With the rapid development of information technology and changes in social structure, the public awareness of health issues has continued to increase, driving the evolution of electronic medical records (EMRs). Traditional EMRs can store and retrieve medical records, but they are often confined to individual hospital database environments and cannot fully meet the demand for cross-hospital data sharing in urgent clinical situations. To address this problem, the concept of the personal health record (PHR) emerged, allowing personal medical data to be stored digitally in the cloud. This makes data available in real time and shareable across institutions while strengthening information security and reducing the risks of data theft and impersonation. In this study, we propose a secure access control mechanism for cloud-based medical information systems, which combines Newton interpolation polynomials, matrix operations, and timestamping to strengthen the stability, timeliness, and flexibility of access control. The mechanism distinguishes user privileges across authorization levels, supports multi-role and hierarchical resource access, and updates authorization information and access status in real time when permissions change to maintain data integrity and confidentiality. The system can also incorporate alerts triggered by abnormal values in continuous sensor readings, so that an elevated risk level, such as a sudden drop in blood pressure or an abnormal glucose level, can prompt immediate privilege adjustments or the routing of data to appropriate medical personnel. By incorporating sensor-derived physiological data from medical devices such as wearable health monitors and IoT-enabled bedside diagnostics, the mechanism can dynamically adjust access privileges and information pathways in response to heart rate, blood oxygen saturation, body temperature, and other physiological measurements. Access control is therefore context-aware: system decisions reflect both user roles and sensor-derived clinical urgency. Through this mechanism, patient data can be shared securely and rapidly across healthcare institutions, potentially reducing data transmission time and enabling real-time access to key medical information during emergencies to support rapid and accurate diagnosis and appropriate treatment planning.