Resource Allocation in a Quantum Key Distribution Network with LEO and GEO trusted-repeaters

Quantum Key Distribution~(QKD) is a technology that enables the exchange of private encryption keys between two legitimate parties, using protocols that involve quantum mechanics principles. The rate at which secret keys can be exchanged depends on the attenuation that is experienced. Therefore, it is more convenient to replace many terrestrial fiber segments (and repeaters) by just few optical satellite links that would enable flexible global coverage. Then, the satellite nodes can take the role of trusted-relays, forwarding the secret keys from source to destination. However, since the rate at which secret keys can be generated in each quantum link is limited, it is very important to select the intermediate satellite nodes to inter-connect ground stations efficiently. This paper studies the most convenient allocation of resources in a QKD network that combines complementary connectivity services of GEO and LEO satellites. The aim of the centralized routing algorithm is to select the most convenient trusted-relays to forward the secret keys between pairs of ground stations, verifying the constraints that satellite-to-ground and inter-satellite quantum channels have.