Secure data transmission over the public channels have high impact and increasingly important due to theft and manipulation in contents. The requirement of public/ private organizations to develop an efficient scheme to provide security to their contents. We developed a digital contents encryption scheme based Arnold scrambling and Lucas series, which is very simple to implement but almost impossible to breach in this article. We perform encryption at standard images by using Lucas series at different iterations of scrambled images of Arnold transform. Numerical simulation analyses performed to analyze the efficiency and effectiveness of the projected structure.

A novel image encryption scheme based on Arnold scrambling and Lucas series

Chaotic maps play a vital role in the development of cryptographic techniques being used in today’s world. Efficient and highly secure algorithms can be constructed based on chaotic maps. Chaotic maps have the intrinsic property of being highly sensitive to initial conditions. In this paper, we have presented a novel scheme for construction and optimization of substitution boxes (S-boxes) based on mixed two dimensional (2D) chaotic maps in which cryptographic properties of S-boxes are optimized based on initial conditions of their parent 2D chaotic map. The proposed scheme and the resulting substitution boxes are analyzed with existing cryptanalysis techniques and their results have been compared with some other algorithms available in literature. The proposed scheme has been found to be more efficacious than other algorithms. The outcomes of security analysis indicate that our proposed technique and resulting optimized non-linear component in the current era of information technology.

Application Based Construction and Optimization of Substitution Boxes Over 2D Mixed Chaotic Maps

Designing chaotic systems with specific features is a hot topic in nonlinear dynamics. In this study, a novel chaotic system is presented with a unique feature of crossing inside and outside of a cylinder repeatedly. This new system is thoroughly analyzed by the help of the bifurcation diagram, Lyapunov exponents’ spectrum, and entropy measurement. Bifurcation analysis of the proposed system with two initiation methods reveals its multistability. As an engineering application, the system’s efficiency is tested in image encryption. The complexity of the chaotic attractor of the proposed system makes it a proper choice for encryption. States of the chaotic attractor are used to shuffle the rows and columns of the image, and then the shuffled image is XORed with the states of chaotic attractor. The unpredictability of the chaotic attractor makes the encryption method very safe. The performance of the encryption method is analyzed using the histogram, correlation coefficient, Shannon entropy, and encryption quality. The results show that the encryption method using the proposed chaotic system has reliable performance.

https://www.mdpi.com/1099-4300/21/10/958/pdf

Entropy Analysis and Image Encryption Application Based on a New Chaotic System Crossing a Cylinder

This contribution proposes a novel chaotic hyperjerk circuit with the new phenomenon of mixed-mode bursting oscillations (MMBOs). The bifurcation analysis of this specific oscillator reveals a relatively rare and complex phenomenon of various coexisting two full Feigenbaum remerging trees. Common nonlinear dynamic systems analysis tools such as bifurcation diagram, phase portraits, time series and Lyapunov exponent are used to uncover the complex behaviours of the circuit with respect to its parameters and initial conditions as well. As one of the major contributions of this work, we introduce a novel hyperjerk circuit with rare phenomena such as the coexistence of a new phenomenon named bubbles of bifurcation (referred as BsB hereafter), the coexistence of two or three asymmetric mixed-mode bursting oscillations, just to name a few. All these phenomena are found simultaneously in a single circuit and thus diverse dissemination. Experimental results support the theoretical analysis.

A novel chaotic hyperjerk circuit with bubbles of bifurcation: mixed-mode bursting oscillations, multistability, and circuit realization

Abstract In this work, we will introduce two novel positivity preserving operator splitting nonstandard finite difference (NSFD) schemes for the numerical solution of SEIR reaction diffusion epidemic model. In epidemic model of infection diseases, positivity is an important property of the continuous system because negative value of a subpopulation is meaningless. The proposed operator splitting NSFD schemes are dynamically consistent with the solution of the continuous model. First scheme is conditionally stable while second operator splitting scheme is unconditionally stable. The stability of the diffusive SEIR model is also verified numerically with the help of Routh-Hurwitz stability condition. Bifurcation value of transmission coefficient is also carried out with and without diffusion. The proposed operator splitting NSFD schemes are compared with the well-known operator splitting finite difference (FD) schemes.

/pdf/positivity-preserving-operator-splitting-nonstandard-finite-sbtueqgmuc.pdf

Bin Zhu

Papers

Bifurcation analysis of two disc dynamos with viscous friction and multiple time delays