Search histories contain detailed and sensitive information about people. Private information retrieval (PIR) aims to hide search histories from service providers by allowing a user to retrieve the wth record of a database without revealing w to the server. However, most known PIR schemes are either very inefficient (and therefore unlikely to gain traction in a practical sense) or reliant on some restrictive assumptions. In this paper, we consider an efficient class of schemes called multi-server PIR. Multi-server PIR assumes that the client communicates with multiple, non-colluding servers, each possessing an identical copy of the database. The current literature does not address the assumption that servers store perfectly-synchronized databases. This seems implausible, especially if servers are not meant to collude. We propose the first multi-server PIR scheme to return the desired record even when servers' databases are not perfectly synchronized. Our scheme asymptotically has the same computational and communication complexity as state-of-the-art PIR schemes for synchronized databases; this comes at the expense of probabilistic success guarantees and two rounds of communication. As a secondary result, our approach can efficiently process multiple concurrent queries in one round of PIR.
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