Paper 2015/1061

On Basing Private Information Retrieval on NP-Hardness

Tianren Liu and Vinod Vaikuntanathan


The possibility of basing the security of cryptographic objects on the (minimal) assumption that $\comp{NP} \nsubseteq \comp{BPP}$ is at the very heart of complexity-theoretic cryptography. Most known results along these lines are negative, showing that assuming widely believed complexity-theoretic conjectures, there are no reductions from an $\comp{NP}$-hard problem to the task of breaking certain cryptographic schemes. We make progress along this line of inquiry by showing that the security of single-server single-round private information retrieval schemes cannot be based on $\comp{NP}$-hardness, unless the polynomial hierarchy collapses. Our main technical contribution is in showing how to break the security of a PIR protocol given an $\comp{SZK}$ oracle. Our result is tight in terms of both the correctness and the privacy parameter of the PIR scheme.

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Publication info
Published by the IACR in TCC 2016
Private Information RetrievalNP-hardnessReductions
Contact author(s)
vinodv @ mit edu
liutr @ mit edu
2015-11-03: last of 2 revisions
2015-10-30: received
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      author = {Tianren Liu and Vinod Vaikuntanathan},
      title = {On Basing Private Information Retrieval on NP-Hardness},
      howpublished = {Cryptology ePrint Archive, Paper 2015/1061},
      year = {2015},
      note = {\url{}},
      url = {}
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