Digital Images Phase Encryption Using Fractional Fourier Transform

Abstract

In the present paper the fractional Fourier transform was used to make phase encryption of color digital images. The image to encrypt is placed as the phase of a complex exponential, then is fractionally transformed three times and multiplied in intermediate steps by two statistically independent random phase masks thus to obtain the encrypted image, to 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 from the decryption process and the original image is obtained this way that had been encrypted. The use of the fractional Fourier transform and the phase encryption of the image add much more complexity to the decryption of the image to who wants decrypt it without being authorized. In the cryptographic algorithm implemented five keys are used, made up of three fractional orders and two random phase masks, all these keys are necessary for proper decryption affording reliability to image transference via transmission networks