Constructing a novel <i>n</i>-dimensional chaotic map with application to image encryption

In this paper, we develop a novel n-dimensional discrete chaotic map. First, the chaotic behaviors of the proposed map are studied. Next, to illustrate the effectiveness of our map, the 4D hyperchaotic map as an example is analyzed using the phase diagram, Lyapunov exponents, bifurcation diagrams and different types of entropy, etc. Moreover, the chaotic signals generated by the proposed map passed the NIST test and were implemented on the hardware DSP. Finally, we apply our chaotic map in image encryption using true numbers and extended XOR. The experimental results express that the presented encryption algorithm has a higher level of security than same other sophisticated methods.