Constant-Rate Oblivious Transfer from Noisy Channels

  • Yuval Ishai
  • Eyal Kushilevitz
  • Rafail Ostrovsky
  • Manoj Prabhakaran
  • Amit Sahai
  • Jürg Wullschleger
Conference paper

DOI: 10.1007/978-3-642-22792-9_38

Part of the Lecture Notes in Computer Science book series (LNCS, volume 6841)
Cite this paper as:
Ishai Y., Kushilevitz E., Ostrovsky R., Prabhakaran M., Sahai A., Wullschleger J. (2011) Constant-Rate Oblivious Transfer from Noisy Channels. In: Rogaway P. (eds) Advances in Cryptology – CRYPTO 2011. CRYPTO 2011. Lecture Notes in Computer Science, vol 6841. Springer, Berlin, Heidelberg

Abstract

A binary symmetric channel (BSC) is a noisy communication channel that flips each bit independently with some fixed error probability 0 < p < 1/2. Crépeau and Kilian (FOCS 1988) showed that oblivious transfer, and hence general secure two-party computation, can be unconditionally realized by communicating over a BSC. There has been a long line of works on improving the efficiency and generality of this construction. However, all known constructions that achieve security against malicious parties require the parties to communicate poly(k) bits over the channel for each instance of oblivious transfer (more precisely, \({2\choose 1}\)-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(spoly(k) complexity of previous constructions.

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Copyright information

© International Association for Cryptologic Research 2011

Authors and Affiliations

  • Yuval Ishai
    • 1
  • Eyal Kushilevitz
    • 1
  • Rafail Ostrovsky
    • 2
  • Manoj Prabhakaran
    • 3
  • Amit Sahai
    • 2
  • Jürg Wullschleger
    • 4
    • 5
  1. 1.TechnionHaifaIsrael
  2. 2.University of CaliforniaLos AngelesUSA
  3. 3.University of IllinoisUrbana-ChampaignUSA
  4. 4.Université of MontréalCanada
  5. 5.McGill UniversityCanada

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