Secret Image Sharing (SIS) transfers an image to mutually suspicious receivers as n meaningless shares, where k or more shares must be present to recover the secret. This paper proposes a (k, n)-SIS system for any image type using polynomial interpolation based on Lagrange polynomials, where the generated shares are of size 1/k of the secret image size. A full encryption system, consisting of substitution and permutation stages, is employed by using the generalized Tent map as a source of randomness. In addition to using a long and sensitive system key, steganography using the Least Significant Bits (LSBs) embedding technique is utilized to improve security. Detailed experimental analysis of the security, robustness and performance of the proposed system is provided, which is more comprehensive than the analyses given in other related works. Security is demonstrated using statistical tests, and robustness against noise and crop attacks is validated. © 2024 IEEE.
Novel Fast Prediction Algorithm for Advanced and High Efficiency Video Coding
This paper introduces an efficient prediction algorithm tailored for advanced and high efficiency video coding, encompassing both H.264 and H.265. The proposed approach aims at replacing the standard intra prediction methodology by employing a streamlined prediction mode, which significantly reduces computational overhead and system complexity while eliminating the requirement for mode decision. By leveraging block comparison criteria, the designed method combines neighboring blocks in a linear fashion to accurately represent the target block. Extensive comparisons are conducted with the H.264 intra prediction using various video sequences and multiple evaluation criteria. The results demonstrate substantial time savings of up to 60% compared to the H.264 standard intra prediction algorithm, with a minor peak signal-to-noise ratio drop. The proposed algorithm holds promise for enhancing real-time video processing and compression in video coding systems, offering notable efficiency gains without sacrificing predictive accuracy. © 2024 IEEE.
Design, implementation and analysis of fully digital 1-D controllable multiscroll chaos
This paper introduces the fully digital implementation of a 1-D multiscroll chaos generator based on a staircase nonlinearity in the 3rd-order jerk system using the Euler approximation. For the first time, digital design is exploited to provide real-time controllability of (i) number of scrolls, (ii) position in 1-D space, (iii) Euler step size and (iv) system parameter. The effect of variations in these fields on the maximum Lyapunov exponent (MLE) is analyzed. The system is implemented using Verilog HDL and synthesized on an Xilinx Virtex 4 FPGA, exhibiting area utilization less than 3.5% and high performance with experimentally verified throughput up to 3.33 Gbits/s. This fully digital system enables applications in modulation schemes and chaos-based cryptosystems without analog to digital conversion. © 2011 IEEE.
The effect of numerical techniques on differential equation based chaotic generators
In this paper, we study the effect of the numerical solution accuracy on the digital implementation of differential chaos generators. Four systems are built on a Xilinx Virtex 4 FPGA using Euler, mid-point, and Runge-Kutta fourth order techniques. The twelve implementations are compared based on the FPGA used area, maximum throughput, maximum Lyapunov exponent, and autocorrelation confidence region. Based on circuit performance and the chaotic response of the different implementations, it was found that less complicated numerical solution has better chaotic response and higher throughput. © 2011 IEEE.
A Secured Lossless Visual Secret Sharing for Color Images Using Arnold Transform
Nowadays, with the rapid growth in information, a fast and secure method is eagerly needed to share images. (n, n)-Visual Secret Sharing (VSS) is used to share a secret image into n shares, where the secret can only be recovered using all the n shares and the recovery must be fast with low computational complexity. This paper proposes a secured lossless (n, n)-VSS system based on Arnold transform and pixel vectorization suitable to be used with binary, grayscale and color images. Multiple security tests were performed such as entropy, correlation, Mean Squared Error (MSE), National Institute of Standards and Technology (NIST) SP-800-22 statistical suite, and differential attacks, which demonstrate the good security of the proposed system. In addition, the time complexity and runtime of the recovery system indicate good efficiency. © 2022 IEEE.
Self-excited attractors in jerk systems: Overview and numerical investigation of chaos production
Chaos theory has attracted the interest of the scientific community because of its broad range of applications, such as in secure communications, cryptography or modeling multi-disciplinary phenomena. Continuous flows, which are expressed in terms of ordinary differential equations, can have numerous types of post transient solutions. Reporting when these systems of differential equations exhibit chaos represents a rich research field. A self-excited chaotic attractor can be detected through a numerical method in which a trajectory starting from a point on the unstable manifold in the neighborhood of an unstable equilibrium reaches an attractor and identifies it. Several simple systems based on jerk-equations and different types of nonlinearities were proposed in the literature. Mathematical analyses of equilibrium points and their stability were provided, as well as electrical circuit implementations of the proposed systems. The purpose of this chapter is double-fold. First, a survey of several self-excited dissipative chaotic attractors based on jerk-equations is provided. The main categories of the included systems are explained from the viewpoint of nonlinearity type and their properties are summarized. Second, maximum Lyapunov exponent values are explored versus the different parameters to identify the presence of chaos in some ranges of the parameters. © 2018, Springer International Publishing AG.
A study on coexistence of different types of synchronization between different dimensional fractional chaotic systems
In this study, robust approaches are proposed to investigate the problem of the coexistence of various types of synchronization between different dimensional fractional chaotic systems. Based on stability theory of linear fractional order systems, the co-existence of full state hybrid function projective synchronization (FSHFPS), inverse generalized synchronization (IGS), inverse full state hybrid projective synchronization (IFSHPS) and generalized synchronization (GS) is demonstrated. Using integer-order Lyapunov stability theory and fractional Lyapunov method, the co-existence of FSHFPS, inverse full state hybrid function projective synchronization (IFSHFPS), IGS and GS is also proved. Finally, numerical results are reported, with the aim to illustrate the capabilities of the novel schemes proposed herein. © Springer International Publishing AG 2017. All rights reserved.
Chaotic properties of various types of hidden attractors in integer and fractional order domains
Nonlinear dynamical systems with chaotic attractors have many engineering applications such as dynamical models or pseudo-random number generators. Discovering systems with hidden attractors has recently received considerable attention because they can lead to unexpected responses to perturbations. In this chapter, several recent examples of hidden attractors, which are classified into several categories from two different viewpoints, are reviewed. From the viewpoint of the equilibrium type, they are classified into systems with no equilibria, with a line of equilibrium points, and with one stable equilibrium. The type of nonlinearity presents another method of categorization. System properties are explored versus the different parameters to identify the values corresponding to the presence of strange attractors. The behavior of the systems is explored for integer order and fractional order derivatives using the suitable numerical techniques. The studied properties include time series, phase portraits, and maximum Lyapunov exponent. © 2018 Elsevier Inc. All rights reserved.
Chaos and bifurcation in controllable jerk-based self-excited attractors
In the recent decades, utilization of chaotic systems has flourished in various engineering applications. Hence, there is an increasing demand on generalized, modified and novel chaotic systems. This chapter combines the general equation of jerk-based chaotic systems with simple scaled discrete chaotic maps. Two continuous chaotic systems based on jerk-equation and discrete maps with scaling parameters are presented. The first system employs the scaled tent map, while the other employs the scaled logistic map. The effects of different parameters on the type of the response of each system are investigated through numerical simulations of time series, phase portraits, bifurcations and Maximum Lyapunov Exponent (MLE) values against all system parameters. Numerical simulations show interesting behaviors and dependencies among these parameters. Analogy between the effects of the scaling parameters is presented for simple one-dimensional discrete chaotic systems and the continuous jerk-based chaotic systems with more complicated dynamics. The impacts of these scaling parameters appear on the effective ranges of other main system parameters and the ranges of the obtained solution. The dependence of equilibrium points on the sign of one of the scaling parameters results in coexisting attractors according to the signs of the parameter and the initial point. In addition, switching can be used to generate double-scroll attractors. Moreover, bifurcation and chaos are studied for fractional-order of the derivative. © 2018, Springer International Publishing AG.
Applications of continuous-time fractional order chaotic systems
The study of nonlinear systems and chaos is of great importance to science and engineering mainly because real systems are inherently nonlinear and linearization is only valid near the operating point. The interest in chaos was increased when Lorenz accidentally discovered the sensitivity to initial condition during his simulation work on weather prediction. When a nonlinear system is exhibiting deterministic chaos, it is very difficult to predict its response under external disturbances. This behavior is a double-edged weapon. From a control and synchronization point of view, this proposes a challenge. On the other hand, from a communications and encryption perspective, this provides a higher level of security. This chapter is a survey of the recent contributions in engineering applications of fractional order chaotic continuous-time systems. The applications include but not limited to: communication and encryption, FPGA implementations, synchronization and control, modeling of electric motors, and biomedical applications. © 2018 Elsevier Inc. All rights reserved.