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Many popular applications use traces of user data to offer various servicesto their users. However, even if user data is anonymized and obfuscated, auser's privacy can be compromised through the use of statistical matchingtechniques that match a user trace to prior user behavior. In this work, wederive the theoretical bounds on the privacy of users in such a scenario. Webuild on our recent study in the area of location privacy, in which weintroduced formal notions of location privacy for anonymization-based locationprivacy-protection mechanisms. Here we derive the fundamental limits of userprivacy when both anonymization and obfuscation-based protection mechanisms areapplied to users' time series of data. We investigate the impact of suchmechanisms on the trade-off between privacy protection and user utility. Wefirst study achievability results for the case where the time-series of usersare governed by an i.i.d. process. The converse results are proved both for thei.i.d. case as well as the more general Markov chain model. We demonstrate thatas the number of users in the network grows, the obfuscation-anonymizationplane can be divided into two regions: in the first region, all users haveperfect privacy; and, in the second region, no user has privacy.

Matching Anonymized and Obfuscated Time Series to Users' Profiles