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.

翻译：2021年加拿大人口普查因其采用了一种独特的隐私保护形式——随机舍入而引人注目，该方法以独立且概率性的方式对离散数值属性值进行舍入处理。在本研究中，我们探讨了离散变量之间的层次加和相关如何使得对2021年加拿大人口普查披露中的属性值进行概率性及精确求解成为可能。我们证明，在某些情况下，无论是否提供总体不变量，都有可能实现“反舍入”并提取舍入前的原始私有值。利用这些方法，我们揭示了2021年加拿大人口普查披露中先前保密的624个属性的精确值。此外，我们以高正确概率推断出超过1000个私有属性的潜在取值。最后，我们提出了一种基于无界离散噪声的简单解决方案，该方案能有效防止精确反舍入，同时在最终产品中保持较高的数据效用。