Private Aggregation from Fewer Anonymous Messages

Ghazi, Badih; Manurangsi, Pasin; Pagh, Rasmus; Velingker, Ameya

Consider the setup where n parties are each given an element [Formula: see text] in the finite field [Formula: see text] and the goal is to compute the sum [Formula: see text] in a secure fashion and with as little communication as possible. We study this problem in the anonymized model of Ishai et al. (FOCS 2006) where each party may broadcast anonymous messages on an insecure channel. We present a new analysis of the one-round “split and mix” protocol of Ishai et al. In order to achieve the same security parameter, our analysis reduces the required number of messages by a [Formula: see text] multiplicative factor. We also prove lower bounds showing that the dependence of the number of messages on the domain size, the number of parties, and the security parameter is essentially tight. Using a reduction of Balle et al. (2019), our improved analysis of the protocol of Ishai et al. yields, in the same model, an [Formula: see text] -differentially private protocol for aggregation that, for any constant [Formula: see text] and any [Formula: see text] , incurs only a constant error and requires only a constant number of messages per party. Previously, such a protocol was known only for [Formula: see text] messages per party.