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The problem of preserving the privacy of individual entries of a databasewhen responding to linear or nonlinear queries with constrained additive noiseis considered. For privacy protection, the response to the query issystematically corrupted with an additive random noise whose support is asubset or equal to a pre-defined constraint set. A measure of privacy using theinverse of the trace of the Fisher information matrix is developed. TheCramer-Rao bound relates the variance of any estimator of the database entriesto the introduced privacy measure. The probability density that minimizes thetrace of the Fisher information (as a proxy for maximizing the measure ofprivacy) is computed. An extension to dynamic problems is also presented.Finally, the results are compared to the differential privacy methodology.

Ensuring Privacy with Constrained Additive Noise by Minimizing Fisher Information