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Journal of Cryptology

, Volume 28, Issue 1, pp 161–175 | Cite as

Quantum Private Information Retrieval has Linear Communication Complexity

  • Ämin Baumeler
  • Anne Broadbent
Article

Abstract

In private information retrieval (PIR), a client queries an \(n\)-bit database in order to retrieve an entry of her choice, while maintaining privacy of her query value. Chor et al. [J ACM 45(6):965–981, 1998] showed that, in the information-theoretical setting, a linear amount of communication is required for classical PIR protocols (thus the trivial protocol is optimal). This linear lower bound was shown by Nayak [FOCS 1999, pp. 369–376, 1999] to hold also in the quantum setting. Here, we extend Nayak’s result by considering approximate privacy, and requiring security only against specious adversaries, which are, in analogy to classical honest-but-curious adversaries, the weakest reasonable quantum adversaries. We show that, even in this weakened scenario, quantum private information retrieval (QPIR) requires \(n\) qubits of communication. From this follows that Le Gall’s recent QPIR protocol with sublinear communication complexity [Theory Comput. 8(1):369–374, 2012] is not information-theoretically private, against the weakest reasonable cryptographic adversary.

Keywords

Private information retrieval Quantum cryptography  Specious adversaries Quantum semi-honest 

Notes

Acknowledgments

We are grateful to Gus Gutoski, Robert König, and Ashwin Nayak for helpful discussions, and to the anonymous referees for helpful comments. Furthermore, we thank Sébastien Gambs for introducing us to PIR. Ä. B. thanks the Institute for Quantum Computing (IQC) and the University of Waterloo for hosting him for a six-month visit, during which these results were established. This work was performed, while A. B. was at the Department of Combinatorics and Optimization, and at the Institute for Quantum Computing (IQC), University of Waterloo. This work was supported by the Canadian Institute for Advanced Research (CIFAR), NSERC Frequency and Industry Canada.

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Copyright information

© International Association for Cryptologic Research 2014

Authors and Affiliations

  1. 1.Faculty of InformaticsUniversità della Svizzera italianaLuganoSwitzerland
  2. 2.Department of Mathematics and StatisticsUniversity of OttawaOttawaCanada

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