Color image encryption scheme based on fractional Hartley transform and chaotic substitution–permutation

We propose a novel opto-digital method of color image encryption which utilizes compound chaotic mappings, the reality preserving fractional Hartley transformation and piecewise linear chaotic map for substitution, optical processing and permutation of image pixels, respectively. The image to be encrypted initially undergoes a chaos-based substitution in the spatial domain through the compound chaotic maps followed by a transformation to the combined time–frequency domain using the fractional Hartley transform. A reality preserving version of the fractional Hartley transform is used to eliminate the complexity associated with transform coefficients. Optical transformation of the image, in the fractional Hartley domain, is followed by a permutation through piecewise linear chaotic maps. Due to the intertwined application of optical transformation and chaos-based substitution and permutation processes, the proposed image encryption scheme possesses higher security. The input parameters (initial conditions, control parameters, and number of iterations) of chaotic maps along with fractional orders of the fractional Hartley transform collectively form the secret keys for encryption/decryption. The proposed scheme is a lossless and symmetric encryption scheme. The level of security provided in terms of high sensitivity to keys, resistivity to brute-force attack, classical attacks, differential attacks, entropy attack, noise and occlusion attack along with the elimination of complex coefficients proves its better efficacy as compared to other similar state-of-the-art schemes.