  The 2021 Canadian census is notable for using a unique form of privacy,
random rounding, which independently and probabilistically rounds discrete
numerical attribute values. In this work, we explore how hierarchical summative
correlation between discrete variables allows for both probabilistic and exact
solutions to attribute values in the 2021 Canadian Census disclosure. We
demonstrate that, in some cases, it is possible to "unround" and extract the
original private values before rounding, both in the presence and absence of
provided population invariants. Using these methods, we expose the exact value
of 624 previously private attributes in the 2021 Canadian census disclosure. We
also infer the potential values of more than 1000 private attributes with a
high probability of correctness. Finally, we propose how a simple solution
based on unbounded discrete noise can effectively negate exact unrounding while
maintaining high utility in the final product.
