# Stealthy Secret Key Generation

## TL;DR

This paper analyzes the capacity of stealthy secret key generation (SSKG) in covert communication systems, showing that stealth constraints do not reduce capacity under certain Markov conditions and providing practical conditions for achieving these bounds.

## Contribution

It demonstrates that SSKG capacity bounds are unaffected by stealth constraints and relaxes conditions for attaining capacity, with practical implications for Gaussian satellite models.

## Key findings

- SSKG capacity bounds are unaffected by stealth constraints.
- Capacity can be achieved under Markov chain conditions.
- Practical conditions for Gaussian satellite models are derived.

## Abstract

In this work, we consider a complete covert communication system, which includes the source-model of a stealthy secret key generation (SSKG) as the first phase. The generated key will be used for the covert communication in the second phase of the current round and also in the first phase of the next round. We investigate the stealthy SK rate performance of the first phase. The derived results show that the SK capacity lower and upper bounds of the source-model SKG are not affected by the additional stealth constraint. This result implies that we can attain the SSKG capacity for free when the sequences observed by the three terminals Alice ($X^n$), Bob ($Y^n$) and Willie ($Z^n$) follow a Markov chain relationship, i.e., $X^n-Y^n-Z^n$. We then prove that the sufficient condition to attain both, the SK capacity as well as the SSK capacity, can be relaxed from physical to stochastic degradedness. In order to underline the practical relevance, we also derive a sufficient condition to attain the degradedness by the usual stochastic order for Maurer's fast fading Gaussian (satellite) model for the source of common randomness.