A Bit More Than a Bit Is More Than a Bit Better

Abstract

We study both the practical and theoretical efficiency of private information retrieval (PIR) protocols in a model wherein several untrusted servers work to obliviously service remote clients’ requests for data and yet no pair of servers colludes in a bid to violate said obliviousness. In exchange for such a strong security assumption, we obtain new PIR protocols exhibiting remarkable efficiency with respect to every cost metric—download, upload, computation, and round complexity—typically considered in the PIR literature. The new constructions extend a multiserver PIR protocol of Shah, Rashmi, and Ramchandran (ISIT 2014), which exhibits a remarkable property of its own: to fetch a b-bit record from a collection of r such records, the client need only download b + 1 bits total. We find that allowing “a bit more” download (and optionally introducing computational assumptions) yields a family of protocols offering very attractive trade-offs. In addition to Shah et al.’s protocol, this family includes as special cases (2-server instances of) the seminal protocol of Chor, Goldreich, Kushilevitz, and Sudan (FOCS 1995) and the recent DPF-based protocol of Boyle, Gilboa, and Ishai (CCS 2016). An implicit “folklore” axiom that dogmatically permeates the research literature on multiserver PIR posits that the latter protocols are the “most efficient” protocols possible in the perfectly and computationally private settings, respectively. Yet our findings soundly refute this supposed axiom: These special cases are (by far) the least performant representatives of our family, with essentially all other parameter settings yielding instances that are significantly faster.

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“…We begin our technical discussion by introducing the basic technologies underlying our construc-tion: Hafiz-Henry computationally 1-private PIR [24], Boolean matrix factorization-based collaborative filtering, and Du-Atallah 3-party multiplication [18]. Additionally, we give a bird's-eye overview of how PIRSONA uses the latter MPC to "glue" the first two (seemingly antithetical) primitives into a seamless, privacypreserving content distribution platform.…”

“…PIR is a cryptographic primitive using which users can fetch items from remote and untrusted database servers without disclosing to the servers which items they fetch. We focus on a specific class of PIR protocols-the so-called "1-private" multiserver scheme of Hafiz and Henry [24]-which provide extremely low download and server-side computation costs. These protocols provide the best-available mix of efficiency and expressiveness for the media delivery applications we target with PIRSONA.…”

Private Aggregate Queries to Untrusted Databases

“…We specifically address the situation where a user wishes to retrieve information from an untrusted database without revealing to the database what specific information they wish to obtain. Private information retrieval (PIR) [3]- [6] is a cryptographic technique that solves this problem. However, while numerous privacy-enhancing technologies, including various PIR protocols, have been conceived over the past two decades to address this problem, the vast majority of them are not viable for facilitating a comprehensive set of statistical queries that might be required for performing data analytics on sensitive databases.…”

“…However, as discussed, this is obviously not practical because databases can be quite large. So we instead explore protocols with total communication costs less than (sublinear to) the database size, as stated in [6], as the non-triviality property of any practical PIR protocols.…”