This paper explores analytical connections between the perturbation methodology of the Australian Bureau of Statistics (ABS) and the differential privacy (DP) framework. We consider a single static counting query function and find the analytical form of the perturbation distribution with symmetric support for the ABS perturbation methodology. We then analytically measure the DP parameters, namely the $(\varepsilon, \delta)$ pair, for the ABS perturbation methodology under this setting. The results and insights obtained about the behaviour of $(\varepsilon, \delta)$ with respect to the perturbation support and variance are used to judiciously select the variance of the perturbation distribution to give a good $\delta$ in the DP framework for a given desired $\varepsilon$ and perturbation support. Finally, we propose a simple sampling scheme to implement the perturbation probability matrix in the ABS Cellkey method. The post sampling $(\varepsilon, \delta)$ pair is numerically analysed as a function of the Cellkey size. It is shown that the best results are obtained for a larger Cellkey size, because the $(\varepsilon, \delta)$ pair post-sampling measures remain almost identical when we compare sampling and theoretical results.

翻译：本文探讨了澳大利亚统计局（ABS）扰动方法与差分隐私（DP）框架之间的分析联系。我们考虑单一静态计数查询函数，推导出具有对称支撑的ABS扰动方法下扰动分布的解析形式。随后在该设定下，我们解析地度量了ABS扰动方法的差分隐私参数，即$(\varepsilon, \delta)$对。关于$(\varepsilon, \delta)$行为相对于扰动支撑与方差的规律与洞见，被用于审慎选择扰动分布的方差，以在给定目标$\varepsilon$和扰动支撑条件下，在DP框架中获得良好的$\delta$值。最后，我们提出一种简单的抽样方案来实现ABS Cellkey方法中的扰动概率矩阵。通过对Cellkey尺寸的函数数值分析，比较了抽样后$(\varepsilon, \delta)$对的表现。结果表明，当采用更大的Cellkey尺寸时效果最佳，这是由于在比较抽样结果与理论结果时，抽样后的$(\varepsilon, \delta)$对度量几乎保持不变。