# 2-Server PIR with Sub-Polynomial Communication

@article{Dvir20142ServerPW,
title={2-Server PIR with Sub-Polynomial Communication},
author={Zeev Dvir and Sivakanth Gopi},
journal={Proceedings of the forty-seventh annual ACM symposium on Theory of Computing},
year={2014}
}
• Published 24 July 2014
• Computer Science, Mathematics
• Proceedings of the forty-seventh annual ACM symposium on Theory of Computing
A 2-server Private Information Retrieval (PIR) scheme allows a user to retrieve the ith bit of an n-bit database replicated among two non-communicating servers, while not revealing any information about i to either server. In this work we construct a 2-server PIR scheme with total communication cost nO√(log log n)/(log n). This improves over current 2-server protocols which all require Ω(n1/3) communication. Our construction circumvents the n1/3 barrier of Razborov and Yekhanin which holds for…
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## References

SHOWING 1-10 OF 36 REFERENCES
An Ω ( n 1 / 3 ) Lower Bound for Bilinear Group Based Private Information Retrieval
• Computer Science
• 2006
The tremendous gap between upper and lower bounds is the focus of this paper, and an Ω(n) lower bound is shown in a restricted model that nevertheless captures all known upper bound techniques of bilinear group based PIR schemes.
An Ω(n) Lower Bound for Bilinear Group Based Private Information Retrieval
• Computer Science
• 2008
The tremendous gap between upper and lower bounds is the focus of this paper, and an Ω(n1/3) lower bound is shown in a restricted model that nevertheless captures all known upper bound techniques.
An \Omega(n^1/3 ) Lower Bound for Bilinear Group Based Private Information Retrieval
• Computer Science
2006 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS'06)
• 2006
The tremendous gap between upper and lower bounds is shown in a restricted model that nevertheless captures all known upper bound techniques and an Omega(n1/3) lower bound applies to bilinear group based PIR schemes.
Breaking the O(n/sup 1/(2k-1)/) barrier for information-theoretic Private Information Retrieval
• Computer Science
The 43rd Annual IEEE Symposium on Foundations of Computer Science, 2002. Proceedings.
• 2002
The complexity of information-theoretic k-server PIR is improved to n/sup O(log log k/k log k)/, and the PIR protocols are more efficient than previous ones for every k/spl ges/3, and the locally decodable codes are shorter for everyk/splges/4.
A geometric approach to information-theoretic private information retrieval
• Computer Science
20th Annual IEEE Conference on Computational Complexity (CCC'05)
• 2005
A new geometric approach to PIR is presented, and a t-private k-server protocol is obtained with communication O((k/sup 2//t) log k n/sup 1//spl lfloor//(2k - 1)/spl rfloor/) removing the (t) term of previous schemes.
Information-Theoretic Private Information Retrieval: A Unified Construction
• Computer Science, Mathematics
ICALP
• 2001
A unified general construction of Private Information Retrieval protocols, whose abstract components can be instantiated to yield both old and new families of PIR protocols, and a main ingredient in the new protocols is a generalization of a solution by Babai, Kimmel, and Lokam to a communication complexity problem in the so-called simultaneous messages model.
A Survey of Single Database PIR: Techniques and Applications
• Computer Science, Mathematics
IACR Cryptol. ePrint Arch.
• 2007
This survey gives an overview of many of the constructions for Single-Database PIR (including an abstract construction based upon homomorphic encryption) and describes some of the connections of PIR to other primitives.
3-query locally decodable codes of subexponential length
This paper gives the first unconditional constant query LDC construction with subexponantial codeword length, which could be extended to higher number of queries.
Private information retrieval
• Computer Science
JACM
• 1998
This work describes schemes that enable a user to access k replicated copies of a database and privately retrieve information stored in the database, so that each individual server gets no information on the identity of the item retrieved by the user.
Query-Efficient Locally Decodable Codes of Subexponential Length
• Computer Science
computational complexity
• 2011
The algebraic theory behind the constructions of Yekhanin and Efremenko is developed, in an attempt to understand the “algebraic niceness” phenomenon in super-polynomial size set-systems with restricted intersections.