A generalized Arnold's Cat Map transformation for image scrambling

Abstract

This study presents a new approach to generate the transformation matrix for Arnold's Cat Map (ACM). Matrices of standard and modified ACM are well known by many users. Since the structure of the possible matrices is known, one can easily select one of them and use it to recover the image with several trials. However, the proposed method generates a larger set of transform matrices. Thus, one will have difficulty in estimating the transform matrix used for scrambling. There is no fixed structure for our matrix as in standard or modified ACM, making it much harder for the transform matrix to be discovered. It is possible to use different type, order and number of operations to generate the transform matrix. The quality of the shuffling process and the strength against brute-force attacks of the proposed method is tested on several benchmark images.