Disclosure Risk from Homogeneity Attack in Differentially Private Frequency Distribution

Abstract

Homogeneity attack allows adversaries to obtain the exact values on the sensitive attributes for his targets without having to re-identify them from released data. Differential privacy (DP) is a mathematical concept that provides robust privacy guarantee against a wide range of privacy attacks. We propose a measure for disclosure risk from homogeneity attack; and derive closed-form relationships between the privacy loss parameters from DP and the disclosure risk from homogeneity attack when released data are multi-dimensional frequency distributions. The availability of the close-form relationships not only saves time and computational resources spent on calculating the relationships numerically, but also assists understanding of DP and privacy loss parameters by putting the abstract concepts in the context of a concrete privacy attack, and offers a different perspective when it comes to choosing privacy loss parameters and implementing differentially private mechanisms for data sanitization and release in practice. We apply the closed-form mathematical relationships in real-life data sets and demonstrate their consistency with the empirical assessment of the disclosure risk due to homogeneity attack on sanitized data.