Cryptanalysis of image encryption scheme based on a new 1D chaotic system

This paper demonstrates cryptanalysis of an image encryption scheme based on a new 1D chaotic system proposed by Zhou et al. (2014). It is claimed to possess high strength because of better chaotic properties of employed chaotic system, and use of random pixel insertion. On the contrary, several issues are identified in this image encryption scheme including improper definition of key-stream generator used in substitution step, static permutation leading to predictable diffusion and no contribution to confusion, fixed and small number of rounds, practical infeasibility of random-pixel insertion step with one-time use of utilized random values.For practical usability, one-time use condition is required to be dropped. In this case, it is analyzed that M × N cipher image can be represented as a set of linear equations (of original pixel values) derivable using O(M.N) chosen plain text images. Original image is then completely recoverable using differential cryptanalysis with single differential image represented as a set of M.N linear equations solvable with O((M.N)3) complexity. Experimental results demonstrate that the original image is completely recovered without any information regarding key or equivalent key-stream making author's claim of large key-space insignificant. Improvements have been proposed, with security analysis, to enhance strength of existing scheme.