  Secure Multiparty Computation (MPC) can improve the security and privacy of
data owners while allowing analysts to perform high quality analytics. Secure
aggregation is a secure distributed mechanism to support federated deep
learning without the need for trusted third parties. In this paper we present a
highly performant secure aggregation protocol with sub-linear communication
complexity.
  Our protocol achieves greater communication and computation efficiencies
through a group-based approach. It is similar to secret sharing protocols
extended to vectors of values-aka gradients-but within groups we add an
additional layer of secret sharing of shares themselves-aka sharding. This
ensures privacy of secret inputs in the standard real/ideal security paradigm,
in both semi-honest and malicious settings where the server may collude with
the adversary.
  In the malicious setting with 5% corrupt clients and 5% dropouts, our
protocol can aggregate over a federation with 100,000,000 members and vectors
of length 100 while requiring each client to communicate with only 350 other
clients. The concrete computation cost for this aggregation is less than half a
second for the server and less than 100ms for the client.
