  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.
