Disclosure Risk from Homogeneity Attack in Differentially Private Frequency Distribution

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.