A Novel Chaotic System with a Line Equilibrium: Analysis and Its Applications to Secure Communication and Random Bit Generation †

Abstract

In this study, a novel two-parameter, three-dimensional chaotic system is constructed. The system has no linear terms and its equilibrium is a line, so it is a system with hidden attractors. The system is first studied by computation of its bifurcation diagrams and diagram of Lyapunov exponents. Then, the system is applied to two encryption related problems. First, the problem of secure communications is considered, using the symmetric chaos shift keying modulation method. Here, the states of the chaotic system are combined with a binary information signal in order to mask it, safely transmit it through a communication channel, and successfully reconstruct the information at the receiver end. In the second problem, the states of the system are utilized to design a simple rule to generate a bit sequence that possesses random properties, and is thus suitable for encryption related applications. For both applications, simulations are performed through Matlab to verify the soundness of the designs.