The Oblivious Transfer Capacity of the Wiretapped Binary Erasure Channel

TL;DR

This paper determines the maximum rate of oblivious transfer over a broadcast binary erasure channel with an eavesdropper, considering different privacy collusion scenarios, advancing understanding of secure communication limits.

Contribution

It derives the oblivious transfer capacity for binary erasure channels under both 2-privacy and 1-privacy conditions, a novel theoretical result.

Findings

Oblivious transfer capacity is characterized for the given channel model.

Capacity differs under 2-privacy and 1-privacy scenarios.

Provides fundamental limits for secure communication over wiretapped channels.

Abstract

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).