  Secure linear aggregation is to linearly aggregate private inputs of
different users with privacy protection. The server in a federated learning
(FL) environment can fulfill any linear computation on private inputs of users
through the secure linear aggregation. At present, based on pseudo-random
number generator and one-time padding technique, one can efficiently compute
the sum of user inputs in FL, but linear calculations of user inputs are not
well supported. Based on decentralized threshold additive homomorphic
encryption (DTAHE) schemes, this paper provides a secure linear aggregation
protocol, which allows the server to multiply the user inputs by any
coefficients and to sum them together, so that the server can build a full
connected layer or a convolution layer on top of user inputs. The protocol
adopts the framework of Bonawitz et al. to provide fault tolerance for user
dropping out, and exploits a blockchain smart contract to encourage the server
honest. The paper gives a security model, security proofs and a concrete
lattice based DTAHE scheme for the protocol. It evaluates the communication and
computation costs of known DTAHE construction methods. The evaluation shows
that an elliptic curve based DTAHE is friendly to users and the lattice based
version leads to a light computation on the server.
