Polylogarithmic private approximations and efficient matching

  • Authors:
  • Piotr Indyk;David Woodruff

  • Affiliations:
  • MIT CSAIL;MIT CSAIL

  • Venue:
  • TCC'06 Proceedings of the Third conference on Theory of Cryptography
  • Year:
  • 2006

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Abstract

In [12] a private approximation of a function f is defined to be another function F that approximates f in the usual sense, but does not reveal any information about x other than what can be deduced from f(x). We give the first two-party private approximation of the l2 distance with polylogarithmic communication. This, in particular, resolves the main open question of [12]. We then look at the private near neighbor problem in which Alice has a query point in {0,1}d and Bob a set of n points in {0,1}d, and Alice should privately learn the point closest to her query. We improve upon existing protocols, resolving open questions of [13,10]. Then, we relax the problem by defining the private approximate near neighbor problem, which requires introducing a notion of secure computation of approximations for functions that return sets of points rather than values. For this problem we give several protocols with sublinear communication.