Communication-efficient distributed oblivious transfer

  • Authors:
  • Amos Beimel;Yeow Meng Chee;Huaxiong Wang;Liang Feng Zhang

  • Affiliations:
  • Department of Computer Science, Ben-Gurion University of the Negev, Beer Sheva, Israel;Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore;Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore;Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore

  • Venue:
  • Journal of Computer and System Sciences
  • Year:
  • 2012

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Abstract

Distributed oblivious transfer (DOT) was introduced by Naor and Pinkas (2000) [31], and then generalized to (k,@?)-DOT-(n1) by Blundo et al. (2007) [8] and Nikov et al. (2002) [34]. In the generalized setting, a (k,@?)-DOT-(n1) allows a sender to communicate one of n secrets to a receiver with the help of @? servers. Specifically, the transfer task of the sender is distributed among @? servers and the receiver interacts with k out of the @? servers in order to retrieve the secret he is interested in. The DOT protocols we consider in this work are information-theoretically secure. The known (k,@?)-DOT-(n1) protocols require linear (in n) communication complexity between the receiver and servers. In this paper, we construct (k,@?)-DOT-(n1) protocols which only require sublinear (in n) communication complexity between the receiver and servers. Our constructions are based on information-theoretic private information retrieval. In particular, we obtain both a specific reduction from (k,@?)-DOT-(n1) to polynomial interpolation-based information-theoretic private information retrieval and a general reduction from (k,@?)-DOT-(n1) to any information-theoretic private information retrieval. The specific reduction yields (t,@t)-private (k,@?)-DOT-(n1) protocols of communication complexity O(n^1^/^@?^(^k^-^@t^-^1^)^/^t^@?) between a semi-honest receiver and servers for any integers t and @t such that 1=