Random (Un)rounding : Vulnerabilities in Discrete Attribute Disclosure in the 2021 Canadian Census

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.