  Privacy and Byzantine resilience are two indispensable requirements for a
federated learning (FL) system. Although there have been extensive studies on
privacy and Byzantine security in their own track, solutions that consider both
remain sparse. This is due to difficulties in reconciling privacy-preserving
and Byzantine-resilient algorithms.
  In this work, we propose a solution to such a two-fold issue. We use our
version of differentially private stochastic gradient descent (DP-SGD)
algorithm to preserve privacy and then apply our Byzantine-resilient
algorithms. We note that while existing works follow this general approach, an
in-depth analysis on the interplay between DP and Byzantine resilience has been
ignored, leading to unsatisfactory performance. Specifically, for the random
noise introduced by DP, previous works strive to reduce its impact on the
Byzantine aggregation. In contrast, we leverage the random noise to construct
an aggregation that effectively rejects many existing Byzantine attacks.
  We provide both theoretical proof and empirical experiments to show our
protocol is effective: retaining high accuracy while preserving the DP
guarantee and Byzantine resilience. Compared with the previous work, our
protocol 1) achieves significantly higher accuracy even in a high privacy
regime; 2) works well even when up to 90% of distributive workers are
Byzantine.
