Differential Privacy — Laplace Mechanism

ε-privacy · sensitivity Δf · noise scale b = Δf/ε · composition theorem

Differential privacy (Dwork 2006): M satisfies ε-DP if for all adjacent datasets D,D' and all outputs S: Pr[M(D)∈S] ≤ e^ε · Pr[M(D')∈S]. Laplace mechanism: M(D) = f(D) + Lap(Δf/ε). Noise scale b = sensitivity/ε. Smaller ε → more privacy → more noise. Sequential composition: k queries with ε_i → total budget Σε_i. Advanced composition: √(2k·ln(1/δ))·ε + k·ε·(e^ε−1) for (ε,δ)-DP.