Image encryption based on the reality-preserving multiple-parameter fractional Fourier transform and chaos permutation

Abstract

In recent years, a number of methods have been proposed in the literature for the encryption of two-dimensional information by use of the fractional Fourier transform, but most of their encryptions are complex value and need digital hologram technique to record their encrypted information, which is inconvenience for digital transmission. In this paper, we first propose a novel reality-preserving multiple-parameter fractional Fourier transform which share real-valuedness outputs as well as most of the properties required for a fractional transform. Then we propose a new approach for image encryption based on the real-valuedness of the reality-preserving multiple-parameter fractional Fourier transform and the decorrelation property of chaotic maps in order to meet the requirements of the secure image transmission. In the proposed scheme, the image is encrypted by juxtaposition of sections of the image in the reality-preserving multiple-parameter fractional Fourier domains and the alignment of sections is determined by chaotic logistic maps. Numerical simulations are performed to demonstrate that the proposed method is reliable and more robust to blind decryption than several existing methods.