An Efficient Image Encryption Algorithm for the Period of Arnold's CAT Map

Abstract

Arnold's CAT Map (ACM) is a chaotic transformation of the 2-dimensional toral automorphism T^2 defined by the mapping Γ ∶ T^2 → T^2. There are many applications of ACM in various research areas such as: steganography, encryption of images, texts and watermarks. The transformation of an image is achieved by the randomized order of pixels. After a finite number of repetitions of the transformation, the original image reappears. In this study, encryption of two images is demonstrated together with a proposed algorithm. Moreover, the periodicity of ACM is discussed and an algorithm to change the period of ACM is suggested. The resultant period obtained from the new algorithm is compared with the period obtained from the usual ACM. The results show that the period of the proposed algorithm grows exponentially while the period of ACM has an upper bound.