A no interference method for image encryption and decryption by an optical system of a fractional fourier transformation and a fourier transformation

Abstract

A no interference encryption and decryption for a digital image is presented in this paper. The encrypting process consists of a fractional Fourier transformation and a Fourier transformation. A digital image is first coded with a random phase plate, then it takes a fractional Fourier transformation. The transformed field function is expanded 4 times and coded with another random phase mask. Meanwhile the system takes a Fourier transformation. The real part of the transformed function is taken as an encrypted image. For the decryption of the digital image, first the encrypted image undergoes an inverse Fourier transformation. Then the upper left corner of the transformed function is cut off. At last the cut-off function takes an inverse fractional Fourier transformation. The original digital image can be extracted from the final transformed function. Compared with optical holography, an interference process is not needed in our program. This will reduce the complexity of optical system. © Springer-Verlag Berlin Heidelberg 2011.