In the digital age, data breaches and misuse are rampant. While we want to make use of data for various beneficial purposes, it's crucial to ensure individual data points cannot be reverse-engineered. Differential Privacy, by adding controlled noise, allows for broad trends in data to be analyzed without revealing specifics about individual data entries, thereby preserving user privacy to a quantifiable standard denoted by \(\epsilon\).
Differential privacy provides a means to quantify the privacy loss in statistical databases. A randomized algorithm \(M\) satisfies \((\epsilon,\delta)\)-differential privacy if, for all datasets \(D_1\) and \(D_2\) differing in a single element, and for any set of possible outputs \(S\), we have: \[ P[M(D_1) \in S] \leq e^\epsilon \times P[M(D_2) \in S] + \delta \] where \(0 \leq \delta < 1\) is a small constant, and \(\epsilon\) is a non-negative parameter that measures the privacy loss.
The term “differential” privacy refers to its emphasis on the dissimilarity between the results produced by a privacy-preserving algorithm on two datasets that differ by just one individual’s data.