Double image encryption based on the reciprocal-orthogonal parametric transform and chaotic maps

In this paper, we propose a double image encryption method based on the reciprocal-orthogonal parametric (Rap) transform and chaotic maps. In this method, a complex-valued image is constructed by two secret real-valued images, one as amplitude and the other as phase. In addition, two chaotic random phase masks are generated using two non-independent chaotic maps; one mask is multiplied by the resulting complex-valued image before applying the two-dimensional (2-D) Rap transform and the other one is multiplied by the resulting matrix in the transform domain. This step is then followed by a chaotic scrambling between the real and imaginary parts before applying another 2-D Rap transform, which yields the encrypted image. The independent parameters of the Rap transforms and the parameters of the chaotic maps used for the masks and scrambling are successfully exploited as an encryption secret key. Simulation results demonstrate the robustness of the proposed method against blind decryption, brute force and statistical attacks.