Image encryption scheme based on fractional-order hyper-chaotic lorenz system with two-stage confusion-diffusion for enhanced pixel randomness

Abstract

This study proposes a novel grayscale image encryption framework integrating a fractional-order 4D hyperchaotic Lorenz system with DNA encoding operations and SHA-256 plaintext-dependent key generation to address the security vulnerabilities in digital data transmission. The encryption pipeline employs a robust two-stage confusion-diffusion architecture designed to maximize pixel randomness and resistance against differential attacks. Stage 1 implements DNA-based confusion-diffusion with chaotic rule selection, while Stage 2 executes a four-round pixel-level permutation and XOR diffusion drixven by fractional-order Grünwald-Letnikov sequences (α = 0.95, d = 5). This multi-layered approach ensures that any infinitesimal change in the plaintext or the secret key results in a completely different cipher image. Hyperchaos is verified through the Lyapunov exponent spectrum (λ1 = +0.973, λ2 = +0.531), confirming two positive exponents and complex dynamical behavior. Experiments on five standard 512 × 512 grayscale images yield near-maximum information entropy (7.9993–7.9994 bits) and negligible pixel correlation (below 0.023). Statistical evaluations show an average NPCR of 99.5992% and UACI of 33.4216%, closely matching theoretical ideals. Key sensitivity analysis demonstrates that a perturbation of only ±10⁻¹⁴ in the initial conditions renders decryption unsuccessful, ensuring high security. In conclusion, the proposed scheme achieves perfect lossless recovery (PSNR = ∞ dB) and successfully passes all NIST SP 800-22 tests, providing a highly secure and reliable solution for protecting sensitive medical or military digital imagery.