  We present RHODE, a novel system that enables privacy-preserving training of
and prediction on Recurrent Neural Networks (RNNs) in a cross-silo federated
learning setting by relying on multiparty homomorphic encryption. RHODE
preserves the confidentiality of the training data, the model, and the
prediction data; and it mitigates federated learning attacks that target the
gradients under a passive-adversary threat model. We propose a packing scheme,
multi-dimensional packing, for a better utilization of Single Instruction,
Multiple Data (SIMD) operations under encryption. With multi-dimensional
packing, RHODE enables the efficient processing, in parallel, of a batch of
samples. To avoid the exploding gradients problem, RHODE provides several
clipping approximations for performing gradient clipping under encryption. We
experimentally show that the model performance with RHODE remains similar to
non-secure solutions both for homogeneous and heterogeneous data distribution
among the data holders. Our experimental evaluation shows that RHODE scales
linearly with the number of data holders and the number of timesteps,
sub-linearly and sub-quadratically with the number of features and the number
of hidden units of RNNs, respectively. To the best of our knowledge, RHODE is
the first system that provides the building blocks for the training of RNNs and
its variants, under encryption in a federated learning setting.
