Secrecy via Sources and Channels

TL;DR

This paper explores the fundamental trade-offs in secret communication and key generation using correlated sources and noisy channels, providing optimal solutions under certain degradation conditions and evaluating the Gaussian case.

Contribution

It introduces an achievable scheme for secret communication and key generation, proving its optimality in degraded parallel channels and sources, including Gaussian scenarios.

Findings

Optimal secrecy region characterized for degraded channels and sources

Achievable scheme proven to be optimal in specific cases

Secrecy trade-offs analyzed for Gaussian sources and channels

Abstract

Alice and Bob want to share a secret key and to communicate an independent message, both of which they desire to be kept secret from an eavesdropper Eve. We study this problem of secret communication and secret key generation when two resources are available -- correlated sources at Alice, Bob, and Eve, and a noisy broadcast channel from Alice to Bob and Eve which is independent of the sources. We are interested in characterizing the fundamental trade-off between the rates of the secret message and secret key. We present an achievable solution and prove its optimality for the parallel channels and sources case when each sub-channel and source component satisfies a degradation order (either in favor of the legitimate receiver or the eavesdropper). This includes the case of jointly Gaussian sources and an additive Gaussian channel, for which the secrecy region is evaluated.