The changing information technology and the constant progress of medical technologies have gradually changed traditional paper-based medical records into low-cost electronic health records. The broad application of electronic health records allows a medical information exchange model being developed, called personal health records (PHR), which are the personal health medical information managed and maintained by the user. In consideration of PHR being a patient's health medical information, the privacy setting and the access authority have to be strictly controlled. In addition to providing users with reasonable access authorities, the PHR system has to avoid the illegal access of unauthorized single users or groups. The idea of publickey cryptosystems and Lagrange interpolating polynomial is applied to construct a high-security and efficient encryption scheme so that PHR users could execute the access system in a secure environment.