Secure image encryption using a 4D chaotic system and Langton’s ant cellular automaton

Abstract

The recent explosion of high-rate multimedia transfer has heightened the need for image ciphers that are lossless, payload-grade, and computationally efficient, yet fully structure-adaptive. Traditional block ciphers are effective for byte streams but do not account for spatial dependencies in images, while many chaos-based methods remain ad hoc, lacking strict invertibility and clear keying or synchronization mechanisms. Motivated by these gaps, we present a keyed image cipher that integrates a four-dimensional (4D) chaotic driver with a rule-adaptive variant of Langton’s Ant cellular automaton. The scheme performs pixel permutation followed by two mutually inverse decimal diffusions with cross-channel feedback, and a symbolic diffusion stage that encodes bytes into Ant symbols intermingled through three distinct, keystream- and rule-dependent operators. The core novelty is a provably bijective symbolic diffusion with an explicit inverse and a branch-number–style local diffusion lower bound, combined with a linear-time streaming implementation. The cipher passes the NIST SP 800-22 statistical tests on both keystream and ciphertext-derived bitstreams. Experiments on standard test images show NPCR UACI Shannon entropy bits/pixel, negligible adjacent-pixel correlations, high key sensitivity, and strong robustness against 20% salt-and-pepper noise and 20% occlusion. The overall key space is approximately, indicating high resistance to brute-force attacks.