Differential privacy
The conceptHow a census can publish town counts without revealing any household
Differential privacy is a promise about a published result: it would look almost the same whether or not your record was in the data. Because no single person changes the output much, nobody can work out what was in your record from it.
The usual way to keep that promise is to add random noise to each answer before release. Say a database of a small town's patients is asked, "How many have diabetes?" The true count is 41. Instead of 41, the system might publish 43 or 39.
The noise is sized to the most one person could change the answer, which is 1 for a count. The size is set by a privacy dial called ε (epsilon). A smaller ε means more noise and stronger privacy.
What it’s forReleases the answer to a question about a dataset with differential privacy (the Laplace mechanism).
output = f(D) + Laplace(Δf / ε)
- f(D)
- the true answer computed on dataset D, e.g. a count of 41
- Δf
- sensitivity: the most one person's record can change the answer, 1 for a count
- ε
- the privacy budget, often between 0.1 and 1. Smaller means more private
- Laplace(b)
- random noise centred on 0 that spreads out more as b grows
What it givesA noisy answer that is accurate for big groups but hides any one person.
- Count query: Δf = 1, ε = 0.5
- Noise scale b = 1 / 0.5 = 2
- True count 41 is published as roughly 41 ± a few, e.g. 43