  Computing the noisy sum of real-valued vectors is an important primitive in
differentially private learning and statistics. In private federated learning
applications, these vectors are held by client devices, leading to a
distributed summation problem. Standard Secure Multiparty Computation (SMC)
protocols for this problem are susceptible to poisoning attacks, where a client
may have a large influence on the sum, without being detected.
  In this work, we propose a poisoning-robust private summation protocol in the
multiple-server setting, recently studied in PRIO. We present a protocol for
vector summation that verifies that the Euclidean norm of each contribution is
approximately bounded. We show that by relaxing the security constraint in SMC
to a differential privacy like guarantee, one can improve over PRIO in terms of
communication requirements as well as the client-side computation. Unlike SMC
algorithms that inevitably cast integers to elements of a large finite field,
our algorithms work over integers/reals, which may allow for additional
efficiencies.
