In this paper, we propose 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, communication load for secret sharing of long
vectors of updates can be very high. To resolve this issue, in the proposed
scheme, local updates are partitioned into smaller sub-vectors and shared 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, the proposed scheme 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.

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