Double image encryption scheme by using random phase encoding and pixel exchanging in the gyrator transform domains

We present a double image encryption scheme by using random pixel exchanging and phase encoding in gyrator domains. Two original images are regarded as the amplitude and phase of a function in the encryption algorithm. The pixels of the two images are exchanged randomly by controlling of a matrix. The same random matrix is used in the process of pixel exchanging and phase encoding for saving space in the application of transmission and storage of key. Some numerical simulation results are made for demonstrating the performance and security of the double image encryption.