# Hierarchical Navigable Small World

In the symmetric-privacy setting where both the query and the database must stay hidden, HNSecW turns HNSW graph-index approximate nearest neighbor search into a fully data-independent procedure that runs under secure multi-party computation, giving single-query online communication and local computation logarithmic complexity. Earlier protocols of this kind mostly used cluster-based pipelines whose online communication grows linearly with database size. On million- to billion-scale benchmarks, HNSecW keeps recall comparable to plaintext HNSW and reaches up to orders-of-magnitude end-to-end speedup over 2PC PANTHER on a wide-area network.

In the symmetric-privacy setting where both the query and the database must stay hidden, HNSecW turns HNSW graph-index approximate nearest neighbor search into a fully data-independent procedure that runs under secure multi-party computation, giving single-query online communication and local computation logarithmic complexity. Earlier protocols of this kind mostly used cluster-based pipelines whose online communication grows linearly with database size. On million- to billion-scale benchmarks, HNSecW keeps recall comparable to plaintext HNSW and reaches up to orders-of-magnitude end-to-end speedup over 2PC PANTHER on a wide-area network.