A Private Information Retrieval (PIR) protocol allows a client to learn the ith row of a database held by one or more servers, without revealing i to the servers. A Random-Index PIR (RPIR) protocol, introduced by Gentry et al. (TCC 2021), is a PIR protocol where, instead of being chosen by the client, i is random. This has applications in e.g. anonymous committee selection. Both PIR and RPIR protocols are interesting only if the communication complexity is smaller than the database size; otherwise, the trivial solution where the servers send the entire database suffices. Unlike PIR, where the client must send at least one message (to encode information about i), RPIR can be executed in a single round of server-to-client communication. In this paper, we study such one-round, information-theoretic RPIR protocols. The only known construction in this setting is SimpleMSRPIR (Gentry et al.), which requires the servers to communicate approximately N/2 bits, N being the database size. We show an Ω(√N) lower bound on communication complexity for one-round two-server information-theoretic RPIR, and a sublinear upper bound. Finally, we show how to use a sublinear amount of database-independent correlated randomness among multiple servers to get near-optimal online communication complexity (the size of one row plus the size of one index description per server).A Private Information Retrieval (PIR) protocol allows a client to learn the ith row of a database held by one or more servers, without revealing i to the servers. A Random-Index PIR (RPIR) protocol, introduced by Gentry et al. (TCC 2021), is a PIR protocol where, instead of being chosen by the client, i is random. This has applications in e.g. anonymous committee selection. Both PIR and RPIR protocols are interesting only if the communication complexity is smaller than the database size; otherwise, the trivial solution where the servers send the entire database suffices. Unlike PIR, where the client must send at least one message (to encode information about i), RPIR can be executed in a single round of server-to-client communication. In this paper, we study such one-round, information-theoretic RPIR protocols. The only known construction in this setting is SimpleMSRPIR (Gentry et al.), which requires the servers to communicate approximately N/2 bits, N being the database size. We show an Ω(√N) lower bound on communication complexity for one-round two-server information-theoretic RPIR, and a sublinear upper bound. Finally, we show how to use a sublinear amount of database-independent correlated randomness among multiple servers to get near-optimal online communication complexity (the size of one row plus the size of one index description per server).

Jan 1, 20250 citations

One-way functions are essential for single-server private information retrieval

Amos Beimel, Yuval Ishai, Eyal Kushilevitz Z +1 more

Private Information Retrieval (PIR) protocols allow a user to read information from a database without revealing to the server storing the database which information he has read.Kushilevitz and Ostrovsky [23] construct, based on the quadratic residuosity assumption, a single-server PIR protc-co1 with small communication complexity.Cachin, Micali, and Stadler [6] present a single-server PIR protocol with a smaller communication complexity, based an the (new) *hiding assumption.A major question, addressed in the present work, is what assumption is the minimal assumption necessary for the construction of single-server private information retrieval protocols with small communication complexity.We prove that if there is a (O-error) PIR protocol in which the server sends less than n bits then one-way functions exist (where n is the number of bits in the database).That is, even saving one bit compared to the naive protocol, in which the entire database is sent, already requires one-way functions.The same result holds (but requires more work) even if we allow the retrieval to fail with probability of at most 1/(8n).Moreover, similar tcomputer sciencePrivate Information Retrieval (PIR) protocols allow a user to read information from a database without revealing to the server storing the database which information he has read.Kushilevitz and Ostrovsky [23] construct, based on the quadratic residuosity assumption, a single-server PIR protc-co1 with small communication complexity.Cachin, Micali, and Stadler [6] present a single-server PIR protocol with a smaller communication complexity, based an the (new) *hiding assumption.A major question, addressed in the present work, is what assumption is the minimal assumption necessary for the construction of single-server private information retrieval protocols with small communication complexity.We prove that if there is a (O-error) PIR protocol in which the server sends less than n bits then one-way functions exist (where n is the number of bits in the database).That is, even saving one bit compared to the naive protocol, in which the entire database is sent, already requires one-way functions.The same result holds (but requires more work) even if we allow the retrieval to fail with probability of at most 1/(8n).Moreover, similar tcomputer science

ACM Symposium on Theory of Computing (STOC)May 1, 199961 citations

Two-Server Private Information Retrieval with Result Verification

Pengzhen Ke, Liang Feng Zhang

Private information retrieval (PIR) allows a client to retrieve any block xifrom a database x = x1xnsuch that i remains hidden from the database servers. PIR •protocols with unconditional privacy and sublinear (in n) communication complexity can be constructed assuming multiple honest-but-curious servers. This assumption however cannot be guaranteed in many real life scenarios such as using cloud servers as database servers. In this paper, we consider an information-theoretic PIR with result verification (PIR-RV) model where the servers may be dishonest (i.e., cheating) and provide incorrect answers but the client can detect the existence of cheating servers. We construct a 2-server PIR-RV protocol with communication complexity ${\mathcal{O}}({n^{1/2}}{\text{log }}p)$ where p is a parameter and controls the probability that the client fails to detect. Our idea may be extended to construct k-server PIR-RV protocols for k ≥ 3.Private information retrieval (PIR) allows a client to retrieve any block xifrom a database x = x1xnsuch that i remains hidden from the database servers. PIR •protocols with unconditional privacy and sublinear (in n) communication complexity can be constructed assuming multiple honest-but-curious servers. This assumption however cannot be guaranteed in many real life scenarios such as using cloud servers as database servers. In this paper, we consider an information-theoretic PIR with result verification (PIR-RV) model where the servers may be dishonest (i.e., cheating) and provide incorrect answers but the client can detect the existence of cheating servers. We construct a 2-server PIR-RV protocol with communication complexity ${\mathcal{O}}({n^{1/2}}{\text{log }}p)$ where p is a parameter and controls the probability that the client fails to detect. Our idea may be extended to construct k-server PIR-RV protocols for k ≥ 3.

IEEE International Symposium on Information Theory (ISIT)Jun 26, 202211 citations

A Linear Lower Bound on the Communication Complexity of Single-Server Private Information Retrieval.

Iftach Haitner, Jonathan J. Hoch, Gil Segev

We study the communication complexity of single-server Private Information Retrieval (PIR) protocolsthat are based on fundamental cryptographic primitives in a black-box manner. In this setting, we establish a tight lower bound on the number of bits communicated by the server in any polynomially-preservingconstruction that relies on trapdoor permutations. More specifically, our main result states that in such constructions \\Omega (n) bits must be communicated by the server, where n is the size of the server's database,and this improves the \\Omega (n / log n) lower bound due to Haitner, Hoch, Reingold and Segev (FOCS '07).Therefore, in the setting under consideration, the naive solution in which the user downloads the entire database turns out to be optimal up to constant multiplicative factors. We note that the lower boundwe establish holds for the most generic form of trapdoor permutations, including in particular enhanced trapdoor permutations.Technically speaking, this paper consists of two main contributions from which our lower bound is obtained. First, we derive a tight lower bound on the number of bits communicated by the sender duringthe commit stage of any black-box construction of a statistically-hiding bit-commitment scheme from a family of trapdoor permutations. This lower bound asymptotically matches the upper bound provided bythe scheme of Naor, Ostrovsky, Venkatesan and Yung (CRYPTO '92). Second, we improve the e fficiencyof the reduction of statistically-hiding commitment schemes to low-communication single-server PIR, due to Beimel, Ishai, Kushilevitz and Malkin (STOC '99). In particular, we present a reduction that essentiallypreserves the communication complexity of the underlying single-server PIR protocol.We study the communication complexity of single-server Private Information Retrieval (PIR) protocolsthat are based on fundamental cryptographic primitives in a black-box manner. In this setting, we establish a tight lower bound on the number of bits communicated by the server in any polynomially-preservingconstruction that relies on trapdoor permutations. More specifically, our main result states that in such constructions \\Omega (n) bits must be communicated by the server, where n is the size of the server's database,and this improves the \\Omega (n / log n) lower bound due to Haitner, Hoch, Reingold and Segev (FOCS '07).Therefore, in the setting under consideration, the naive solution in which the user downloads the entire database turns out to be optimal up to constant multiplicative factors. We note that the lower boundwe establish holds for the most generic form of trapdoor permutations, including in particular enhanced trapdoor permutations.Technically speaking, this paper consists of two main contributions from which our lower bound is obtained. First, we derive a tight lower bound on the number of bits communicated by the sender duringthe commit stage of any black-box construction of a statistically-hiding bit-commitment scheme from a family of trapdoor permutations. This lower bound asymptotically matches the upper bound provided bythe scheme of Naor, Ostrovsky, Venkatesan and Yung (CRYPTO '92). Second, we improve the e fficiencyof the reduction of statistically-hiding commitment schemes to low-communication single-server PIR, due to Beimel, Ishai, Kushilevitz and Malkin (STOC '99). In particular, we present a reduction that essentiallypreserves the communication complexity of the underlying single-server PIR protocol.

Jan 1, 20070 citations

On Quantum Advantage in Information Theoretic Single-Server PIR

Dorit Aharonov, Zvika Brakerski, Kai-Min Chung +3 more

In (single-server) Private Information Retrieval (PIR), a server holds a large database $DB$ of size $n$ , and a client holds an index $i \in [n]$ and wishes to retrieve $DB[i]$ without revealing $i$ to the server. It is well known that information theoretic privacy even against an `honest but curious' server requires $Ω(n)$ communication complexity. This is true even if quantum communication is allowed and is due to the ability of such an adversarial server to execute the protocol on a superposition of databases instead of on a specific database (`input purification attack'). Nevertheless, there have been some proposals of protocols that achieve sub-linear communication and appear to provide some notion of privacy. Most notably, a protocol due to Le Gall (ToC 2012) with communication complexity $O(\sqrt{n})$ , and a protocol by Kerenidis et al. (QIC 2016) with communication complexity $O(\log(n))$ , and $O(n)$ shared entanglement. We show that, in a sense, input purification is the only potent adversarial strategy, and protocols such as the two protocols above are secure in a restricted variant of the quantum honest but curious (a.k.a specious) model. More explicitly, we propose a restricted privacy notion called \emph{anchored privacy}, where the adversary is forced to execute on a classical database (i.e. the execution is anchored to a classical database). We show that for measurement-free protocols, anchored security against honest adversarial servers implies anchored privacy even against specious adversaries. Finally, we prove that even with (unlimited) pre-shared entanglement it is impossible to achieve security in the standard specious model with sub-linear communication, thus further substantiating the necessity of our relaxation. This lower bound may be of independent interest (in particular recalling that PIR is a special case of Fully Homomorphic Encryption).In (single-server) Private Information Retrieval (PIR), a server holds a large database $DB$ of size $n$, and a client holds an index $i \in [n]$ and wishes to retrieve $DB[i]$ without revealing $i$ to the server. It is well known that information theoretic privacy even against an `honest but curious' server requires $Ω(n)$ communication complexity. This is true even if quantum communication is allowed and is due to the ability of such an adversarial server to execute the protocol on a superposition of databases instead of on a specific database (`input purification attack'). Nevertheless, there have been some proposals of protocols that achieve sub-linear communication and appear to provide some notion of privacy. Most notably, a protocol due to Le Gall (ToC 2012) with communication complexity $O(\sqrt{n})$, and a protocol by Kerenidis et al. (QIC 2016) with communication complexity $O(\log(n))$, and $O(n)$ shared entanglement. We show that, in a sense, input purification is the only potent adversarial strategy, and protocols such as the two protocols above are secure in a restricted variant of the quantum honest but curious (a.k.a specious) model. More explicitly, we propose a restricted privacy notion called \emph{anchored privacy}, where the adversary is forced to execute on a classical database (i.e. the execution is anchored to a classical database). We show that for measurement-free protocols, anchored security against honest adversarial servers implies anchored privacy even against specious adversaries. Finally, we prove that even with (unlimited) pre-shared entanglement it is impossible to achieve security in the standard specious model with sub-linear communication, thus further substantiating the necessity of our relaxation. This lower bound may be of independent interest (in particular recalling that PIR is a special case of Fully Homomorphic Encryption).

arXiv:1902.09768Feb 26, 20190 citations

The Capacity of Symmetric Private Information Retrieval

Hua Sun, Syed A. Jafar

Private information retrieval (PIR) is the problem of retrieving as efficiently as possible, one out of K messages from N non-communicating replicated databases (each holds all K messages) while keeping the identity of the desired message index a secret from each individual database. Symmetric PIR (SPIR) is a generalization of PIR to include the requirement that beyond the desired message, the user learns nothing about the other K - 1 messages. The information theoretic capacity of SPIR (equivalently, the reciprocal of minimum download cost) is the maximum number of bits of desired information that can be privately retrieved per bit of downloaded information. We show that the capacity of SPIR is 1-1/N regardless of the number of messages K, if the databases have access to common randomness (not available to the user) that is independent of the messages, in the amount that is at least 1/(N -1) bits per desired message bit, and zero otherwise.Private information retrieval (PIR) is the problem of retrieving as efficiently as possible, one out of K messages from N non-communicating replicated databases (each holds all K messages) while keeping the identity of the desired message index a secret from each individual database. Symmetric PIR (SPIR) is a generalization of PIR to include the requirement that beyond the desired message, the user learns nothing about the other K - 1 messages. The information theoretic capacity of SPIR (equivalently, the reciprocal of minimum download cost) is the maximum number of bits of desired information that can be privately retrieved per bit of downloaded information. We show that the capacity of SPIR is 1-1/N regardless of the number of messages K, if the databases have access to common randomness (not available to the user) that is independent of the messages, in the amount that is at least 1/(N -1) bits per desired message bit, and zero otherwise.

IEEE Globecom Workshops (GC Wkshps)Dec 1, 201651 citations

{\mathcal{O}}({n^{1/2}}{\text{log }}p)

where p is a parameter and controls the probability that the client fails to detect. Our idea may be extended to construct k-server PIR-RV protocols for k ≥ 3.

In (single-server) Private Information Retrieval (PIR), a server holds a large database

DB

of size

n

, and a client holds an index

i \in [n]

and wishes to retrieve

DB[i]

without revealing

i

to the server. It is well known that information theoretic privacy even against an `honest but curious' server requires

Ω(n)

communication complexity. This is true even if quantum communication is allowed and is due to the ability of such an adversarial server to execute the protocol on a superposition of databases instead of on a specific database (`input purification attack'). Nevertheless, there have been some proposals of protocols that achieve sub-linear communication and appear to provide some notion of privacy. Most notably, a protocol due to Le Gall (ToC 2012) with communication complexity

O(\sqrt{n})

, and a protocol by Kerenidis et al. (QIC 2016) with communication complexity

O(\log(n))

, and

O(n)

shared entanglement. We show that, in a sense, input purification is the only potent adversarial strategy, and protocols such as the two protocols above are secure in a restricted variant of the quantum honest but curious (a.k.a specious) model. More explicitly, we propose a restricted privacy notion called \emph{anchored privacy}, where the adversary is forced to execute on a classical database (i.e. the execution is anchored to a classical database). We show that for measurement-free protocols, anchored security against honest adversarial servers implies anchored privacy even against specious adversaries. Finally, we prove that even with (unlimited) pre-shared entanglement it is impossible to achieve security in the standard specious model with sub-linear communication, thus further substantiating the necessity of our relaxation. This lower bound may be of independent interest (in particular recalling that PIR is a special case of Fully Homomorphic Encryption).