---
abstract: 'Modern applications significantly enhance user experience by adapting to each user’s individual condition and/or preferences. While this adaptation can greatly improve a user’s experience or be essential for the application to work, the exposure of user data to the application presents a significant privacy threat to the userseven when the traces are anonymized (since the statistical matching of an anonymized trace to prior user behavior can identify a user and their habits). Because of the current and growing algorithmic and computational capabilities of adversaries, provable privacy guarantees as a function of the degree of anonymization and obfuscation of the traces are necessary. Our previous work has established the requirements on anonymization and obfuscation in the case that data traces are independent between users. However, the data traces of different users will be dependent in many applications, and an adversary can potentially exploit such. In this paper, we consider the impact of correlation between user traces on their privacy. First, we demonstrate that the adversary can readily identify the association graph, revealing which user data traces are correlated. Next, we demonstrate that the adversary can use this association graph to break user privacy with significantly shorter traces than in the case of independent users, and that obfuscating data traces independently across users is often insufficient to remedy such leakage. Finally, we discuss how users can employ data trace dependency to improve privacy by performing better obfuscation.'
author:
- 'Nazanin Takbiri  Amir Houmansadr  Dennis Goeckel  Hossein Pishro-Nik  [^1] [^2] [^3] [^4]'
bibliography:
- 'REF.bib'
title: Privacy of Dependent Users Against Statistical Matching
---

Internet of Things (IoT), Privacy-Protection Mechanisms (PPM), Information Theoretic Privacy, Anonymization, Obfuscation, Multi-user Correlation, Correlation Coefficient.

[^1]: N. Takbiri is with the Department of Electrical and Computer Engineering, University of Massachusetts, Amherst, MA, 01003 USA e-mail: (ntakbiri@umass.edu).

[^2]: A. Houmansadr is with the College of Information and Computer Sciences, University of Massachusetts, Amherst, MA, 01003 USA e-mail:(amir@cs.umass.edu)

[^3]: H. Pishro-Nik and D. Goeckel are with the Department of Electrical and Computer Engineering, University of Massachusetts, Amherst, MA, 01003 USA e-mail:(pishro@ecs.umass.edu)

[^4]: This work was supported by National Science Foundation under grants CCF–1421957 and CNS1739462.

    This work was presented in part in IEEE International Symposium on Information Theory (ISIT 2018) [@nazanin_ISIT2018].
