Cryptanalyzing a novel image cipher based on mixed transformed logistic maps

Abstract

Recently, a novel image cipher [Multimed Tools Appl (2012) 56:315–330] was proposed based on mixed transformed logistic maps. The cipher includes three parts: initial permutation of all the pixels with six odd keys, nonlinear diffusion using the first chaotic keystream and xoring the second chaotic keystream with the resultant values, and Zig-Zag diffusion with the third chaotic keystream. It was claimed that the nonlinear diffusion using the first chaotic map, xoring with the second chaotic map and the Zig-Zag diffusion with the third chaotic map are done to improve the security against the known/chosen plaintext attack. However, the cipher is insecure against chosen plaintext attack. In this paper, we analyze the security weakness of the cipher. As for different images, three chaotic keys keep unchanged so that three chaotic keystreams are also fixed. Our target is to reveal six odd integer keys and three chaotic keystreams equivalent to three chaotic keys. By applying chosen plaintext attack, we can reveal them through two different methods. Experimental results also verify our assertion.