Stealthy keyless secret key generation from degraded sources

To conceal the behavior of communications, we may adopt covert or stealthy communications under different scenarios and demands. However, when legitimate users have worse channels than the eavesdropper, the legitimate users may need additional keys to attain the concealment. Normal secret key generation (SKG) schemes may raise Willie's attention due to the public discussion breaking the concealment. Therefore, in this work, we investigate how to conceal the SKG itself, especially according to the stealth constraint. We prove that if the virtual channel between the common random source observed by the legitimate Alice and Bob, namely, X and Y, respectively, is more capable than that between Bob and Willie (the warden), namely, Y and Z, respectively, the same stealthy SK rate as in the case without stealth constraint can be achieved. Furthermore, if (X, Y, Z) form a Markov chain, then the key capacity of the SKG with the stealth constraint can be achieved for free.