  The paper aims to give an overview of various approaches to statistical
disclosure control based on random noise that are currently being discussed for
official population statistics and censuses. A particular focus is on a
stringent delineation between different concepts influencing the discussion: we
separate clearly between risk measures, noise distributions and output
mechanisms - putting these concepts into scope and into relation with each
other.
  After recapitulating differential privacy as a risk measure, the paper also
remarks on utility and risk aspects of some specific output mechanisms and
parameter setups, with special attention on static outputs that are rather
typical in official population statistics. In particular, it is argued that
unbounded noise distributions, such as plain Laplace, may jeopardise key unique
census features without a clear need from a risk perspective. On the other
hand, bounded noise distributions, such as the truncated Laplace or the cell
key method, can be set up to keep unique census features while controlling
disclosure risks in census-like outputs.
  Finally, the paper analyses some typical attack scenarios to constrain
generic noise parameter ranges that suggest a good risk/utility compromise for
the 2021 EU census output scenario. The analysis also shows that strictly
differentially private mechanisms would be severely constrained in this
scenario.
