On the security of 3D Cat map based symmetric image encryption scheme

A 3D Cat map based symmetric image encryption algorithm, which significantly increases the resistance against statistical and differential attacks, has been proposed recently. It employs a 3D Cat map to shuffle the positions of image pixels and uses the Logistic map to diffuse the relationship between the cipher-image and the plain-image. Based on the factor that it is sufficient to break this cryptosystem only with the equivalent control parameters, some fundamental weaknesses of the cryptosystem are pointed out. With the knowledge of symbolic dynamics and some specially designed plain-images, we can calculate the equivalent initial condition of diffusion process and rebuild a valid equivalent 3D Cat matrix. In this Letter, we will propose a successful chosen-plain-text cryptanalytic attack, which is composed of two mutually independent procedures: the cryptanalysis of the diffusion process and the cryptanalysis of the spatial permutation process. Both theoretical and experimental results show that the lack of security discourages the use of these cryptosystems for practical applications.