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

Covariance Zink 

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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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