Abstract
Useful quantum-key supply from intermittent satellite contacts depends on finite-block security, authentication, relay inventories, and application demand, not optical transmittance alone. We simulate a trusted high-altitude-platform (HAP) relay between a ground station and a 500 km low-Earth-orbit satellite using three-intensity decoy-state BB84, finite-key estimation, authenticated key inventories, and a 200-pass service model. The comparator is the satellite-to-ground (S→G) downlink; a groundto-satellite uplink is not simulated, so the margins apply only to this downlink. With a 0.20 m HAP receive radius, the relay yields 13.175 Mbit/pass, 15.65% of the 84.185 Mbit/pass direct yield. With a 0.50 m HAP radius, the relay yield rises to 116.981 Mbit/pass, 38.77% above the 84.298 Mbit/pass direct yield. The unchanged direct-link estimates vary by under 0.2% from independent Monte Carlo sampling. The advantage remains 29.57% under a common contact window and 28.42% with equal elevation masks. Protocol tuning raises the 0.20 m relay yield by 36.74% without closing its gap to the direct link. For workloads derived from the 0.20 m relay supply, a 30 Mbit buffer produced no starved schedules for the 0.50 m relay in 10,000 simulations per demand. Receive-aperture collection is the main modeled condition for relay advantage under the stated assumptions.