Differential privacy (DP) provides a robust model to achieve privacy guarantees for released information. We examine the protection potency of sanitized multi-dimensional frequency distributions via DP randomization mechanisms against homogeneity attack (HA). HA allows adversaries to obtain the exact values on sensitive attributes for their targets without having to identify them from the released data. We propose measures for disclosure risk from HA and derive closed-form relationships between the privacy loss parameters in DP and the disclosure risk from HA. The availability of the closed-form relationships assists understanding the abstract concepts of DP and privacy loss parameters by putting them in the context of a concrete privacy attack and offers a perspective for choosing privacy loss parameters when employing DP mechanisms in information sanitization and release in practice. We apply the closed-form mathematical relationships in real-life datasets to demonstrate the assessment of disclosure risk due to HA on differentially private sanitized frequency distributions at various privacy loss parameters.

翻译：差分隐私（DP）为已发布信息提供了实现隐私保证的稳健模型。我们研究了通过DP随机化机制净化的多维频率分布对抗同质性攻击（HA）的保护效力。HA使攻击者能够直接获取其目标在敏感属性上的精确值，而无需从已发布数据中识别出这些目标。我们提出了从HA中泄露风险的度量方法，并推导出DP中隐私损失参数与HA泄露风险之间的闭式关系。这些闭式关系的可用性有助于将DP及隐私损失参数的抽象概念置于具体隐私攻击的背景下进行理解，并为在实际信息净化和发布中采用DP机制时选择隐私损失参数提供了视角。我们将这些闭式数学关系应用于真实数据集，展示了在不同隐私损失参数下，对经过差分隐私净化的频率分布因HA导致的泄露风险进行评估。