  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 optimal communication loads within diminishing gaps. Specifically, in
presence of at most $D=o(N)$ dropout users, SwiftAgg+ achieves a per-user
communication load of $(1+\mathcal{O}(\frac{1}{N}))L$ symbols and a server
communication load of $(1+\mathcal{O}(\frac{1}{N}))L$ symbols, with a
worst-case information-theoretic security guarantee, against any subset of up
to $T=o(N)$ semi-honest users who may also collude with the curious server.
Moreover, the proposed SwiftAgg+ allows for a flexible trade-off between
communication loads and the number of active communication links. In
particular, for $T<N-D$ and for any $K\in\mathbb{N}$, SwiftAgg+ can achieve the
server communication load of $(1+\frac{T}{K})L$ symbols, and per-user
communication load of up to $(1+\frac{T+D}{K})L$ symbols, where the number of
pair-wise active connections in the network is $\frac{N}{2}(K+T+D+1)$.
