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 (KDF). The user-provided key material—a 12-character, human-readable key and four salt words—is transformed by the KDF into 256 bits of high-entropy data, which is then converted into 96 balanced decimal digits to seed the chaotic system. Encryption operates in the real number domain through a chaotic partition–permutation stage followed by modular diffusion. Experimental results confirm perfect reversibility, high randomness (Shannon entropy ≈7.9981), and negligible adjacent-pixel correlation. The method resists known- and chosen-plaintext attacks, showing no statistical dependence between plain and cipher images. Differential analysis yields NPCR≈99.6% and UACI≈33.9%, demonstrating complete diffusion. The PBKDF2-based key derivation expands the effective key space to 2256, eliminates weak-key conditions, and ensures full reproducibility. The proposed approach bridges deterministic chaos and modern cryptography, offering a secure, verifiable framework for protecting sensitive images.
Valencia et al. (Thu,) studied this question.