Optical color image hiding scheme by using Gerchberg–Saxton algorithm in fractional Fourier domain

•The main key and extra keys are introduced for hiding secret image to enhance the security.•The Gerchberg–Saxton retrieval transform is employed for the color image hiding scheme.•The three components of color secret image are mixed in the algorithm.

We proposed an optical color image hiding algorithm based on Gerchberg–Saxton retrieval algorithm in fractional Fourier domain. The RGB components of the color image are converted into a scrambled image by using 3D Arnold transform before the hiding operation simultaneously and these changed images are regarded as the amplitude of fractional Fourier spectrum. Subsequently the unknown phase functions in fractional Fourier domain are calculated by the retrieval algorithm, in which the host RBG components are the part of amplitude of the input functions. The 3D Arnold transform is performed with different parameters to enhance the security of the hiding and extracting algorithm. Some numerical simulations are made to test the validity and capability of the proposed color hiding encryption algorithm.