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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

  1. 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

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

  3. Scope x − → M − → z marco@stronati.org (PETS’14) Predictive Mechanism July 2014 3 / 18

  4. Scope x − → M − → z Privacy through reduced accuracy Utility accuracy of reported location marco@stronati.org (PETS’14) Predictive Mechanism July 2014 3 / 18

  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

  6. Privacy Definition Geo-indistinguishability d P ( 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

  7. Privacy Mechanism Noise mechanism N ( ǫ N ) marco@stronati.org (PETS’14) Predictive Mechanism July 2014 5 / 18

  8. Privacy Mechanism Noise mechanism N ( ǫ N ) marco@stronati.org (PETS’14) Predictive Mechanism July 2014 5 / 18

  9. Mobility Traces Independent Mechanism IM (¯ x ) that uses N ( ǫ N )( x ) is n · ǫ N 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

  10. Correlation real traces are strongly correlated not every point has the same value marco@stronati.org (PETS’14) Predictive Mechanism July 2014 7 / 18

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

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

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

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

  15. 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

  16. 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

  17. 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

  18. Testing for accuracy Deterministic test breaks d-privacy: two close secrets always report different observables D-Private test Θ( ǫ θ , l ) adds again laplacian noise on the distance between secret and prediction marco@stronati.org (PETS’14) Predictive Mechanism July 2014 9 / 18

  19. Testing for accuracy Deterministic test breaks d-privacy: two close secrets always report different observables D-Private test Θ( ǫ θ , 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

  20. Predictive Mechanism Predictive Mechanism PM ( ǫ θ , ǫ N , l ) prediction function d-private test Θ( ǫ θ , l ) noise mechanism N ( ǫ N ) Results the mechanism is indeed d-private the budget used at each step is ǫ θ (easy) or ǫ θ + ǫ N (hard) global budget depends on the run (on the trace) marco@stronati.org (PETS’14) Predictive Mechanism July 2014 10 / 18

  21. Budget Managers Parameters Local: ( ǫ θ , ǫ N , l ) Global: ( ǫ, α, n ) Budget Manager: Global → Local marco@stronati.org (PETS’14) Predictive Mechanism July 2014 11 / 18

  22. Budget Managers Parameters Local: ( ǫ θ , ǫ N , l ) Global: ( ǫ, α, n ) Budget Manager: Global → Local Privacy fixed ǫ we define two strategies Fixed Accuracy Fixed Rate What is saved is spent to decrease α What is saved is spent to increase n marco@stronati.org (PETS’14) Predictive Mechanism July 2014 11 / 18

  23. Parrot prediction - simple yet effective marco@stronati.org (PETS’14) Predictive Mechanism July 2014 12 / 18

  24. Parrot prediction - simple yet effective repeats the last observable marco@stronati.org (PETS’14) Predictive Mechanism July 2014 12 / 18

  25. Geolife and TDrive from Microsoft marco@stronati.org (PETS’14) Predictive Mechanism July 2014 13 / 18

  26. 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

  27. Experimental results Geolife: Fixed Accuracy 3 km with skip marco@stronati.org (PETS’14) Predictive Mechanism July 2014 15 / 18

  28. Experimental results Geolife: Fixed Rate 3.3% with skip marco@stronati.org (PETS’14) Predictive Mechanism July 2014 16 / 18

  29. 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

  30. 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

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