On the security of a class of image encryption schemes

Recently four chaos-based image encryption schemes were proposed. Essentially, the four schemes can be classified into one, which is composed of two basic parts: permutation of positions and diffusion of pixel values with the same cipher-text feedback function. The operations involved in the two basic parts are determined by a pseudo random number sequence (PRNS) generated from iterating a chaotic dynamic system. According to the security requirement, the two basic parts are performed alternatively for some rounds. Despite the claim that the schemes are of high quality, we found the following security problems: 1) the schemes are not sensitive to the changes of plain-images; 2) the schemes are not sensitive to the changes of the key streams generated by any secret key; 3) there exists a serious flaw of the diffusion function; 4) the schemes can be broken with no more than [log <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</sub> (MN)] + 3 chosen-images when only one iteration is used, where MN is the size of the plain- image and L is the number of different pixel values. Moreover, we found that the cryptanalysis on one of these schemes proposed by another research group is quite questionable.