Generalized oblivious transfer by secret sharing

The notion of Generalized Oblivious Transfer (GOT) was introduced by Ishai and Kushilevitz (Proceeding of ISTCS97, IEEE Computer Society, pp 174-184, 1997). In a GOT protocol, Alice holds a set U of messages. A decreasing monotone collection of subsets of U defines the retrieval restrictions. Bob is allowed to learn any permissable subset of messages from that collection, but nothing else, while Alice must remain oblivious regarding the selection that Bob made. We propose a simple and efficient GOT protocol that employs secret sharing. We compare it to another secret sharing based solution for that problem that was recently proposed in Shankar et al. (Proceeding of ICDCN08, LNCS 4904, pp 304-309, 2008). In particular, we show that the access structures that are realized by the two solutions are related through a duality-type relation that we introduce here. We show that there are examples which favor our solution over the second one, while in other examples the contrary holds. Two applications of GOT are considered-priced oblivious transfer, and oblivious evaluation of multivariate polynomials.