# Optimizing Noise Level for Perturbing Geo-location Data

## Abstract

With the tremendous increase in the number of smart phones, App stores have been overwhelmed with applications requiring geo-location access in order to provide their users better services through personalization. Revealing a user’s location to these third party Apps, no matter at what frequency, is a severe privacy breach which can have unpleasant social consequences. In order to prevent inference attacks derived from geo-location data, a number of location obfuscation techniques have been proposed in the literature. However, none of them provides any *objective* measure of privacy guarantee. Some work has been done to define differential privacy for geo-location data in the form of geo-indistinguishability with *l* privacy guarantee. These techniques do not utilize any prior background information about the Points of Interest (*PoI*s) of a user and apply Laplacian noise to perturb all the location coordinates. Intuitively, the utility of such a mechanism can be improved if the noise distribution is derived after considering some prior information about *PoI*s. In this paper, we apply the standard definition of differential privacy on geo-location data. We use first principles to model various privacy and utility constraints, prior background information available about the *PoI*s (distribution of PoI locations in a 1D plane) and the granularity of the input required by different types of apps, in order to produce a more accurate and a utility maximizing differentially private algorithm for geo-location data at the OS level. We investigate this for a particular category of Apps and for some specific scenarios. This will also help us to verify whether Laplacian noise is still the optimal perturbation when we have such prior information.

## Keywords

Differential privacy Utility Points of interest Geo-location data Laplacian noise## Notes

### Acknowledgement

We would like to thank Dr. Aleksandra Korolova for being the guiding light throughout the course of this paper.

## References

- 1.Bindschaedler, V., Shokri, R.: Synthesizing plausible privacy preserving location traces. IEEE, August 2016Google Scholar
- 2.Andrés, M., Bordenable, N.E., Chatzikokolakis, K., Palamidessi, C.: Geo-indistinguishability: differential privacy for location-based systems. Springer, Switzerland (2015)Google Scholar
- 3.Andreś, M., Bordenable, N.E., Chatzikokolakis, K., Palamidessi, C.: Optimal geo-indistinguishable mechanisms for location privacy. In: Proceedings of the 2014 ACM SIGSAC, Conference on Computer and Communications SecurityGoogle Scholar
- 4.
- 5.Polakis, I., Argyros, G., Petsios, T., Sivakorn, S., Keromytis, A.D.: Where’s Wally? Precise user discovery attacks in location proximity services. In: Proceedings of the 22nd ACM SIGSAC Conference on Computer and Communications Security (2015)Google Scholar
- 6.Srivastava, V., Naik, V., Gupta, A.: Privacy breach of social relation from location based mobile applications. In: IEEE CS Home, pp. 324–328 (2014)Google Scholar
- 7.Liao, L., Fox, D., Kautz, H.: Extracting places and activities from GPS traces using hierarchical conditional random fields. Int. J. Robot. Res. Arch.
**26**(1), 119–134 (2007)CrossRefGoogle Scholar - 8.Brenner, H., Nissim, K.: Impossibility of differentially private universally optimal mechanisms. In: 2010 51st Annual IEEE Symposium Foundations of Computer Science (FOCS)Google Scholar
- 9.Nunez, M., Frignal, J.: Geo–location inference attacks: from modelling to privacy risk assessment. In: EDCC 2014 Proceedings of the 2014 Tenth European Dependable Computing ConferenceGoogle Scholar
- 10.Gruteser, M., Grunwald, D.: Anonymous usage of location–based service through spatial and temporal cloaking. In: Proceeding MobiSys 2003 Proceedings of the 1st International Conference on Mobile Systems, Applications and ServicesGoogle Scholar
- 11.Kulik, L., Duckham, M.: A Formal Model of Obfuscation and Negotiation for Location Privacy. PERVASIVE Springer-Verlag, Heidelberg (2005)Google Scholar
- 12.Ardagna, C.A., Cremonini, M., Damiani, E., Samarati, P.: Location privacy protection through obfuscation–based techniques. In: IFIP Annual Conference on Data and Applications Security and Privacy DBSec 2007: Data and Applications SecurityGoogle Scholar
- 13.Chatzikokolakis, K., Elsalamouny, E., Palamidessi, C.: Practical Mechanisms for Location Privacy. Inria and LIX, cole PolytechniqueGoogle Scholar
- 14.ElSalamouny, E., Gambs, S.: Differential privacy models for location based services. Trans. Data Priv.
**9**, 15–48 (2016). INRIA, FranceGoogle Scholar