We introduce some different chaotic maps and analyze the resulting simulation by using MATLAB (R 2013b), with processor Core2 Duo (2.16 GHz) and 2 GB RAM on Windows 8.
2.1. Arnold Cat Map
The Arnold cat map is one of the most important 2-D chaotic map (Shang, Ren, & Zhang, 2008; Liehuang, Wenzhuo, Lejian, & Hong, 2006). It is used in image encryption to shuffle the pixel positions of the plain image. Without any losses in generality, we assume the dimension of the original image to be N 
N. The Arnold Cat map can be described as follows:
(1) where p and q are positive integers, Determinant (A) = 1. When Arnold Cat map is performed once the position of the pixel
will be in the new position
, after applying Arnold Cat map with number of iteration iterating R, it satisfied that
it reaches to its original case this depend on the number of iteration R to and parameters p, q and the size N of the original image. So that we use parameters p, q, and the number of iterations R as the secret keys in the proposed scheme, since the 2-D Arnold Cat map performs a linear transformation, and using mod function, it shuffles the pixel positions with good result in the correlation coefficient among the adjacent pixels.