Privacy vulnerabilities with background information in data perturbation

The issue of data privacy is considered a significant hindrance to the development and industrial applications of database publishing and data mining techniques. Among many privacy-preserving methodologies, data perturbation is a popular technique for achieving a balance between data utility and information privacy. It is known that the attacker's background information about the original data can play a significant role in breaching data privacy. In this paper, we analyze data perturbation's potential privacy vulnerability in the presence of known background information in privacy-preserving database publishing and data mining based on the eigenspace of the perturbed data under some constraints. We study the situation in which data privacy may be compromised with the leakage of a few original data records. We first show that additive perturbation preserves the angle between data records during the perturbation. Based on this angle-preservation property, we show that, in a general perturbation model, even the leakage of only one single original data probably degrades the privacy of perturbed data in some cases. We theoretically and experimentally show that a general data perturbation model is vulnerable from this type of background privacy breach.