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Proceedings on Privacy Enhancing Technologies

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Optimal Rate Private Information Retrieval from Homomorphic Encryption

Aggelos Kiayias
  • National and Kapodistrian University of Athens, Greece
/ Nikos Leonardos
  • Université Paris Diderot – Paris 7, France
/ Helger Lipmaa
  • University of Tartu, Estonia
/ Kateryna Pavlyk
  • University of Tartu, Estonia
/ Qiang Tang
  • University of Connecticut, USA
Published Online: 2015-06-22 | DOI: https://doi.org/10.1515/popets-2015-0016

Abstract

We consider the problem of minimizing the communication in single-database private information retrieval protocols in the case where the length of the data to be transmitted is large. We present first rate-optimal protocols for 1-out-of-n computationallyprivate information retrieval (CPIR), oblivious transfer (OT), and strong conditional oblivious transfer (SCOT). These protocols are based on a new optimalrate leveled homomorphic encryption scheme for large-output polynomial-size branching programs, that might be of independent interest. The analysis of the new scheme is intricate: the optimal rate is achieved if a certain parameter s is set equal to the only positive root of a degree-(m + 1) polynomial, where m is the length of the branching program. We show, by using Galois theory, that even when m = 4, this polynomial cannot be solved in radicals. We employ the Newton-Puiseux algorithm to find a Puiseux series for s, and based on this, propose a Θ (logm)-time algorithm to find an integer approximation to s.

Keywords: Branching programs; CPIR; Galois theory; homomorphic encryption; OT; Puiseux series; SCOT

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Received: 2015-02-15

Revised: 2015-05-15

Accepted: 2015-05-15

Published Online: 2015-06-22

Published in Print: 2015-06-01


Citation Information: Proceedings on Privacy Enhancing Technologies. Volume 2015, Issue 2, Pages 222–243, ISSN (Online) 2299-0984, DOI: https://doi.org/10.1515/popets-2015-0016, June 2015

© Aggelos Kiayias et al.. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. (CC BY-NC-ND 3.0)

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