Chaos-Based Digital Image Encryption Using Arnold’s Cat Map Permutation and Duffing Map Diffusion: A Python Desktop Implementation

Digital images are widely used for identification, communication, and information exchange, yet their large size, high pixel correlation, and uneven intensity distribution make them vulnerable to theft, manipulation, and statistical inference, thereby requiring encryption mechanisms tailored to image characteristics.Purpose: This study proposes a chaos-based permutation–diffusion scheme that combines Arnold’s Cat Map for pixel permutation and the Duffing Map as a keystream generator for diffusion to strengthen digital image encryption and improve resistance to unauthorized analysis. Methodology: An experimental quantitative approach was conducted through the development of a Python-based desktop application. Ten test images (RGB and grayscale) with varying resolutions were encrypted and decrypted using predefined key settings. Security and performance were evaluated using histogram analysis, entropy, pixel correlation, key sensitivity, processing time, and key space. Findings: The encrypted images exhibit near-uniform histograms, entropy values approaching the ideal for 8-bit images (≈8), and pixel correlation values close to zero, indicating strong statistical concealment. The scheme also demonstrates high key sensitivity, where small key changes prevent meaningful decryption, and a large key space that supports brute-force resistance. Processing time increases with image size but remains practically feasible for desktop implementation. Implications: The proposed scheme can be applied to protect sensitive image data in local desktop environments and image exchange scenarios, reducing risks of statistical attacks and brute-force attempts while maintaining acceptable runtime for common image sizes. Originality: This study delivers an end-to-end integration of Arnold’s Cat Map and the Duffing Map within a permutation–diffusion structure implemented as a Python desktop application, supported by structured security and efficiency evaluation, thereby providing a practical and reproducible contribution to chaos-based image cryptography.