Design of Synchronized Large-Scale Chaos Random Number Generators and Its Application to Secure Communication

This paper is concerned with the design of synchronized large-scale chaos random number generators (CRNGs) and its application to secure communication. In order to increase the diversity of chaotic signals, we firstly introduce additional modulation parameters in the original chaotic Duffing map system to modulate the amplitude and DC offset of the chaotic states. Then according to the butterfly effect, we implement modulated Duffing map systems with different initial values by using the microcontroller and complete the design of large-scale CRNGs. Next, a discrete sliding mode scheme is proposed to solve the synchronization problem of the master-slave large-scale CRNGs. Finally, we integrate the aforementioned results to implement an innovative secure communication system.

Novel Image Encryption Scheme Based on Chebyshev Polynomial and Duffing Map

We present a novel image encryption algorithm using Chebyshev polynomial based on permutation and substitution and Duffing map based on substitution. Comprehensive security analysis has been performed on the designed scheme using key space analysis, visual testing, histogram analysis, information entropy calculation, correlation coefficient analysis, differential analysis, key sensitivity test, and speed test. The study demonstrates that the proposed image encryption algorithm shows advantages of more than10113key space and desirable level of security based on the good statistical results and theoretical arguments.

Projective Synchronization of Chaotic Systems Via Backstepping Design

Chaos synchronization of discrete dynamical systems is investigated. An algorithm is proposed for projective synchronization of chaotic 2D Duffing map and chaotic Tinkerbell map. The control law was derived from the Lyapunov stability theory. Numerical simulation results are presented to verify the effectiveness of the proposed algorithm

An Algorithm to Automatically Detect the Smale Horseshoes

Smale horseshoes, curvilinear rectangles and their U-shaped images patterned on Smale's famous example, provide a rigorous way to study chaos in dynamical systems. The paper is devoted to constructing them in two-dimensional diffeomorphisms with the existence of transversal homoclinic saddles. We first propose an algorithm to automatically construct “horizontal” and “vertical” sides of the curvilinear rectangle near to segments of the stable and of the unstable manifolds, respectively, and then apply it to four classical chaotic maps (the Duffing map, the Hénon map, the Ikeda map, and the Lozi map) to verify its effectiveness.