We consider the problem of ON-OFF privacy in which a user is interested in the latest message generated by one of n sources available at a server. The user has the choice to turn privacy ON or OFF depending on whether he wants to hide his interest at the time or not. The challenge of allowing the privacy to be toggled between ON and OFF is that the user's online behavior is correlated over time. Therefore, the user cannot simply ignore the privacy requirement when privacy is OFF.We represent the user's correlated requests by an n-state Markov chain. Our goal is to design ON-OFF privacy schemes with optimal download rate that ensure privacy for past and future requests. We devise a polynomial-time algorithm to construct an ON-OFF privacy scheme. Moreover, we present an upper bound on the achievable rate. We show that the proposed scheme is optimal and the upper bound is tight for some special families of Markov chains. We also give an implicit characterization of the optimal achievable rate as a linear programming (LP).Index Terms-Information-theoretic privacy, private information retrieval, Markov chains
I. INTRODUCTION
A. MotivationIn the current data-driven world, users' information is always being collected online, and its privacy has become a significant concern. Many users wish to keep private their personal information, such as their age, sex, political views, health disorders, etc. Significant research has been devoted to study algorithms that preserve users' privacy. Some of the proposed approaches include applying anonymization techniques [1], differential privacy algorithms [2], and private information retrieval methods [3].Privacy, however, comes at a cost. Privacy-preserving algorithms typically incur higher overheads in terms of computation, memory, and delay. These incurred costs motivate one to think of privacy as an expensive commodity and, therefore, to allow the user to request it, i.e., turn privacy ON, only when needed; otherwise, turn it OFF. The user may choose to switch between privacy being ON and OFF depending on several criteria, such as location (country, workplace vs. home, etc.), network connection (public or private network), devices (shared vs. personal machines) being used, or service quality (privacy-preserving algorithms typically induce more overheads), to name a few.At a conceptual level, ON-OFF privacy algorithms enable privacy to be switched between ON and OFF whenever desired. One of the main challenges in designing such algorithms