Medical care has become one of the most indispensable parts of human lives, leading to a dramatic increase in medical big data. To streamline the diagnosis and treatment process, healthcare professionals are now adopting Internet of Things (IoT)-based wearable technology. Recent years have witnessed billions of sensors, devices, and vehicles being connected through the Internet. One such technology—remote patient monitoring—is common nowadays for the treatment and care of patients. However, these technologies also pose grave privacy risks and security concerns about the data transfer and the logging of data transactions. These security and privacy problems of medical data could result from a delay in treatment progress, even endangering the patient’s life. We propose the use of a blockchain to provide secure management and analysis of healthcare big data. However, blockchains are computationally expensive, demand high bandwidth and extra computational power, and are therefore not completely suitable for most resource-constrained IoT devices meant for smart cities. In this work, we try to resolve the above-mentioned issues of using blockchain with IoT devices. We propose a novel framework of modified blockchain models suitable for IoT devices that rely on their distributed nature and other additional privacy and security properties of the network. These additional privacy and security properties in our model are based on advanced cryptographic primitives. The solutions given here make IoT application data and transactions more secure and anonymous over a blockchain-based network.