Topology-Oblivious Random-Walk Key Relaying in Quantum Key Distribution Networks

Quantum key distribution (QKD) networks require relaying when distant key management entities share no direct quantum link. Most relay strategies, however, rely on centralized control or globally maintained routing state. This paper asks whether useful security and efficiency can still be obtained with topology-oblivious stochastic forwarding. It studies the security-overhead trade-off in a model in which fragmented key material is relayed via random-walk variants and reconstructed under privacy amplification. Under a restricted model with at most one compromised relay, the analysis asks whether strictly local forwarding can retain useful information-theoretic security. Evaluation on the GÉANT topology, representing a European academic backbone network, shows clear differences between random-walk variants. The proposed highest-score-neighbor local path-diversification heuristic reduces the risk that relayed key material passes through a compromised node. The evaluation also shows that a preliminary loop-erasure step significantly shortens sampled routes and improves throughput in the model. These findings position topology-oblivious stochastic forwarding as a decentralized alternative to global-state maintenance or centralized orchestration in QKD networks.