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This paper considers the secure aggregation problem for federated learningunder an information theoretic cryptographic formulation, where distributedtraining nodes (referred to as users) train models based on their own localdata and a curious-but-honest server aggregates the trained models withoutretrieving other information about users' local data. Secure aggregationgenerally contains two phases, namely key sharing phase and model aggregationphase. Due to the common effect of user dropouts in federated learning, themodel aggregation phase should contain two rounds, where in the first round theusers transmit masked models and, in the second round, according to theidentity of surviving users after the first round, these surviving userstransmit some further messages to help the server decrypt the sum of users'trained models. The objective of the considered information theoreticformulation is to characterize the capacity region of the communication ratesin the two rounds from the users to the server in the model aggregation phase,assuming that key sharing has already been performed offline in prior. In thiscontext, Zhao and Sun completely characterized the capacity region under theassumption that the keys can be arbitrary random variables. More recently, anadditional constraint, known as "uncoded groupwise keys," has been introduced.This constraint entails the presence of multiple independent keys within thesystem, with each key being shared by precisely S users. The capacity regionfor the information-theoretic secure aggregation problem with uncoded groupwisekeys was established in our recent work subject to the condition S > K - U,where K is the number of total users and U is the designed minimum number ofsurviving users. In this paper we fully characterize of the the capacity regionfor this problem by proposing a new converse bound and an achievable scheme.

The Capacity Region of Information Theoretic Secure Aggregation with Uncoded Groupwise Keys