Post-quantum soundness for topology-hiding connectivity assurance

Develop a variant of the multigraph-based, topology-hiding connectivity-assurance protocol for QKD inter-networking that achieves post-quantum soundness while preserving statistical privacy of the zero-knowledge connectivity proofs. Specifically, replace the current reliance on number-theoretic assumptions (such as SDH/q-SDH-based graph signatures) with post-quantum-secure primitives and prove soundness without degrading the privacy guarantees for hidden endpoints and padded path lengths.

Background

The paper presents a topology-hiding connectivity-assurance protocol for QKD inter-networking that extends graph-signature techniques to multigraphs and supports hidden endpoints. The construction enables zero-knowledge proofs of path existence while concealing topology details such as internal hops and boundary nodes.

The current realization relies on number-theoretic assumptions (e.g., SDH/q-SDH-based signatures) for soundness. The authors note that this reliance limits post-quantum robustness and explicitly identify as an open challenge the design of a variant that maintains statistical privacy while achieving post-quantum soundness.