Developed a novel function computation scheme Gaussian Functional mechanism that ensures strict privacy guaratnee and offers much better utility than existing methods. Additionally, we extend our novel mechanism such that it works seemlessly in decentralized-data settings and propose capeFM, which offers the same privacy-utility trade-off as centralized schemes. This theoretical work is also validated on several real datasets for regression and classification. This work led to this Entropy Information Theory, Probability and Statistics publication.