Abstract: With the digitization and networking development of medical imaging, medical images that exist in single-channel grayscale form are more prone to privacy leakage and tampering risks during transmission and storage. Compared to three-channel color images, their encryption effectiveness is more difficult to guarantee. To address this, this paper proposes a geometric rotation encryption algorithm based on a novel spatiotemporal chaotic system. The new system is built using the Sine map and the classical CML system as the foundational models. A pixel scrambling and diffusion algorithm based on geometric rotation thinking is designed in combination with the Cartesian coordinate system. The rules of scrambling and diffusion are still influenced by the numerical characteristics of the pixel values themselves, and the pixel characteristic-driven features are reflected algorithmically based on the theory of coordinate rotation. Finally, simulation analysis concludes that the encryption effect of this algorithm can effectively ensure the security and confidentiality of medical images. Additionally, employing the concept of coordinate system rotation allows students to easily and efficiently understand the essential meaning of image encryption.