Differential Privacy Vocabulary Exercises

1 / 5

A privacy engineer says: "The mechanism satisfies ε-differential privacy."

What does differential privacy (DP) formally guarantee?

Differential privacy — formal definition (Dwork 2006):

A randomised mechanism M satisfies (ε, δ)-DP if for all datasets D, D' differing by one record, and all outputs S:
Pr[M(D) ∈ S] ≤ e^ε · Pr[M(D') ∈ S] + δ

Parameter	Meaning
ε (epsilon)	Privacy budget — smaller = stronger privacy
δ (delta)	Failure probability — probability DP guarantee breaks

Key vocabulary: privacy guarantee, neighbouring datasets, indistinguishability, randomised mechanism.

2 / 5

Two algorithms are compared: Algorithm A uses ε = 0.1, Algorithm B uses ε = 10.

Which provides stronger privacy and why?

Epsilon (ε) as privacy budget:

ε value	Privacy level	Typical use
ε ≈ 0.1	Very strong	Highly sensitive data (medical, financial)
ε ≈ 1	Strong	Census, telemetry (Apple, Google)
ε ≈ 10	Weak	Utility-focused, low privacy concern

Key vocabulary: privacy budget, budget consumption, epsilon accounting, privacy-utility trade-off, "spending epsilon".

3 / 5

A paper uses the Laplace mechanism to release a differentially private count query.

What does the Laplace mechanism do?

Laplace mechanism for numeric queries:

M(x) = f(x) + Lap(sensitivity / ε)

Term	Meaning
f(x)	The true query result
Sensitivity	Max change in f when one record changes
ε	Privacy budget

Gaussian mechanism: uses Gaussian noise, satisfies (ε, δ)-DP. Key vocabulary: noise calibration, sensitivity of a function (L1/L2), noise scale, privacy-accuracy trade-off.

4 / 5

A product team discusses implementing local differential privacy (LDP) vs. global (central) differential privacy.

What is the key architectural difference?

Local vs. global DP architecture:

Model	Where noise is added	Trust assumption	Example
Local DP	On user's device	No trusted server needed	Apple iOS telemetry, Google RAPPOR
Global DP	At the curator/server	Requires trusted curator	US Census DP, TensorFlow Privacy

Trade-off: LDP has worse accuracy for the same ε because noise is applied before aggregation. Key vocabulary: randomised response, shuffler model, trusted curator, federated learning + DP.

5 / 5

An engineer says: "The function has a sensitivity of 1 for this query."

What does sensitivity of a function mean in differential privacy?

Global sensitivity = max change in output over all pairs of neighbouring datasets:

Query	L1 sensitivity	Why
COUNT(*)	1	Adding/removing one record changes count by at most 1
SUM(age) — age 0–100	100	One record can contribute up to 100
MEAN(age)	100/n	Changes by at most range/n

Higher sensitivity → more noise needed → less accuracy. Key vocabulary: L1 sensitivity (Manhattan), L2 sensitivity (Euclidean), local sensitivity, smooth sensitivity, clipping to bound sensitivity.