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The popularity of mobile devices and location-based services (LBS) hascreated great concern regarding the location privacy of their users.Anonymization is a common technique that is often used to protect the locationprivacy of LBS users. Here, we present an information-theoretic approach todefine the notion of perfect location privacy. We show how LBS's should use theanonymization method to ensure that their users can achieve perfect locationprivacy. First, we assume that a user's current location is independent fromher past locations. Using this i.i.d model, we show that if the pseudonym ofthe user is changed before $O(n^{\frac{2}{r-1}})$ observations are made by theadversary for that user, then the user has perfect location privacy. Here, n isthe number of the users in the network and r is the number of all possiblelocations that users can go to. Next, we model users' movements using Markovchains to better model real-world movement patterns. We show that perfectlocation privacy is achievable for a user if the user's pseudonym is changedbefore $O(n^{\frac{2}{|E|-r}})$ observations are collected by the adversary forthe user, where |E| is the number of edges in the user's Markov chain model.

Achieving Perfect Location Privacy in Wireless Devices Using Anonymization