  We propose a secure inference protocol for a distributed setting involving a
single server node and multiple client nodes. We assume that the observed data
vector is partitioned across multiple client nodes while the deep learning
model is located at the server node. Each client node is required to encrypt
its portion of the data vector and transmit the resulting ciphertext to the
server node. The server node is required to collect the ciphertexts and perform
inference in the encrypted domain. We demonstrate an application of multi-party
homomorphic encryption (MPHE) to satisfy these requirements. We propose a
packing scheme, that enables the server to form the ciphertext of the complete
data by aggregating the ciphertext of data subsets encrypted using MPHE. While
our proposed protocol builds upon prior horizontal federated training
protocol~\cite{sav2020poseidon}, we focus on the inference for vertically
partitioned data and avoid the transmission of (encrypted) model weights from
the server node to the client nodes.
