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International Conference on Cryptology in India

Symmetrically Private Information Retrieval (Extended Abstract)

Sanjeev Kumar Mishra, Palash Sarkar

Published Jan 1, 2000• 0 citations
OpenAlex

Abstract

Abstract. In this paper we present a single-round, single-server symmetrically private information retrieval scheme, in which privacy of user follows from intractability of the quadratic residuacity problem and the privacy of the database follows from the XOR assumption for quadratic residues introduced in this paper. The communication complexity of the proposed scheme for retrieving one bit can be made O(n ɛ), for any ɛ>0, where n is the number of bits in the database. We extend the protocol to a block retrieval scheme which is specially efficient when the number of records in the database is equal to the size of each record.

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On Symmetrically Private Information Retrieval.

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In today's age of information it is very important that, information about the information which you are seeking should not be leaked even to the server who is going to provide you the desired information. On the other hand, considering information as commodity, it is age old wisdom that one should get only as much as he pays. In this paper we essentially consider this problem and provide suitable solutions. Under a new number theoretic assumption, XOR Assumption, we give single-round symmetrically private information retrieval (SPIR) scheme for bit retrieval with communication complexity O(n...

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Abstract Private information retrieval (PIR) is one of the promising techniques to preserve user privacy in the presence of trusted-but-curious servers. The information theoretically private query construction assures the highest user privacy over curious and unbounded computation servers. Therefore, the need for information-theoretic private retrieval was fulfilled by various schemes in a variety of PIR settings. But, there is a lack of efficient encryption switching scheme which supports efficient switching between information-theoretic to/from computationally bounded PIRs. We propose a combination of new bit connection methods called rail-shape and signal-shape and new quadratic residuosity assumption based family of trapdoor functions for generic single database private block retrieval (PBR). The main goal of this work is to show that the possibility of mapping from computationally bounded privacy to information theoretic privacy or vice-versa in a single database setting using newly constructed bit connection and trapdoor function combinations. Notably, the proposed schemes are single round, memoryless and plain database schemes (at their basic constructions).

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

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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 science

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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, 2025•0 citations
Abstract. In this paper we present a single-round, single-server symmetrically private information retrieval scheme, in which privacy of user follows from intractability of the quadratic residuacity problem and the privacy of the database follows from the XOR assumption for quadratic residues introduced in this paper. The communication complexity of the proposed scheme for retrieving one bit can be made O(n ɛ), for any ɛ>0, where n is the number of bits in the database. We extend the protocol to a block retrieval scheme which is specially efficient when the number of records in the database is equal to the size of each record.
In today's age of information it is very important that, information about the information which you are seeking should not be leaked even to the server who is going to provide you the desired information. On the other hand, considering information as commodity, it is age old wisdom that one should get only as much as he pays. In this paper we essentially consider this problem and provide suitable solutions. Under a new number theoretic assumption, XOR Assumption, we give single-round symmetrically private information retrieval (SPIR) scheme for bit retrieval with communication complexity O(n...
Abstract Private information retrieval (PIR) is one of the promising techniques to preserve user privacy in the presence of trusted-but-curious servers. The information theoretically private query construction assures the highest user privacy over curious and unbounded computation servers. Therefore, the need for information-theoretic private retrieval was fulfilled by various schemes in a variety of PIR settings. But, there is a lack of efficient encryption switching scheme which supports efficient switching between information-theoretic to/from computationally bounded PIRs. We propose a combination of new bit connection methods called rail-shape and signal-shape and new quadratic residuosity assumption based family of trapdoor functions for generic single database private block retrieval (PBR). The main goal of this work is to show that the possibility of mapping from computationally bounded privacy to information theoretic privacy or vice-versa in a single database setting using newly constructed bit connection and trapdoor function combinations. Notably, the proposed schemes are single round, memoryless and plain database schemes (at their basic constructions).
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 science
The Private Information Retrieval protocol(PIR) is an important secure multi-party computation protocol.In PIR,a user can perform a query from a database without revealing his private information;meanwhile the privacy of the database will be protected,too.This paper proposes a new scheme in which we apply cryptographic technology on the auxiliary random servers protocol to solve the problem of PIR.This scheme is efficient in computational complexity and doesn't increase the cost of communication.It is very practical and can retrieve a block of bits.Detailed analysis of security,computational complexity and communicational complexity to the scheme is also given in this paper.
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).