Breaking the O(n/sup 1/(2k-1)/) barrier for information-theoretic Private Information Retrieval

Beimel, Amos; Ishai, Yuval; Kushilevitz, Eyal; Raymond, Jean-François

doi:10.1109/sfcs.2002.1181949

Cited by 167 publications

(228 citation statements)

References 16 publications

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“…But there are also other types of applications which seem to benefit from the use of replicated secret-sharing in different, and sometimes unexpected, ways. For instance, replicated shares yield the most efficient information-theoretic private information retrieval protocols and locally decodable codes [5], the best round complexity for verifiable secret-sharing [18], and the simplest protocols for secure multiparty computation with respect to generalized adversaries [3,25]. Our results on share conversion provide an explanation for the usefulness of the replicated scheme, suggesting that anything that can be achieved using linear secret-sharing can also be achieved (up to an n t overhead) using this specific scheme.…”

Section: Our Resultsmentioning

confidence: 99%

“…Our results on share conversion provide an explanation for the usefulness of the replicated scheme, suggesting that anything that can be achieved using linear secret-sharing can also be achieved (up to an n t overhead) using this specific scheme. This may also serve as a useful guideline for the design of cryptographic protocols (e.g., when attempting to improve [5]). …”

Section: Our Resultsmentioning

confidence: 99%

“…5 On the other hand, the pseudo-random function is used as a black-box and hence any pseudo-random function can be used. By Proposition 1, our solution is optimal among a class of generic schemes making a black-box use of a PRF.…”

Section: Lemmamentioning

confidence: 99%

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Share Conversion, Pseudorandom Secret-Sharing and Applications to Secure Computation

Cramer

Damgård

Ishai

2005

Lecture Notes in Computer Science

177

114

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Abstract. We present a method for converting shares of a secret into shares of the same secret in a different secret-sharing scheme using only local computation and no communication between players. In particular, shares in a replicated scheme based on a CNF representation of the access structure can be converted into shares from any linear scheme for the same structure. We show how this can be combined with any pseudorandom function to create, from initially distributed randomness, any number of Shamir secret-sharings of (pseudo)random values without communication. We apply this technique to obtain efficient non-interactive protocols for secure computation of low-degree polynomials, which in turn give rise to other applications in secure computation and threshold cryptography. For instance, we can make the Cramer-Shoup threshold cryptosystem by Canetti and Goldwasser fully non-interactive, or construct noninteractive threshold signature schemes secure without random oracles. The latter solutions are practical only for a relatively small number of players. However, in our main applications the number of players is typically small, and furthermore it can be argued that no solution that makes a black-box use of a pseudorandom function can be more efficient.

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Section: Our Resultsmentioning

confidence: 99%

Section: Our Resultsmentioning

confidence: 99%

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Share Conversion, Pseudorandom Secret-Sharing and Applications to Secure Computation

Cramer

Damgård

Ishai

2005

Lecture Notes in Computer Science

177

114

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“…All known PIR protocols realization can be divided into two classes: single-server protocols (see [2][3][4][5][6][7][8][9][10]) and multi-servers ones (see [11][12][13][14]). …”

Section: Existing Schemesmentioning

confidence: 99%

Сomputationally efficient private information retrieval protocol

Afanasyeva¹,

Bezzateev²

2016

Naučno-teh. vestn. inf. tehnol. meh. opt.

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“…The other direction focussed on constructing the locally decodable codes. Important constructions in this direction for constant query length appeared in [3,4]. Unfortunately, all these constructions yield codes that are exponentially long in k i .…”

Section: Introductionmentioning

confidence: 99%

Private Locally Decodable Codes

Ostrovsky

Pandey

Sahai

Automata, Languages and Programming

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We consider the problem of constructing efficient locally decodable codes in the presence of a computationally bounded adversary. Assuming the existence of one-way functions, we construct efficient locally decodable codes with positive information rate and low (almost optimal) query complexity which can correctly decode any given bit of the message from constant channel error rate ρ. This compares favorably to our state of knowledge locally-decodable codes without cryptographic assumptions. For all our constructions, the probability for any polynomial-time adversary, that the decoding algorithm incorrectly decodes any bit of the message is negligible in the security parameter.

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Breaking the O(n/sup 1/(2k-1)/) barrier for information-theoretic Private Information Retrieval

Cited by 167 publications

References 16 publications

Share Conversion, Pseudorandom Secret-Sharing and Applications to Secure Computation

Share Conversion, Pseudorandom Secret-Sharing and Applications to Secure Computation

Сomputationally efficient private information retrieval protocol

Private Locally Decodable Codes

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