Periodicity analysis of Arnold Cat Map and its application to image encryption

Image encryption and decryption are important as there is a lot of information transfer in the digital world. An interesting topic of discussion could be the periodicity of the Arnold Cat Map (ACM) used for image encryption. Determining the exact or even approximate value of the period for the particular size of the image is much appreciated. In this paper, the periodicity of the ACM map is analyzed to enhance the chaotic behaviour of the Arnold Cat Map so as to overcome the limitation of ACM algorithm owing to its periodicity. Also modified ACM-2D and ACM-3D maps are proposed for image encryption and its efficiency is proved by histogram and key sensitivity analysis.