuzzy activation function based zeroing neural network for dynamic Arnold Map image cryptography

As an effective method for time-varying problems solving, zeroing neural network (ZNN) has been frequently applied in science and engineering. In order to improve its performances in practical applications, a fuzzy activation function (FAF) is designed by introducing the fuzzy logic technology, and a fuzzy activation function based zeroing neural network (FAF-ZNN) model for fast solving time-varying matrix inversion (TVMI) is proposed. Rigorous mathematical analysis and comparative simulation experiments with other models guarantee its superior convergence and robustness to noises. In addition, based on the proposed FAF-ZNN model, a new dynamic Arnold map image cryptography algorithm is designed. Specifically, in the new dynamic image encryption, a dynamic key matrix is introduced, and the FAF-ZNN model is applied to fast compute the inversion of the dynamic key matrix for the dynamic Arnold map image cryptography decryption process. The effectiveness of the dynamic image encryption algorithm is verified by experiment results, which enhances the security of existing image encryption algorithms.

Securing Images using Bifid Cipher associated with Arnold Map

In this paper, a scheme for image data security is designed by using Bifid cipher and Arnold map. The conventional 2D-Bifid cipher is changed to handle the encryption and decryption of color images. Further, a block-based method is realized using Arnold map to encrypt and decrypt the image data of square as well as non-square sizes. The proposed scheme is constructed on a widely adopted cryptographic framework, i.e., substitution-permutation design, where Bifid cipher-based scheme acts as a substitution layer and Arnold map-based scheme acts as a diffusion layer. The designed scheme has a huge key space with key sensitivity not only to accurate keys but also to their accurate orders. The practicability and performance of the designed scheme is validated by conducting a detailed analysis along with a comparative study. This paper contributes to a simple, efficient and secure image encryption method, which outperforms to the related works.

Image Watermarking Using Discrete Wavelet Transform and Singular Value Decomposition for Enhanced Imperceptibility and Robustness

Digital multimedia elements such as text, image, audio, and video can be easily manipulated because of the rapid rise of multimedia technology, making data protection a prime concern. Hence, copyright protection, content authentication, and integrity verification are today’s new challenging issues. To address these issues, digital image watermarking techniques have been proposed by several researchers. Image watermarking can be conducted through several transformations, such as discrete wavelet transform (DWT), singular value decomposition (SVD), orthogonal matrix Q and upper triangular matrix R (QR) decomposition, and non-subsampled contourlet transform (NSCT). However, a single transformation cannot simultaneously satisfy all the design requirements of image watermarking, which makes a platform to design a hybrid invisible image watermarking technique in this work. The proposed work combines four-level (4L) DWT and two-level (2L) SVD. The Arnold map initially encrypts the watermark image, and 2L SVD is applied to it to extract the s components of the watermark image. A 4L DWT is applied to the host image to extract the LL sub-band, and then 2L SVD is applied to extract s components that are embedded into the host image to generate the watermarked image. The dynamic-sized watermark maintains a balanced visual impact and non-blind watermarking preserves the quality and integrity of the host image. We have evaluated the performance after applying several intentional and unintentional attacks and found high imperceptibility and improved robustness with enhanced security to the system than existing state-of-the-art methods.

Performance Analysis of Image Watermarking for Different Sub-bands Using LWT and Arnold Map

In this paper, blind image watermarking is proposed for grey-scale images using LWT and Arnold maps. A comprehensive analysis of robustness and imperceptibility for different sub-band is analyzed, and a robust sub-band against different attacks is determined for designing a system robust against intentional attacks or combined attacks. The importance of embedding a watermark in several sub-bands has been examined to increase the robustness against various image attacks while retaining a reasonable level of imperceptibility. During the study, robustness is analyzed and watched against the number of attacks such as compression attacks, noisy attacks, de-noising attacks, and geometric attacks. It is moreover seen that higher sub-bands are seen to offer good imperceptibility, and robustness performance depends on the nature of attacks. It has also been noticed that entire attacks affect the watermarked image in a different way. A standard image dataset is used to test the suggested concept, and it is discovered that sub-band 1 performs admirably for strength (robustness) and imperceptibility against different image attacks.

Color image encryption base on a 2D hyperchaotic enhanced Henon map and cross diffusion

The parameter range of traditional 2D chaotic maps is small, limiting the sequence generation performance. In order to improve security and efficiency, it is necessary to develop a new 2D chaotic map for image encryption. This paper proposes an enhanced version of the Henon Map, called 2D-HHMSC, which has better sequence generation performance than the Henon Map under the same parameters. In addition, 2D-HHMSC has ample parameter space, enhancing the generated sequences’ randomness. The proposed method is a new color image encryption algorithm. To prevent the algorithm from being subjected to brute force attacks, two hash functions are used to generate the parameters and initial values of the Arnold map and 2D-HHMSC. The key space of the algorithm can reach 2̂1024. In the scrambling phase, the three channels of the color image are scrambled using Arnold maps with different parameters and then combined into a grayscale image. In order to fully diffuse the scrambled image, use the key stream generated by 2D-HHMSC to diffuse the grayscale image, starting from the center position of the grayscale image The correlation coefficients of the proposed encryption algorithm are 0.002, 0.0012, and −0.0006, and the information entropy is 7.9993. Experimental results show that the algorithm can resist common attacks, proving its robustness and reliability.

Coexisting point attractors, multi-transient behaviors, area-preserving chaotic systems, non-degenerate hyperchaotic systems derived from a simple 3D discrete system

In this paper, we propose a simple 3D discrete system with a variety of interesting dynamic behaviors. When the control parameters of the discrete system are set to different appropriate values, the system is transformed into four distinct systems, namely a discrete system with coexisting point attractors, a discrete system with novel multi-transient behaviors, an area-preserving map, and a non-degenerate hyperchaotic system. This transient transition behavior is manifested as a switch between multiple quasi-periodic flows. This multi-transient behavior is rarely reported in discrete systems. In addition, to meet the requirements of chaotic secure communication, relevant experiments prove that the pixel scrambling effect of the proposed area-preserving map is better than that of the 3D digital Arnold map. Moreover, a PRNG is constructed by quantizing the proposed non-degenerate hyperchaotic system, and the PRNG can pass the NIST SP-800-22 test and show good randomness.

Cryptographic Encryption and Optimization for Internet of Things Based Medical Image Security

The expansion of the Internet of Things is expected to lead to the emergence of the Internet of Medical Things (IoMT), which will revolutionize the health-care industry (IoT). The Internet of Things (IoT) revolution is outpacing current human services thanks to its bright mechanical, economical, and social future. Security is essential because most patient information is housed on a cloud platform in the hospital. The security of medical images in the Internet of Things was investigated in this research using a new cryptographic model and optimization approaches. For the effective storage and safe transfer of patient data along with medical images, a separate framework is required. The key management and optimization will be chosen utilizing the Rivest–Shamir–Adleman-based Arnold map (RSA-AM), hostile orchestration (HO), and obstruction bloom breeding optimization (OBBO) to increase the encryption and decryption processes’ level of security. The effectiveness of the suggested strategy is measured using peak signal-to-noise ratio (PSNR), entropy, mean square error (MSE), bit error rate (BER), structural similarity index (SSI), and correlation coefficient (CC). The investigation shows that the recommended approach provides greater security than other current systems.

A novel multi-layer color image encryption based on RSA cryptosystem, RP2DFrHT and generalized 2D Arnold map

A novel multi-layer color image encryption based on RSA cryptosystem, RP2DFrHT and generalized 2D Arnold map

Blockchain-Driven Image Encryption Process with Arithmetic Optimization Algorithm for Security in Emerging Virtual Environments

The real world is bounded by people, hospitals, industries, buildings, businesses, vehicles, cognitive cities, and billions of devices that offer various services and interact with the world. Recent technologies, including AR, VR, XR, and the digital twin concept, provide advanced solutions to create a new virtual world. Due to the ongoing development of information communication technologies and broadcast channels, data security has become a major concern. Blockchain (BC) technology is an open, decentralized, and transparent distributed database that can be maintained by the group. BC’s major features are high credibility, decentralization, transparency, versatility, autonomy, traceability, anonymity, intelligence, reward mechanisms, and irreversibility. This study presents a blockchain-driven image encryption technique using arithmetic optimization with a fractional-order Lorenz system (BDIE-AOFOLS). The BDIE-AOFOLS technique uses the FOLS method, which integrates the Arnold map, tent map, and fractional Lorenz system. Besides this, an arithmetic optimization algorithm (AOA) was carried out for the optimum key generation process to achieve the maximum PSNR value. The design of an AOA-based optimal generation of keys for the FOLS technique determines the novelty of the current work. Moreover, the cryptographical pixel values of the images can be stored securely in the BC, guaranteeing image security. We compared the outcomes of the proposed BDIE-AOFOLS technique against benchmark color images. The comparative analysis demonstrated the improved security efficiency of the BDIE-AOFOLS technique over other approaches, with a mean square error of 0.0430 and a peak signal-to-noise ratio of 61.80 dB.

An Encryption Application and FPGA Realization of a Fractional Memristive Chaotic System

The work in this paper extends a memristive chaotic system with transcendental nonlinearities to the fractional-order domain. The extended system’s chaotic properties were validated through bifurcation analysis and spectral entropy. The presented system was employed in the substitution stage of an image encryption algorithm, including a generalized Arnold map for the permutation. The encryption scheme demonstrated its efficiency through statistical tests, key sensitivity analysis and resistance to brute force and differential attacks. The fractional-order memristive system includes a reconfigurable coordinate rotation digital computer (CORDIC) and Grünwald–Letnikov (GL) architectures, which are essential for trigonometric and hyperbolic functions and fractional-order operator implementations, respectively. The proposed system was implemented on the Artix-7 FPGA board, achieving a throughput of 0.396 Gbit/s.

Advanced 5D logistic and DNA encoding for medical images

ABSTRACT Since patient diagnostic data such as X-rays, MRIs, CT scans, etc. contain very sensitive information about a patient's health, it must be encrypted to prevent unauthorized access. In chaotic-based image encryption methods, the lower-dimensional chaotic maps are insufficient because they can be estimated through some signal estimation technologies; therefore, a higher-order novel 5D logistic chaotic map along with DNA encoding and the Arnold map for medical image encryption is presented to overcome the vital medical breaching that could cost a life. In this work, the advantages of DNA principles and high-dimensional chaotic maps are used to develop an efficient encryption method for the protection of medical images. The strategy is useful due to the fact that the higher order makes the system more complicated and tough to penetrate. The large keyspace up to, anti attack capabilities, and comparison of various standard parameters with different literatures illustrate the algorithm's superiority.

Quad Key-Secured 3D Gauss Encryption Compression System with Lyapunov Exponent Validation for Digital Images

High-dimensional systems are more secure than their lower-order counterparts. However, high security with these complex sets of equations and parameters reduces the transmission system’s processing speed, necessitating the development of an algorithm that secures and makes the system lightweight, ensuring that the processing speed is not compromised. This study provides a digital image compression–encryption technique based on the idea of a novel quad key-secured 3D Gauss chaotic map with singular value decomposition (SVD) and hybrid chaos, which employs SVD to compress the digital image and a four-key-protected encryption via a novel 3D Gauss map, logistic map, Arnold map, or sine map. The algorithm has three benefits: First, the compression method enables the user to select the appropriate compression level based on the application using a unique number. Second, it features a confusion method in which the image’s pixel coordinates are jumbled using four chaotic maps. The pixel position is randomized, resulting in a communication-safe cipher text image. Third, the four keys are produced using a novel 3D Gauss map, logistic map, Arnold map, or sine map, which are nonlinear and chaotic and, hence, very secure with greater key spaces (2498). Moreover, the novel 3D Gauss map satisfies the Lyapunov exponent distribution, which characterizes any chaotic system. As a result, the technique is extremely safe while simultaneously conserving storage space. The experimental findings demonstrate that the method provides reliable reconstruction with a good PSNR on various singular values. Moreover, the applied attacks demonstrated in the result section prove that the proposed method can firmly withstand the urge of attacks.

Multi-layer security based multiple image encryption technique

This paper designs a novel multiple image encryption technique utilizing affine Hill cipher (AHC), reality-preserving two-dimensional discrete fractional Hartley transform (RP2DFrHT) and generalized two-dimensional (2D) Arnold map (AM). In our technique, three indexed images are obtained from three color images. Afterwards, AHC performs a strong degree of confusion and diffusion operations and RP2DFrHT provides real domain output image. Lastly, 2D AM dislocates the image pixel position. After the encryption process, single-channel real-valued encrypted image is obtained which gives convenience in the display, storage and transmission of an image over an unsecured network. The proposed technique is multi-layer secured in the time, frequency and co-ordinate domains. Moreover, the secret keys, arrangements and positions of used parameters all are imperative for the correct decryption process of our technique. Simulation results, security analysis, statistical analysis and comparison analysis ensure that the proposed technique has an excellent encryption effect, sufficient security and robustness.

Using chaotic dynamics to characterize the complexity of rough surfaces.

In this work, we use the basic ingredients of chaotic dynamics (stretching and folding of phase space points) for the characterization of the complexity of microscopy images of rough surfaces. The key idea is to use an image as the initial condition of a chaotic discrete dynamical system, such as the Arnold cat map, and track its transformations during the first iterations of the map. Since the basic effects of the Arnold map are the stretching and folding of image texture, the application of the map leads to an enhancement of the high frequency content of images along with an increase of discontinuities in pixel intensities. We exploit these effects to quantify the complexity of S type (lying between homogeneity and randomness) of the image texture since the first (enhancement of high frequencies) can be used to quantify the distance of texture from randomness and noise and the second (the proliferation of discontinuities) the distance from order and homogeneity. The method is validated in synthetic images which are generated from computer generated surfaces with controlled correlation length and fractal dimension and it is applied in real images of nanostructured surfaces obtained from a scanning electron microscope with very interesting results.

Medical Image Encryption Based on Josephus Traversing and Hyperchaotic Lorenz System.

This study proposes a new medical image encryption scheme based on Josephus traversing and hyperchaotic Lorenz system. First, a chaotic sequence is generated through hyperchaotic system. This hyperchaotic sequence is used in the scrambling and diffusion stages of the algorithm. Second, in the scrambling process, the image is initially confused by Josephus scrambling, and then the image is further confused by Arnold map. Finally, generated hyperchaos sequence and exclusive OR operation is used for the image to carry on the positive and reverse diffusion to change the pixel value of the image and further hide the effective information of the image. In addition, the information of the plaintext image is used to generate keys used in the algorithm, which increases the ability of resisting plaintext attack. Experimental results and security analysis show that the scheme can effectively hide plaintext image information according to the characteristics of medical images, and is resistant to common types of attacks. In addition, this scheme performs well in the experiments of robustness, which shows that the scheme can solve the problem of image damage in telemedicine. It has a positive significance for the future research.

Efficient Scrambling-Substitution Image Security Scheme using Chaotic Arnold-Logistic Maps in the Discrete Cosine Transform

This paper introduces an efficient scrambling-substitution image security scheme using chaotic Arnold and Logistic (Arnold-Logistic) maps in the discrete cosine transform (DCT). The Arnold map is employed as a scrambling stage while the Logistic map is employed as a substitution stage. The hybrid Arnold-Logistic mapping is performed in the DCT. The encipherment phase of the introduced DCT-based Arnold-Logistic security scheme begins by applying the DCT to the plainimage and the resulted DCT coefficient of the plainimage are scrambled for m iterations using the Arnold transformation. Then, the Arnold-based transformed DCT coefficients are substituted for n iterations using the Logistic map and the inverse of DCT (IDCT) is employed to produce the cipherimage. The decipherment phase of the introduced DCTbased Arnold-Logistic security scheme is the inverse of the encryption stage and begins by applying the DCT to the cipherimage. The resulted DCT coefficient of the cipherimage is inversely substituted for n iterations using the inverse Logistic map. Then, the inverse Logistic-based transformed DCT coefficients are inversely scrambled for m iterations using the inverse Arnold map and the IDCT is employed to produce the decrypted image. A series of test experiments are applied to investigate the introduced DCTbased Arnold-Logistic security scheme. The outcome results demonstrated the superiority of the introduced DCT-based Arnold-Logistic security scheme from the security point of view.

New image encryption scheme based on Arnold map and cuckoo search optimization algorithm

New image encryption scheme based on Arnold map and cuckoo search optimization algorithm

Complex entropy based encryption and decryption technique for securing medical images

During medical picture transmission, the most pressing concern is security. Medical images must be encrypted since they are extremely sensitive. Watermarking, digital fingerprinting/signature, and encoding are some of the available image security techniques. Images and movies, for example, must be highly encrypted and decoded without losing any content information. Medical photos, for example, require extra protection, and protecting medical images is a critical issue when medical images and related patient information are transferred over public networks. This research work proposes a visual encryption strategy to secure medical pictures before being transmitted or stored in the cloud. This technique makes such pictures of unauthorized people unavailable and also maintains confidentiality, a prime safety requirement. The process made use of a pixel shuffling-based encryption technique and a secret key created from the image. In this research, we encrypted the medical image using modified Arnold Map Encryption and generated secret key values. Therefore, the image is encrypted, and henceforth it is decrypted as well. So this work gave us the encrypted image and decrypted image/original image as well. The modified Arnold Map Encryption tries to add more randomness, thus increasing the entropy of the image and thus makes it harder to decrypt. The modified Arnold Map Encryption is also compared to other algorithms such as Hyper Chaotic, Secure Hash Algorithm-13 (SHA-13), Ten Logistic Maps, Bakers Map, HenonMap, Cross Chaos Map, and 2D Logistic Map and shows better results in terms of encryption speed and Number of Pixel Change Rate (NPCR) value.

Retraction Note to: A secure medical image transmission algorithm based on binary bits and Arnold map

Retraction Note to: A secure medical image transmission algorithm based on binary bits and Arnold map

A Blind Video Copyright Protection Technique in Maximum and Minimum Energy Frames Based on The Fast Walsh Hadamard Transform (FWHT) and Discrete Wavelet Transform (DWT) and Arnold Map

Video copyright protection is the most generally acknowledged method of preventing data piracy. This paper proposes a blind video copyright protection technique based on the Fast Walsh Hadamard Transform (FWHT), Discrete Wavelet Transform (DWT), and Arnold Map. The proposed method chooses only frames with maximum and minimum energy features to host the watermark. It also exploits the advantages of both the fast Walsh Hadamard transform (FWHT) and discrete wavelet transforms (DWT) for watermark embedding. The Arnold map encrypts watermarks before the embedding process and decrypts watermarks after extraction. The results show that the proposed method can achieve a fast embedding time, good transparency, and robustness against various attacks.