  In this paper, we propose ByzSecAgg, an efficient secure aggregation scheme
for federated learning that is protected against Byzantine attacks and privacy
leakages. Processing individual updates to manage adversarial behavior, while
preserving privacy of data against colluding nodes, requires some sort of
secure secret sharing. However, the communication load for secret sharing of
long vectors of updates can be very high. ByzSecAgg solves this problem by
partitioning local updates into smaller sub-vectors and sharing them using ramp
secret sharing. However, this sharing method does not admit bi-linear
computations, such as pairwise distance calculations, needed by
outlier-detection algorithms. To overcome this issue, each user runs another
round of ramp sharing, with different embedding of data in the sharing
polynomial. This technique, motivated by ideas from coded computing, enables
secure computation of pairwise distance. In addition, to maintain the integrity
and privacy of the local update, ByzSecAgg also uses a vector commitment
method, in which the commitment size remains constant (i.e. does not increase
with the length of the local update), while simultaneously allowing
verification of the secret sharing process. In terms of communication loads,
ByzSecAgg significantly outperforms the state-of-the-art scheme, known as BREA.
