An efficient image encryption scheme using Fresnelet transform and elliptic curve based scrambling

This work introduces a novel and more efficient image encryption scheme, that deploys Fresnelet diffraction in the wave-propagation domain in conjunction with image scrambling effect, based on a specific elliptic curve group, that substantially reduces the computational cost for the desired outcome. Significantly elevated security of the encrypted image is guaranteed by highly complex algebraic structure of the elliptic curve over the Galois field F24\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathbb {F}_{2}^{4}$\end{document}, in association with Fresnelet transform-based data-decomposition. At first stage, the proposed scheme, propagates confidential information, with selected wavelength at ceratin specific distance, using the Fresnelet transform. During this process confidential data decomposes into four complex sub-bands. We further separate these sub-bands into real and imaginary sub-band data. Then, at the second stage, elliptic curve group law is deployed to add confusion by scrambling the net sub-band data. The security and quality of the presented technique is examined through highly significant tools and we prove that when compared with other prevailing schemes, the proposed scheme offers coherent outcomes.