Deep Learning and Chaos: A combined Approach To Image Encryption and Decryption

TL;DR

Simulation results and comparative analyses illustrate that the proposed encryption scheme possesses excellent visual security, decryption quality, and computational efficiency, and thus, it is efficient for secure image transmission and storage in big data applications.

Abstract

In this paper, we introduce a novel image encryption and decryption algorithm using hyperchaotic signals from the novel 3D hyperchaotic map, 2D memristor map, Convolutional Neural Network (CNN), and key sensitivity analysis to achieve robust security and high efficiency. The encryption starts with the scrambling of gray images by using a 3D hyperchaotic map to yield complex sequences under disruption of pixel values; the robustness of this original encryption is further reinforced by employing a CNN to learn the intricate patterns and add the safety layer. The robustness of the encryption algorithm is shown by key sensitivity analysis, i.e., the average sensitivity of the algorithm to key elements. The other factors and systems of unauthorized decryption, even with slight variations in the keys, can alter the decryption procedure, resulting in the ineffective recreation of the decrypted image. Statistical analysis includes entropy analysis, correlation analysis, histogram analysis, and other security analyses like anomaly detection, all of which confirm the high security and effectiveness of the proposed encryption method. Testing of the algorithm under various noisy conditions is carried out to test robustness against Gaussian noise. Metrics for differential analysis, such as the NPCR (Number of Pixel Change Rate)and UACI (Unified Average Change Intensity), are also used to determine the strength of encryption. At the same time, the empirical validation was performed on several test images, which showed that the proposed encryption techniques have practical applicability and are robust to noise. Simulation results and comparative analyses illustrate that our encryption scheme possesses excellent visual security, decryption quality, and computational efficiency, and thus, it is efficient for secure image transmission and storage in big data applications.

Figures (13)

• Figure 1: The figure depicts three separate three-dimensional scatter-density plots pertaining to three different trajectories in a three-dimensional hyperchaotic map; the $x$, $y$, and $z$ axes display the value of the three variables involved. The trajectory in (a) is confined to such a small region of phase space that this is almost certainly the least chaotic of the three. In (b), the trajectory spreads out over a larger portion of phase space, indicating a more chaotic system than a. And (c) is even more spread out, indicating a highly chaotic system.
• Figure 2: Bifurcation diagram and Lyapunov exponent spectrum of 3D hyperchaotic map is givenmuni2024. It shows that this system is showing very complex hyperchaotic behaviour as the parameter $b_2$ of the system changes its values. Figure (a) represents the Bifurcation diagram for a 3D hyperchaotic map. Figure (b) Lyapunov exponent diagram for the above 3D hyperchaotic map clearly indicates the stability and chaotic region as a function of changing parameters.
• Figure 3: Evolution of hyperchaotic behaviour of 2D memristor map is shown. Fig(a) here illustrates the phase space at $k = 1.74$, which is a hyperchaotic regime. Fig(b) here illustrates the phase space at $k = 1.75$, which lies in a hyperchaotic regime. Fig(c) here illustrates the phase space at $k = 1.76$, which lies in two disjoint cyclic hyperchaotic regimes.
• Figure 4: The bifurcation diagram and Lyapunov exponent spectrum of the 2D memristor map are shown. (a) shows the bifurcation diagram showing the state of the system developing as it depends on the parameter $k$; (b) shows the Lyapunov exponent spectrum showing the existence of hyperchaos depending on the parameter $k$.
• Figure 5: An original greyscale image (a) is encrypted by a 3D hyperchaotic equation and converted into an unreadable, scrambled image (b). A backward process leads to the decryption of the picture and its return to its original format (c). Therefore, it is possible to examine how efficiently a technique encrypts or decrypts a picture.