Constant-rate oblivious transfer from noisy channels

  • Authors:
  • Yuval Ishai;Eyal Kushilevitz;Rafail Ostrovsky;Manoj Prabhakaran;Amit Sahai;Jürg Wullschleger

  • Affiliations:
  • Technion, Haifa, Israel;Technion, Haifa, Israel;University of California, Los Angeles;University of Illinois, Urbana-Champaign;University of California, Los Angeles;Université of Montréal and McGill University

  • Venue:
  • CRYPTO'11 Proceedings of the 31st annual conference on Advances in cryptology
  • Year:
  • 2011

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Abstract

A binary symmetric channel (BSC) is a noisy communication channel that flips each bit independently with some fixed error probability 0 poly(k) bits over the channel for each instance of oblivious transfer (more precisely, (2/1)- bit-OT) being realized, where k is a statistical security parameter. The question of achieving a constant (positive) rate was left open, even in the easier case of realizing a single oblivious transfer of a long string. We settle this question in the affirmative by showing how to realize n independent instances of oblivious transfer, with statistical error that vanishes with n, by communicating just O(n) bits over a BSC. As a corollary, any boolean circuit of size s can be securely evaluated by two parties with O(s)+poly(k) bits of communication over a BSC, improving over the O(s) ċ poly(k) complexity of previous constructions.