Double Image Encryption Based on 2D Discrete Fractional Fourier Transform and Piecewise Nonlinear Chaotic Map

Abstract

Secure transmission of sensitive data over open networks is a challenge in the present scenario of digital signal transmissions. Especially in 2D image signals, the adjacent pixel correlation is high which makes it a challenge to encrypt or hide the information from being fraudulently interpreted. Optical signal processing is preferred for image encryption owing to its high speed parallel processing. Fractional transforms are used for the digital implementation of the optical processing due to the fact that fractional orders enable to analyze a time variant signal where each fractional order correspond to an arbitrary angle of rotation. In this work, we apply a fractional Fourier transform for double image encryption, as fractional orders provide randomness and serve as secret key. The complex outcome of transform becomes a limitation due to requirement of double memory for storage and transmission besides computational complexity. To overcome this issue, a reality preserving scheme is applied to obtain real output from transform. A piecewise nonlinear chaotic map is used to introduce chaotic blending in the double image data. The larger key space of PWNCA based blending offers yet another security layer to the optical transform based encryption. The simulation results give testimony to the acquired randomness in the encrypted data. The proposed scheme is quite sensitive to keys and is robust against potential attacks.