Hybrid privacy-aware semantic search: SVD-truncated document geometry and CKKS-encrypted query reranking under a restricted threat model

Semantic search creates an asymmetric disclosure problem: query embeddings may reveal user intent, while returning exact provider vectors distributes reusable representations. We evaluate a deliberately restricted hybrid design. A public corpus-fitted SVD basis and PQ index support client-side candidate selection; candidate IDs are disclosed, while the projected query is encrypted with CKKS. A block-SIMD kernel scores 100 plaintext provider vectors and returns one ciphertext. At 672 dimensions, median server time falls from 1689.1 to 224.5 ms and response size by a factor of 99.5; provider-only saturation reaches 25.99 requests/s with 16 workers. In a frozen post-exploratory revision-analysis subset, disjoint from validation and containing 3,235 canonical BEIR queries, five of six collections satisfy a +/-0.002 nDCG@10 equivalence rule between actual CKKS and plaintext reranking of the same shortlist, while ArguAna is inconclusive. Projection controls favor SVD over random and coordinate truncation. Leakage audits show that disclosed candidate sets are highly linkable and reproduce part of the exact neighbourhood, while public PQ reveals approximate corpus geometry. The design therefore conditionally hides numerical query slots, but does not provide semantic-query, document, unlinkability, circuit, or access-pattern privacy.