The Oblivious Transfer Capacity of the Wiretapped Binary Erasure Channel

We consider oblivious transfer between Alice and Bob in the presence of an eavesdropper Eve when there is a broadcast channel from Alice to Bob and Eve. In addition to the secrecy constraints of Alice and Bob, Eve should not learn the private data of Alice and Bob. When the broadcast channel consists of two independent binary erasure channels, we derive the oblivious transfer capacity for both 2-privacy (where the eavesdropper may collude with either party) and 1-privacy (where there are no collusions).Comment: This is an extended version of the paper "The Oblivious Transfer Capacity of the Wiretapped Binary Erasure Channel" to be presented at ISIT 201

On the Oblivious Transfer Capacity of the Degraded Wiretapped Binary Erasure Channel

We study oblivious transfer (OT) between Alice and Bob in the presence of an eavesdropper Eve over a degraded wiretapped binary erasure channel from Alice to Bob and Eve. In addition to the privacy goals of oblivious transfer between Alice and Bob, we require privacy of Alice and Bob's private data from Eve. In previous work we derived the OT capacity (in the honest-but-curious model) of the wiretapped binary independent erasure channel where the erasure processes of Bob and Eve are independent. Here we derive a lower bound on the OT capacity in the same secrecy model when the wiretapped binary erasure channel is degraded in favour of Bob.Comment: To be presented at the IEEE International Symposium on Information Theory (ISIT 2015), Hong Kon