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Wiretapped Oblivious Transfer

Abstract

In this paper, we study the problem of obtaining 11-of-22 string oblivious transfer (OT) between users Alice and Bob, in the presence of a passive eavesdropper Eve. The resource enabling OT in our setup is a noisy broadcast channel from Alice to Bob and Eve. Apart from the OT requirements between the users, Eve is not allowed to learn anything about the users' inputs. When Alice and Bob are honest-but-curious and the noisy broadcast channel is made up of two independent binary erasure channels (connecting Alice-Bob and Alice-Eve), we derive the 11-of-22 string OT capacity for both 22-privacy (when Eve can collude with either Alice or Bob) and 11-privacy (when no such collusion is allowed). We generalize these capacity results to 11-of-NN string OT and study other variants of this problem. When Alice and/or Bob are malicious, we present a different scheme based on interactive hashing. This scheme is shown to be optimal for certain parameter regimes. We present a new formulation of multiple, simultaneous OTs between Alice-Bob and Alice-Cathy. For this new setup, we present schemes and outer bounds that match in all but one regime of parameters. Finally, we consider the setup where the broadcast channel is made up of a cascade of two independent binary erasure channels (connecting Alice-Bob and Bob-Eve) and 11-of-22 string OT is desired between Alice and Bob with 11-privacy. For this setup, we derive an upper and lower bound on the 11-of-22 string OT capacity which match in one of two possible parameter regimes.

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