Generalized Oblivious Transfer
k-n Oblivious transfer is a special case of Generalized oblivious transfer, which was presented by Ishai and Kushilevitz7. In that setting, the sender has a set U of n messages, and the transfer constraints are specified by a collection A of permissible subsets of U. The receiver may obtain any subset of the messages in U that appears in the collection A. The sender should remain oblivious of the selection made by the receiver, while the receiver cannot learn the value of the messages outside the subset of messages that he chose to obtain. The collection A is monotone decreasing, in the sense that it is closed under containment (i.e., if a given subset B is in the collection A, so are all of the subsets of B). The solution proposed by Ishai and Kushilevitz uses parallel invocations of 1-2 oblivious transfer while making use of a special model of private protocols. Later on, other solutions that are based on secret sharing were published --- one by Bhavani Shankar, Kannan Srinathan, and C. Pandu Rangan8, and another by Tamir Tassa9.
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