Cryptanalysis of an image cryptosystem based on logistic map

In recent years, the studies of chaos-based image encryption have become an important aspect of the security of image transmission. So far, a large amount of chaotic maps have been used in image encryption with the permutation–diffusion architecture, such as logistic map, cat map, tent map and so on. In this paper, a defect of designing an image cryptosystem based on logistic map is proposed. According to the cryptanalysis of the defect, the initial value of logistic which is used to encrypt plain-image can be deduced by the decreased key space, when the parameter of logistic map is given. Finally, the theoretical analysis and numerical experimental results show that the defect could be used to break the image cryptosystem based on logistic map.