COMPSCI-3IS3 Information Security Homework 3 – Due: 03/31/2022 Approximate Differential Privacy
TAs: Keivan and Wei
1. Let Z ∼ N (0, 1) be a Gaussian random variable and q be a query with sensitivity ∆. Let γ, δ > 0 and a dataset D be given. Consider the following mechanism
1 MD=qD+ γ∆ logδ Z.
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For what value of ε, this mechanism is (ε, δ)-DP?
2. Let q1, . . . , qk be k queries each with sensitivity one. Consider the following two settings:
• Queries are non-adaptive and (ε0, δ0)-DP Gaussian mechanisms M1, . . . , Mk are used to release
their values.
• Queries are adaptive and ε0 -DP Laplace mechanisms N1 , . . . , Nk are used to release their values.
Which setting leads to a better utility? Explain.
3. Suppose a data-holder company allows only Gaussian or Laplace mechanisms with variance 1 to be used in their data release schemes (due to a utility constraint). What is the maximum number of queries that this company can answer if the overall privacy guarantee needs to be ε = 1 and δ = 10−5? Provide the answer in four cases: All mechanisms are assumed to be either Laplace or Gaussian and queries are either adaptive or non-adaptive. [If you cannot solve an equation, you can use any numerical techniques (e.g., Matlab, Python, R, Mathematica) to give an approximate solution.]
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