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Annual Symposium on Foundations of Computer Science

Replication is not needed: single database, computationally-private information retrieval

Eyal Kushilevitz Z, Rafail Ostrovsky

Published Nov 22, 2002• 933 citations
Publisher

Abstract

We establish the following, quite unexpected, result: replication of data for the computational private information retrieval problem is not necessary. More specifically, based on the quadratic residuosity assumption, we present a single database, computationally private information retrieval scheme with O(n/sup /spl epsiv//) communication complexity for any /spl epsiv/>0.

DOI
10.1109/sfcs.1997.646125

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We establish the following, quite unexpected, result: replication of data for the computational private information retrieval problem is not necessary. More specifically, based on the quadratic residuosity assumption, we present a single database, computationally private information retrieval scheme with O(n/sup /spl epsiv//) communication complexity for any /spl epsiv/>0.
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
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.
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) is an important protocol in cryptographic community to ensure privacy of the user when retrieving information from untrusted databases. In a variation to this problem, symmetric private information retrieval (SPIR) is a protocol which ensures the privacy of user as well as databases. A major drawback for the majority of existing works on information theoretic PIR and SPIR is that they focus on scenarios where all databases store the entire data set (i.e. replicated databases). The goal of this thesis is to present PIR and SPIR schemes for storage constrained databases. For both PIR and SPIR, we present a systematic approach to utilize storage constrained databases. The technical contribution involves two main parts: (a) a careful storage scheme to split and store messages across databases; and (b) construction of information theoretic PIR and SPIR schemes from such databases. We also compare our results to the fully replicated scenario, as well as compare the differences between the communication overhead of PIR and SPIR schemes.
Oblivious transfer is such a strong cryptographic tool that it is directly used both in private data retrieval techniques and secure, multi-party computation paradigms. We propose an optimal oblivious transfer, where the communication complexity is logarithmic in size of the database with minimum computation overhead - the computational complexity in any oblivious transfer protocol is at least linear in the size of the database. Our communication-efficient oblivious transfer protocol is a non-interactive, single-database scheme that is generally based on homomorphic encryption functions.
We introduce the problem of symmetric private information retrieval (SPIR) on replicated databases modeled by a simple graph. In this model, each vertex corresponds to a server, and a message is replicated on two servers if and only if there is an edge between them. We consider the setting where the server-side common randomness necessary to accomplish SPIR is also replicated at the servers according to the graph, and we call this as message-specific common randomness. In this setting, we establish a lower bound on the SPIR capacity, i.e., the maximum download rate, for general graphs, by proposing an achievable SPIR scheme. Next, we prove that, for any SPIR scheme to be feasible, the minimum size of message-specific randomness should be equal to the size of a message. Finally, by providing matching upper bounds, we derive the exact SPIR capacity for the class of path and regular graphs.