Key and Message Semantic-Security over State-Dependent Channels

TL;DR

This paper investigates the optimal trade-off between secret message and key rates over state-dependent wiretap channels with non-causal channel state information, introducing a new capacity region that improves upon previous bounds.

Contribution

It derives a new inner bound on the semantic-security capacity region for SD-WTCs with non-causal CSI, using superposition coding and strong soft-covering lemmas, surpassing prior results.

Findings

The new region attains capacity for certain SD-WTC classes.

It improves upon previous SM-SK trade-off bounds.

The region is strictly larger than earlier known bounds.

Abstract

We study the trade-off between secret message (SM) and secret key (SK) rates, simultaneously achievable over a state-dependent (SD) wiretap channel (WTC) with non-causal channel state information (CSI) at the encoder. This model subsumes other instances of CSI availability as special cases, and calls for efficient utilization of the state sequence for both reliability and security purposes. An inner bound on the semantic-security (SS) SM-SK capacity region is derived based on a superposition coding scheme inspired by a past work of the authors. The region is shown to attain capacity for a certain class of SD-WTCs. SS is established by virtue of two versions of the strong soft-covering lemma. The derived region yields an improvement upon the previously best known SM-SK trade-off result reported by Prabhakaran et al., and, to the best of our knowledge, upon all other existing lower bounds for either SM or SK for this setup, even if the semantic security requirement is relaxed to weak secrecy. It is demonstrated that our region can be strictly larger than those reported in the preceding works.