Chaotic CS Encryption:An Efficient Image Encryption Algorithm Based on Chebyshev Chaotic System and Compressive Sensing

Images are the most important carrier of human information. Moreover, how to safely transmit digital imagesthrough public channels has become an urgent problem. In this paper, we propose a novel image encryptionalgorithm, called chaotic compressive sensing (CS) encryption (CCSE), which can not only improve the efficiencyof image transmission but also introduce the high security of the chaotic system. Specifically, the proposed CCSEcan fully leverage the advantages of the Chebyshev chaotic system and CS, enabling it to withstand various attacks,such as differential attacks, and exhibit robustness. First, we use a sparse trans-form to sparse the plaintext imageand then use theArnold transformto perturb the image pixels. After that,we elaborate aChebyshev Toeplitz chaoticsensing matrix for CCSE. By using this Toeplitz matrix, the perturbed image is compressed and sampled to reducethe transmission bandwidth and the amount of data. Finally, a bilateral diffusion operator and a chaotic encryptionoperator are used to perturb and expand the image pixels to change the pixel position and value of the compressedimage, and ultimately obtain an encrypted image. Experimental results show that our method can be resistant tovarious attacks, such as the statistical attack and noise attack, and can outperform its current competitors.

Double quantum images encryption scheme based on chaotic system

This paper explores a double quantum images representation(DNEQR)model that allows for simultaneous storage of two digital images in a quantum superposition state.Additionally,a new type of two-dimensional hyperchaotic system based on sine and logistic maps is investigated,offering a wider parameter space and better chaotic behavior compared to the sine and logistic maps.Based on the DNEQR model and the hyperchaotic system,a double quantum images encryption algorithm is proposed.Firstly,two classical plaintext images are transformed into quantum states using the DNEQR model.Then,the proposed hyperchaotic system is employed to iteratively generate pseudo-random sequences.These chaotic sequences are utilized to perform pixel value and position operations on the quantum image,resulting in changes to both pixel values and positions.Finally,the ciphertext image can be obtained by qubit-level diffusion using two XOR operations between the position-permutated image and the pseudo-random sequences.The corresponding quantum circuits are also given.Experimental results demonstrate that the proposed scheme ensures the security of the images during transmission,improves the encryption efficiency,and enhances anti-interference and anti-attack capabilities.

Chaotic Map-Based Authentication and Key Agreement Protocol with Low-Latency for Metasystem

With the rapid advancement in exploring perceptual interactions and digital twins,metaverse technology has emerged to transcend the constraints of space-time and reality,facilitating remote AI-based collaboration.In this dynamic metasystem environment,frequent information exchanges necessitate robust security measures,with Authentication and Key Agreement(AKA)serving as the primary line of defense to ensure communication security.However,traditional AKA protocols fall short in meeting the low-latency requirements essential for synchronous interactions within the metaverse.To address this challenge and enable nearly latency-free interactions,a novel low-latency AKA protocol based on chaotic maps is proposed.This protocol not only ensures mutual authentication of entities within the metasystem but also generates secure session keys.The security of these session keys is rigorously validated through formal proofs,formal verification,and informal proofs.When confronted with the Dolev-Yao(DY)threat model,the session keys are formally demonstrated to be secure under the Real-or-Random(ROR)model.The proposed protocol is further validated through simulations conducted using VMware workstation compiled in HLPSL language and C language.The simulation results affirm the protocol’s effectiveness in resisting well-known attacks while achieving the desired low latency for optimal metaverse interactions.

A color image encryption scheme based on a 2D coupled chaotic system and diagonal scrambling algorithm

A novel color image encryption scheme is developed to enhance the security of encryption without increasing the complexity. Firstly, the plain color image is decomposed into three grayscale plain images, which are converted into the frequency domain coefficient matrices(FDCM) with discrete cosine transform(DCT) operation. After that, a twodimensional(2D) coupled chaotic system is developed and used to generate one group of embedded matrices and another group of encryption matrices, respectively. The embedded matrices are integrated with the FDCM to fulfill the frequency domain encryption, and then the inverse DCT processing is implemented to recover the spatial domain signal. Eventually,under the function of the encryption matrices and the proposed diagonal scrambling algorithm, the final color ciphertext is obtained. The experimental results show that the proposed method can not only ensure efficient encryption but also satisfy various sizes of image encryption. Besides, it has better performance than other similar techniques in statistical feature analysis, such as key space, key sensitivity, anti-differential attack, information entropy, noise attack, etc.

Bipolar-growth multi-wing attractors and diverse coexisting attractors in a new memristive chaotic system

This article proposes a non-ideal flux-controlled memristor with a bisymmetric sawtooth piecewise function, and a new multi-wing memristive chaotic system(MMCS) based on the memristor is generated. Compared with other existing MMCSs, the most eye-catching point of the proposed MMCS is that the amplitude of the wing will enlarge towards the poles as the number of wings increases. Diverse coexisting attractors are numerically found in the MMCS, including chaos,quasi-period, and stable point. The circuits of the proposed memristor and MMCS are designed and the obtained results demonstrate their validity and reliability.

Rucklidge-based memristive chaotic system:Dynamic analysis and image encryption

A new four-dimensional(4D)memristive chaotic system is obtained by introducing a memristor into the Rucklidge chaotic system,and a detailed dynamic analysis of the system is performed.The sensitivity of the system to parameters allows it obtains 16 different attractors by changing only one parameter.The various transient behaviors and excellent spectral entropy and C0 complexity values of the system can also reflect the high complexity of the system.A circuit is designed and verified the feasibility of the system from the physical level.Finally,the system is applied to image encryption,and the security of the encryption system is analyzed from multiple aspects,providing a reference for the application of such memristive chaotic systems.

A Speech Cryptosystem Using the New Chaotic System with a Capsule-Shaped Equilibrium Curve

In recent years,there are numerous studies on chaotic systems with special equilibrium curves having various shapes such as circle,butterfly,heart and apple.This paper describes a new 3-D chaotic dynamical system with a capsule-shaped equilibrium curve.The proposed chaotic system has two quadratic,two cubic and two quartic nonlinear terms.It is noted that the proposed chaotic system has a hidden attractor since it has an infinite number of equilibrium points.It is also established that the proposed chaotic system exhibits multi-stability with two coexisting chaotic attractors for the same parameter values but differential initial states.A detailed bifurcation analysis with respect to variations in the system parameters is portrayed for the new chaotic system with capsule equilibrium curve.We have shown MATLAB plots to illustrate the capsule equilibrium curve,phase orbits of the new chaotic system,bifurcation diagrams and multi-stability.As an engineering application,we have proposed a speech cryptosystem with a numerical algorithm,which is based on our novel 3-D chaotic system with a capsule-shaped equilibrium curve.The proposed speech cryptosystem follows its security evolution and implementation on Field Programmable Gate Array(FPGA)platform.Experimental results show that the proposed encryption system utilizes 33%of the FPGA,while the maximum clock frequency is 178.28 MHz.

Data encryption based on a 9D complex chaotic system with quaternion for smart grid

With the development of smart grid, operation and control of a power system can be realized through the power communication network, especially the power production and enterprise management business involve a large amount of sensitive information, and the requirements for data security and real-time transmission are gradually improved. In this paper, a new 9-dimensional(9D) complex chaotic system with quaternion is proposed for the encryption of smart grid data. Firstly, we present the mathematical model of the system, and analyze its attractors, bifurcation diagram, complexity,and 0–1 test. Secondly, the pseudo-random sequences are generated by the new chaotic system to encrypt power data.Finally, the proposed encryption algorithm is verified with power data and images in the smart grid, which can ensure the encryption security and real time. The verification results show that the proposed encryption scheme is technically feasible and available for power data and image encryption in smart grid.

Realizing reliable XOR logic operation via logical chaotic resonance in a triple-well potential system

There exists an optimal range of intensity of a chaotic force in which the behavior of a chaos-driven bistable system with two weak inputs can be consistently mapped to a specific logic output. This phenomenon is called logical chaotic resonance(LCR). However, realization of a reliable exclusive disjunction(XOR) through LCR has not been reported.Here, we explore the possibility of using chaos to enhance the reliability of XOR logic operation in a triple-well potential system via LCR. The success probability P of obtaining XOR logic operation can take the maximum value of 1 in an optimal window of intensity D of a chaotic force. Namely, success probability P displays characteristic bell-shaped behavior by altering the intensity of the chaotic driving force, indicating the occurrence of LCR. Further, the effects of periodic force on LCR have been investigated. For a subthreshold chaotic force, a periodic force with appropriate amplitude and frequency can help enhance the reliability of XOR logic operation. Thus, LCR can be effectively regulated by changing the amplitude and frequency of the periodic force.

A Novel Internet of Medical Thing Cryptosystem Based on Jigsaw Transformation and Ikeda Chaotic Map

Image encryption has attracted much interest as a robust security solution for preventing unauthorized access to critical image data.Medical picture encryption is a crucial step in many cloud-based and healthcare applications.In this study,a strong cryptosystem based on a 2D chaotic map and Jigsaw transformation is presented for the encryption of medical photos in private Internet of Medical Things(IoMT)and cloud storage.A disorganized three-dimensional map is the foundation of the proposed cipher.The dispersion of pixel values and the permutation of their places in this map are accomplished using a nonlinear encoding process.The suggested cryptosystem enhances the security of the delivered medical images by performing many operations.To validate the efficiency of the recommended cryptosystem,various medical image kinds are used,each with its unique characteristics.Several measures are used to evaluate the proposed cryptosystem,which all support its robust security.The simulation results confirm the supplied cryptosystem’s secrecy.Furthermore,it provides strong robustness and suggested protection standards for cloud service applications,healthcare,and IoMT.It is seen that the proposed 3D chaotic cryptosystem obtains an average entropy of 7.9998,which is near its most excellent value of 8,and a typical NPCR value of 99.62%,which is also near its extreme value of 99.60%.Moreover,the recommended cryptosystem outperforms conventional security systems across the test assessment criteria.

Numerical Simulation of the Fractional-Order Lorenz Chaotic Systems with Caputo Fractional Derivative

Although some numerical methods of the fractional-order chaotic systems have been announced,high-precision numerical methods have always been the direction that researchers strive to pursue.Based on this problem,this paper introduces a high-precision numerical approach.Some complex dynamic behavior of fractional-order Lorenz chaotic systems are shown by using the present method.We observe some novel dynamic behavior in numerical experiments which are unlike any that have been previously discovered in numerical experiments or theoretical studies.We investigate the influence of α_(1),α_(2),α_(3) on the numerical solution of fractional-order Lorenz chaotic systems.The simulation results of integer order are in good agreement with those of othermethods.The simulation results of numerical experiments demonstrate the effectiveness of the present method.

Bayesian system identification and chaotic prediction from data for stochastic Mathieu-van der Pol-Duffing energy harvester

In this paper,the approximate Bayesian computation combines the particle swarm optimization and se-quential Monte Carlo methods,which identify the parameters of the Mathieu-van der Pol-Duffing chaotic energy harvester system.Then the proposed method is applied to estimate the coefficients of the chaotic model and the response output paths of the identified coefficients compared with the observed,which verifies the effectiveness of the proposed method.Finally,a partial response sample of the regular and chaotic responses,determined by the maximum Lyapunov exponent,is applied to detect whether chaotic motion occurs in them by a 0-1 test.This paper can provide a reference for data-based parameter iden-tification and chaotic prediction of chaotic vibration energy harvester systems.

Video Transmission Secrecy Improvement Based on Fractional Order Hyper Chaotic System

In the Digital World scenario,the confidentiality of information in video transmission plays an important role.Chaotic systems have been shown to be effective for video signal encryption.To improve video transmission secrecy,compressive encryption method is proposed to accomplish compression and encryption based on fractional order hyper chaotic system that incorporates Compressive Sensing(CS),pixel level,bit level scrambling and nucleotide Sequences operations.The measurement matrix generates by the fractional order hyper chaotic system strengthens the efficiency of the encryption process.To avoid plain text attack,the CS measurement is scrambled to its pixel level,bit level scrambling decreases the similarity between the adjacent measurements and the nucleotide sequence operations are done on the scrambled bits,increasing the encryption.Two stages are comprised in the reconstruction technique,the first stage uses the intra-frame similarity and offers robust preliminary retrieval for each frame,and the second stage iteratively improves the efficiency of reconstruction by integrating inter frame Multi Hypothesis(MH)estimation and weighted residual sparsity modeling.In each iteration,the residual coefficient weights are modified using a mathematical approach based on the MH predictions,and the Split Bregman iteration algorithm is defined to resolve weighted l1 regularization.Experimental findings show that the proposed algorithm provides good compression of video coupled with an efficient encryption method that is resistant to multiple attacks.

CNN-LSTM based incremental attention mechanism enabled phase-space reconstruction for chaotic time series prediction

To improve the prediction accuracy of chaotic time series and reconstruct a more reasonable phase space structure of the prediction network,we propose a convolutional neural network-long short-term memory(CNN-LSTM)prediction model based on the incremental attention mechanism.Firstly,a traversal search is conducted through the traversal layer for finite parameters in the phase space.Then,an incremental attention layer is utilized for parameter judgment based on the dimension weight criteria(DWC).The phase space parameters that best meet DWC are selected and fed into the input layer.Finally,the constructed CNN-LSTM network extracts spatio-temporal features and provides the final prediction results.The model is verified using Logistic,Lorenz,and sunspot chaotic time series,and the performance is compared from the two dimensions of prediction accuracy and network phase space structure.Additionally,the CNN-LSTM network based on incremental attention is compared with long short-term memory(LSTM),convolutional neural network(CNN),recurrent neural network(RNN),and support vector regression(SVR)for prediction accuracy.The experiment results indicate that the proposed composite network model possesses enhanced capability in extracting temporal features and achieves higher prediction accuracy.Also,the algorithm to estimate the phase space parameter is compared with the traditional CAO,false nearest neighbor,and C-C,three typical methods for determining the chaotic phase space parameters.The experiments reveal that the phase space parameter estimation algorithm based on the incremental attention mechanism is superior in prediction accuracy compared with the traditional phase space reconstruction method in five networks,including CNN-LSTM,LSTM,CNN,RNN,and SVR.

Theoretical and experimental investigation of the resonance responses and chaotic dynamics of a bistable laminated composite shell in the dynamic snap-through mode

The dynamic model of a bistable laminated composite shell simply supported by four corners is further developed to investigate the resonance responses and chaotic behaviors.The existence of the 1:1 resonance relationship between two order vibration modes of the system is verified.The resonance response of this class of bistable structures in the dynamic snap-through mode is investigated,and the four-dimensional(4D)nonlinear modulation equations are derived based on the 1:1 internal resonance relationship by means of the multiple scales method.The Hopf bifurcation and instability interval of the amplitude frequency and force amplitude curves are analyzed.The discussion focuses on investigating the effects of key parameters,e.g.,excitation amplitude,damping coefficient,and detuning parameters,on the resonance responses.The numerical simulations show that the foundation excitation and the degree of coupling between the vibration modes exert a substantial effect on the chaotic dynamics of the system.Furthermore,the significant motions under particular excitation conditions are visualized by bifurcation diagrams,time histories,phase portraits,three-dimensional(3D)phase portraits,and Poincare maps.Finally,the vibration experiment is carried out to study the amplitude frequency responses and bifurcation characteristics for the bistable laminated composite shell,yielding results that are qualitatively consistent with the theoretical results.

Suppression and synchronization of chaos in uncertain time-delay physical system

The mechanical horizontal platform(MHP)system exhibits a rich chaotic behavior.The chaotic MHP system has applications in the earthquake and offshore industries.This article proposes a robust adaptive continuous control(RACC)algorithm.It investigates the control and synchronization of chaos in the uncertain MHP system with time-delay in the presence of unknown state-dependent and time-dependent disturbances.The closed-loop system contains most of the nonlinear terms that enhance the complexity of the dynamical system;it improves the efficiency of the closed-loop.The proposed RACC approach(a)accomplishes faster convergence of the perturbed state variables(synchronization errors)to the desired steady-state,(b)eradicates the effect of unknown state-dependent and time-dependent disturbances,and(c)suppresses undesirable chattering in the feedback control inputs.This paper describes a detailed closed-loop stability analysis based on the Lyapunov-Krasovskii functional theory and Lyapunov stability technique.It provides parameter adaptation laws that confirm the convergence of the uncertain parameters to some constant values.The computer simulation results endorse the theoretical findings and provide a comparative performance.

A chaotic hierarchical encryption/watermark embedding scheme for multi-medical images based on row-column confusion and closed-loop bi-directional diffusion

Security during remote transmission has been an important concern for researchers in recent years.In this paper,a hierarchical encryption multi-image encryption scheme for people with different security levels is designed,and a multiimage encryption(MIE)algorithm with row and column confusion and closed-loop bi-directional diffusion is adopted in the paper.While ensuring secure communication of medical image information,people with different security levels have different levels of decryption keys,and differentiated visual effects can be obtained by using the strong sensitivity of chaotic keys.The highest security level can obtain decrypted images without watermarks,and at the same time,patient information and copyright attribution can be verified by obtaining watermark images.The experimental results show that the scheme is sufficiently secure as an MIE scheme with visualized differences and the encryption and decryption efficiency is significantly improved compared to other works.

Intrusion Detection Model Using Chaotic MAP for Network Coding Enabled Mobile Small Cells

Wireless Network security management is difficult because of the ever-increasing number of wireless network malfunctions,vulnerabilities,and assaults.Complex security systems,such as Intrusion Detection Systems(IDS),are essential due to the limitations of simpler security measures,such as cryptography and firewalls.Due to their compact nature and low energy reserves,wireless networks present a significant challenge for security procedures.The features of small cells can cause threats to the network.Network Coding(NC)enabled small cells are vulnerable to various types of attacks.Avoiding attacks and performing secure“peer”to“peer”data transmission is a challenging task in small cells.Due to the low power and memory requirements of the proposed model,it is well suited to use with constrained small cells.An attacker cannot change the contents of data and generate a new Hashed Homomorphic Message Authentication Code(HHMAC)hash between transmissions since the HMAC function is generated using the shared secret.In this research,a chaotic sequence mapping based low overhead 1D Improved Logistic Map is used to secure“peer”to“peer”data transmission model using lightweight H-MAC(1D-LM-P2P-LHHMAC)is proposed with accurate intrusion detection.The proposed model is evaluated with the traditional models by considering various evaluation metrics like Vector Set Generation Accuracy Levels,Key Pair Generation Time Levels,Chaotic Map Accuracy Levels,Intrusion Detection Accuracy Levels,and the results represent that the proposed model performance in chaotic map accuracy level is 98%and intrusion detection is 98.2%.The proposed model is compared with the traditional models and the results represent that the proposed model secure data transmission levels are high.

Space-Time Chaos Filtering for the Incoherent Paradigm for 6G Wireless System Design from Theoretic Perspective

The following material is devoted to the generalization of the chaos modeling to random fields in communication channels and its application on the space-time filtering for the incoherent paradigm;that is the purpose of this research. The approach, presented hereafter, is based on the “Markovian” trend in modeling of random fields, and it is applied for the first time to the chaos field modeling through the well-known concept of the random “treatment” of deterministic dynamic systems, first presented by A. Kolmogorov, M. Born, etc. The material presents the generalized Stratonovich-Kushner Equations (SKE) for the optimum filtering of chaotic models of random fields and its simplified quasi-optimum solutions. In addition to this, the application of the multi-moment algorithms for quasi-optimum solutions is considered and, it is shown, that for scenarios, when the covariation interval of the input random field is less than the distance between the antenna elements, the gain of the space-time algorithms against their “time” analogies is significant. This is the general result presented in the following.

Distributional Chaoticity of the Minimal Subshift of Shift Operators

This paper focus on the chaotic properties of minimal subshift of shift operators. It is proved that the minimal subshift of shift operators is uniformly distributional chaotic, distributional chaotic in a sequence, distributional chaotic of type k ( k∈{ 1,2,2 1 2 ,3 } ), and ( 0,1 ) -distribution.