Asymptotic Privacy Loss Due to Time Series Matching of Dependent Users

Abstract

The Internet of Things (IoT) promises to improve user utility by tuning applications to a user’s current behavior, but the user’s behavior can be matched to characteristics learned from prior observations to compromise the user’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’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.