Cat Map Research Articles

Resource optimized Region Based Image Encryption Using Chaotic Maps

Securing medical images becomes a major concern to avoid leaking confidential data. This problem motivated the development of many low computational complexity methods to encrypt these medical images. In this research work, block cipher-based region of interest medical image encryption with multiple maps is proposed. Primarily, region of interest (ROI) regions and region of background (ROB) are extracted with the help of Laplacian edge detection operator. Further, important ROI regions are permuted in a circular fashion with the help of Arnold cat map and angle value. Then permuted ROI part is encrypted using the duffling system and unimportant regions are unchanged. The advantage of the work is that it encrypts only selected/important parts and that will achieve fast execution speed and reduction in computation complexity. The approach presented here enables the storage and transmission of medical image data within an open network. These results show that the security in the proposed method is much better than many chaotic encryption algorithms proposed in the recent times.

Robust Chaos-Based Medical Image Cryptosystem

In In this paper, we propose an efficient cryptosystem for medical images. While the confusion stage is ensured by an Arnold's cat map allowing the permutation of pixels; the diffusion stage is alleviated by an improved logistic map used by the chaotic key-based algorithm (CKBA). The simulation results attest that the proposed algorithm has superior security and enables efficient encryption/decryption of medical images. Performances were evaluated by several security analyses: the NPCR and UACI are improved over 99.60% and 33.46% respectively, and entropy is reported close to 7.8. What makes this new cipher much stronger security.

Circulate Matrix and Compression Sensing Based Multi-Level Image Encryption

Digital data security is a broad research area in the field of science and technology. A lot of research was focused on information security-based mechanism for secure communication. This paper presents a novel image encryption as well as compression based on measurement matrix, pixel exchange and logistic cat map, which includes the permutation, compression, and diffusion processes. Initially the image is divided into four equal sizes of blocks and then each block is transformed into horizontal and vertical low and high frequency band. Then a random matrix multiplication function is applied to achieve an encrypted and scrambling frequency component and apply inverse DWT procedure to get first level of scrambled blocks, and further we apply the second level of security mechanism. Here each adjacent block pixel is exchanged by using the random matrices. For providing the high level of compression we design measurement matrices in compressive sensing by utilizing the circulate matrices and controlling the original column vectors of the circulate matrices with Arnold cat map. With the help of measurement matrix again the blocks are encrypted. Experimental results and performance analyses validate the good compression performance and high security of the given algorithm.

Secure Image Encryption Using Chaotic, Hybrid Chaotic and Block Cipher Approach.

Secure image transmission is one of the most challenging problems in the age of communication technology. Millions of people use and transfer images for either personal or commercial purposes over the internet. One way of achieving secure image transmission over the network is encryption techniques that convert the original image into a non-understandable or scrambled form, called a cipher image, so that even if the attacker gets access to the cipher they would not be able to retrieve the original image. In this study, chaos-based image encryption and block cipher techniques are implemented and analyzed for image encryption. Arnold cat map in combination with a logistic map are used as native chaotic and hybrid chaotic approaches respectively whereas advanced encryption standard (AES) is used as a block cipher approach. The chaotic and AES methods are applied to encrypt images and are subjected to measures of different performance parameters such as peak signal to noise ratio (PSNR), number of pixels change rate (NPCR), unified average changing intensity (UACI), and histogram and computation time analysis to measure the strength of each algorithm. The results show that the hybrid chaotic map has better NPCR and UACI values which makes it more robust to differential attacks or chosen plain text attacks. The Arnold cat map is computationally efficient in comparison to the other two approaches. However, AES has a lower PSNR value (7.53 to 11.93) and has more variation between histograms of original and cipher images, thereby indicating that it is more resistant to statistical attacks than the other two approaches.

An improved artificial bee Colony algorithm based on cat mapping and differential variation

An improved artificial bee Colony algorithm based on cat mapping and differential variation

A Novel Solar Photovoltaic Array Reconfiguration Technique Using Two-Dimensional Generalized Arnold's Cat Map

Abstract This paper presents a highly efficient image encryption-based Arnold's cat map (ACM) technique to reconfigure the photovoltaic (PV) array to enhance the output and mitigate the mismatch losses due to partial shading (PS). The proposed ACM technique concentrates on alleviating the power loss by effectively dispersing the shade over the entire PV array without modifying its electrical circuitry. The proposed reconfiguration technique is investigated and analyzed with conventional series–parallel and total-cross-tied configurations along with the recently reported chaotic Baker's map, odd–even, odd–even–prime pattern-based configurations. The proposed technique is examined for symmetrical 6 × 6 PV array and unsymmetrical 6 × 9 PV array under distinct nonuniform and uniform PS cases. To confirm the potency and superior performance of the proposed technique, the system has been extensively examined with nine performance parameters such as global maximum power, mismatch power, power loss, efficiency, fill factor, array yield, capacity factor, performance ratio, and the number of maximum power peaks. An experimental setup of a 4 × 4 array reconfiguration system prototype is developed and tested in a real-time environment to validate the effectiveness of the proposed technique over the existing ones. From the comprehensive investigation, it is regarded that the proposed technique offers consistently superior performance with the least percentage mismatch losses and maximum power enhancement of 48.8%, 31.03%, and 27.5% for various shading cases of 6 × 6 and 6 × 9 PV arrays.

Image encryption based on fractional chaotic pseudo-random number generator and DNA encryption method

Nonlinear dynamic systems and chaotic systems have been quite exhaustively researched in the domain of cryptography. However, the possibility of using fractional chaotic systems in the cryptosystem design has been much less explored while it bears advantages such as enlarged keyspace and better resistance to attack compared to classical nonlinear systems. This paper, therefore, proposes a novel structure for the pseudo-random number generator based on 3 different fractional chaotic systems, namely fractional Chen system, Lu system, and fractional generalized double-humped logistic map. Then, the outputs of this fractional chaotic pseudo-random number generator are used as a keystream for an image encryption scheme. The confusion layer of the scheme is conducted by a dynamic DNA encoding and decoding method combined with a 2D cat map for the permutation in the DNA bases level. The diffusion layer is performed through the adoption of a 32 bits discrete logistic map. The performance and security analyses have been conducted for the above-designed cryptosystem, proving that the proposed cryptosystem is practical and efficient, and can be successfully implemented in image encryption.

SecDH: Security of COVID-19 images based on data hiding with PCA

Nowadays, image security and copyright protection become challenging, especially after the COVID-19 pandemic. In the paper, we develop SecDH as a medical data hiding scheme, which can guarantee the security and copyright protection of the COVID-19 images. Firstly, the cover image is normalized, which offers high resistance against the geometric attacks. Secondly, the normalized principal component as embedding factor is computed, which are calculated based on principal component analysis (PCA) between cover and mark image. Thirdly, the medical image is invisibly marked with secret mark based on normalized component, redundant discrete wavelet transform (RDWT) and randomized singular value decomposition (RSVD) is introduced. Finally, Arnold cat map scheme employed to ensure the security of the watermarking system. Under the experimental evaluation, our SecDH tool is not only imperceptible, but also has a satisfactory advantage in robustness and security compared with the traditional watermarking schemes.

A new color image encryption algorithm using multiple chaotic maps with the intersecting planes method

This paper proposes a new and efficient color image encryption algorithm based on multiple chaotic maps (Logistic map, Sine map, and Chebyshev map) and the intersecting planes method inside a cube. All maps were used to fill the three adjacent faces of the cube. These faces represent the three channels of the color image (red, green, and blue). The first phase of our method begins with extracting all the pixels from the original image and looking for the corresponding values of each pixel on the three faces of the cube. Then, we used a circular rotation operation based on the position of each pixel (row, column). This rotation prevents two identical pixels to have the same encrypted value. Afterward, we used the intersecting planes method with the corresponding face to encrypt the pixels. For the confusion part, we chose the 2D transformation Arnold Cat Map to shuffle all the pixels and change their positions according to the parameters calculated from all the pixels of the original image. We evaluated the performance of our algorithm against various differential and statistical attacks and based on multiple factors, such as histogram, entropy, correlation coefficient, UACI, NPCR, and PSNR. We compared the proposed method with several efficient methods in the field. The various results got by our method show its performance and reliability in terms of safety, precision, confidentiality, and robustness.

Resource Optimized Selective Image Encryption of Medical Images Using Multiple Chaotic Systems

Medical images typically contain personal and diagnostic information about patients and are typically shared among hospitals, doctors, and patients via public networks. As a result, they must be kept secure while being stored and transported to protect the patient's privacy. However, due to the unique qualities of digital image data, such as significant redundancy and correlation between pixels and their huge size, traditional cryptographic techniques are ineffective for providing proper security while encrypting them. The necessity to develop enhanced and specialized image encryption algorithms arise as traditional techniques cease to be a trustworthy option. This problem motivated them to develop many low computational complexity methods to encrypt these medical images. In this research work, Block Cipher based Region of interest medical image encryption with multiple maps is proposed. Primarily, Region of Interest (ROI) regions are extracted with the help of a Laplacian edge detection operator, and then based on the edges in the blocks, the image is classified into wanted (ROI) and unwanted (RONI or ROB) parts. Next, the important ROI regions are permuted circularly with the help of Arnold's cat map and angle value. Then permuted ROI part is encrypted using the duffling system and unimportant regions are unaltered. Finally, the ROI encrypted image is obtained by concating the ROI encrypted part and the Region of Background (ROB) unaltered part. The encryption algorithm proposed has better security performance which is demonstrated in the experiments such as attacks on data loss, differential attacks, statistical attacks, and brute force attacks. These results show that the security in the proposed method is much better than many chaotic encryption algorithms proposed in recent times.

Enhanced design and hardware implementation of a chaos-based block cipher for image protection

Nowadays chaos-based cryptography systems are widely used to protect sensitive data. A variety of chaos-based cryptosystems with software implementation has been published in the literature. However, due to the rapid growth of connected devices, the development of hardware secure and low-resource cryptographic systems is necessary. In this paper, we enhance the design of one of our software cryptosystems and then we address its FPGA-based implementation. The improvement in the design consists essentially to introduce an Initial Vector (IV) entry to the Chaotic Pseudo Random Number Generator (CPRNG) thus allowing to generate a new dynamic keys for the confusion layer (using a modified 2-D cat map) and diffusion layer (using a logistic map) with each new execution of the system. The CPRNG is formed by XORred a discrete Skew Tent Map (STM) with a discrete Piecewise Linear Chaotic Map (PWLCM). The proposed cryptosystem, which operates in Cipher Block Chaining (CBC) mode, is controlled by a Finite State Machine (FSM) to ensure that both the encryption and decryption are performed by the same reconfigurable architecture. The system is implemented on a Xilinx XC7Z020 ZYNQ FPGA platform. The results obtained in terms of hardware implementation costs (logic resources, throughput, and efficiency) and in terms of security against cryptographic attacks demonstrate the effectiveness of the proposed chaos-based cryptosystem.

Performance Analysis of Chaotic Neural Network and Chaotic Cat Map Based Image Encryption

Nowadays, chaotic systems are used quite often, especially in image encryption applications. Hypersensitivity to the initial conditions, limited field-changing signs and irregular movements make these systems one of the critical elements in scientific matters such as cryptography. These systems are divided in two parts as discrete time and continuous time in terms of their dimensions and properties. Gray level image encryption applications generally use one-dimensional and color image encryption applications generally use multi-dimensional chaotic systems. In this study, Tent Map, Cat Map, Lorenz, Chua, Lu chaotic systems were used for chaotic neural network based image coding application and Logistic Map and 3D Cat Map chaotic systems were used for 3D chaotic Cat Map based image encryption application. The encrypted image and the original image were examined by various analysis methods. As a result of these analyzes, it was seen that both applications gave very successful results. Analyzes have shown that the chaotic neural network based image coding algorithm is more secure and successful.

Robustness of Modified Non-Separable HaarWavelet Transform and Singular Value Decomposition for Non-blind Digital Image Watermarking

Security is a matter of significant concern for image media. An effective way to protect images is by digital watermarking. This paper introduces a non-blind digital watermarking scheme using modified non-separable Haar wavelet transform (NSHWT), singular value decomposition (SVD), Arnold's cat map, and Rabin-p cryptosystem to embed a binary watermark image into a color cover image. Aside from robustness, security is also prioritized in the scheme. High robustness is achieved using two transform domain techniques, discrete wavelet transform (DWT) and SVD, while security is heightened with the double encryption by Arnold's cat map scrambling and Rabin-p cryptosystem. A disadvantage of the discrete wavelet transform in digital image watermarking is the calculation complexity and the high cost of changing memory and time. The proposed algorithm uses a modified NSHWT instead of the traditional method of DWT. Therefore, the load of the process on the hardware can significantly be reduced while still maintaining the advantages of DWT. The algorithm is objectively evaluated in terms of imperceptibility, robustness, and embedding capacity for both binary and color watermarks, as well as efficiency. It has been concluded that the proposed scheme performs competently compared with other recent watermarking techniques based on DWT and SVD.

Optimal reconfiguration of PV array based on digital image encryption algorithm: A comprehensive simulation and experimental investigation

Harvesting the optimal output from partially shaded PV arrays is a crucial issue. To address this, various reconfiguration techniques are reported in the literature. However, most of these techniques inherit numerous drawbacks such as compatibility issues, ineffective shade dispersal, numerous power peaks, inconsistent performance, increased mismatch, etc. Therefore, a novel reconfiguration approach based on Arnold’s Cat Map which is widely employed in image encryption is proposed in this work to overcome all the aforementioned issues. The proposed approach is tested for various symmetrical 9 × 9, 7 × 7, 6 × 6, 5 × 5, 4 × 4, and unsymmetrical 3 × 5, 4 × 3, 5 × 9, and 6 × 20 PV arrays under 100 shading cases. The performance of the proposed technique is compared with the 41 existing reconfiguration techniques for various array sizes. The proposed technique is experimentally validated in both indoor laboratory and outdoor environments for 4 × 4 and 3 × 5 PV arrays under distinct shading conditions. Further, to confirm the effectiveness and consistency of the proposed technique over the existing ones statistically, a Non-parametric Wilcoxon Signed-Rank test with a significant difference of 0.05 is considered for evaluation. The proposed technique yields the maximum enhancement in output by 30.81%, 36.36%, 38.15%, 33.77%, 16.62%, 21.8%, 18.42%, and 16.79% for 9 × 9, 7 × 7, 6 × 6, 5 × 5, 4 × 4, 4 × 3, 5 × 9, and 6 × 20 PV arrays respectively. From the comprehensive analysis, it is remarked that the lowest mismatch is obtained by the proposed encryption based-technique under all shading conditions.

On the implementation of large period piece-wise linear Arnold cat map

This paper presents a piece-wise linear cat map (PWLCM) obtained by perturbing the conventional quantized Arnold cat map (QACM) with a nonlinear term. The effect of the nonlinear term on the dynamics of the QACM is investigated. We show that the eigenvalues, hence the Lyapunov exponents of the PWLCM depend on the initial conditions, which is not the case for the QACM. As a result, the proposed PWLCM is a generalized form of the QACM, whose the period exponentially increases with respect to the precision, thus taking as value 1.09 × 10513 for only 10-bit precision; while that of the corresponding QACM is only 768. The nonlinear term increases the sensitivity of the system to the initial conditions, which contributes to increase its period, hence to enhance its complexity. An electronic implementation of both the QACM and the PWLCM in the case of 4-bit precision using Multisim is presented. The proposed architecture of both the QACM and the PWLCM are implemented using Verilog and prototyped on the Zynq 7020 FPGA board. For 4-bit precision, the FPGA implementation performs 1.072 Gbps throughput at 134 MHz maximum frequency. We verified that experimental and simulation behaviors of the proposed system perfectly match, thus confirming the effectiveness of the proposed electronic circuit for exhibiting the expected dynamics in real-time.

Management of Education and Correction of Problem Teenagers Based on Information Encryption Storage Method

In order to effectively realize the management of educational correction for problem teenagers, improve the security and reliability of encrypted storage of educational correction information for problem teenagers, and shorten the encrypted storage time of educational correction information for problem teenagers, educational correction management for problem teenagers based on information encryption storage method is proposed. Analyze the information encryption storage method and combine it with the necessary theoretical foundation of education and correction of issue teenagers to create an encryption and secure storage management method for education and correction of problem teenagers’ information. The CP-ABE algorithm is used to obtain the initial key of the system, express the encrypted cipher-text, specify the attributes of each user in the problematic youth education and correction user permission list, and obtain the problem youth education and correction user permission control structure. Using tent mapping and cat mapping methods, the key parameters are calculated, respectively, and the encrypted file is piecewise, linearly mapped. Then, XOR is the plaintext bytes and key bytes of the encrypted and safe storage of the problem youth’s education and correction information, completing the encrypted and safe storage of the data information in the problem youth’s education and correction management and realizing the problem youth’s education and correction management. The results of the experiments show that the proposed technology is secure and reliable and that it can efficiently reduce the encryption storage time of educational corrective material for troubled teenagers.

An 8-bit precision cipher for fast image encryption

Implementing chaos based ciphers usually involves 32-bit floating-point arithmetics that is hardware resources costly. The limitation of the computational precision is hardware imposed and transforms chaotic orbits into limit cycles with short periods, hence alters their randomness. In cryptographic applications, short period dynamics and weak randomness result in security issues. In order to address this concern, we propose an 8-bit precision cipher that can be implemented with low-end microprocessors running 8-bit integer arithmetics. The cipher includes a quantized pseudo-random number generator (QPRNG) based on a 16-dimensional quantized Arnold’s cat map (QACM). We used entropy measure, statistical, sensitivity and key space analyses to evaluate its security level under limited computational precision. Simulation results attest that it is as highly secure as those involving real-number arithmetics, even for only 8-bit precision. We also showed that the period of the proposed QACM can be chosen such that Tx > 1027, which is very large as compared to existing QACM. Such a large period implies a high randomness of the derived QPRNG that is confirmed by statistical NIST tests. Contrary to existing ciphers that include other chaotic systems than the QACM for strengthening the security level, ours is exclusively based on the QACM and is fast, despite the included high-dimensional QACM.

4-Weighted Fractional Fourier Transform based Multiple Image Encryption Approach with PAN

In this manuscript, a new encryption approach for multiple images is proposed based on 4-weighted fractionalfrequency transform (4-WFRFT) domain. First, the low frequency-components of all the images are obtained byapplying Fourier Transform on each image, which positioned at corner position of image, shifted to the centralposition. Low-frequency component of each individual image is then scrambled with help of Arnold cat mapwith its parameters and combined all scrambled image to form a single image with the same size that of originalimage which is now ready for encryption process. Here, parameters of Arnold cat map and transform order of 4-WFRFT treated as secret keys which are converted from Permanent Account Number (PAN) of authorize person.The encrypted image information generated by authorize person can be recovered by applying PAN at receiverside.

A novel image encryption scheme based on Arnold cat map, Newton-Leipnik system and Logistic Gaussian map

A novel image encryption scheme based on Arnold cat map, Newton-Leipnik system and Logistic Gaussian map

A Family of Non-Monotonic Toral Mixing Maps

We establish the mixing property for a family of Lebesgue measure preserving toral maps composed of two piecewise linear shears, the first of which is non-monotonic. The maps serve as a basic model for the ‘stretching and folding’ action in laminar fluid mixing, in particular flows where boundary conditions give rise to non-monotonic flow profiles. The family can be viewed as the parameter space between two well-known systems, Arnold’s Cat Map and a map due to Cerbelli and Giona, both of which possess finite Markov partitions and straightforward to prove mixing properties. However, no such finite Markov partitions appear to exist for the present family, so establishing mixing properties requires a different approach. In particular, we follow a scheme of Katok and Strelcyn, proving strong mixing properties with respect to the Lebesgue measure on two open parameter spaces. Finally, we comment on the challenges in extending these mixing windows and the potential for using the same approach to prove mixing properties in similar systems.