Stealthy secret key generation

In this work, we aim to design a stealthy secret key generation (SSKG) scheme for a completely concealed communication system. More specifically, the data transmission is accomplished by covert communications, which requires additional keys to guarantee the covertness when Bob's channel quality is worse than a warden Willie's in a special definition. However, normal SKG schemes may raise Willie's attention and violate the design goal. Therefore, we resort to the SSKG. 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 stealthy SKG capacity for free when the common randomness observed at each node forms a Markov chain. We then prove that the sufficient condition to attain the SK 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 the fast fading Gaussian Maurer's (satellite) model for the source of common randomness.