 Differential privacy

A randomized mechanism $M$ satisfies differential privacy with parameters $(\epsilon ,\delta )$ if, for every ordered pair of adjacent datasets $D,D^{\prime }$ and measurable output event $S$,Adjacency specifies the contribution of one individual, such as adding or removing one record. The probability is over the mechanism's randomness.

For an integer count query with sensitivity one under add/remove adjacency, releasing the count plus independent Laplace distribution noise of scale $1/\epsilon$ gives $(\epsilon ,0)$ privacy. The ratio of output densities is at most $e^{\epsilon }$ by the triangle inequality. The guarantee limits distinguishability between neighboring inputs; it does not require publishing identical results or certify that every statistical estimate is accurate.^[ref]

Differential privacy is a mathematical framework designed to provide a rigorous privacy guarantee when sharing or analyzing data that may contain sensitive information about individuals. The primary goal of differential privacy is to enable the release of useful statistical information while ensuring that the privacy of individual data points is preserved. The core idea is to ensure that the outcome of a data analysis (like a query or a statistical result) does not significantly change when any single individual's data is added or removed from the dataset.