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The textbook defences are extremes - encrypting the whole search homomorphically is sound but too slow at million-document scale, while privacy noise degrades ranking long before it protects. We study a middle path exploiting the asymmetry between the static collection and the dynamic query. The collection is protected geometrically: each vector is truncated onto a lower-dimensional SVD subspace and rotated by a secret orthogonal transform known only to the owner. The query is protected cryptographically: it is reranked under CKKS homomorphic encryption, so an honest-but-curious server never sees the query or the scores. CKKS parameters come from a small offline benchmark.\n  We prove a tight lower bound on the reconstruction ","title":"Hybrid privacy-aware semantic search: SVD-truncated document geometry and CKKS-encrypted query reranking under a restricted threat model","url":"https://arxiv.org/abs/2606.26373","vendor":"arxiv_cs_ai"},"summary":"arXiv:2606.26373v1 Announce Type: cross \nAbstract: Dense embeddings power semantic search and retrieval-augmented generation, but embedding-inversion attacks can reconstruct source text from a vector: when a vector database leaks, the documents behind it leak too. The textbook defences are extremes - encrypting the whole search homomorphically is sound but too slow at million-document scale, while privacy noise degrades ranking long before it protects. We study a middle path exploiting the asymmetry between the static collection and the dynamic query. The collection is protected geometrically: each vector is truncated onto a lower-dimensional SVD subspace and rotated by a secret orthogonal transform known only to the owner. The query is protected cryptographically: it is reranked under CKKS homomorphic encryption, so an honest-but-curious server never sees the query or the scores. 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