Information diffusion in images through encryption with Jerk chaotic systems

Abstract

In the ongoing work a Jerk-type Duffing system with a sixth-order damped potential is applied into an image encryption
algorithm, due to the sensitivity and non-periodicity of the response of system under different initial conditions. In most cases,
image encryption generally consists of three main stages. First, the pseudorandom generation of the encryption key. Second,
the shuffling of the image pixels. Third, the intensity of the pixel values is changed in a pseudorandom manner (diffusion).
The proposed encryption algorithm based on diffusion, relies on a deterministic and chaotic Jerk-type dynamical system, whose
purpose is to generate pseudo-random data used to modify the pixel intensity values. The image is encrypted only through the
diffusion process, considering a known key generated by the user. To verify the reliability of the encryption process, the statistical
properties of the plain image are compared with the encrypted image, taking as reference the statistical properties corresponding to
an image with uniform distribution. The comparison is made by evaluating the correlation between adjacent pixels of each of the
images and the Shannon information entropy, which quantifies information content or randomness in the image by measuring
the uncertainty in pixel values, a high entropy indicates a complex image with diverse pixel values and low entropy indicates
a uniform, simple image. It is found that the Jerk chaotic system optimally hides the image information by obtaining a high
information entropy.