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：差分隐私为发布信息提供了实现隐私保障的鲁棒模型。本文考察了经差分隐私随机化机制处理的多维频率分布对同质性攻击的保护效力。同质性攻击使攻击者无需从发布数据中识别目标个体，即可获取其敏感属性的精确值。我们提出了针对同质性攻击的披露风险度量指标，并推导出差分隐私中的隐私损失参数与同质性攻击披露风险之间的闭式关系。这些闭式关系通过将抽象概念置于具体隐私攻击场景中，有助于理解差分隐私及隐私损失参数的抽象概念，并为此类机制在实际信息清洗与发布中选取隐私损失参数提供了视角。我们将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，针对经差分隐私净化的频率分布，由同质性攻击导致的披露风险评估方法。