Chaotic Image Cryptography Systems: A Review

In recent decades, image encryption has been a popular and important field of research. The image encryption techniques have been studied thoroughly to ensure the safety of digital images on transmission through the networks. A large range of algorithms for chaotic-based cryptographic systems has been suggested and submitted to enhance the efficiency of the encryption methods. The chaotic map is one technique to guarantee security. The benefits of chaotic image encryption include the fact that it is simple to implement; it has a faster encryption speed, and it is powerful against attacks. Due to their extreme sensitivity to initial conditions, unpredictability, and random-like behaviours, many image encryption systems using chaotic maps have been proposed. This study paper presents a scientific review of many types of researches during the (2014-2020) years that used chaotic with its various types (one-dimensional, multi-dimensional, or hyper-chaotic) to process the digital images in the encryption stage or the scrambling phase. Furthermore, it presents a future reading of researches that has a wider role in developing the cryptography field by improving the efficiency of Algorithms where using a chaotic map with other methods gives better results than using chaotic alone in scrambling and encryption methods.

Lorenz-63 Model as a Metaphor for Transient Complexity in Climate

Dynamical systems like the one described by the three-variable Lorenz-63 model may serve as metaphors for complex natural systems such as climate systems. When these systems are perturbed by external forcing factors, they tend to relax back to their equilibrium conditions after the forcing has shut off. Here we investigate the behavior of such transients in the Lorenz-63 model by studying its trajectories initialized far away from the asymptotic attractor. Counterintuitively, these transient trajectories exhibit complex routes and, in particular, the sensitivity to initial conditions is akin to that of the asymptotic behavior on the attractor. Thus, similar extreme events may lead to widely different variations before the perturbed system returns back to its statistical equilibrium.

Dynamic Analysis and Cryptographic Application of a Sinusoidal-polynomial Composite Chaotic System

Owning 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 the 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 SPCCS. Detailed simulation results verify effectiveness of the proposed image encryption algorithm.

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.

Whale optimization based synchronization and control of two identical fractional order financial chaotic systems

This paper proposes a scheme to synchronize fractional order chaotic systems employing fractional PID controller. The parameters of FOPID are tuned using Swarm based optimization techniques, viz.: Whale optimization algorithm and Particle swarm optimization techniques. To assert the complete synchronization, master-slave method has been implemented. Chaotic systems are highly dependent upon initial conditions and parameter perturbations. Therefore, taking these properties into consideration, synchronization of two identical fractional order financial chaotic systems is performed with distinct initial conditions. To show the efficacy of the proposed method, analysis is performed for orders between 0 to 1, and also for sensitivity to initial conditions.

A New Image Encryption Scheme Using Dual Chaotic Map Synchronization

Chaotic systems behavior attracts many researchers in the field of image encryption. The major advantage of using chaos as the basis for developing a crypto-system is due to its sensitivity to initial conditions and parameter tunning as well as the random-like behavior which resembles the main ingredients of a good cipher namely the confusion and diffusion properties. In this article, we present a new scheme based on the synchronization of dual chaotic systems namely Lorenz and Chen chaotic systems and prove that those chaotic maps can be completely synchronized with other under suitable conditions and specific parameters that make a new addition to the chaotic based encryption systems. This addition provides a master-slave configuration that is utilized to construct the proposed dual synchronized chaos-based cipher scheme. The common security analyses are performed to validate the effectiveness of the proposed scheme. Based on all experiments and analyses, we can conclude that this scheme is secure, efficient, robust, reliable, and can be directly applied successfully for many practical security applications in insecure network channels such as the Internet

Robustness in Neural Circuits

Complex systems are found everywhere – from scheduling to traffic, food to climate, economics to ecology, the brain, and the universe. Complex systems typically have many elements, many modes of interconnectedness of those elements, and often exhibit sensitivity to initial conditions. Complex systems by their nature are generally unpredictable and can be highly unstable.

Forest Climax Phenomenon: An Invariance of Scale

We can think of forests as multiscale multispecies networks, constantly evolving toward a climax or potential natural community—the successional process-pattern of natural regeneration that exhibits sensitivity to initial conditions. This is why I look into forest succession in light of the Red Queen hypothesis and focus on the key aspects of ecological self-organisation: dynamical criticality, evolvability and intransitivity. The idea of the review is that forest climax should be associated with habitat dynamics driven by a large continuum of ecologically equivalent time scales, so that the same ecological conclusions could be drawn statistically from any scale. A synthesis of the literature is undertaken in order to (1) present the framework for assessing habitat dynamics and (2) present the types of successional trajectories based on tree regeneration mode in forest gaps. In general, there are four types of successional trajectories within the process-pattern of forest regeneration that exhibits sensitivity to initial conditions: advance reproduction specialists, advance reproduction generalists, early reproduction generalists and early reproduction specialists. A successional trajectory is an expression of a fractal connectivity among certain patterns of natural regeneration in the multiscale multispecies networks of landscape habitats. Theoretically, the organically derived measures of pattern diversity, integrity and complexity, determined by the rates of recruitment, growth and mortality of forest tree species, are the means to test the efficacy of specific interventions to avert the disturbance-related decline in forest regeneration. That is of relevance to the emerging field of biocomplexity research.