  In this paper, we address the problem of privacy-preserving training and
evaluation of neural networks in an $N$-party, federated learning setting. We
propose a novel system, POSEIDON, the first of its kind in the regime of
privacy-preserving neural network training. It employs multiparty lattice-based
cryptography to preserve the confidentiality of the training data, the model,
and the evaluation data, under a passive-adversary model and collusions between
up to $N-1$ parties. To efficiently execute the secure backpropagation
algorithm for training neural networks, we provide a generic packing approach
that enables Single Instruction, Multiple Data (SIMD) operations on encrypted
data. We also introduce arbitrary linear transformations within the
cryptographic bootstrapping operation, optimizing the costly cryptographic
computations over the parties, and we define a constrained optimization problem
for choosing the cryptographic parameters. Our experimental results show that
POSEIDON achieves accuracy similar to centralized or decentralized non-private
approaches and that its computation and communication overhead scales linearly
with the number of parties. POSEIDON trains a 3-layer neural network on the
MNIST dataset with 784 features and 60K samples distributed among 10 parties in
less than 2 hours.
