Reversible data hiding in encrypted images (RDH-EI) has emerged as a critical paradigm for high-security image systems, where both data confidentiality and lossless image recovery are mandatory. This paper proposes a cryptography-oriented reversible data hiding scheme that integrates encryption-assisted embedding with median-based prediction and grayscale invariance to achieve high payload capacity, low distortion, and strong cryptanalytic robustness. In the proposed framework, the original grayscale image is first encrypted using a lightweight stream cipher to ensure visual confidentiality. A median predictor is then employed on spatially correlated pixels to generate compact prediction errors, which are adaptively modulated for reversible embedding. To preserve visual consistency and reduce embedding artifacts, a grayscale invariance constraint is imposed, ensuring that the pixel intensity transitions remain statistically stable after data insertion. The embedded bitstream is protected using a secret-key-controlled permutation, providing resistance against statistical and differential steganalysis. At the receiver side, the hidden data and the original image are perfectly recovered without auxiliary side information, demonstrating strict reversibility.