Privacy-Amplifying Sketching for Federated Learning: Secure and Decoupled Designs

Communication efficiency and client-level privacy are two central considerations in federated learning (FL). Privacy-amplifying sketching, as instantiated by the Federated Sketched Gaussian Mechanism (Fed-SGM) of li2025sketched, uses random sketching both to compress client updates and to strengthen privacy when the sketch randomness remains hidden from the server. This creates a deployment tension: communication-efficient aggregation requires participating clients to share a common sketch, whereas privacy amplification requires its randomness to remain hidden from the honest-but-curious server. We develop two complementary designs for resolving this tension. First, we securely realize a shared, server-hidden sketching matrix for Fed-SGM through a threshold-resilient seed-sharing protocol that protects against server–client collusion under an honest-majority assumption. Second, as our main result, we propose Fed-DSSGM, which eliminates the shared-hidden-sketch requirement of Fed-SGM by decoupling privacy amplification from communication compression: each client uses a private sketch for the privacy mechanism, while a separate shared global sketch is used solely for communication efficiency. We establish privacy, security, and convergence guarantees for these designs. Experiments on vision and language benchmarks show that Fed-DSSGM closely matches the utility of Fed-SGM across privacy budgets, while being considerably more robust due to the decoupled design.