An extended image encryption with Markov processes in solutions images dynamical system of non-linear differential equations

Abstract

The process of hiding texts or images into images and signals has been remained contemporary topics over more than decades in Information Sciences. An attempt has been made to hide information or images into the solutions of non-linear differential equations of some especial type like Lorezn and Rossler’s equations, these equations have great importance in almost all practical applications from engineering, geography (weather forecasting) and even in stock markets due to its chaotic behavior of solutions which is dependent on initial conditions. The chaotic nature and the aperiodicity of such solutions have become the main source of attraction for encryptions. The 3D parametric (time) series of solutions of Lorenz and Rossler’s equations are produced phase vectors, and one of these phase vectors is chosen for the purpose of text or image embedding into its error (noise). The error (noise) is a part of chaotic solutions behaved aperiodicity in phase vectors. This attracted the embedding of manipulated text or image into it. Modified or reconstructed phase vector embedded with text or image when reproduced in the form of phase surfaces are quite similar to the original solutions surfaces. So Lorenz and Rossler solutions are used for embedding benchmark images like Lena, Fruits and Vegetables. Having embedded these images into series solutions, we found Lorenz solutions are more appropriate over the Rossler solutions. A thorough statistical analysis together with histograms of both original images and embedded images are reported. Experiments with RGB values of embedded images are also reported. In the present research, we have further extended this technique by using Markov processes to our target images and converted into encrypted images before embedding into solution phase vector of Lorenz and Rossler’s equations. Markov processes are made more confusing/diffusing the target images and has become difficult for intruders to attack for retrieval.