Wiretapped Commitment over Binary Channels

TL;DR

This paper introduces the concept of wiretapped commitment over noisy channels, analyzing the maximum secure commitment rate in the presence of an eavesdropper with different collusion scenarios.

Contribution

It defines the wiretapped commitment capacity and explores its limits under various collusion assumptions between the eavesdropper and parties.

Findings

Capacity results for 1-private regime

Capacity results for 2-private regime

Impact of collusion on security

Abstract

We propose the problem of wiretapped commitment, where two parties, say committer Alice and receiver Bob, engage in a commitment protocol using a noisy channel as a resource, in the presence of an eavesdropper, say Eve. Noisy versions of Alice's transmission over the wiretap channel are received at both Bob and Eve. We seek to determine the maximum commitment throughput in the presence of an eavesdropper, i.e., wiretapped commitment capacity, where in addition to the standard security requirements for two-party commitment, one seeks to ensure that Eve doesn't learn about the commit string. A key interest in this work is to explore the effect of collusion (or lack of it) between the eavesdropper Eve and either Alice or Bob. Toward the same, we present results on the wiretapped commitment capacity under the so-called 1-private regime (when Alice or Bob cannot collude with Eve) and the 2-private regime (when Alice or Bob may possibly collude with Eve).