Fully Homomorphic Encryption (FHE) enables computations on encrypted data without requiring decryption. However, each computation increases the noise level in ciphertext, which can eventually cause decryption failures once ciphertext noise is above the threshold. In this work, we revisit BFV homomorphic encryption used by Fan et al. [1] and present an optimized noise growth approach by swapping the sample space for secret key and error distribution. Later, we check the hardness of proposed scheme using lattice estimator. Our analysis demonstrates that the proposed method achieves more than 128-bit security and achieves a lower noise bound than existing techniques.