  Homomorphic encryption is a very useful gradient protection technique used in
privacy preserving federated learning. However, existing encrypted federated
learning systems need a trusted third party to generate and distribute key
pairs to connected participants, making them unsuited for federated learning
and vulnerable to security risks. Moreover, encrypting all model parameters is
computationally intensive, especially for large machine learning models such as
deep neural networks. In order to mitigate these issues, we develop a
practical, computationally efficient encryption based protocol for federated
deep learning, where the key pairs are collaboratively generated without the
help of a third party. By quantization of the model parameters on the clients
and an approximated aggregation on the server, the proposed method avoids
encryption and decryption of the entire model. In addition, a threshold based
secret sharing technique is designed so that no one can hold the global private
key for decryption, while aggregated ciphertexts can be successfully decrypted
by a threshold number of clients even if some clients are offline. Our
experimental results confirm that the proposed method significantly reduces the
communication costs and computational complexity compared to existing encrypted
federated learning without compromising the performance and security.
