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Sequences II pp 360-368 | Cite as

Efficient Reduction among Oblivious Transfer Protocols based on New Self-Intersecting Codes

  • Claude Crépeau
  • Miklós Sántha

Abstract

A 1 2 -OT2 (one-out-of-two Bit Oblivious Transfer) is a technique by which a party S owning two secret bits b 0, b 1, can transfer one of them b c to another party R, who chooses c. This is done in a way that does not release any bias about b c to R nor any bias about c to S. One interesting extension of this transfer is the 1 2 -OT 1 k (one-out-of-two String O.T.) in which the two secrets q 0, q 1 are elements of GF k (2) instead of bits. A reduction of 1 2 -OT 1 k to 1 2 -OT2 presented in [BCR86] uses O(k lo 2 3) calls to 1 2 -OT2 and thus raises an interesting combinatorial question: how many calls to 1 2 -OT2 are necessary and sufficient to achieve a 1 2 -OT 1 k ?

In the current paper we answer this question quite precisely. We accomplish this reduction using Θ(k) calls to 1 2 -OT2. First, we show by probabilistic methods how to obtain such a reduction with probability essentially 1 and second, we give a deterministic polynomial time construction based on the algebraic codes of Goppa [Gop81].

Keywords

Linear Code Oblivious Transfer Line Vector Modular Curf Goppa Code 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag New York, Inc. 1993

Authors and Affiliations

  • Claude Crépeau
    • 1
  • Miklós Sántha
    • 1
  1. 1.Laboratoire de Recherche en InformatiqueUniversité Paris-SudOrsayFrance

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