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

TL;DR

This paper reveals vulnerabilities in the 2021 Canadian Census's random rounding privacy method, demonstrating how hierarchical correlations can be exploited to recover private data, and proposes a noise-based solution to mitigate this risk.

Contribution

It introduces methods to unround and recover private census data using hierarchical correlations and proposes a noise-based approach to preserve privacy.

Findings

Exact values of 624 attributes were recovered.

Potential values of over 1000 attributes inferred with high confidence.

A noise-based method can prevent unrounding while maintaining data utility.

Abstract

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.