Geometric Spread Routing for Security-Oriented Communication in Mega LEO Constellations

Predictable relay reuse in regular inter-satellite-link meshes can expose repeated low Earth orbit communications to traffic-aware observation even when payloads are encrypted. This paper formulates a bounded relay-observation model and introduces Geometric Path Entropy (GPE), which jointly measures path-use uncertainty and probability-weighted geometric separation. We then design Geometric Spread Routing (GSR), which performs combinadic path selection offline and provides O(1) next-hop lookup within each topology epoch. Across 31 physically filtered snapshots and 12 stratified geographic demands, GSR increases GPE by 103%, reduces shared-link overlap by 53%, and raises the greedy full-coverage relay cost by 25% relative to the strongest baselines on common-routable cases. Under cumulative adaptive observation, it increases the 90-min full-coverage cost by 21.9%. On seven literature-aligned three-ISL graphs, the topology-aware variant improves normalized GPE by 12.8% and reduces overlap by 27.8% on average. Hardware-in-the-loop evaluation confirms forwarding consistency and low per-hop latency. These results validate GSR's resistance to bounded traffic-aware relay coverage across feasible topology epochs and routing demands.