Image Encryption and Two Dimensional Discrete M-Parameter Fractional Fourier Transform

We propose a novel fractional Fourier transform named M-parameter fractional Fourier transform (MPFRFT), and using this MPFRFT algorithm successfully acquire a new image encryption method. This MPFRFT is not only a fractionization of Fourier transform, but also an extension of four-item weighted fractional Fourier transform defined by Shih, and it owns four free parameters in the weight coefficients. Without any increase of the computational complexity, the MPFRFT-based image encryption method owns more secret keys than the encryption methods operated by other fractional Fourier transforms. On the other hand, even though the order of the fractional Fourier transform which is treated as a secret key is known, one still can't decrypt the image correctly, so do the four free parameters. What's more, not only the security of image information increases, but also the encryption process is simpler. Digital simulations are presented to verify the validity and efficiency of the algorithm.