  In this work we analyze a measurement-device-independent (MDI) protocol to
establish continuous-variable (CV) quantum key distribution (QKD) between two
ground stations. We assume communication occurs between the ground stations via
satellite over two independent atmospheric-fading channels dominated by
turbulence-induced beam wander. In this MDI protocol the measurement device is
the satellite itself, and the security of the protocol is analyzed through an
equivalent entanglement-based swapping scheme. We quantify the positive impact
the fading channels can have on the final quantum key rates, demonstrating how
the protocol is able to generate a positive key rate even over high-loss
atmospheric channels. This is somewhat counter-intuitive given that the same
outcome is only possible in the low-loss regime for a measurement device
centrally positioned in a fiber-optic channel. Our results show that useful
space-based quantum key generation rates between two ground stations are
possible even when the relay satellite is held by an adversary. The cost in key
rate incurred by altering the status of the satellite from trustworthy to
untrustworthy is presented.
