Bounded privacy-utility monotonicity indicating bounded tradeoff of differential privacy mechanisms

Abstract

Differential privacy can achieve the tradeoff between privacy and utility by using privacy metric and utility metric. However, since privacy metric and utility metric may not be bounded, differential privacy can not provide the bounded tradeoff. Moreover, there is no unified method to indicate the bounded tradeoff of differential privacy in the current work. To this end, we proposed the bounded privacy-utility monotonicity indicating the bounded tradeoff of differential privacy. First, we gave the definition of the bounded tradeoff of differential privacy, and we presented the bounded privacy-utility monotonicity of differential privacy based on computational indistinguishability. Second, we theoretically proved the bounded privacy-utility monotonicity of several differential privacy mechanisms based on the bounded metrics of modulus of characteristic function and normalized entropy, including the Laplace mechanism, discrete Laplace mechanism, Gaussian mechanism, exponential mechanism, optimal mechanism, and quaternary mechanism. We also showed that these mechanisms had the bounded privacy-utility monotonicity in the multivariate case. Third, our numerical results further demonstrated that these several differential privacy mechanisms obtained the bounded privacy-utility monotonicity. Finally, we gave an instance of achieving the bounded tradeoff of differential privacy mechanisms based on the bounded privacy-utility monotonicity under semi-honest model, and we discussed the goal of optimization of the bounded tradeoff of differential privacy based on the bounded privacy-utility monotonicity under semi-honest model. Therefore, the bounded privacy-utility monotonicity can be used to indicate the bounded tradeoff of differential privacy under semi-honest model. Furthermore, the bounded privacy-utility monotonicity plays an important role of optimizing the bounded tradeoff of differential privacy under semi-honest model.