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The 2021 Canadian census is notable for using a unique form of privacy,random rounding, which independently and probabilistically rounds discretenumerical attribute values. In this work, we explore how hierarchical summativecorrelation between discrete variables allows for both probabilistic and exactsolutions to attribute values in the 2021 Canadian Census disclosure. Wedemonstrate that, in some cases, it is possible to "unround" and extract theoriginal private values before rounding, both in the presence and absence ofprovided population invariants. Using these methods, we expose the exact valueof 624 previously private attributes in the 2021 Canadian census disclosure. Wealso infer the potential values of more than 1000 private attributes with ahigh probability of correctness. Finally, we propose how a simple solutionbased on unbounded discrete noise can effectively negate exact unrounding whilemaintaining high utility in the final product.

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