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The Internet of Things (IoT) promises to improve user utility by tuning applications to a user&#x2019;s current behavior, but the user&#x2019;s behavior can be matched to characteristics learned from prior observations to compromise the user&#x2019;s identity and hence privacy. Our previous work has established the rate at which anonymization must be performed to prevent such matching in a Bayesian setting when faced with a powerful adversary who has extensive knowledge of each user&#x2019;s past behavior. However, even sophisticated adversaries do not often have such extensive knowledge; hence, in this letter, we turn our attention to an adversary who must learn user behavior from past data traces of limited length under the assumptions that: (i) there exists dependency between data traces of different users; and (ii) the data points of each user are drawn from a normal distribution. Results on the lengths of training sequences and rates of anonymization for the data sequences that result in a loss of user privacy are presented.

Asymptotic Privacy Loss Due to Time Series Matching of Dependent Users