Image Encryption Method Based on Logarithmic Chaotic System and DNA Mutation

Existing chaos-based image ciphers may suffer from limited dynamical complexity in low-dimensional maps and insufficient diversification of encryption-control sequences across different encryption instances. To address these limitations, a one-dimensional logarithmic chaotic map and a plaintext-dependent encryption scheme with dynamic DNA point mutation are presented. The map combines logarithmic stretching with modular folding and exhibits persistent complex dynamics over the investigated parameter interval. Compared with the logistic map and the one-dimensional Cosine Logistic compound map (1DCLC), it shows a broader positive-Lyapunov-exponent region and more stable normalized permutation entropy, while derived binary sequences satisfy the adopted NIST SP 800-22 criteria. The encryption architecture integrates block-reversal permutation, dynamic DNA encoding, involutive point mutation, and chaotic XOR masking. A SHA-512 plaintext digest, a fresh 128-bit public nonce, and a 256-bit master key are processed through HMAC-SHA-256 and HKDF-SHA-256 to derive the chaotic parameters. Experiments on standard grayscale images show near-uniform ciphertext distributions, negligible adjacent-pixel correlations, near-maximal entropy, differential characteristics close to theoretical references, and pronounced one-bit key sensitivity. The MATLAB implementation achieves encryption and decryption throughputs of approximately 1 MB/s.