  Federated learning (FL) has been proposed to allow collaborative training of
machine learning (ML) models among multiple parties where each party can keep
its data private. In this paradigm, only model updates, such as model weights
or gradients, are shared. Many existing approaches have focused on horizontal
FL, where each party has the entire feature set and labels in the training data
set. However, many real scenarios follow a vertically-partitioned FL setup,
where a complete feature set is formed only when all the datasets from the
parties are combined, and the labels are only available to a single party.
Privacy-preserving vertical FL is challenging because complete sets of labels
and features are not owned by one entity. Existing approaches for vertical FL
require multiple peer-to-peer communications among parties, leading to lengthy
training times, and are restricted to (approximated) linear models and just two
parties. To close this gap, we propose FedV, a framework for secure gradient
computation in vertical settings for several widely used ML models such as
linear models, logistic regression, and support vector machines. FedV removes
the need for peer-to-peer communication among parties by using functional
encryption schemes; this allows FedV to achieve faster training times. It also
works for larger and changing sets of parties. We empirically demonstrate the
applicability for multiple types of ML models and show a reduction of 10%-70%
of training time and 80% to 90% in data transfer with respect to the
state-of-the-art approaches.
