A Predictive Differentially-Private Mechanism for Mobility Traces - - PowerPoint PPT Presentation

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A Predictive Differentially-Private Mechanism for Mobility Traces - - PowerPoint PPT Presentation

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A Predictive Differentially-Private Mechanism for Mobility Traces Marco Stronati marco@stronati.org joint work with K. Chatzikokolakis and C. Palamidessi marco@stronati.org (PETS14) Predictive Mechanism July 2014 1 / 18 Location Based

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A Predictive Differentially-Private Mechanism for Mobility Traces

Marco Stronati marco@stronati.org joint work with

  • K. Chatzikokolakis and C. Palamidessi

marco@stronati.org (PETS’14) Predictive Mechanism July 2014 1 / 18

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SLIDE 2

Location Based Service

marco@stronati.org (PETS’14) Predictive Mechanism July 2014 2 / 18

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Scope

x − → M − → z

marco@stronati.org (PETS’14) Predictive Mechanism July 2014 3 / 18

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Scope

x − → M − → z

Privacy

through reduced accuracy

Utility

accuracy of reported location

marco@stronati.org (PETS’14) Predictive Mechanism July 2014 3 / 18

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SLIDE 5

Scope

x − → M − → z

Privacy

through reduced accuracy

Utility

accuracy of reported location

Contribution

in traces with considerable correlation we provide better utility

marco@stronati.org (PETS’14) Predictive Mechanism July 2014 3 / 18

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Privacy Definition

Geo-indistinguishability

dP(M(x), M(x′)) ≤ ǫ·d(x, x′) ∀x, x′

Andr´ es, Bordenabe, Chatzikokolakis, Palamidessi: Geo-indistinguishability: differential privacy for location-based

  • systems. In: Proc. of CCS, ACM (2013) 901–914

marco@stronati.org (PETS’14) Predictive Mechanism July 2014 4 / 18

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Privacy Mechanism

Noise mechanism

N(ǫN)

marco@stronati.org (PETS’14) Predictive Mechanism July 2014 5 / 18

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SLIDE 8

Privacy Mechanism

Noise mechanism

N(ǫN)

marco@stronati.org (PETS’14) Predictive Mechanism July 2014 5 / 18

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Mobility Traces

Independent Mechanism

IM(¯ x) that uses N(ǫN)(x) is n · ǫN d-private works on any trace (including random teleporting) budget is linear with the length of the trace

marco@stronati.org (PETS’14) Predictive Mechanism July 2014 6 / 18

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Correlation

real traces are strongly correlated not every point has the same value

marco@stronati.org (PETS’14) Predictive Mechanism July 2014 7 / 18

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Predictive Mechanism (broken)

Predictive Mechanism (broken)

Equip the noise mechanism with a prediction function a test function with a threshold l

Cost

easy points are free hard points cost ǫN

marco@stronati.org (PETS’14) Predictive Mechanism July 2014 8 / 18

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Predictive Mechanism (broken)

Predictive Mechanism (broken)

Equip the noise mechanism with a prediction function a test function with a threshold l

Cost

easy points are free hard points cost ǫN

marco@stronati.org (PETS’14) Predictive Mechanism July 2014 8 / 18

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SLIDE 13

Predictive Mechanism (broken)

Predictive Mechanism (broken)

Equip the noise mechanism with a prediction function a test function with a threshold l

Cost

easy points are free hard points cost ǫN

marco@stronati.org (PETS’14) Predictive Mechanism July 2014 8 / 18

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SLIDE 14

Predictive Mechanism (broken)

Predictive Mechanism (broken)

Equip the noise mechanism with a prediction function a test function with a threshold l

Cost

easy points are free hard points cost ǫN

marco@stronati.org (PETS’14) Predictive Mechanism July 2014 8 / 18

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Testing for accuracy

Deterministic test

breaks d-privacy: two close secrets always report different observables

marco@stronati.org (PETS’14) Predictive Mechanism July 2014 9 / 18

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Testing for accuracy

Deterministic test

breaks d-privacy: two close secrets always report different observables

marco@stronati.org (PETS’14) Predictive Mechanism July 2014 9 / 18

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Testing for accuracy

Deterministic test

breaks d-privacy: two close secrets always report different observables

marco@stronati.org (PETS’14) Predictive Mechanism July 2014 9 / 18

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Testing for accuracy

Deterministic test

breaks d-privacy: two close secrets always report different observables

D-Private test

Θ(ǫθ, l) adds again laplacian noise on the distance between secret and prediction

marco@stronati.org (PETS’14) Predictive Mechanism July 2014 9 / 18

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Testing for accuracy

Deterministic test

breaks d-privacy: two close secrets always report different observables

D-Private test

Θ(ǫθ, l) adds again laplacian noise on the distance between secret and prediction

Skip the test

testing is still linear in n

marco@stronati.org (PETS’14) Predictive Mechanism July 2014 9 / 18

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Predictive Mechanism

Predictive Mechanism

PM(ǫθ, ǫN, l) prediction function d-private test Θ(ǫθ, l) noise mechanism N(ǫN)

Results

the mechanism is indeed d-private the budget used at each step is ǫθ (easy) or ǫθ + ǫN (hard) global budget depends on the run (on the trace)

marco@stronati.org (PETS’14) Predictive Mechanism July 2014 10 / 18

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Budget Managers

Parameters

Local: (ǫθ, ǫN, l) Global: (ǫ, α, n) Budget Manager: Global → Local

marco@stronati.org (PETS’14) Predictive Mechanism July 2014 11 / 18

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Budget Managers

Parameters

Local: (ǫθ, ǫN, l) Global: (ǫ, α, n) Budget Manager: Global → Local

Privacy

fixed ǫ we define two strategies

Fixed Accuracy

What is saved is spent to increase n

Fixed Rate

What is saved is spent to decrease α

marco@stronati.org (PETS’14) Predictive Mechanism July 2014 11 / 18

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Parrot prediction - simple yet effective

marco@stronati.org (PETS’14) Predictive Mechanism July 2014 12 / 18

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Parrot prediction - simple yet effective

repeats the last observable

marco@stronati.org (PETS’14) Predictive Mechanism July 2014 12 / 18

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Geolife and TDrive from Microsoft

marco@stronati.org (PETS’14) Predictive Mechanism July 2014 13 / 18

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Sampling

Sampled the traces with different frequencies 1 minutes 1 hour (a jump) Original trace Sampled trace Reported trace

marco@stronati.org (PETS’14) Predictive Mechanism July 2014 14 / 18

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Experimental results

Geolife: Fixed Accuracy 3 km with skip

marco@stronati.org (PETS’14) Predictive Mechanism July 2014 15 / 18

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Experimental results

Geolife: Fixed Rate 3.3% with skip

marco@stronati.org (PETS’14) Predictive Mechanism July 2014 16 / 18

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What to take home

composition of private and deterministic components budget managers allows to move cost from privacy to accuracy or rate 99% predictive mechanism is reusable considerable correlation is needed to make up for the test cost

marco@stronati.org (PETS’14) Predictive Mechanism July 2014 17 / 18

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Thanks

Questions?

Location Guard for Chrome and Firefox

https://github.com/chatziko/location-guard

marco@stronati.org (PETS’14) Predictive Mechanism July 2014 18 / 18