On the relationship between (secure) multi-party computation and (secure) federated learning

The contribution of this short note, contains the following two parts: in the first part, we are able to show that the federate learning (FL) procedure presented by Kairouz et al. \cite{Kairouz1901}, is a random processing. Namely, an $m$-ary functionality for the FL procedure can be defined in the context of multi-party computation (MPC); Furthermore, an instance of FL protocol along Kairouz et al.'s definition can be viewed as an implementation of the defined $m$-ary functionality. As such, an instance of FL procedure is also an instance of MPC protocol. In short, FL is a subset of MPC. To privately computing the defined FL (m-ary) functionality, various techniques such as homomorphic encryption (HE), secure multi-party computation (SMPC) and differential privacy (DP) have been deployed. In the second part, we are able to show that if the underlying FL instance privately computes the defined $m$-ary functionality in the simulation-based framework, then the simulation-based FL solution is also an instance of SMPC. Consequently, SFL is a subset of SMPC.