From chaos to encryption using fractional order Lorenz-Stenflo model with flux-controlled feedback memristor

Abstract

To add complexity to a chaotic system, a new five-dimensional fractional-order chaotic system is proposed based on the Lorenz-Stenflo model with a feedback memristor. By analyzing the phase portraits, equilibrium points, bifurcation analysis, and Poincaré maps, the system generates a two-wing attractor with symmetrical coexistence, which implies that the newly developed chaotic system has abundant dynamical characteristics. The Routh–Hurwitz stability criterion, eigenvalues, and Lyapunov exponents were calculated for a memristive-based system, suggesting that the developed system is unstable and hyperchaotic. The chaotic system is executed with analogue circuits for both the open-loop and closed-loop feedback memristive systems. The transfer function technique was used for the fractional operator. The simulation results showed excellent agreement between the circuit and numerical simulations. Finally, random data information from a chaotic system is utilized to process multimedia encryption. A new cryptographic scheme is presented with the idea of an image as a key, which is introduced and tested with security analysis in support of the provision that images and chaotic systems together can form a viable key.