Geodesic
On Distributed Oblivious Transfer
Serdica Journal of Computing, Tome 1 (2007) no. 3, pp. 313-336.

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This paper is about unconditionally secure distributed protocols for oblivious transfer, as proposed by Naor and Pinkas and generalized by Blundo et al. In this setting a Sender has ζ secrets and a Receiver is interested in one of them. The Sender distributes the information about the secrets to n servers, and a Receiver must contact a threshold of the servers in order to compute the secret. We present a non-existence result and a lower bound for the existence of one-round, threshold, distributed oblivious transfer protocols, generalizing the results of Blundo et al. A threshold based construction implementing 1-out-of-ζ distributed oblivious transfer achieving this lower bound is described. A condition for existence of distributed oblivious transfer schemes based on general access structures is proven. We also present a general access structure protocol implementing 1-out-of-ζ distributed oblivious transfer.
Keywords: Cryptographic Protocols, Oblivious Transfer 
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Nikov, Ventzislav; Nikova, Svetla; Preneel, Bart. On Distributed Oblivious Transfer. Serdica Journal of Computing, Tome 1 (2007) no. 3, pp. 313-336. http://geodesic.mathdoc.fr/item/SJC_2007_1_3_a6/