Image Encryption Using Chaotic Box Partition–Permutation and Modular Diffusion with PBKDF2 Key Derivation

This work presents a hybrid chaotic–cryptographic image encryption method that integrates a physical two-dimensional delta-kicked oscillator with a PBKDF2-HMAC-SHA256 key derivation function. The key consists in a 12-symbol human key and four user-defined salt words into 256-bit high-entropy material, later converted for the KDF into 96 balanced decimal digits that seed the chaotic functions. The encryption occurs on the real domain, using a partition–permutation mechanism followed by modular diffusion, both governed by chaos. Experimental results confirm the perfect reversibility of the process, high randomness (entropy = 7.9981), and zero adjacent-pixel correlation. Known and chosen plaintext attacks revealed no statistical dependence between cipher and plain images, while NPCR≈99.6% and UACI≈33.9% demonstrate complete diffusion. The PBKDF2-based key derivation expands the key space to 2256 combinations, effectively eliminating weak-key conditions and enhancing reproducibility. The proposed approach bridges deterministic chaos and modern cryptography, offering a secure and verifiable method for protecting sensitive images.