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In this paper, we study the problem of the 1-of-2 string oblivious transfer(OT) between Alice and Bob in the presence of a passive eavesdropper Eve. Theeavesdropper Eve is not allowed to get any information about the private dataof Alice or Bob. When Alice and Bob are honest-but-curious users, we propose aprotocol that satisfies $1$-private (neither Alice nor Bob colludes with Eve)OT requirements for the binary erasure symmetric broadcast channel, in whichthe channel provides dependent erasure patterns to Bob and Eve. We find thatwhen the erasure probabilities satisfy certain conditions, the derived lowerand upper bounds on the wiretapped OT capacity meet. Our results generalize andimprove upon the results on wiretapped OT capacity by Mishra et al. Finally, wepropose a protocol for a larger class of wiretapped channels and derive a lowerbound on the wiretapped OT capacity.

Capacity Results for the Wiretapped Oblivious Transfer