A Low-Complexity 4D Discrete Chaotic System for Secure Image Encryption Based on Reversible Neural Network

Area of Science:

• Cryptography and Information Security
• Nonlinear Dynamics and Chaos Theory

Background:

• Existing chaotic systems often suffer from complex structures and potential degradation.
• There is a need for robust and simple chaotic systems for secure applications like image encryption.

Purpose of the Study:

• To propose a novel four-dimensional discrete chaotic system (4D-DCS) with a simple structure.
• To develop an image encryption algorithm utilizing the proposed 4D-DCS for enhanced security and practicality.

Main Methods:

• Constructed a 4D-DCS by integrating a feedback controller and modulo operation into a linear discrete-time system.
• Employed mathematical analysis (Li-Yorke chaos) and numerical simulations (Lyapunov exponent, 0-1 test, NIST SP 800-22) to validate chaotic and pseudorandom properties.
• Developed an image encryption algorithm using SHA-256 for key generation, row-column permutation, and a reversible neural network for diffusion.

Main Results:

• The 4D-DCS exhibits hyperchaotic characteristics and excellent pseudorandomness.
• The encryption algorithm achieved high NPCR (∼99.61%) and UACI (∼33.46%), a large key space (2^216), high information entropy (near 8), and low correlation coefficients (near 0).
• Demonstrated strong robustness against differential, cropping, noise, and chosen-plaintext attacks.

Conclusions:

• The proposed 4D-DCS offers structural simplicity and stability compared to existing systems.
• The image encryption algorithm provides superior security and practicality, making it suitable for security-critical applications.