  With the advance of machine learning and the internet of things (IoT),
security and privacy have become key concerns in mobile services and networks.
Transferring data to a central unit violates privacy as well as protection of
sensitive data while increasing bandwidth demands.Federated learning mitigates
this need to transfer local data by sharing model updates only. However, data
leakage still remains an issue. In this paper, we propose xMK-CKKS, a multi-key
homomorphic encryption protocol to design a novel privacy-preserving federated
learning scheme. In this scheme, model updates are encrypted via an aggregated
public key before sharing with a server for aggregation. For decryption,
collaboration between all participating devices is required. This scheme
prevents privacy leakage from publicly shared information in federated
learning, and is robust to collusion between $k<N-1$ participating devices and
the server. Our experimental evaluation demonstrates that the scheme preserves
model accuracy against traditional federated learning as well as secure
federated learning with homomorphic encryption (MK-CKKS, Paillier) and reduces
computational cost compared to Paillier based federated learning. The average
energy consumption is 2.4 Watts, so that it is suited to IoT scenarios.
