Image Encryption by Redirection and Cyclical Shift

摘要

In this paper, we present a novel method for encrypting and decrypting large amounts of data such as two-dimensional (2-D) images, both gray-scale and color, without the loss of information, and using private keys of varying lengths. The proposed method is based on the concept of the tensor representation of an image and splitting the 2-D discrete Fourier transform (DFT) by one-dimensional (1-D) DFTs of signals from the tensor representation, or transform. The splitting of the transform is accomplished in a three-dimensional (3-D) space, namely on the 3-D lattice placed on the torus. Each splitting-signal of the image defines the 2-D DFT along the frequency-points located on the spirals on the torus. Spirals have different form and cover the lattice on the torus in a complex form, which makes them very effective when moving data through and between the spirals, and data along the spirals. The encryption consists of several iterative applications of mapping the 3-D torus into several ones of smaller sizes, and rotates then moves the data around the spirals on all tori. The encryption results in the image which is uncorrelated. The decryption algorithm uses the encrypted data, and processes them in inverse order with an identical number of iterations. The proposed method can be extended to encrypt and decrypt documents as well as other types of digital media. Simulation results of the purposed method are presented to show the performance for image encryption.