The Smart Healthcare System (SHS) represents a ground-breaking evolution in healthcare, integrating Internet of Things (IoT), Fog computing, and Cloud computing. This innovation deploys miniature IoT wearables for real-time patient health data collection, enabling remote monitoring, early anomaly detection, and personalized care. SHS strategically utilizes cloud computing for scalable data analytics and storage, while Fog computing enables swift data processing at intermediate nodes. The pivotal role of IoT is emphasized, with wearable devices serving as continuous data conduits for remote monitoring and data-driven healthcare. However, SHS faces security challenges, including unauthorized access, data manipulation, and cyber threats to the interconnected healthcare devices. Cryptography is essential to address these issues, however, due to inherent resource limitations of smart miniature biosensor devices, the applicability of conventional security protocols remains questionable. This research work compares NTRU Encrypt and ECC as potential candidates for SHS, demonstrating their superiority in rapid encryption, quick processing times, and efficient resource utilization.