With the tremendous growth of technology, providing data security to critical applications such as smart grid, health care, and military is indispensable. On the other hand, due to the proliferation of external data threats in these applications, the loss incurred is incredibly high. Standard encryption algorithms such as RSA, ElGamal, and ECC facilitate in protecting sensitive data from outside attackers; however, they cannot perform computations on sensitive data while being encrypted. To perform computations and to process encrypted query on encrypted data, various homomorphic encryption (HE) schemes are proposed. Each of the schemes has its own shortcomings either related to performance or with storage that acts as the barrier for applying in real-time applications. With that conception, our objective is to design HE schemes that are simple by design, efficient in performance, and highly unimpeachable against attacks. Our first proposed scheme is based on Carmichael's Theorem, referred to as Carmichael's Theorem-based Homomorphic Encryption (CTHE), and the second is an improved version of Gorti's Enhanced Homomorphic Encryption Scheme, referred to as Modified Enhanced Homomorphic Encryption (MEHE). For brevity, the schemes are referred to as CTHE and MEHE. Both the schemes are provably secure under the hardness of integer factorization, discrete logarithm, and quadratic residuosity problems. To reduce the noise in these schemes, the modulus switching method is adopted and proved theoretically. The schemes' efficiency is proven by collecting the data from cardiovascular dataset (statically)/blood pressure monitor (dynamically) and is homomorphically encrypted in the edge server. Further analysis on encrypted data is carried out to identify whether a person has hypotension or hypertension with the aid of parameters, namely, mean arterial pressure. As the schemes are probabilistic in nature, breaking the schemes by a polynomial time adversary is impossible and is proven in the article.