Double image encryption based on symmetry of 2D-DFT and equal modulus decomposition

Abstract

This paper introduces a double image encryption scheme mainly based on symmetry of two-dimensional discrete Fourier transform (2D-DFT) and equal modulus decomposition (EMD). Firstly, the plural form is adopted to encode double image as a whole and the 2D-DFT is performed. To obtain matrices satisfying property of conjugate symmetry, the spectra are implemented addition and subtraction. Followed by truncation-superposition operations, another complex value matrix is attained and equal modulus decomposition is carried out to get two phase templates, which are further gyrator transformed to enhance security. With an orthogonal matrix, the real and imaginary parts are shared and spliced together to produce a real-valued cipherimage, which aims to make storage and transmission convenient. The initial states of 2D logistic map are closely related to the plaintext images and is employed to generate phase mask, rotation angles as well as the input of Gaussian matrix, which ensures the high level of security. Experimental results have demonstrated the feasibility and validity of the proposal in restituting plaintext images, security and resisting Gaussian noise attack.