Lattice based distributed threshold additive homomorphic encryption with application in federated learning

In federated learning (FL), a parameter server needs to aggregate user gradients and a user needs to protect the value of their gradients. Among all the possible solutions to the problem, those based on additive homomorphic encryption (AHE) are natural. As users may drop out in FL and an adversary could corrupt some users and the parameter server, we require a dropout-resilient AHE scheme with a distributed key generation algorithm. In this paper, we aim to provide a lattice based distributed threshold AHE (DTAHE) scheme and to show their applications in FL. The main merit of the DTAHE scheme is to save communication bandwidth compared with other latticed based DTAHE schemes. Embedding the scheme into FL, we get two secure aggregation protocols. One is secure against a semi-honest adversary and the other is secure against an active adversary. The latter exploits a smart contract in a ledger. Finally, we provide security proofs and performance analysis for the scheme and protocols.