Scaling Analysis of an Image Encryption Scheme Based on Chaotic Dynamical Systems.

L E Reyes-López,M T Ramírez-Torres,H González-Aguilar,M Mejía-Carlos,J O Armijo-Correa,J S Murguía

doi:10.3390/e23060672

L E Reyes-López, M T Ramírez-Torres + Show 4 more

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https://doi.org/10.3390/e23060672

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Abstract

Despite that many image encryption systems based on chaotic or hyperchaotic systems have been proposed to protect different kinds of information, it has been crucial to achieve as much security as possible in such systems. In this sense, we numerically implement a known image encryption system with some variants, making special emphasis when two operations are considered in the scrambling stage. The variants of such an encryption system are based on some hyperchaotic systems, which generated some substitution boxes and the keys of the system. With the aim to have a more complete evaluation, some internal stages of the image encryption scheme have been evaluated by using common statistical tests, and also the scaling behavior of the encrypted images has been calculated by means of a two-dimensional detrended fluctuation analysis (2D-DFA). Our results show that the image encryption systems that include two operations or transformations in the scrambling stage present a better performance than those encryption systems that consider just one operation. In fact, the 2D-DFA approach was more sensitive than some common statistical tests to determine more clearly the impact of multiple operations in the scrambling process, confirming that this scaling method can be used as a perceptual security metric, and it may contribute to having better image encryption systems.

Highlights

Introduction published maps and institutional affilNowadays, the way in which society communicates has radically changed with the fast development of computers and the internet
We considered the hyperchaotic approach in [2] to generate two particular S-boxes based on the hyperchaotic systems of Lorenz and Chen, whose dynamics are very well modeled by the set of differential equations of (1)–(2), respectively
To measure the impact of the scrambling process on the quality and the robustness of the image encryption system, some common statistical tests have considered such as the histogram analysis, the correlation among the adjacent pixels, the entropy, and the

Summary

Introduction

The way in which society communicates has radically changed with the fast development of computers and the internet. Multimedia communication has been gaining momentum in the exchange of information at all social levels. In recent years, security and confidentiality have been of considerable interest. Due to the demand to have a secure transmission through any means of communication, a great variety of encryption systems has been proposed [1,2,3,4,5]. Chaos theory is used in many fields of science due to its special properties, and cryptography is no exception. Many visual data encryption systems based on chaos theory consider the principle of applying chaotic maps to obtain highly mixing properties, which are similar to cryptographic systems. Encryption systems that involve chaotic systems iations

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