On the security of image encryption schemes based on Multiple Parameters Transforms

Recent developments of generalized forms of signal processing transforms with a large number of independent parameters, such as the Multiple Parameter Fractional Fourier Transform and the Discrete Fractional Cosine Transform, have encouraged many researchers to propose image encryption algorithms based on a single or multiple applications of these transforms. In order to claim a high level of security of these parameterized transforms-based schemes, their authors usually use the argument that the encrypted image is visually indistinguishable from random noise. In this paper, we show that these algorithms represent typical textbook examples of insecure ciphers; all the building blocks of these schemes are linear, and hence, breaking these scheme, using a known plaintext attack, is equivalent to solving a set of linear equations. We also invalidate the argument of relying on the visual quality of the encrypted image ciphertext by presenting an example for a trivially insecure system that produces ciphertext images with the same property. An agreement against the claimed efficiency of these schemes is also provided.