Two-dimensional DFA scaling analysis applied to encrypted images

Abstract

The technique of detrended fluctuation analysis (DFA) has been widely used to unveil scaling properties of many different signals. In this paper, we determine scaling properties in the encrypted images by means of a two-dimensional DFA approach. To carry out the image encryption, we use an enhanced cryptosystem based on a rule-90 cellular automaton and we compare the results obtained with its unmodified version and the encryption system AES. The numerical results show that the encrypted images present a persistent behavior which is close to that of the 1/f-noise. These results point to the possibility that the DFA scaling exponent can be used to measure the quality of the encrypted image content.

Discriminating image textures with the multiscale two-dimensional complexity-entropy causality plane

“…Actually, recent effective applications in heterogeneous fields confirm that these fractal techniques are highly valuable tools, e.g. identification of lesion regions of crop leaf affected by diseases [10], Hurst exponent estimation performed on satellite images to measure changes on the Earth's surface [11], and determination of scaling properties in encrypted images [12]. Despite all these significant efforts, the development of a robust methodology to detect and quantify spatial structures in images still represents an open and subtle problem.…”

A highly nonlinear S-box based on a fractional linear transformation

“… 2014 ; Vargas-Olmos et al. 2015 , 2016 ). During the image encryption process distortions occur and the strength of the encryption algorithm used is characterized by the type of these distortions.…”

Design and Implementation of a Configurable Encryption System for Power-Constrained Devices

“…To measure the efficiency of the encryption system, the most common tests applied in cryptography [31], [34]- [36] were carried out, such as statistical tests including histogram analysis, correlation analysis, entropy analysis and PSNR analysis, as well as sensitivity tests such as differential attacks analysis and key sensitivity analysis. In addition to these tests, detrended fluctuation analysis (DFA) was performed to evaluate the performance of the system [37]. The tests were performed on a database of 60 images 1…”

“…DFA is a technique used to analyze singular or fractal behaviors that can be present in images. This is done by extracting the Hurst indices of sequences in the plane of the image, and then, the average of the scaling exponent can be estimated [37]. To resist a common attack, a good cryptosystem should map the plain-image to a random cipher-image without exhibiting any pattern, and the image pixels should take as many random values as possible [38].…”

“…The values α = 1 and α = 1.5, correspond to 1/f noise and Brownian motion, respectively [41]. For secure encryption, the scaling exponent should be close to 0.5 and 1 for one-dimensional DFA and 2D-DFA, respectively [37], [39].…”