We investigate the dynamics of a two-dimensional chaotic Duffing map which
exhibits the occurrence of coexisting chaotic attractors as well as periodic
orbits with a typical set of system parameters. Such unusual behaviors in
low-dimensional maps is inadmissible 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 asymmetric 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 a high-level security.Comment: 15 pages, 15 figure