Dynamic Analysis and Circuit Design of a New 3D Highly Chaotic System and its Application to Pseudo Random Number Generator (PRNG) and Image Encryption

In this paper, a new 3D dynamical system with four quadratic nonlinear terms is presented. It is shown that the proposed chaotic system has two saddle-foci, unstable, equilibrium points. Thus, the proposed chaotic system exhibits self-excited chaotic attractors. Dynamical analysis methods such as Lyapunov exponents spectrum, bifurcation diagrams, and phase portraits are used to explore the complex dynamical behaviors of the proposed chaotic system and analyze its basic qualitative properties. It is shown that the maximal Lyapunov exponent (MLE) of the new chaotic system is 7.196, which is a high value. The proposed highly chaotic system exhibits high complexity and it will be very useful for applications in cryptography, encryption and secure communications. The physical feasibility of the proposed system is verified by implementing its electronic circuit schematic using Multisim software. Additionally, a PRNG has been developed using the derived state variables and analyze with NIST-800–22 test. Lastly, we developed a PRNG-based image encryption and employ it for an encryption. The experimental outcomes obtained prove that the 3D chaotic system-based encryption application presented in this section has a very good performance.