Enhancing chaos in multistability regions of Duffing map for an image encryption algorithm

We investigate the dynamics of a 2D chaotic Duffing map that exhibits coexisting chaotic attractors and periodic orbits with a typical set of system parameters. Such unusual behaviors in low-dimensional maps are unacceptable, especially in the applications of chaos-based cryptography. To this end, the Sine-Cosine chaotification technique is used to propose a modified Duffing map in enhancing its chaos complexity in the multistable regions. Based on the enhanced Duffing map, a new image encryption algorithm is developed with the principles of confusion and diffusion. While in the former, hyperchaotic sequences are generated for scrambling of plain-image pixels, the latter is accomplished by the elliptic curves, S-box, and hyperchaotic sequences. Simulation results and security analysis reveal that the proposed encryption algorithm can effectively encrypt and decrypt various kinds of digital images with high-level security.