Single-server private information retrieval (PIR) schemes are known to require linear query time. Recent works circumvent these classical lower bounds by leveraging preprocessing to answer queries in sublinear time. We prove computation lower bounds for PIR with preprocessing schemes making blackbox usage of any cryptography (such as random oracles or virtual blackbox obfuscation). If the client stores $s$ bits about an $n$ -bit database, then answering $k = Ω(s)$ queries requires either $Ω(n/s)$ amortized online communication or $Ω(n/s)$ amortized server cryptographic operations. This is tight, as known constructions match either bound while outperforming the other. Our lower bound is unconditional and allows arbitrary query protocols, weakened privacy, and server-side database encodings (including doubly efficient PIR) whenever the encoding is independent of the blackbox cryptography. Previous bounds were only known conditionally and for restricted classes of preprocessing, e.g., under non-encoding assumptions. Our framework also yields $Ω(n/s)$ communication lower bounds for schemes with $o(n/s)$ server cryptographic operations, communication-determined server cryptography, or perfect privacy in the idealized model. Finally, we prove lower bounds for symmetric PIR with client preprocessing in the random oracle model and give a matching construction using only one-way functions in the online phase.Single-server private information retrieval (PIR) schemes are known to require linear query time. Recent works circumvent these classical lower bounds by leveraging preprocessing to answer queries in sublinear time. We prove computation lower bounds for PIR with preprocessing schemes making blackbox usage of any cryptography (such as random oracles or virtual blackbox obfuscation). If the client stores $s$ bits about an $n$-bit database, then answering $k = Ω(s)$ queries requires either $Ω(n/s)$ amortized online communication or $Ω(n/s)$ amortized server cryptographic operations. This is tight, as known constructions match either bound while outperforming the other. Our lower bound is unconditional and allows arbitrary query protocols, weakened privacy, and server-side database encodings (including doubly efficient PIR) whenever the encoding is independent of the blackbox cryptography. Previous bounds were only known conditionally and for restricted classes of preprocessing, e.g., under non-encoding assumptions. Our framework also yields $Ω(n/s)$ communication lower bounds for schemes with $o(n/s)$ server cryptographic operations, communication-determined server cryptography, or perfect privacy in the idealized model. Finally, we prove lower bounds for symmetric PIR with client preprocessing in the random oracle model and give a matching construction using only one-way functions in the online phase.

arXiv:2607.06451Jul 7, 20260 citations

Almost Optimal Private Information Retrieval

Dmitri Asonov, Johann-Christoph Freytag

Lecture notes in computer scienceJan 1, 200367 citations

Towards Practical Private Information Retrieval

Robert Huijie Deng

Jan 1, 20064 citations

Capacity of Quantum Private Information Retrieval with Collusion of All But One of Servers

Seunghoan Song, Masahito Hayashi

Quantum private information retrieval (QPIR) is the problem to retrieve one of f classical files by downloading quantum systems from non-communicating n servers each of which contains the copy of f files, while the identity of the retrieved file is unknown to each server. As an extension, we consider the (n-1)-private QPIR that the identity of the retrieved file is secret even if any n-1 servers collude, and derive the QPIR capacity for this problem which is defined as the maximum rate of the retrieved file size over the download size. For an even number n of servers, we show that the capacity of the (n-1)-private QPIR is 2/n, when we assume that there are preexisting entanglements among the servers and require that no information of the nonretrieved files is downloaded. We construct an (n - 1)-private QPIR protocol of rate Γn/21-1and prove that the capacity is upper bounded by 2/n. The (n - 1)-private QPIR capacity is strictly greater than the classical counterpart. The full version of this paper is accessible at: https://arxiv.org/pdf/1903.12556.Quantum private information retrieval (QPIR) is the problem to retrieve one of f classical files by downloading quantum systems from non-communicating n servers each of which contains the copy of f files, while the identity of the retrieved file is unknown to each server. As an extension, we consider the (n-1)-private QPIR that the identity of the retrieved file is secret even if any n-1 servers collude, and derive the QPIR capacity for this problem which is defined as the maximum rate of the retrieved file size over the download size. For an even number n of servers, we show that the capacity of the (n-1)-private QPIR is 2/n, when we assume that there are preexisting entanglements among the servers and require that no information of the nonretrieved files is downloaded. We construct an (n - 1)-private QPIR protocol of rate Γn/21-1and prove that the capacity is upper bounded by 2/n. The (n - 1)-private QPIR capacity is strictly greater than the classical counterpart. The full version of this paper is accessible at: https://arxiv.org/pdf/1903.12556.

IEEE Information Theory Workshop (ITW)Aug 1, 201910 citations

s

bits about an

n

-bit database, then answering

k = Ω(s)

queries requires either

Ω(n/s)

amortized online communication or

Ω(n/s)

amortized server cryptographic operations. This is tight, as known constructions match either bound while outperforming the other. Our lower bound is unconditional and allows arbitrary query protocols, weakened privacy, and server-side database encodings (including doubly efficient PIR) whenever the encoding is independent of the blackbox cryptography. Previous bounds were only known conditionally and for restricted classes of preprocessing, e.g., under non-encoding assumptions. Our framework also yields

Ω(n/s)

communication lower bounds for schemes with

o(n/s)

server cryptographic operations, communication-determined server cryptography, or perfect privacy in the idealized model. Finally, we prove lower bounds for symmetric PIR with client preprocessing in the random oracle model and give a matching construction using only one-way functions in the online phase.