  With the emergence of privacy leaks in federated learning, secure aggregation
protocols that mainly adopt either homomorphic encryption or threshold secret
sharing have been widely developed for federated learning to protect the
privacy of the local training data of each client. However, these existing
protocols suffer from many shortcomings, such as the dependence on a trusted
third party, the vulnerability to clients being corrupted, low efficiency, the
trade-off between security and fault tolerance, etc. To solve these
disadvantages, we propose an efficient and multi-private key secure aggregation
scheme for federated learning. Specifically, we skillfully modify the variant
ElGamal encryption technique to achieve homomorphic addition operation, which
has two important advantages: 1) The server and each client can freely select
public and private keys without introducing a trust third party and 2) Compared
to the variant ElGamal encryption, the plaintext space is relatively large,
which is more suitable for the deep model. Besides, for the high dimensional
deep model parameter, we introduce a super-increasing sequence to compress
multi-dimensional data into 1-D, which can greatly reduce encryption and
decryption times as well as communication for ciphertext transmission. Detailed
security analyses show that our proposed scheme achieves the semantic security
of both individual local gradients and the aggregated result while achieving
optimal robustness in tolerating both client collusion and dropped clients.
Extensive simulations demonstrate that the accuracy of our scheme is almost the
same as the non-private approach, while the efficiency of our scheme is much
better than the state-of-the-art homomorphic encryption-based secure
aggregation schemes. More importantly, the efficiency advantages of our scheme
will become increasingly prominent as the number of model parameters increases.
