A Privacy-Preserving Game Model for Local Differential Privacy by Using Information-Theoretic Approach

Local differential privacy (LDP) is an effective privacy-preserving model to address the problems which do not have a trusted entity. The main idea of the LDP is to add randomness in real data to guarantee individual's private sensitive information. Here, the technology of randomized response is an effective method to realize the LDP mechanism. In fact, the randomized response is a probabilistic mapping from the real data to perturbed data, which can be modeled as an information-theoretic lossy compression mechanism. What's more, the privacy budget ϵ has become a de facto standard to quantify the worst-case privacy leakage. However, such a metrics can not capture the question that which one is the optimal privacy mechanism in a set of equivalent ϵ-privacy mechanisms. Besides, the privacy and utility are closely correlated with the privacy mechanism, and existing methods do not consider the strategic adversary's behavior. In this paper, we tackle the problem of tradeoffs privacy and utility under the rational framework within an information-theoretic approach as the metrics. To address the problem, we first formulate this trade-off as a minimax information leakage problem. Then, we propose a privacy preserving attack and defense (PPAD) game framework, that is, a two-person zero-sum (TPZS) game. Further, we develop an alternating optimization algorithm to compute the saddle point of the proposed PPAD game. As a case study, we apply our method to compare several alternative ln2-privacy mechanisms, the experimental result demonstrates that can provide an effective method to compare equivalent ϵ-privacy mechanisms. Furthermore, the numeric simulation result confirms that the proposed method also be useful for the protector to assess privacy disclosure risks.