Design and Analysis of a Three-Dimensional Discrete Memristive Chaotic System with Infinite Wide Parameter Range

In this paper, a new discrete memristive chaotic system with infinitely wide parameter range is designed. Firstly, a discrete memristor based on a triangular wave function is constructed. The memristor conforms to the definition of generalized memristor, and a new three-dimensional memristive chaotic system is designed based on it. Numerical simulations show that it can generate chaotic sequences with high complexity.Otherwise, an improved perturbation method is proposed to estimate the output sequence of the differential system. At the same time, it is proved mathematically that the new system can always be in chaotic or hyperchaotic state with infinitely wide parameter range under certain conditions. By observing the Lyapunov exponent spectrum and the phase diagram, it is found as the absolute value of the parameter increases, the output range and ergodicity of the new system are also enhanced, and the new system has super multi-stability. This paper analyzes the mechanism of the discrete memristive chaotic system generating infinitely coexisting attractors, puts forward a method to make ordinary chaotic systems easier to obtain super multi-stability, and verifies it. The results show it is effective. Finally, the DSP hardware platform is used to implement the new system, which proves the physical existence and realizability of the system.

Secure OFDM with Peak-to-Average Power Ratio Reduction Using the Spectral Phase of Chaotic Signals

In this paper, a new physical layer security technique is proposed for Orthogonal Frequency Division Multiplexing (OFDM) communication systems. The security is achieved by modifying the OFDM symbols using the phase information of chaos in the frequency spectrum. In addition, this scheme reduces the Peak to Average Power Ratio (PAPR), which is one of the major drawbacks of OFDM. The Selected Mapping (SLM) technique for PAPR reduction is employed to exploit the random characteristics of chaotic sequences. The reduction with this algorithm is shown to be similar to that of other SLM schemes, but it has lower computational complexity and side information does not have to be sent to the receiver. The security of this technique stems from the noise like behavior of chaotic sequences and their dependence on the initial conditions of the chaotic generator (which are used as the key). Even a slight difference in the initial conditions will result in a different phase sequence, which prevents an eavesdropper from recovering the transmitted OFDM symbols.

Generating novel multi-scroll chaotic attractors via fractal transformation

The fractal and chaos are bound tightly, and their relevant researches are well-established. Few of them, however, concentrates on the research of the possibility of combining the fractal and the chaotic systems to generate multi-scroll chaotic attractors. This paper presents a novel non-equilibrium point chaotic system, exhibiting extremely rich and complex hidden behaviors including chaos, hyper-chaos, multi-scroll attractors, extreme multi-stability and initial offset-boosting. The proposed system is combined with fractal transformation respectively, and a new class of multi-scroll attractors, such as multi-ring attractors and separated-scroll attractors, is observed. Particularly, swallow-shaped attractors for the first time is found. Moreover, another efficient method to generate a different class of chaotic attractors uses parabola transformation and triangle transformation. Additionally, the spectrum entropy ( SE ) complexity is employed to discuss the complexity of the proposed system before and after fractal, resulting in a chaotic sequences with fractal transformation that has higher complexity. Finally, we develop a hardware platform to implement the presented attractors before and after fractal in a way to confirm the accuracy of the numerical simulations, providing a theoretical basis for the next application in image encryption.

A Color Image Encryption Scheme Based on a Hybrid Cascaded Chaotic System

As image is an important way of information representation, researchers pay more and more attention on image encryption. In order to improve the performance of image encryption, a novel image encryption scheme based on a hybrid cascaded chaotic system and sectoral segmentation is proposed in this paper. Hybrid cascaded chaotic system has a larger key space, higher complexity, more sensitivity to initial conditions. Four chaotic sequences relevant to a plain image are generated by this system, which strengthen plaintext correlation and the randomness. During the scrambling process, sectoral segmentation focuses on how to extract a sequence from the disk storing data, which can not only reduce the correlation between the three components of the image, but also hide image information to a large extent. Further, a DNA algorithm is used in the diffusion process. Simulation shows that the proposed scheme can effectively resist various attacks and improve the encryption performance.

A Novel Compressive Image Encryption with an Improved 2D Coupled Map Lattice Model

The digital image, as the critical component of information transmission and storage, has been widely used in the fields of big data, cloud and frog computing, Internet of things, and so on. Due to large amounts of private information in the digital image, the image protection is fairly essential, and the designing of the encryption image scheme has become a hot issue in recent years. In this paper, to resolve the shortcoming that the probability density distribution (PDD) of the chaotic sequences generated in the original two-dimensional coupled map lattice (2D CML) model is uneven, we firstly proposed an improved 2D CML model according to adding the offsets for each node after every iteration of the original model, which possesses much better chaotic performance than the original one, and also its chaotic sequences become uniform. Based on the improved 2D CML model, we designed a compressive image encryption scheme. Under the condition of different keys, the uniform chaotic sequences generated by the improved 2D CML model are utilized for compressing, confusing, and diffusing, respectively. Meanwhile, the message authentication code (MAC) is employed for guaranteeing that the encryption image be integration. Finally, theoretical analysis and simulation tests both demonstrate that the proposed image encryption scheme owns outstanding statistical, well encryption performance, and high security. It has great potential for ensuring the digital image security in application.

A new image encryption algorithm based on the OF-LSTMS and chaotic sequences

In this paper, a novel image encryption algorithm based on the Once Forward Long Short Term Memory Structure (OF-LSTMS) and the Two-Dimensional Coupled Map Lattice (2DCML) fractional-order chaotic system is proposed. The original image is divided into several image blocks, each of which is input into the OF-LSTMS as a pixel sub-sequence. According to the chaotic sequences generated by the 2DCML fractional-order chaotic system, the parameters of the input gate, output gate and memory unit of the OF-LSTMS are initialized, and the pixel positions are changed at the same time of changing the pixel values, achieving the synchronization of permutation and diffusion operations, which greatly improves the efficiency of image encryption and reduces the time consumption. In addition the 2DCML fractional-order chaotic system has better chaotic ergodicity and the values of chaotic sequences are larger than the traditional chaotic system. Therefore, it is very suitable to image encryption. Many simulation results show that the proposed scheme has higher security and efficiency comparing with previous schemes.

A novel multi-image cryptosystem based on weighted plain images and using combined chaotic maps

This paper introduces a new multi-image cryptosystem based on modified Henon map and nonlinear combination of chaotic seed maps. Based on the degree of correlation between the adjacent pixels of the plain image, a unique weight is assigned to the plain image. First, the coordinates of plain images are disrupted by modified Henon map as confusion phase. In the first step of diffusion phase, the pixels content of images are changed separately by XOR operation between confused images and matrices with suitable nonlinear combination of seed maps sequences. These combination of seed maps are selected depending on the weight of plain images as well as bifurcation properties of mentioned chaotic maps. After concatenating the matrices obtained from the first step of diffusion phase, the bitwise XOR operation is applied between newly developed matrix and the other produced matrix from the chaotic sequences of the Logistic-Tent-Sine hybrid system, as second step of diffusion phase. The encrypted image is obtained after applying shift and exchange operations. The results of the implementation using graphs and histograms show that the proposed scheme, compared to some existing methods, can effectively resist common attacks and can be used as a secure method for encrypting digital images.

A Two-Step Compressed Sensing Approach for Single-Snapshot DOA Estimation of Closely Spaced Signals

Single-snapshot direction-of-arrival (DOA) estimation plays an important role in dynamic target detection and tracking applications. Because a single-snapshot signal provides few information for statistics calculation, recently compressed sensing (CS) theory is applied to solve single-snapshot DOA estimation, instead of the traditional DOA methods based on statistics. However, when the unknown sources are closely located, the spatial signals are highly correlated, and its overcomplete dictionary is made up of dense grids, which leads to a serious decrease in the estimation accuracy of the CS-based algorithm. In order to solve this problem, this paper proposed a two-step compressed sensing-based algorithm for the single-snapshot DOA estimation of closely spaced signals. The overcomplete dictionaries with coarse and refined grids are used in the two steps, respectively. The measurement matrix is constructed by using a very sparse projection scheme based on chaotic sequences because chaotic sequences have determinism and pseudo-randomness property. Such measurement matrix is mainly proposed for compressing the overcomplete dictionary in preestimation step, while it is well designed by choosing the steering vectors of true DOA in the accurate estimation step, in which the neighborhood information around the true DOAs partly solved in the previous step will be used. Monte Carlo simulation results demonstrate that the proposed algorithm can perform better than other existing single-snapshot DOA estimation methods. Especially, it can work well to solve the issues caused by closely spaced signals and single snapshot.