On Distributed Oblivious Transfer

The paper has been presented at the International Conference Pioneers of Bulgarian Mathematics, Dedicated to Nikola Obreshkoff and Lubomir Tschakaloff , Sofia, July, 2006. The material in this paper was presented in part at INDOCRYPT 2002

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.