Hybrid image encryption algorithm based on Galois fields and chaotic structures

Abstract

Almost every industry relies heavily on images, including the medical field, video conferencing, weather forecasting, the military, and most social media applications. Attackers can hack and obtain sensitive data that is not encrypted or has inadequate security due to the widespread use of modern technology. Securely transmitting secret images through an unreliable network necessitates using a solid image cryptosystem. This paper presents a novel image encryption algorithm that synergistically combines the mathematical robustness of Galois fields with the dynamic complexity of Allee’s effect-influenced logistic maps. The proposed method leverages the properties of Galois fields to enhance cryptographic security and operational efficiency. At the same time, the Allee’s effect, integrated into logistic maps, introduces a new dimension of chaotic behaviour that intensifies encryption unpredictability. Our approach begins with an image preprocessing phase using Galois field transformations to disperse pixel values uniformly. Elements of $GF\left(2^8\right)$ are applied to Allee’s effect with a logistic map to obtain substitution boxes of high non-linearity. These boxes are used for substitution and permutation purposes. A two-dimensional logistic map generates the key for the bitwise XOR operation. Comparative analyses with existing encryption techniques demonstrate that our algorithm offers superior resistance to common cryptographic attacks, including statistical, differential, and brute-force attacks. Experimental results highlight the algorithm’s capability to maintain image quality and integrity post-decryption, making it a viable solution for secure image transmission in diverse applications. Integrating Galois fields and Allee’s effect in logistic maps establishes a robust framework for advancing image encryption methodologies.