  Federated Learning (FL) is an interesting strategy that enables the
collaborative training of an AI model among different data owners without
revealing their private datasets. Even so, FL has some privacy vulnerabilities
that have been tried to be overcome by applying some techniques like
Differential Privacy (DP), Homomorphic Encryption (HE), or Secure Multi-Party
Computation (SMPC). However, these techniques have some important drawbacks
that might narrow their range of application: problems to work with non-linear
functions and to operate large matrix multiplications and high communication
and computational costs to manage semi-honest nodes. In this context, we
propose a solution to guarantee privacy in FL schemes that simultaneously
solves the previously mentioned problems. Our proposal is based on the Berrut
Approximated Coded Computing, a technique from the Coded Distributed Computing
paradigm, adapted to a Secret Sharing configuration, to provide input privacy
to FL in a scalable way. It can be applied for computing non-linear functions
and treats the special case of distributed matrix multiplication, a key
primitive at the core of many automated learning tasks. Because of these
characteristics, it could be applied in a wide range of FL scenarios, since it
is independent of the machine learning models or aggregation algorithms used in
the FL scheme. We provide analysis of the achieve privacy and complexity of our
solution and, due to the extensive numerical results performed, it can be
observed a good trade-off between privacy and precision.
