AbstractHealth monitoring sensors are widely available to monitor patients' health remotely. The collected sensor data are sent to cloud storage and processed in a remote health monitoring system. The Internet of Things (IoT) with cloud support offers a promising answer to data exploding concerns for the ability to constrain specific gadgets. However, IoT faces many security issues when sharing data between two users because of the cloud's leverage nature. In the case of a private cloud, simple encryption techniques can ensure security. But, in the case of a public cloud, maintaining data privacy is a significant issue. To overcome this concern, an optimized Brakerski‐Gentry‐Vaikuntanathan fully homomorphic encryption (BGV‐FHE) encryption method for secured data mutuality is proposed in this article. In this method, IoT medical data are initially acquired and then encrypted using two key schemes, and the data are stored in cloud storage. The main objective of these key schemes is to select optimal key parameters. Key parameters are chosen using the glow‐worm swarm optimization and used for the encryption phase. Storing data in the cloud using a public key provides access to requested users. Meanwhile, sensitive data are encrypted using a private key and cannot be accessed unless authenticated. This proposed approach has two levels of encryption, and thus it is an efficient data secured protocol for cloud resources. Implementing the optimized BGV‐FHE scheme based encryption scheme in Python, two datasets result in an accuracy level of 77% and 91%, respectively.