Amos Beimel, Yuval Ishai, Eyal Kushilevitz and Tal Malkin. One-Way Functions Are Essential for Single-Server Private Information Retrieval. STOC 1999: 89-98  Home/Search   Document Details and Download   Summary   Related Articles   Check

....Supported in part by the Mitchell Schoref program at the Technion. interested in retrieving from x is modeled as the i th bit of x; that is, x i , for some index i. The notion of PIR was introduced by Chor et. al [9] and since then was the subject of a significant amount of work [2, 6, 7, 8, 11, 12, 13, 15, 17]. If information theoretic privacy is required and there is a single server available, then there is no better solution other than the user asking for a copy of the whole database from the server (which is obviously very inefficient) 9] However, if identical copies of the database are replicated ....

A. Beimel, Y. Ishai, E. Kushilevitz, and T. Malkin. One-way functions are essential for single-server private information retrieval. In Proc. of the 31th Annu. ACM Symp. on the Theory of Computing, 1999.

.... represented by public key encryption (PKE) and includes trapdoor permutation (TDP) trapdoor function (TDF) oblivious transfer (OT) private information retrieval (PIR) and key agreement (KA) One wayness turns out to be essential as these primitives all are known to imply one way functions [11, 19, 1, 2, 7]. For private cryptography, one wayness basically is also sucient as one way functions can be used to construct all the primitives therein, except one way permutations. For public cryptography, additional properties are required on top of one wayness, and the relationships among primitives appear ....

Amos Beimel, Yuval Ishai, Eyal Kushilevitz, and Tal Malkin. One-way functions are essential for single-server private information retrieval. In Proceedings of the 31st Annual ACM Symposium on Theory of Computing, pages 89-98, 1999.

....primitive cryptographic terminologies which will be used in the remaining sections of the paper are reviewed. One way function, is a function which is relatively easy to compute, but significantly hard to reverse. That is, given x it is easy to compute (x) but given f(x) it is hard to compute x [Beimel et al. 1999]. Breaking a plate is a good example of a one way function. It is easy to smash a plate into a thousand tiny pieces. However, it is not easy to put all of those tiny pieces back together into a plate. Hash function, h(x) is a hash function. For a given Y it is computationally hard to find a x ....

Beimel A., Ishai Y., Kushilevitz E., and Malkin T.(1999). One-way functions are essential for single server private information retrieval. In Proc. of the 31st Annu. ACM Syrup. on the Theory of Computing (STOC), pages 89-98.

....and work, and O(N 1 # ) extra storage bits. The targeted web advertising without revealing user preferences (a problem similar to PIR) is investigated in [36] Comparative Security Analysis of PIR Relationships between different security primitives and the PIR problem are lighted in [23, 41, 39, 11, 20]. 3.6 Related Work We briefly mention in this section the work, which does not directly solve the PIR problem, but some ideas from this related work may be used or are already used to construct a PIR protocol. Protocols for Theoretical PIR in [19, 4] have used ideas from instance hiding problem ....

A. Beimel, Y. Ishai, E. Kushilevitz, and T. Malkin. One-way functions are essential for single-server private information retrieval. In Proc. of 31st STOC, 1999.

.... December 19, 2000 Abstract The private information retrieval (PIR) primitive has received a significant amount of attention from the scientific community since it was first proposed by Chor et al. 9, 10] Extensions to the model [8, 11, 13, 14, 17] relation with other cryptographic primitives [6, 12] and improved upper bounds [3, 16] have been obtained. In this paper, we continue along this path and give an improved upper bound for information theoretic PIR. Our protocol and proofs extend the algebraic methods of Ishai and Kushilevitz [16] keywords: Private information retrieval, privacy, ....

BEIMEL, A., ISHAI, Y., KUSHILEVITZ, E., AND MALKIN, T. One-way functions are essential for single-server private information retrieval. In Proceedings of the 31st ACM Symposium on Theory of Computing (1999), ACM Press.

....the construction of [11] to use any trapdoor predicate with certain homomorphic properties. Speci cally, such predicates exist under the decisional Die Hellman assumptions and under the assumption that it is hard to approximate the shortest vector in a lattice. PIR problem was also studied in [9, 21, 52, 53, 55]. Recently, 43] have shown a single database PIR based on any one way trapdoor permutations, though their communication, while less than n, is bigger than Schemes based on speci c number theoretic assumptions [20, 11, 22, 23] On the other hand [21] have shown that any nontrivial single database ....

.... PIR problem was also studied in [9, 21, 52, 53, 55] Recently, 43] have shown a single database PIR based on any one way trapdoor permutations, though their communication, while less than n, is bigger than Schemes based on speci c number theoretic assumptions [20, 11, 22, 23] On the other hand [21] have shown that any nontrivial single database PIR implies the existence of one way functions. Chor et al. 3] also de nes several extensions of the PIR problem: 5 Private Retrieval of Blocks or Records: The database is consists of n blocks of m bits each. The user wants to retrieve the i th ....

A. Beimel, Y. Ishai, E. Kushilevitz, and T. Malkin. One way functions are essential for singleserver private information retrieval. In Proceedings of the 31th Annual ACM Symposium on Theory of Computing, 1999.

....Supported in part by the Mitchell Schoref program at the Technion. interested in retrieving from x is modeled as the i th bit of x; that is, x i , for some index i. The notion of PIR was introduced by Chor et. al [9] and since then was the subject of a significant amount of work [2, 6, 7, 8, 11, 12, 13, 15, 17]. If information theoretic privacy is required and there is a single server available, then there is no better solution other than the user asking for a copy of the whole database from the server (which is obviously very inefficient) 9] However, if identical copies of the database are replicated ....

A. Beimel, Y. Ishai, E. Kushilevitz, and T. Malkin. One-way functions are essential for single-server private information retrieval. In Proc. of the 31th Annu. ACM Symp. on the Theory of Computing, 1999.

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A. Beimel, Y. Ishai, E. Kushilevitz, and T. Malkin. One-way functions are essential for single-server private information retrieval. In Proc. of the 31th Annu. ACM Symp. on the Theory of Computing, 1999.

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A. Beimel, Y. Ishai, E. Kushilevitz, and T. Malkin. One-Way Functions Are Essential for Single-Server Private Information Retrieval. Proc. of 31st STOC, pp. 89--98, 1999.

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A. Beimel, Y. Ishai, E. Kushilevitz, and T. Malkin. One-Way Functions are Essential for Single-Server Private Information Retrieval. In Proc. of 31st STOC, 1999.

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A. Beimel, Y. Ishai, E. Kushilevitz, and T. Malkin. One-Way Functions are Essential for Single-Server Private Information Retrieval. In Proc. of 31st STOC, 1999.

....make the problem more concrete, the database is modeled as an n bit string x, and the user has some index i and is interested in privately retrieving the value of x i . Since its introduction, PIR has been an area of active research, and various settings and extensions have been considered (e.g. [2, 25, 10, 20, 18,17, 14, 9, 8, 19, 15, 21, 1]) Most of the initial work on PIR has focused on the goal of minimizing the communication, which was considered the most expensive resource. However, despite considerable success in realizing this goal, the real life applicability of the proposed solutions remains questionable. One of the most ....

....every constant # 0, a single server protocol with communication complexity of O (n ) bits. Cachin, Micali, and Stadler [9] present a single server protocol with polylogarithmic communication complexity, based on a new number theoretic intractability assumption. Other works in this setting are [25, 24, 27, 8, 15, 21, 1]. The only previous work that has addressed the servers computation is that of Gertner, Goldwasser, and Malkin [17] see also [23] who present a model for PIR utilizing special purpose privacy servers, achieving stronger privacy guarantees and small computation for the original server holding ....

A. Beimel, Y. Ishai, E. Kushilevitz, and T. Malkin. One-way functions are essential for single-server private information retrieval. In 31th STOC, pages 89--98, 1999.

....model of private information retrieval, provide formal de nitions for it, and survey previous work. In Chapter 5 we explore the necessary assumptions for computational (single server) PIR. The work presented in this chapter is based on joint works with Amos Beimel, Yuval Ishai and Eyal Kushilevitz [BIKM99], and with Giovanni Di Crescenzo and Rafail Ostrovsky [DMO99] In Chapter 6 we introduce the model of SPIR, and prove our results for the information theoretic setting and for the computational setting. The work presented in this chapter is based on joint works with Yael Gertner, Yuval Ishai and ....

A. Beimel, Y. Ishai, E. Kushilevitz, and T. Malkin. One-way functions are essential for single-server private information retrieval. In Proc. of the 31th Annu. ACM Symp. on the Theory of Computing, pages 89-98, 1999.

....make the problem more concrete, the database is modeled as an n bit string x, and the user has some index i and is interested in privately retrieving the value of x i . Since its introduction, PIR has been an area of active research, and various settings and extensions have been considered (e.g. [2, 25, 10, 20, 18, 17, 14, 9, 8, 19, 15, 21, 1]) Most of the initial work on PIR has focused on the goal of minimizing the communication, which was considered the most expensive resource. However, despite considerable success in realizing this goal, the real life applicability of the proposed solutions remains questionable. One of the most ....

....constant 0, a single server protocol with communication complexity of O (n ) bits. Cachin, Micali, and Stadler [9] present a single server protocol with polylogarithmic communication complexity, based on a new number theoretic intractability assumption. Other works in this setting are [25, 24, 27, 8, 15, 21, 1]. The only previous work that has addressed the servers computation is that of Gertner, Goldwasser, and Malkin [17] see also [23] who present a model for PIR utilizing special purpose privacy servers, achieving stronger privacy guarantees and small computation for the original server holding ....

A. Beimel, Y. Ishai, E. Kushilevitz, and T. Malkin. One-way functions are essential for single-server private information retrieval. In 31th STOC, pages 89-98, 1999.

....stored in the server without revealing to the server which item is being retrieved. For concreteness, the database is viewed as an n bit string x and the entry to be retrieved is the i th bit of x. This problem was introduced by Chor et al. 9] and various aspects of it were further studied in [1, 8, 32, 27, 11, 15, 16, 28, 39, 12, 2, 7, 24, 30]. A naive solution for hiding which particular item is being retrieved (i.e. the index i) is to retrieve the entire database x. The communication complexity of this solution is n bits. Solutions that are more efficient than the naive one, in a setting where there are identical copies of the ....

.... private information retrieval On the lower bound front, in addition to the information theoretic lower bound [9] recent work has established that single server private information retrieval with less than n communication (even n Gamma 1 bits) already implies the existence of one way functions [2] and, more gener 1 In [8] it is shown, in the setting where there are several servers storing identical database x, that intractability assumptions might be of help in constructing efficient PIR protocols. 2 ally, the existence of Oblivious Transfer (OT) protocols [12] the connection between ....

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A. Beimel, Y. Ishai, E. Kushilevitz, and T. Malkin. One-way functions are essential for single-server private information retrieval. In Proc. of the 31th Annu. ACM Symp. on the Theory of Computing, 1999.

....the entire data string to the user (i.e. c(n) n) thus satisfying the PIR privacy requirement in the information theoretic sense. We call any PIR protocol with c(n) n non trivial. The problem of constructing non trivial PIR was originally introduced by Chor et al. 8] and further studied in [8, 1, 7, 33, 27, 29, 3, 12, 16, 15, 6, 23, 28]. In [8] this problem was studied in the setting of multiple non communicating copies of the database (further improvements were given in [1, 23] That is, 8] show that if there are at least two or more copies of the database, then non trivial PIR (for example, with two copies of the database, ....

....databases. 2 be at least poly logarithmic in n. Recently, 28] have shown a single database PIR based on any one way trapdoor permutation, though their communication, while less then n, is bigger than schemes based on specific number theoretic assumptions [27, 29, 37, 6] On the other hand, [3] have shown that any non trivial single database PIR implies the existence of a one way function. Oblivious Transfer. The Oblivious Transfer (OT) protocol was introduced by Rabin [35] one out of two Oblivious Transfer, denoted i 2 1 j OT , was introduced in [13] and one out of n Oblivious ....

[Article contains additional citation context not shown here]

A. Beimel, Y. Ishai, E. Kushilevitz, and T. Malkin. One-Way Functions are Essential for Single-Server Private Information Retrieval. In Proc. of 31st STOC, 1999.

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Amos Beimel, Yuval Ishai, Eyal Kushilevitz and Tal Malkin. One-Way Functions Are Essential for Single-Server Private Information Retrieval. STOC 1999: 89-98

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A. Beimel, Y. Ishai, E. Kushilevitz and T. Malkin. One-way functions are essential for single-server private information retrieval. In proceedings of STOC `99.

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A. Beimel, Y. Ishai, E. Kushilevitz, and T. Malkin. One-way functions are essential for singleserver private information retrieval. In Proc. of the 31th ACM Sym. on Theory of Computing, 1999.

No context found.

A. Beimel, Y. Ishai, E. Kushilevitz, and T. Malkin, One-Way Functions are essential for Single-Server Private Information Retrieval, Proc. of the 31st Annual ACM Symposium on Theory of Computing (STOC), pp. 89-98, 1999.

No context found.

A. Beimel, Y. Ishai, E. Kushilevitz, and T. Malkin. One-way functions are essential for singleserver private information retrieval. In Proc. of the 31th ACM Sym. on Theory of Computing, 1999.

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A. Beimel, Y. Ishai, E. Kushilevitz and T. Malki. One-way functions are essential for single-server private information retrieval. In Proceedings of the Thirty- rst Annual ACM Symposium on Theory of Computing, Atlanta, Georgia, USA, May 1-4, 1999.

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