There is broad consensus that remote health monitoring will benefit all stakeholders in the healthcare system and that it has the potential to save billions of dollars. Among the major concerns that are preventing the patients from widely adopting this technology are data privacy and security. Wireless Medical Sensor Networks (MSNs) are the building blocks for remote health monitoring systems. This paper helps to identify the most challenging security issues in the existing authentication protocols for remote patient monitoring and presents a lightweight public-key-based authentication protocol for MSNs. In MSNs, the nodes are classified into sensors that report measurements about the human body and actuators that receive commands from the medical staff and perform actions. Authenticating these commands is a critical security issue, as any alteration may lead to serious consequences. The proposed protocol is based on the Rabin authentication algorithm, which is modified in this paper to improve its signature signing process, making it suitable for delay-sensitive MSN applications. To prove the efficiency of the Rabin algorithm, we implemented the algorithm with different hardware settings using Tmote Sky motes and also programmed the algorithm on an FPGA to evaluate its design and performance. Furthermore, the proposed protocol is implemented and tested using the MIRACL (Multiprecision Integer and Rational Arithmetic C/C++) library. The results show that secure, direct, instant and authenticated commands can be delivered from the medical staff to the MSN nodes