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## Breaking the O(n<sup>1/(2k-1)</sup>) Barrier for Information-Theoretic Private Information Retrieval

Vancouver, BC, Canada

Nov. 16, 2002 to Nov. 19, 2002

ISBN: 0-7695-1822-2

pp: 261

Amos Beimel , Ben-Gurion University

Yuval Ishai , Technion

Eyal Kushilevitz , Technion

Jean-François Raymond , McGill University

ABSTRACT

<p>Private Information Retrieval (PIR) protocols allow a user to retrieve a data item from a database while hiding the identity of the item being retrieved. Specifically, in information-theoretic, k-server PIR protocols the database is replicated among k servers, and each server learns nothing about the item the user retrieves. The cost of such protocols is measured by the communication complexity of retrieving one out of n bits of data. For any fixed k, the complexity of the best protocols prior to our work was 0(n^{\frac{1}{{2k - 1}}}) (Ambainis, 1997). Since then several methods were developed in an attempt to beat this bound, but all these methods yielded the same asymptotic bound.</p> <p>In this work, this barrier is finally broken and the complexity of information-theoretic k-server PIR is improved to n^{0(\frac{{\log \log k}}{{k\log k}})}. The new PIR protocols can also be used to construct k-query binary locally decodable codes of length exp (n^{0(\frac{{\log \log k}}{{k\log k}})}), compared to exp (n^{\frac{1}{{k - 1}}}) in previous constructions. The improvements presented in this paper apply even for small values of k: the PIR protocols are more efficient than previous ones for every k \geqslant 3, and the locally decodable codes are shorter for every k \geqslant 4.</p>

INDEX TERMS

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CITATION

Amos Beimel,
Yuval Ishai,
Eyal Kushilevitz,
Jean-François Raymond,
"Breaking the O(n<sup>1/(2k-1)</sup>) Barrier for Information-Theoretic Private Information Retrieval",

*FOCS*, 2002, 2013 IEEE 54th Annual Symposium on Foundations of Computer Science, 2013 IEEE 54th Annual Symposium on Foundations of Computer Science 2002, pp. 261, doi:10.1109/SFCS.2002.1181949