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Oblivious transfers and intersecting codes

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3 Author(s)
Brassard, G. ; Dept. d''Inf. et de Recherche Oper., Montreal Univ., Que., Canada ; Crepeau, C. ; Santha, M.

Assume A owns t secret k-bit strings. She is willing to disclose one of them to B, at his choosing, provided he does not learn anything about the other strings. Conversely, B does not want A to learn which secret he chose to learn. A protocol for the above task is said to implement one-out-of-t string oblivious transfer, denoted (t 1)-OTk2. This primitive is particularly useful in a variety of cryptographic settings. An apparently simpler task corresponds to the case k=1 and t=2 of two 1-bit secrets: this is known as one-out-of-two bit oblivious transfer, denoted (2 1)-OT2. We address the question of implementing ( t1)-OTk2 assuming the existence of a (21)-OT2. In particular, we prove that unconditionally secure (21)-OTk 2 can be implemented from Θ(k) calls to (2 1)-OT2. This is optimal up to a small multiplicative constant. Our solution is based on the notion of self-intersecting codes. Of independent interest, we give several efficient new constructions for such codes. Another contribution of this paper is a set of information-theoretic definitions for correctness and privacy of unconditionally secure oblivious transfer

Published in:

Information Theory, IEEE Transactions on  (Volume:42 ,  Issue: 6 )

Date of Publication:

Nov 1996

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