Narrow Results

To ensure the confidentiality of the data that are transferred over cloud networks including sensitive information like medical images and money transaction is significant and requires severe security mechanism to protect the personal information from hackers as well as malicious users as breaches in security affect the privacy and reputation of the user. Hence, an image-based cryptographic method is developed for improving security performance. Here, the time-bound encryption approach is established for protecting confidential medical images which is implemented in e-healthcare. Further, it traverses through a Lupus Coyote optimization (LCO) algorithm which utilizes the systematic chaotic maps (CM), since it performs based on the parameters which may be either discrete or consistent time parameters, and the inception of chaotic signals prevents the prohibited accesses. The proposed LCO optimizes the process of pixel assembling by determining the right parameter values for formulating the chaotic patterns to provide a robust cryptography method. Finally, the permutation as well as the properties of diffusion is controlled in the entire system to deal with the complexity of control pixel shuffling as well as the operations of substitution. Additionally, the correlation between neighboring pixels is interrupted which adds complexity to extracting the information by the attackers and the diffusion algorithm assists in eliminating the storage issue. Thus, the performance of the LCO-based time bound image encryption using the CM model is improved than the other systems, in which the performance metrics such as cosine similarity (CS), histogram correlation (HC), mean square error (MSE), peak signal to noise ratio (PSNR), root mean square error (RMSE), and structural similarity index measure (SSIM) attained the values of 86.53, 0.935, 4.12, 39.51, 4.54, and 0.94 dB, respectively, at number of images 50 with the size of population 250.

In this paper, a hierarchy of coupled maps in synchronized state is introduced. Then some discussions about the individual properties of these chaotic maps are presented, from a dynamical systems viewpoint. Also, one of these chaotic map is used as a Nonlinear Pseudo Random Generator (NPRNG). This paper addresses the chaotic features of this map which are useful for generating nonlinear pseudo random numbers. Results of the analysis and extensive tests such as the NIST, DIEHARD and ENT test suites indicate that the NPRNG exhibits good statistical randomness properties.

A novel encryption algorithm to cipher digital images is presented in this work. The digital image is rendering into a three-dimensional (3D) lattice and the protocol consists of two phases: the confusion phase where 24 chaotic Cat maps are applied and the diffusion phase where a 3D cellular automata is evolved. The encryption method is shown to be secure against the most important cryptanalytic attacks.

This paper presents a hybrid approach based discrete Particle Swarm Optimization (PSO) and chaotic strategies for solving multi-objective task scheduling problem in cloud computing. The main purpose is to allocate the summited tasks to the available resources in the cloud environment with minimum makespan (i.e. schedule length) and processing cost while maximizing resource utilization without violating Service Level Agreement (SLA) among users and cloud providers. The main challenges faced by Particle Swarm Optimization (PSO) when used to solve scheduling problems are premature convergence and trapping into local optimum. This paper presents an enhanced Particle Swarm Optimization algorithm hybridized with Chaotic Map strategies. The proposed approach is called Enhanced Particle Swarm Optimization based Chaotic Strategies (EPSOCHO) algorithm. Our proposed approach suggests two Chaotic Map strategies: sinusoidal iterator and Lorenz attractor to enhanced PSO algorithm in order to get good convergence and diversity for optimizing the task scheduling in cloud computing. The proposed approach is simulated and implemented in Cloudsim simulator. The performance of the proposed approach is compared with the standard PSO algorithm, the improved PSO algorithm with Longest job to fastest processor (LJFP-PSO), and the improved PSO algorithm with minimum completion time (MCT-PSO) using different sizes of tasks and various benchmark datasets. The results clearly demonstrate the efficiency of the proposed approach in terms of makespan, processing cost and resources utilization.

This paper proposes a new block encryption algorithm. The chaotic trajectories are computed by weighting. Then the result is used to mask the plaintext. Multiple blocks of plaintext are encrypted at the same time and this decreases the chaotic iterations. So the encryption speed is improved to some extent. The proposed algorithm is flexible. When the number of weights is increased, the number of the encrypted plaintext block at the same time is increased and the encryption speed is improved. The simulation result shows that the proposed algorithm has fast encryption speed and fine security.

Chaotic maps with higher chaotic complexity are urgently needed in many application scenarios. This paper proposes a chaotification model based on sine and cosecant functions (CMSC) to improve the dynamic properties of existing chaotic maps. CMSC can generate a new map with higher chaotic complexity by using the existing one-dimensional (1D) chaotic map as a seed map. To discuss the performance of CMSC, the chaos properties of CMSC are analyzed based on the mathematical definition of the Lyapunov exponent (LE). Then, three new maps are generated by applying three classical 1D chaotic maps to CMSC respectively, and the dynamic behaviors of the new maps are analyzed in terms of fixed point, bifurcation diagram, sample entropy (SE), etc. The results of the analysis demonstrate that the new maps have a larger chaotic region and excellent chaotic characteristics.

Chaotic map is applied to numerous research fields, such as encryption of data and information. In this paper, a novel bit-level scrambling encryption based on three-dimensional trigonometric chaotic sequence is proposed. This encryption is operated on grayscale images because pixel value of which is between 0 and 255, which can be converted into 8-bit binary number, then each image can be converted into eight binary images. Combine binary images a three-dimensional matrix as input, which have three index values width, height, and page. Generate three numbers by the chaotic sequence to locate the value of the matrix need to be changed. After the value is located, change its value 0 to 1 or 1 to 0, this is the basic encryption scheme. This paper makes a three-dimensional binary matrix with 32 images to test the encryption scheme, and get average value of images’ number of pixel change rate at 0.9603, unified averaged change intensity at 31.27%, information entropy at 7.9891, also the histograms. And correlation coefficients of each pixel from three directions are small. There are comparisons with other encryptions too. The key space of this encryption is more than 10${}^{255}$.

This paper proposes solving short-term unit commitment (UC) problems with security constraints by hybrid chaotic particle swarm optimization (CPSO). The objective of security-constrained UC (SC-UC) is to minimize the total generation cost, which is the sum of both transition cost and production cost of the scheduled combination units. The proposed CPSO method, which involves the chaotic map and the chaotic turbulence, can avoid premature convergence of PSO and escape local minima. Moreover, the proposed hybrid CPSO method has the ability of solving both the continuous and the discrete optimal programming problems. Two power systems are demonstrated for verifying the feasibility and effectiveness of the proposed method in solving SC-UC problems with constraints of a nonlinear generator and operation security assessment taken into consideration. The simulation results show that the proposed CPSO-based SC-UC method is indeed capable of obtaining efficiently high-quality UC solutions and enhancing the system security of UC operation.

In this paper, an online chatting system with an embedded real-time chaotic encryption/decryption method is designed for the Internet. Such system not only provides a real-time communication platform, but also ensures a secure channel for communication. By the use of cipher feedback and the skew tent map, the input text can be real-time encoded and the cipher text is sent via TCP/IP. With the properties of randomness of the map, and its sensitivity on system parameters and the initial conditions, the encrypted transmitting messages are difficult to be eavesdropped. The implemented method is simple and can be easily embedded in any existing systems.

Let X be a dendrite and f : X → X be a continuous map. Denote by R(f) and P(f) the sets of recurrent points and periodic points of f respectively. In this paper we show that, if the cardinal number Card(End(X)) of the set of endpoints of X is less than the cardinal number c of the continuum, then . From this we derive that, if Card(End(X)) < c, then f is chaotic in the sense of Devaney if and only if f is transitive.

The close relationship between chaos and cryptography makes chaotic encryption a natural candidate for secure communication and cryptography. In this manuscript, we prove that a class of maps that have been proposed as suitable for scrambling signals possess the property of sensitive dependence on initial conditions (s.d.i.c.) necessary for chaos and cryptography. Our result can also be used for generating other maps with s.d.i.c., through a suitable semiconjugacy between their input and output parts. Using the condition of semiconjugacy we also establish for this class of maps rigorous criteria for the existence and stability of their fixed points and limit cycles.

In this paper, we propose a new one-dimensional, two-segmental nonlinear map by combining tent, triangle and parabola curve functions. We call the proposed map, Mehrab map since its return maps shape is similar to an altar (which we call it "Mehrab"). Definition and properties of Mehrab map along with orbit diagrams, Lyapunov exponents, and its histograms are considered. To generate more uniform density function maps, two modified versions of the proposed Mehrab map are also defined. In the first modification of Mehrab map (FMM), vertical symmetry and transformation to the right are used. Sensitivity to initial condition and total chaotic range of FMM are medium. Probability density function of FMM map is uniform and its histograms show this uniformity. In the second modification of Mehrab (SMM) map, vertical and horizontal symmetry and transformation to the right are used. According to the orbit diagrams and Lyapunov exponents, the sensitivity to initial condition and the total chaotic range of SMM map are large. This property gives more chaotic region to the map. Its histograms prove that the probability density function of SMM is also uniform.

This work presents novel discrete-time chaotic systems with some known physical system nonlinearities. Dynamic behaviors of the models are examined with numerical methods and Arduino microcontroller-based experimental studies. Many new chaotic maps are generated in the form of $x(k+1)=rx(k)+f(x(k))$ and high-dimensional chaotic systems are obtained by weak coupling or cross-coupling the same or different chaotic maps. An application of the chaotic maps is realized with Arduino for chaotic pulse width modulation to drive electrical machines. It is expected that the new chaotic maps and their microcontroller implementations will facilitate practical chaos-based applications in different fields.

In the paper “Some Open Problems in Chaos Theory and Dynamics” by Zeraoulia and Sprott, the two-dimensional map $(x,y)\mapsto (-ax{(1+y^2)}^{-1},x+by)$ was considered and the problem on the analytical study of the boundedness of its attractors was formulated. In the present paper, the boundedness of its attractors is studied, the corresponding analytical estimation of absorbing set is obtained, and thus an answer to the problem is given.

This paper proposes a chaotic secure video remote communication scheme that can perform on real WAN networks, and implements it on a smartphone hardware platform. First, a joint encryption and compression scheme is designed by embedding a chaotic encryption scheme into the MJPG-Streamer source codes. Then, multiuser smartphone communications between the sender and the receiver are implemented via WAN remote transmission. Finally, the transmitted video data are received with the given IP address and port in an Android smartphone. It should be noted that, this is the first time that chaotic video encryption schemes are implemented on such a hardware platform. The experimental results demonstrate that the technical challenges on hardware implementation of secure video communication are successfully solved, reaching a balance amongst sufficient security level, real-time processing of massive video data, and utilization of available resources in the hardware environment. The proposed scheme can serve as a good application example of chaotic secure communications for smartphone and other mobile facilities in the future.

This paper proposes an image encryption algorithm based on a chaotic map and information entropy. Unlike Fridrich’s structure, the proposed method contains permutation, modulation, and diffusion (PMD) operations. This method avoids the shortcoming in traditional schemes of strictly shuffling the pixel positions before diffusion encryption. Information entropy is employed to influence the generation of the keystream. The initial keys used in the permutation and diffusion stages interact with each other. As a result, the algorithm acts as an indivisible entity to enhance security. Experimental results and security analyses demonstrate the good performance of the proposed algorithm as a secure and effective communication method for images.

This paper presents cryptanalysis of a color image encryption scheme. DNA encoding and multiple 1D chaotic maps are used in the encryption process which increases its computational speed. The key streams generated in this scheme are dependent on secret keys, updated using the sum of pixel intensities of plain image of size $W\times H\times 3$. This paper analyzes the security of encryption scheme against the chosen plaintext attack and finds that only ${𝒪}(768WH)$ different key matrices for diffusion are possible, an equivalent version of which can be revealed with ${𝒪}(768WH)$ chosen plain images. Experimental results are presented to prove that equivalent diffusion keys and block permutation sequence can be effectively revealed through the attack. In addition, low sensitivity of keys towards changes in plaintext along with insecure diffusion process involved in encryption process is also reported. Finally, to remedy the shortcomings of the original encryption scheme, an enhanced encryption scheme is generated that can resist chosen/known plaintext attack while maintaining the merits of the original encryption scheme.

We present a rigorous convergence analysis of a linear spline Markov finite approximation method for computing stationary densities of random maps with position dependent probabilities, which consist of several chaotic maps. The whole analysis is based on a new Lasota–Yorke-type inequality for the Markov operator associated with the random map, which is better than the previous one in the literature and much simpler to obtain. We also present numerical results to support our theoretical analysis.

This paper reports the complex dynamics of a class of two-dimensional maps containing hidden attractors via linear augmentation. Firstly, the method of linear augmentation for continuous dynamical systems is generalized to discrete dynamical systems. Then three cases of a class of two-dimensional maps that exhibit hidden dynamics, the maps with no fixed point and the maps with one stable fixed point, are studied. Our numerical simulations show the effectiveness of the linear augmentation method. As the coupling strength of the controller increases or decreases, hidden attractor can be annihilated or altered to be self-excited, and multistability of the map can be controlled to being bistable or monostable.

Chaotic dynamical systems without fixed points are promising in the generation of pseudo-random sequences because orbits will not converge to a fixed point. In this class of systems there are no final fixed points, so the basin of attraction of a fixed point does not exist. The absence of fixed points makes it difficult to analyze the dynamics of the systems because a fixed point gives us a lot of information about the dynamics of the system. In addition, if there is an amplitude control parameter for the generated chaotic signals, the tolerance and adaptability are higher and better in the application process. In view of the aforementioned, in this paper, a novel class of discrete maps is presented and described by a kind of piecewise linear (PWL) maps. Necessary and sufficient conditions are given to guarantee that this class of discrete maps does not have any fixed point. Furthermore, we introduce families of these PWL discrete maps without fixed points that present positive Lyapunov exponents and have chaotic dynamics with amplitude control. From these families, we select one particular map, which is analyzed theoretically and proved to be chaotic in the sense of Devaney.