Chaotic Matrix Research Articles

Optimation of image encryption using fractal Tromino and polynomial Chebyshev based on chaotic matrix

Optimation of image encryption using fractal Tromino and polynomial Chebyshev based on chaotic matrix

A novel chaotic map-based encryption scheme for surveillance videos

The widespread use of surveillance cameras has initiated privacy concerns among individuals being captured by these devices. Due to the limited internal storage capacity, these cameras often transmit recorded videos over unreliable networks. This situation creates opportunities for attackers to exploit vulnerabilities, such as launching Man-in-the-Middle attacks, replayed scene attacks, and tampering with the video content. Considering these risks, this paper introduces a new chaotic map-based encryption scheme for surveillance videos. The work proposes a novel chaotic map using cascading and coupling operations on functions and is referred to as a Cascaded Coupled Logistic-Sine-Cosine (CCLSC) map. The chaotic performance of the novel CCLSC map has been evaluated using the Lyapunov exponent and the Bifurcation diagram. The scheme to encrypt surveillance videos is designed using the novel CCLSC map and our earlier designed Sine-Tangent-Sine (STS) chaotic map. The process involves extracting individual frames from the video and subsequently encrypts each frame as a digital image. The encryption of each frame involves three steps. The first step generates a Dynamic Chaotic Matrix (DCM) using CCLSC and STS map. The second phase is pixel scrambling using DCM and the final step changes the pixel values using DCM. Our results validate the security, robustness, and effectiveness of the proposed method.

Expanded multi-scroll attractor system analysis and application for remote sensing image encryption

Exploring special multi-scroll chaotic systems is meaningful work. This paper studies an expanded multi-scroll chaotic system consisting of eight terms with one nonlinearity. It is generated by modifying the nonlinear term of the newly constructed chaotic system by a polynomial function. The unique mathematical model makes the unstable index-2 equilibria increase in four dimensions, which contributes to the number of scrolls expanding in each phase plane unidirectionally. Dynamic analysis finds that the system can yield complex nested multi-scroll attractors and has single-parameter-based synchronization control of amplitude and offset boosting behavior. Moreover, circuit implementation verifies the physical existence of the proposed system. Also, an image encryption algorithm for remote sensing images is established. Permutation and diffusion operations are performed using new pixel coordinates derived from the data of the chaotic matrix, which comes from the same position as the pixel matrix. Relevant tests suggest that the algorithm is secure and able to resist undesirable interference.

A random optimization strategy of microgrid dispatching based on stochastic response surface method considering uncertainty of renewable energy supplies and load demands

The stochastic response of microgrid regulation under the influence of uncertainty should be considered in the day-ahead optimal dispatching. This paper focuses on the Stochastic Response Surface Method (SRSM) modelling and Second-Order Cone Programming (SOCP) optimal solution for the stochastic optimization strategy of microgrid dispatching considering the random fluctuations of renewable energy supplies and load demands. Based on the SRSM theory, the random distributions of uncertainty are converted into independent standard normal distributions by Nataf transformation, then by means of a small amount of standardized SRSM samples of random fluctuations, the Hermite Chaotic Polynomials can be formulated to describe the random response process of microgrid adjustment. And the Hermite Chaotic Matrix establishes the linear constraint functions for the probability distribution characteristics of stochastic response process of microgrid adjustment considering uncertainty. On this basis, the SRSM based stochastic optimization (SO) model with multi-objective functions are constructed for the optimal economic operation, control of cost fluctuation and lower carbon emissions. In addition, to reduce operation risk, the constraints of extreme power shortage are introduced into the model. To ensure the convexity of the optimization model, the Second-Order Cone Relaxation is applied to all the quadratic terms in the model. Thus, the proposed SO model of microgrid dispatching can be transformed into an SOCP optimization problem. And the Yalmip-Gurobi solver is adopted for the solution of the proposed SO model, which has an efficient operation speed and stability. The effectiveness of the proposed scheme is demonstrated by the case studies using Monte Carlo sampling simulation.

Color Image Encryption Algorithm Based on Cross-Spiral Transformation and Zone Diffusion

Due to their rich information, color images are frequently utilized in many different industries, but the network’s security in handling their delivery of images must be taken into account. To improve the security and efficiency of color images, this paper proposed a color image encryption algorithm based on cross-spiral transformation and zone diffusion. The proposed algorithm is based on Chen’s system and the piecewise linear chaotic map, and uses the chaotic sequences generated by them for related operations. Firstly, the R, G and B planes are extracted, and the spiral starting point of each plane is randomly selected by the chaotic sequence to implement the cross-spiral transformation. Secondly, the bit-level image matrix is constructed by the scrambled image matrix, and the bit-level chaotic matrix is constructed by the chaotic sequence. Finally, the three-dimensional matrix is divided into four zones by a dividing line, and partition diffusion is carried out to obtain the encrypted image. Simulation results and algorithm analyses indicate that the proposed algorithm has superior performance and can resist a wide range of attacks.

A Novel Fractional Sine Chaotic Map and Its Application to Image Encryption and Watermarking

This article addresses the telecommunications industry’s priority of ensuring information security during the transition to next-generation networks. It proposes an image encryption system that combines watermarking techniques and a discrete fractional sine chaotic map. The authors also incorporate the principles of blockchain to enhance the security of transmitted and received image data. The proposed system utilizes a newly developed sine chaotic map with a fractional difference operator, exhibiting long-term chaotic dynamics. The complexity of this map is demonstrated by comparing it with three other fractional chaotic maps from existing literature, using bifurcation diagrams and the largest Lyapunov exponent. The authors also show the map’s sensitivity to changes in initial conditions through time-series diagrams. To encrypt images, the authors suggest a method involving watermarking of two secret images and encryption based on blockchain technology. The cover image is watermarked with the two hidden images using discrete wavelet transformations. Then, the image pixels undergo diffusion using a chaotic matrix generated from the discrete fractional sine chaotic map. This encryption process aims to protect the image data and make it resistant to unauthorized access. To evaluate the algorithm, the authors perform statistical analysis and critical sensitivity analysis to examine its characteristics. They also analyse different attacks to assess the algorithm’s ability to resist such threats and maintain image quality after decryption. The results demonstrate that the proposed algorithm effectively defends against attacks and ensures image security.

Image encryption algorithm based on a new chaotic system with Rubik's cube transform and Brownian motion model

In this paper a new two-dimensional chaotic map based on Logistic map and Chebyshev map is proposed. The performance analysis and evaluation show the proposed map has a very wide range of chaos and good ergodicity. Further, a new image encryption algorithm is designed using the chaotic map with Rubik's Cube transform and Brownian motion model. The encryption process is ‘confusion - Rubik's cube transformation - diffusion’. In the confusion stage, a method combining Brownian motion theory and chaotic sequence is proposed. Then combining the advantages of chaotic system and Rubik's cube, a Rubik's Cube transformation algorithm is proposed. The scrambled pixel matrix and the chaotic matrix are spliced into a hexahedron structure, and the Rubik's Cube is dynamically scrambled through a pseudo-random sequence. Finally, the XOR operation is performed on the basis of the two-dimensional Hénon chaotic map. The experimental results show that the algorithm has the advantages of large key space, strong robustness and high security, and can resist common cryptanalysis attacks.

A novel cancelable fingerprint scheme based on random security sampling mechanism and relocation bloom filter

The existing cancellable fingerprint template based on the bloom filter either suffers from a lack of template security or low recognition performance. To solve the above problems, the paper proposes a novel cancelable fingerprint protection scheme based on a random sampling mechanism and relocation bloom filter. The security matrix is generated by a random sampling mechanism to increase the security and recognition accuracy of the scheme. The structure of a random sampling mechanism is as follows. Firstly, we use the key management system to generate keys and a chaotic matrix with randomness. Secondly, the key is used as a random initial address to extract overlapping feature sub-blocks from fingerprint features. Then the feature sub-blocks are combined to generate a feature matrix. Therefore, the feature matrix has richer fingerprint information than the original fingerprint features. Finally, a security matrix is generated by the XOR fusion of features matrix and chaotic matrix. Furthermore, we designed a relocation bloom filter with a parallel structure, which provides a way to avoid the decrease in performance caused by hash conflicts. What is more, it increased the security of the scheme that the relocatable bloom uses an irreversible function mapping function to transform the security matrix into a cancelable fingerprint template. The experimental results demonstrate that this scheme has state-of-the-art accuracy performance on benchmark FVC2002 and FVC2004 fingerprint databases. The security analysis shows that the scheme meets the cancellable biometrics protection scheme criteria and has higher security.

Image Encryption Algorithm Based on a Novel Wide-Range Discrete Hyperchaotic Map

Existing hyperchaotic systems suffer from a small parameter range and small key space. Therefore, we propose herein a novel wide-range discrete hyperchaotic map(3D-SCC) based on the mathematical model of the Sine map. Dynamic numerical analysis shows that this map has a wide-range of parameters, high sensitive, high sensitivity of sequences and good ergodicity, which proves that the system is well suited to the field of communication encryption. Moreover, this paper proposes an image encryption algorithm based on a dynamic cycle shift scramble algorithm and image-sensitive function. First, the image feature is extracted by the image-sensitive function to input into the chaos map. Then, the plaintext image is decomposed by an integer wavelet, and the low-frequency part is scrambled by a dynamic cyclic shifting algorithm. The shuffled low-frequency part and high-frequency parts are reconstructed by wavelet, and the chaotic matrix image is bitwise XOR with it to obtain the final ciphertext. The experimental results show that the average NPCR is 99.6024%, the average UACI is 33.4630%, and the average local Shannon entropy is 7.9029, indicating that the statistical properties of the ciphertext are closer to the ideal value. The anti-attack test shows that the algorithm can effectively resist cutting attacks and noise attacks. Therefore, the algorithm has great application value in the field of image encryption.

Blockchain enabled optimal Hopfield Chaotic Neural network based secure encryption technique for industrial internet of things environment

Industrial Internet of Things (IIoT) denotes a network of interlinked sensors, instruments, and other devices for industrial applications in the domains of manufacturing, logistics, transportation, etc. IIoT security is a major crucial research area for several applications. Image encryption techniques gained popularity in the recent years, thanks to increasing requirements for secure image transmission in IIoT environments. At the same time, conventional security solutions built for sensitive data protection are getting outdated in IIoT environment due to the participation of third party. Blockchain (BC) is one of the recent solutions used for security purpose which eliminates the involvement of a third party. With this motivation, the current research article presents a new BC-Enabled Shark Smell Optimization with Hopfield Chaotic Neural Network (SSO-HCNN) for secure encryption in IoT environment. The proposed SSO-HCNN model exploits a composite Chaotic Map (CM) which is integrated into staged logistic and tent maps to initially process the images and develop the variables needed for Arnold mapping. In addition, the SSO algorithm is developed with maximum PSNR and coefficient fitness function to select the optimum secret and public keys of the system amongst the random numbers. Besides, the diffusion phase utilizes HCNN to create a self-diffusion chaotic matrix whereas the jumbled image performs XOR operation using the keys to obtain the cipher image. In SSO-HCNN model, the cryptographic pixel value in the image is saved on BC thus guaranteeing the security and privacy of the images. To examine the superior performance of SSO-HCNN model over state-of-the-art methods, a set of simulations was conducted on benchmark test images. The simulation results of the proposed SSO-HCNN model were promising under different evaluation parameters.

Secure collaborative cognitive radio based on chaotic modulation and compressive sensing

Cognitive radio (CR) is a wireless technology that is used to overcome the spectrum scarcity problem. CR includes several stages, spectrum sensing is the first stage in the CR cycle. Traditional spectrum sensing (SS) techniques have many challenges in the wideband spectrum. CR security is an important problem, since when an attacker from outside the network access the sensing information this produces an increase in sensing time and reduces the opportunities for exploiting vacant band. Compressive sensing (CS) is proposed to capture all the wideband spectrum at the same time to solve the challenges and improve the performance in the traditional techniques and then one of the traditional SS techniques are applied to the reconstructed signal for detection purpose. The sensing matrix is the core of CS must be designed in a way that produces a low reconstruction error with high compression. There are many types of sensing matrices, the chaotic matrix is the best type in terms of security, memory storage, and system performance. Few works in the literature use the chaotic matrix in CS based CR and these works have many challenges: they used sample distance in the chaotic map to generate a chaotic sequence which consumes high resources, they did not take into consideration the security in reporting channel, and they did not measure their works using real primary user (PU) signal of a practical application under fading channel and low SNR values. In this paper, we propose a chaotic CS based collaborative scenario to solve all challenges that have been presented. We proposed a chaotic matrix based on the Henon map and use the differential chaotic shift keying (DCSK) modulation to transmit the measurement vector through the reporting channel to increase the security and improve the performance under fading channel. The simulation results are tested based on a recorded real-TV signal as PU and Compressive Sampling Matching Pursuit (CoSaMP) recovery algorithm under AWGN and TDL-C fading channels in collaborative and non-collaborative scenarios. The performance of the proposed system has been measured using recovery error, mean square error (MSE), derived probability of detection (Pdrec), and sensitivity to initial values. To measure the improvement introduced by the proposed system, it is evaluated in comparison with selected chaotic and random matrices. The results show that the proposed system provides low recovery error, MSE, with high Pdrec, security, and compression under SNR equal to −30 dB in AWGN and TDL-C fading channels as compared to other matrices in the literature.

Dynamic analysis and image encryption application of a sinusoidal-polynomial composite chaotic system

Due to complex properties of ergodicity, non-periodic ability and sensitivity to initial states, chaotic systems are widely used in cryptography. In this paper, we propose a sinusoidal-polynomial composite chaotic system (SPCCS), and prove that it satisfies Devaney’s definition of chaos: the sensitivity to initial conditions, topological transitivity and density of periodic points. The experimental results show that SPCCS has better unpredictability and more complex chaotic behavior than the classical chaotic maps. Furthermore, we provide a new image encryption algorithm combining pixel segmentation operation, block chaotic matrix confusing operation and pixel diffusion operation with the proposed SPCCS. The detailed simulation results verify superiority and effectiveness of the proposed image encryption algorithm.

Compressive sensing based on novel chaotic matrix for cognitive radio

SummaryCognitive radio (CR) is an emerging technology for optimum spectrum utilization. Spectrum sensing (SS) is the first step of CR. Important challenge in the next generations is wideband SS. Compressive sensing (CS) can be used as an SS in CR to solve this challenge. Sensing matrix (SM) plays an important role in CS. For better performance, SM must have low mutual coherence. The existing matrices in the literature are random and chaotic. All random matrices have a good performance, but they have problems of large memory storage, complexity, sharing bandwidth, and low security. Chaotic matrices (CMs) are the best but still have some problems including the use of sample distance in chaotic sequence that consumes high storage resources, low performance and compression under low signal‐to‐noise ratio (SNR), and low security. In this paper, we propose a new 1‐D chaotic map for constructing a novel SM. The proposed map has simple structure, wide range chaotic behavior, and high security. Its chaotic behavior is confirmed using Lyapunov exponent, bifurcation, and trajectory. The CS performance based on novel CM is measured using absolute error ( , mutual coherence, memory cost, computational complexity, and MSE (mean square error), while evaluated through comparisons with matrices in the literature. The simulation and mathematical results show that the proposed map is a hyperchaotic with efficient chaotic behavior in wide range of parameters and low memory storage and complexity. The results also show that it has low , MSE, and mutual coherence at low SNR with high compression.

Enhancing the Security of Digital Image Encryption using Diagonalize Multidimensional Nonlinear Chaotic System

This paper describes a new efficient cryptosystem for the color image encryption technique, based on a combination of multidimensional proposed chaos systems. This chaos system consists of six bisections: T_1 (x),T_2 (x),T_2 (y),T_3 (x),T_3 (y), andT_3 (z). They induce three chaotic matrix keys and three chaotic vector keys. We use a multidimensional chaotic system together with an encryption algorithm to provide better security and wide key spaces. The proposed cryptosystem uses four levels of random pixel diffusions and permutations simultaneously and ω - times interchange between rows and columns. The correlations between the RGB components of the plain image are reduced. The level of security, the computational complexity, the quality of decoding a decrypted image under closure threat is improved. The simulation results showed that the algorithm shows a high level of security, and the assurance that the image recovered at the receiving point is identified as the image at the transmission point.

CHAOTIC COMPRESSIVE SENSING OF TV –UHF BAND IN IRAQ USING CHEBYSHEV GRAM SCHMIDT SENSING MATRIX

Cognitive radio (CR) is a promising technology for solving spectrum sacristy problem. Spectrum sensing is the main step of CR. Sensing the wideband spectrum produces more challenges. Compressive sensing (CS) is a technology used as spectrum sening in CR to solve these challenges. CS consists of three stages: sparse representation, encoding and decoding. In encoding stage sensing matrix are required, and it plays an important role for performance of CS. The design of efficient sensing matrix requires achieving low mutual coherence . In decoding stage the recovery algorithm is applied to reconstruct a sparse signal. İn this paper a new chaotic matrix is proposed based on Chebyshev map and modified gram Schmidt (MGS). The CS based proposed matrix is applied for sensing real TV signal as a PU. The proposed system is tested under two types of recovery algorithms. The performance of CS based proposed matrix is measured using recovery error (Re), mean square error (MSE), and probability of detection (Pd) and evaluated by comparing it with Gaussian, Bernoulli and chaotic matrix in the literature. The simulation results show that the proposed system has low Re and high Pd under low SNR values and has low MSE with high compression.

Medical image encryption algorithm based on a new five-dimensional three-leaf chaotic system and genetic operation.

Current image encryption methods have many shortcomings for the medical image encryption with high resolution, strong correlation and large storage space, and it is difficult to obtain reliable clinically applicable medical images. Therefore, this paper proposes a medical image encryption algorithm based on a new five-dimensional three-leaf chaotic system and genetic operation. And the dynamic analysis of the phase diagram and bifurcation diagram of the five-dimensional three-leaf chaotic system selected in this paper is carried out, and NIST is used to test the randomness of its chaotic sequence. This algorithm follows the diffusion-scrambling framework, especially using the principle of DNA recombination combined with the five-dimensional three-leaf chaotic system to generate a chaotic matrix that participates in the operation. The bit-level DNA mutation operation is introduced in the diffusion, and the scrambling and diffusion effects have been further improved. Algorithm security and randomness have been enhanced. This paper evaluates the efficiency of this algorithm for medical image encryption in terms of security analysis and time performance. Security analysis is carried out from key space, information entropy, histogram, similarity between decrypted image and original image, PSNR, correlation, sensitivity, noise attack, cropping attack and so on. Perform time efficiency analysis from the perspective of time performance. The comparison between this algorithm and the experimental results obtained by some of the latest medical image encryption algorithms shows that this algorithm is superior to the existing medical image encryption algorithms to a certain extent in terms of security and time efficiency.

Multi-channel monitoring data compression method for industrial robot based on compressed sensing

To address the problems of considerable redundancy and weak transmission security of multi-channel real-time vibration monitoring data of industrial robots, in this research a compressed sensing (CS)-based method to compress multi-channel industrial robot monitoring data has been proposed. Firstly, the multi-sensor data of the robot is fused into a comprehensive signal by the cross-correlation function fusion algorithm, which can significantly reduce the signal redundancy among sensors and improve the signal quality. Then, the discrete cosine transform matrix is used for sparse decomposition analysis of the synthetic signal. Finally, CS technology and chaotic matrix are used to encrypt and compress the integrated signal to achieve efficient encryption transmission. The experimental results show that the method can significantly reduce the amount of data transmitted and enhance the encryption performance during transmission without sacrificing helpful information and ensuring signal transmission efficiency and security.

Depositional Heterogeneities and Brittleness of Mudstone Lithofacies in the Marcellus Subgroup, Appalachian Basin, New York, U.S.A.

Organic-rich rocks of the Marcellus subgroup in the study area consist of a diverse suite of mudstone lithofacies that were deposited in distinct facies belts. Lithofacies in the succession range in composition from argillaceous to siliceous, calcareous, and carbonaceous mudstone. Heterogeneities in the succession occurs in the form of varying mineralogical composition, slightly bioturbated to highly bioturbated chaotic matrix, organic-rich and organic-lean laminae, scattered fossil shells in the matrix, and fossils acting as lamination planes. Lithofacies were deposited in three facies belts from the proximal to the distal zone of the depositional system. Bedded siliceous mudstone (BSM) facies occur in the proximal facies belt and consists of a high quartz content in addition to clay minerals and pyrite. In the medial part of the facies belt lies the laminated argillaceous mudstone (LAM), bedded calcareous mudstone (BCaM), and bedded carbonaceous mudstone (BCM). The size of detrital mineral grains in the lithofacies of the medial facies belt is larger than bedded argillaceous mudstone (BAM) of the distal facies belt, characterized by clay-rich matrix with occasional fossil shells and horizontally aligned fossils. Two types of horizontal traces and one type of fecal string characterize the proximal mud-stone facies, whereas only single horizontal trace fossil is found in the mudstones of the medial and distal facies belt. Parallel alignment of fossil shells and fossil lags in lithofacies indicate that bed-load transport was active periodically from the proximal source of the depositional system. Bioturbation has heavily affected all of the lithofacies and presence of mottled burrows as well as Devonian fauna indicate that oxic to dysoxic conditions prevailed during deposition. The deposition of this organic-rich mudstone succession through dynamic processes in an overall oxic to dysoxic environment is different from conventional anoxic depositional models interpreted for most of the organic rich black shales worldwide. Total organic content (TOC) varies from top to bottom in the succession and is highest in BCM facies. The brittleness index, calculated on the basis of mineralogy, allowed classification of the lithofacies into three distinct zones, i.e., a brittle zone, a less brittle zone, and a ductile zone with a general proximal to distal decrease in the brittle behavior due to a decrease in the size of the sediments.

Image encryption algorithm based on the fractional Hermite transform

A new image encryption algorithm is proposed by combining fractional Hermite transform (FHT) with hyper-chaos map. In the first round of pixel scrambling, the original image is performed by the Zigzag operation and the Arnold transform. Then the scrambled image matrix is XORed with an encryption sequence composed of an 8-bit linear feedback shift register. Compared with the traditional Hermite transform, the FHT has better noise tolerance, and it could process the non-stationary input signals better. Subsequently, the encrypted data is re-encrypted by the cyclic shift operation based on the hyper-chaotic system. The four initial values of the hyper-chaotic system are obtained by combining plaintext image with SHA-512. Finally, the processed image matrix is XORed with a chaotic matrix generated by the three-dimensional Logistic-sine-coupling map. The presented image encryption algorithm has a large key space and strong anti-noise ability. Simulation results show that the proposed algorithm is feasible, secure and effective.

An efficient image encryption scheme based on fractal Tromino and Chebyshev polynomial

The security of digital content during transmission and storage through insecure communication links and databases is a challenging issue in today's world. In this article, an encryption scheme based on fractal Tromino and Chebyshev polynomial-based generated chaotic matrix is presented. The scheme fulfills the most fundamental aspect of encryption that is diffusion and confusion. For confusion highly non-linear, pre-defined S-boxes are used. The proposed scheme has been tested using state-of-the-art key performance indicators including differential analysis, statistical analysis. Information entropy analysis, mean square error, and NIST-based randomness analysis. The encrypted images have the highest practically achievable entropy of 7.999 and the time analysis shows that the proposed system is suitable for real-time implementation. The rest of the results indicates that the proposed cryptosystem possesses high immunity toward various attacks. The security analysis compared with the existing scheme shows the strength of the suggested scheme.