In the presence of convenience, cloud computing services have increasingly become used to resolve low-latency and high-efficiency issues. In particular, they can help medical staff remotely obtain patients' data. The radio frequency identification (RFID) system is popularly used to collect the physiological signals of patients in e-Healthcare, which include their heartbeat, blood pressure, pulse, brain activity, and others. Although cloud computing services and RFID systems are used in many environments, they have some problems that are associated with security and efficiency. For example, the RFID system cannot be used to perform time-consuming and burdensome computations. Therefore, the public-key cryptosystem is difficult to be used. In addition, due to the overload of cloud servers when a large number of devices join, the use of traditional cryptosystems is not feasible. Recently, many protocols have been proposed to resolve the above issues. However, most of them consider only the authentication of communicating entities rather than authenticated key agreement for secure data transmission. Some protocols are not secure against possible attacks. Thus, this study proposes authentication key agreement protocols for e-Healthcare systems to solve the problems of efficiency using lightweight operations and to enhance security by adopting the physical unclonable function (PUF). Since PUFs use the uniqueness and randomness of their circuits to perform computation, they have message fingerprints that act as authentication keys. A PUF is lightweight and suitable for use in e-Healthcare systems with limited resources. The proposed protocols satisfy more security requirements than related authentication protocols, require fewer computational resources, and are more efficient.