Fractional Fourier Transform Applied to Digital Images Encryption

In the present paper a digital algorithm was developed to make phase encryption of digital indexed images to color using the fractional Fourier transform (the images in RGB are converted to indexed before to encrypt). The indexed images are represented by a matrix of MXN pixels (where M defines the height and N is the Width of the image) and a color map (it's a matrix of CX3 elements, where C indicates the colors number of the image and the number 3 indicates the three columns associated with the color components: Red, Green and Blue of each pixel of the matrix of MXN) associated to the matrix of pixels to suitably represent the color information of the image. The indexed image (matrix of MXN pixels) to encrypt is placed as the phase of a complex exponential, then is transformed three times and multiplied in intermediate steps by two random phase masks statistically independent thus to obtain the encrypted image, for decrypt the coding image the encryption procedure is applied in the inverse sense to the conjugated complex of the encrypted image, then is taken the negative of the phase of the resulting function of the decryption process and the original image is obtained this way that had been encrypted; For the color map equal procedure is applied in the encryption/decryption process described previously for the matrix of MXN pixels. In the implemented cryptographic algorithm five keys are used, constituted by three fractional orders and two random phase masks, all these keys are necessary for a correct decryption providing a dependability to the transference of images by means of the communications nets.