A novel hybrid chaotic map-based image encryption scheme with entropy-driven security analysis

This paper proposes a reproducible image encryption algorithm utilizing two two-dimensional chaotic maps, denoted by System I and System II. In response to the need for a more complete dynamical and cryptographic validation, the revised study extends the original Lyapunov-exponent, phase-portrait, and bifurcation analyses by adding equilibrium-point equations, piecewise Jacobian matrices, local stability criteria, and a basin-of-attraction investigation protocol. The maps are embedded in a plaintext-related confusion–diffusion architecture in which SHA-256 is used to derive the initial conditions and control parameters through explicit conversion equations. Security is evaluated using histogram uniformity, correlation coefficients, key sensitivity, differential metrics, bit-level and pixel-level avalanche tests, Shannon entropy, approximate entropy, sample entropy, and NIST SP 800-22 randomness testing. The manuscript also clarifies the practical meaning of key-space estimation under finite-precision arithmetic, provides a formal discussion of chosen-plaintext resistance, and reports the experimental conditions required for fair computational comparison. Robustness against noise and occlusion is quantified through PSNR, SSIM, BER, and recovery accuracy. The comparative discussion has been revised to avoid unsupported superiority claims and to present the proposed method as competitive with recent chaos-, cellular-automata-, ECC-, and hybrid-based image encryption schemes.