Private Aggregation from Fewer Anonymous Messages

Consider the setup where n parties are each given an element \\(x_i\\) in the finite field \\(\\mathbb {F}_q\\) and the goal is to compute the sum \\(\\sum _i x_i\\) 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.