Back to the Drawing Board: Revisiting the Design of Optimal - PowerPoint PPT Presentation

Back to the Drawing Board: Revisiting the Design of Optimal Location Privacy-preserving Mechanisms Simon Oya, Carmela Troncoso, Fernando Pérez-González 1

Motivation. Obfuscation-Based Location Privacy. • Location information is sensitive. I want to use location services • Solution: obfuscation mechanisms without disclosing my location Service I’m at the fake location provider , closest ? Here you go! • We get some privacy. In this work • We lose some quality of service. We study some flaws in the • There are many ways to evaluate the privacy and traditional evaluation approach and quality loss of obfuscation mechanisms . how to solve them. 2

System Model Prior of real locations Real location Obfuscation mechanism Service Provider Obfuscated and adversary location Provides ...at the cost ? utility … of privacy 3

Traditional Evaluation: Metrics • Quality Loss: Average Loss Real location Euclidean, Hamming, semantic , … • Privacy: Average Adversary Error Obfuscated location Estimated Adversary’s estimation of the location real location Euclidean, Hamming, semantic , … 4 Shokri, Reza, et al. "Quantifying location privacy." Security and privacy (sp), 2011 ieee symposium on . IEEE, 2011.

Optimal Remapping [1] How to compute the optimal remapping of a mechanism f. The generated output is the Step 2: Compute the posterior Step 1: Generate a random output after the remapping. and remap to its “center”. location using the mechanism 5 [1] Chatzikokolakis, K., Elsalamouny, E., & Palamidessi, C. “Efficient Utility Improvement for Location Privacy .” PETS’17 .

Traditional Evaluation: Example and Remapping Traditional evaluation compares average error • Theorem : if d Q =d P , the optimal with average loss. remapping gives an optimal mechanism in terms of . • Lemma : the set of optimal mechanisms forms a convex polytope. Remapped mechanism Original mechanism • This means there are many optimal mechanisms… are all of them “equally good”? 6

Problems of the Traditional Evaluation The Coin Mechanism Flip a biased coin Real location p 1-p “Center” of the map Tails! Heads! = = Report real Report central location location H ow “good” is this mechanism? No privacy! Seems OK… 7

Problems of the Traditional Evaluation The Coin Mechanism • The coin mechanism is useless in practice… Flip a biased coin • … yet it is optimal in terms of . p 1-p • How do we identify and avoid these “undesirable” Tails! Heads! mechanisms? = = • Our proposal: use additional privacy and/or Report real Report central quality loss metrics. location location • We will see two: • H ow “good” is this mechanism? Conditional Entropy coin • Polytope of Worst-Case Loss No privacy! Seems OK… optimal 2 mechanisms No utility! 8

Solution 1: Conditional Entropy • The Conditional Entropy is a privacy metric.* Real location Obfuscated location 9 * Shokri, Reza, et al. "Quantifying location privacy." Security and privacy (sp), 2011 ieee symposium on . IEEE, 2011.

Conditional Entropy II • How does it help us? Optimal CE 1-p p Tails! Heads! = = Coin Report central Report real location location • The conditional entropy is concave! • The coin performs poorly. • The conditional entropy reveals “binary” mechanisms such as the coin. 10

Conditional Entropy III • Is a mechanism that maximizes the conditional entropy “good” enough? • Consider this adversary posterior: • This is undesirable for the user… yet it achieves large conditional entropy. • Therefore, we have to design mechanisms using CE as a complementary metric . 11

Conditional Entropy IV. Design. • How to design a mechanism that performs well in terms of AE and CE? Rate-Distortion: Blahut-Arimoto • Algorithm: Summary: • Tries to make an exponential posterior (we call it ExPost ). • For computational reasons, we need to perform approximations. • The more computational power we have, the closer it is to the optimal mechanism in terms of CE. • Iterative. • Uses remapping to achieve optimal AE. 12

Solution 2: Worst-Case Loss • How does it help us? • Tails  Huge loss • Having a constraint on the WC loss avoids this. • This constraint makes sense in real applications where we need a minimum utility (e.g., search nearby points of interest). 1.5km radius • Implementation: add a WC loss constraint to the design problem, use truncation, etc. 13

Multi-Dimensional Notion of Privacy • Both mechanisms are • The two-dimensional approach is misleading. • Consider privacy as a multi-dimensional optimal with respect to this privacy and quality notion . loss notions. 14

Evaluation I. Mechanisms. • Selection of relevant mechanisms. • Two from our work Optimal AE [2] Laplacian [1] Gaussian Exponential Posterior (ExPost) Circular Exponential Linear program! Only feasible in The coin We also perform an optimal remapping simple scenarios. after these mechanisms to improve them. [1] Chatzikokolakis, K., Elsalamouny, E., & Palamidessi, C. “Efficient Utility Improvement for Location Privacy .” PETS’17 . 15 [2] Shokri, Reza, et al. "Protecting location privacy: optimal strategy against localization attacks." CCS’12

Evaluation II. Continuous Scenario. Datasets: Gowalla, Brightkite With Worst-Case Loss = 1.5km Without Worst-Case Loss San Francisco region 16

Evaluation II. Continuous Scenario. Datasets: Gowalla, Brightkite With Worst-Case Loss = 1.5km Without Worst-Case Loss San Francisco region No mechanism fares well in all the metrics!!! Looking at a single privacy metric is misleading 17

Evaluation III. Discrete Scenario (Semantic) • • We evaluate Shokri et. al optimal mechanism We consider a [2], optimized for the semantic metric. semantic metric. 18 [2] Shokri, Reza, et al. "Protecting location privacy: optimal strategy against localization attacks." CCS’12

Evaluation III. Discrete Scenario (Semantic) • • We evaluate Shokri et. al optimal mechanism We consider a [2], optimized for the semantic metric. semantic metric. No mechanism fares well in all the metrics!!! Careful with the multiple solutions of the same program! 19 [2] Shokri, Reza, et al. "Protecting location privacy: optimal strategy against localization attacks." CCS’12

Conclusions This might give “bad” Most of them are Many location-privacy mechanisms. Design and evaluated following a evaluation should be done mechanisms are being two-dimensional considering privacy as a proposed approach multidimensional notion . Thank you!! simonoya@gts.uvigo.es 20