Genqiang Wu

Genqiang Wu, Xiaoying Zhang, Yu Qi et al.

The exponential growth of data collection necessitates robust privacy protections that preserve data utility. We address information disclosure against adversaries with bounded prior knowledge, modeled by an entropy constraint $H(X) \geq b$. Within this information privacy framework -- which replaces differential privacy's independence assumption with a bounded-knowledge model -- we study three core problems: maximal per-record leakage, the primal leakage-distortion tradeoff (minimizing worst-case leakage under distortion $D$), and the dual distortion minimization (minimizing distortion under leakage constraint $L$). These problems resemble classical information-theoretic ones (channel capacity, rate-distortion) but are more complex due to high dimensionality and the entropy constraint. We develop efficient alternating optimization algorithms that exploit convexity-concavity duality, with theoretical guarantees including local convergence for the primal problem and convergence to a stationary point for the dual. Experiments on binary symmetric channels and modular sum queries validate the algorithms, showing improved privacy-utility tradeoffs over classical differential privacy mechanisms. This work provides a computational framework for auditing privacy risks and designing certified mechanisms under realistic adversary assumptions.

Genqiang Wu

Data privacy protection studies how to query a dataset while preserving the privacy of individuals whose sensitive information is contained in the dataset. The information privacy model protects the privacy of an individual by using a noisy channel, called privacy channel, to filter out most information of the individual from the query's output. This paper studies how to construct privacy channels, which is challenging since it needs to evaluate the maximal amount of disclosed information of each individual contained in the query's output, called individual channel capacity. Our main contribution is an interesting result which can transform the problem of evaluating a privacy channel's individual channel capacity, which equals the problem of evaluating the capacities of an infinite number of channels, into the problem of evaluating the capacities of a finite number of channels. This result gives us a way to utilize the results in the information theory to construct privacy channels. As some examples, it is used to construct several basic privacy channels, such as the random response privacy channel, the exponential privacy channel and the Gaussian privacy channel, which are respective counterparts of the random response mechanism, the exponential mechanism and the Gaussian mechanism of differential privacy.

Genqiang Wu

How to query a dataset in the way of preserving the privacy of individuals whose data is included in the dataset is an important problem. The information privacy model, a variant of Shannon's information theoretic model to the encryption systems, protects the privacy of an individual by controlling the amount of information of the individual's data obtained by each adversary from the query's output. This model also assumes that each adversary's uncertainty to the queried dataset is not so small in order to improve the data utility. In this paper, we prove some results to the group privacy and the composition privacy properties of this model, where the group privacy ensures a group of individuals' privacy is preserved, and where the composition privacy ensures multiple queries also preserve the privacy of an individual. Explicitly, we reduce the proof of the two properties to the estimation of the difference of two channel capacities. Our proofs are greatly benefited from some information-theoretic tools and approaches.

Genqiang Wu, Xianyao Xia, Yeping He

Current differential privacy frameworks face significant challenges: vulnerability to correlated data attacks and suboptimal utility-privacy tradeoffs. To address these limitations, we establish a novel information-theoretic foundation for Dalenius' privacy vision using Shannon's perfect secrecy framework. By leveraging the fundamental distinction between cryptographic systems (small secret keys) and privacy mechanisms (massive datasets), we replace differential privacy's restrictive independence assumption with practical partial knowledge constraints ($H(X) \geq b$). We propose an information privacy framework achieving Dalenius security with quantifiable utility-privacy tradeoffs. Crucially, we prove that foundational mechanisms -- random response, exponential, and Gaussian channels -- satisfy Dalenius' requirements while preserving group privacy and composition properties. Our channel capacity analysis reduces infinite-dimensional evaluations to finite convex optimizations, enabling direct application of information-theoretic tools. Empirical evaluation demonstrates that individual channel capacity (maximal information leakage of each individual) decreases with increasing entropy constraint $b$, and our framework achieves superior utility-privacy tradeoffs compared to classical differential privacy mechanisms under equivalent privacy guarantees. The framework is extended to computationally bounded adversaries via Yao's theory, unifying cryptographic and statistical privacy paradigms. Collectively, these contributions provide a theoretically grounded path toward practical, composable privacy -- subject to future resolution of the tradeoff characterization -- with enhanced resilience to correlation attacks.

Genqiang Wu, Xianyao Xia, Yeping He

The purpose of this paper is to develop a mathematical analysis theory to solve differential privacy problems. The heart of our approaches is to use analytic tools to characterize the correlations among the outputs of different datasets, which makes it feasible to represent a differentially private mechanism with minimal number of parameters. These results are then used to construct differentially private mechanisms analytically. Furthermore, our approaches are universal to almost all query functions. We believe that the approaches and results of this paper are indispensable complements to the current studies of differential privacy that are ruled by the ad hoc and algorithmic approaches.

Genqiang Wu, Yeping He, Jingzheng Wu et al.

How to achieve differential privacy in the distributed setting, where the dataset is distributed among the distrustful parties, is an important problem. We consider in what condition can a protocol inherit the differential privacy property of a function it computes. The heart of the problem is the secure multiparty computation of randomized function. A notion \emph{obliviousness} is introduced, which captures the key security problems when computing a randomized function from a deterministic one in the distributed setting. By this observation, a sufficient and necessary condition about computing a randomized function from a deterministic one is given. The above result can not only be used to determine whether a protocol computing differentially private function is secure, but also be used to construct secure one. Then we prove that the differential privacy property of a function can be inherited by the protocol computing it if the protocol privately computes it. A composition theorem of differentially private protocols is also presented. We also construct some protocols to generate random variate in the distributed setting, such as the uniform random variates and the inversion method. By using these fundamental protocols, we construct protocols of the Gaussian mechanism, the Laplace mechanism and the Exponential mechanism. Importantly, all these protocols satisfy obliviousness and so can be proved to be secure in a simulation based manner. We also provide a complexity bound of computing randomized function in the distribute setting. Finally, to show that our results are fundamental and powerful to multiparty differential privacy, we construct a differentially private empirical risk minimization protocol.