Relations among different privacy notions

Abstract

We present a comprehensive view of the relations among several privacy notions: differential privacy (DP) [1], Bayesian differential privacy (BDP) [2], semantic privacy (SP) [3], and membership privacy (MP) [4]. The results are organized into two parts. In part one, we extend the notion of semantic privacy (SP) to Bayesian semantic privacy (BSP) and show its essential equivalence with Bayesian differential privacy (BDP) in the quantitative sense. We prove the relations between BDP, BSP, and SP as follows: ǫ-BDP ⇐= 1 2 − 1 e ǫ +1 -BSP, and ǫ-BDP =⇒ (e 2ǫ − 1)-BSP =⇒ (e 2ǫ − 1)-SP. In addition, we obtain a minor result ǫ-DP ⇐= 1 2 − 1 e ǫ +1 -SP, which improves the result of Kasiviswanathan and Smith [3] stating ǫ-DP ⇐= ǫ/6-SP for ǫ ≤ 1.35. In part two, we establish the relations between BDP and MP. First, ǫ-BDP =⇒ ǫ-MP. Second, for a family of distributions that are downward scalable in the sense of Li et al. [4], it is shown that ǫ-BDP ⇐= ǫ-MP.

Composition properties of Bayesian differential privacy

“…Although differential privacy has received considerable interest in the literature [25]- [35], it has been observed by Kifer and Machanavajjhala [11] (see also [12]- [18]) that differential privacy may not work as expected when the data tuples have dependencies. To extend differential privacy for correlated data, prior studies have investigated various privacy metrics [13]- [18], [36]. One of the metrics receiving much attention is the notion of Bayesian differential privacy introduced by Yang et al [19].…”