A robust chaos-based image encryption scheme over $${\mathbb{F}}_{256}$$ using predefined reversible functions

Abstract

This article presents a novel image-encryption approach based on dynamic, reversible chaotic-algebraic transformations formulated over a general finite field $${\mathbb{F}}_{{\text{P}}^{\text{n}}}$$ and instantiated, for byte-aligned data, at p = 2 and n = 8, that is, over $${\mathbb{F}}_{256}={\mathbb{F}}_{2}\left[x\right]/p\left(x\right)$$ , by randomly picking an irreducible polynomial p(x) from 30 choices and a field generator from 128 choices. This approach exploits the mathematical richness of finite fields to create invertible, nonlinear, and general transformations, performed pixel by pixel, with a guarantee of exact decryption based on parametric reversibility conditions, as well as improved confusion. Simultaneously, they also deploy chaotic maps to create sensitive control parameters and pseudo-random sequences to improve diffusion, key sensitivity, and resistance to statistical attacks. The proposed scheme relies on characteristics of digital images, such as redundancy and strong correlation between pixels. Secure encryption can be achieved by combining predefined reversible functions with chaos-driven permutation mechanisms. In-depth security analyses, including histogram uniformity, information entropy, pixel correlation, NPCR, UACI, AE, key sensitivity, and reconstruction fidelity, confirm that our approach is effective and robust. This study provides a common and well-founded hybrid encryption approach, contributing to the existing body of knowledge in the literature on image cryptography in finite fields.