Information Theoretic Secure Aggregation With User Dropouts

In the robust secure aggregation problem, a server wishes to learn and only sum of inputs number users while some may drop out (i.e., not respond). The identity dropped is known priori needs securely recover remaining surviving users. We consider following minimal two-round model aggregation. Over first round, any set no fewer than $U$ notation="LaTeX">$K$ respond wants all responding are viewed as dropped. second dropouts still possible over round) from information obtained two rounds, can decode desired sum. security constraint that even if colludes with notation="LaTeX">$T$ messages received by (e.g., delayed packets), able infer additional beyond in theoretic sense. For this we characterize optimal communication cost. When notation="LaTeX">$U \leq T$ , feasible, when > compute one symbol sum, minimum symbols sent each user 1 notation="LaTeX">$1/(U-T)$ round.