  Uniformity testing, or testing whether independent observations are uniformly
distributed, is the prototypical question in distribution testing. Over the
past years, a line of work has been focusing on uniformity testing under
privacy constraints on the data, and obtained private and data-efficient
algorithms under various privacy models such as central differential privacy
(DP), local privacy (LDP), pan-privacy, and, very recently, the shuffle model
of differential privacy.
  In this work, we considerably simplify the analysis of the known uniformity
testing algorithm in the shuffle model, and, using a recent result on "privacy
amplification via shuffling," provide an alternative algorithm attaining the
same guarantees with an elementary and streamlined argument.
