This paper addresses the challenge of preserving privacy in Federated Learning (FL) within centralized systems, focusing on both trusted and untrusted server scenarios.We analyze this setting within the Stochastic Convex Optimization (SCO) framework, and devise methods that ensure Differential Privacy (DP) while maintaining optimal convergence rates for homogeneous and heterogeneous data distributions.Our approach, based on a recent stochastic optimization technique, offers linear computational complexity, comparable to non-private FL methods, and reduced gradient obfuscation.This work enhances the practicality of DP in FL, balancing privacy, efficiency, and robustness in a variety of server trust environments.