Ensuring Privacy with Constrained Additive Noise by Minimizing Fisher Information
For database privacy, this work provides a theoretical framework for optimizing additive noise under constraints, but it is incremental as it builds on existing Fisher information and Cramér-Rao bound concepts.
The paper develops a privacy measure based on Fisher information for linear and nonlinear queries with constrained additive noise, and computes the noise distribution that minimizes Fisher information to maximize privacy. The approach is compared to differential privacy.
The problem of preserving the privacy of individual entries of a database when responding to linear or nonlinear queries with constrained additive noise is considered. For privacy protection, the response to the query is systematically corrupted with an additive random noise whose support is a subset or equal to a pre-defined constraint set. A measure of privacy using the inverse of the trace of the Fisher information matrix is developed. The Cramer-Rao bound relates the variance of any estimator of the database entries to the introduced privacy measure. The probability density that minimizes the trace of the Fisher information (as a proxy for maximizing the measure of privacy) is computed. An extension to dynamic problems is also presented. Finally, the results are compared to the differential privacy methodology.