<p>This paper presents a novel medical image encryption scheme that integrates a synchronously updated chaotic logical Boolean <i>network with the Four-Color Theorem to achieve high security and structural obfuscation. The proposed Boolean network,</i> constructed through the semi-tensor product and derived from the Hénon map, exhibits enhanced dynamical properties, such as increased sensitivity to initial conditions and stronger chaotic behavior, thereby improving cryptographic unpredictability and robustness. To preserve clinically significant image information, a color-labeling strategy is employed to identify and encode diagnostically relevant regions within the image. A color label matrix, generated according to the Ffour-Color Theorem and matched to the dimensions of the plaintext image, is subsequently employed to guide pixel position scrambling. This process effectively conceals anatomical and pathological features while maintaining computational efficiency. Experimental results confirm the robustness of the proposed scheme, demonstrating strong resistance against statistical and differential attacks.</p>