Secure Aggregation with Uncoded Groupwise Keys Against User Collusion

In this paper, we study the information theoretic secure aggregation problem, where the server node aims to aggregate K users' locally trained models, without revealing any other information about the users' local data. To ensure security, some keys are shared among the users, which is referred to as the key sharing phase. Uncoded groupwise keys are considered, where each key is shared by a subset of S users and is independent from other keys. After the key sharing phase, each user masks its trained model and sends to the server, which is referred to as the model aggregation phase. In the presence of users' dropouts (i.e., up to K – U user may drop during the model aggregation phase and the identity of the dropped users cannot be predicted), to guarantee the information theoretic security, two-round transmissions are necessary. Our objective is to characterize the capacity region of the transmission rates (i.e., the normalized numbers of two-round transmissions by each user) in the two rounds. When
$\mathsf{S}\geq \mathsf{K}- \mathsf{U}+1$
, the capacity region was recently characterized. In this paper, we additionally consider the potential effect of user collusion, where there may exist up to T users colluding with the server. With the presence of the colluding users, the security constraint becomes that, except the sum of trained models, the server cannot learn any information about the other users' local data even if it colludes with any set of up to T users. For this new problem, we propose two secure aggregation schemes, which work for the cases of
$\mathsf{S} = \mathsf{K}-\mathsf{U}+1$
and of
$\mathsf{K}-\mathsf{U}+1\leq \mathsf{S}\leq \mathsf{K} - \mathsf{T}$
, respectively. The first scheme is then proven to achieve the capacity region.