SwiftAgg+: Achieving Asymptotically Optimal Communication Load in Secure Aggregation for Federated Learning

We propose SwiftAgg+, a novel secure aggregation protocol for federated learning systems, where a central server aggregates local models of $N\in\mathbb{N}$ distributed users, each of size $L \in \mathbb{N}$, trained on their local data, in a privacy-preserving manner. SwiftAgg+ can significantly reduce the communication overheads without any compromise on security, and achieve the optimum communication load within a diminishing gap. Specifically, in presence of at most $D$ dropout users, SwiftAgg+ achieves average per-user communication load of $(1+\mathcal{O}(\frac{1}{N}))L$ and the server communication load of $(1+\mathcal{O}(\frac{1}{N}))L$, with a worst-case information-theoretic security guarantee, against any subset of up to $T$ semi-honest users who may also collude with the curious server. The proposed SwiftAgg+ has also a flexibility to reduce the number of active communication links at the cost of increasing the the communication load between the users and the server. In particular, for any $K\in\mathbb{N}$, SwiftAgg+ can achieve the uplink communication load of $(1+\frac{T}{K})L$, and per-user communication load of up to $(1-\frac{1}{N})(1+\frac{T+D}{K})L$, where the number of pair-wise active connections in the network is $\frac{N}{2}(K+T+D+1)$.