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Fully homomorphic search is sound but far too slow at million-document scale, while privacy noise degrades ranking before it protects. We study a middle path built on an asymmetry: the static document collection is protected geometrically - each vector is SVD-truncated onto a lower-dimensional subspace and rotated by a secret orthogonal transform held only by the data owner - while the dynamic query is protected cryptographically under CKKS, so an honest-but-curious server never sees query values or similarity scores. We prove a tight lower bound on the reconstruction error of any decoder confined to the protected subspace. On a one-million-document corpus with five encoders the protection preserves - and on the strongest encoders slightly i","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:2606.26373v2 Announce Type: replace-cross \nAbstract: Dense embeddings power semantic search and retrieval-augmented generation, yet a leaked vector database also leaks the text behind it, because embeddings can be inverted with high fidelity. Fully homomorphic search is sound but far too slow at million-document scale, while privacy noise degrades ranking before it protects. We study a middle path built on an asymmetry: the static document collection is protected geometrically - each vector is SVD-truncated onto a lower-dimensional subspace and rotated by a secret orthogonal transform held only by the data owner - while the dynamic query is protected cryptographically under CKKS, so an honest-but-curious server never sees query values or similarity scores. We prove a tight lower bound on the reconstruction error of any decoder confined to the protected subspace. On a one-million-document corpus with five encoders the protection preserves - and on the strongest encoders slightly i","title":"Hybrid privacy-aware semantic search: SVD-truncated document geometry and CKKS-encrypted query reranking under a restricted threat model","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-06-30T04:43:04Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2606.26373"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:21d4cebcbb0b1f104ba8d043a5c2711b5c086def7a7bbf43f70d4c275b799a72d23178d548600dde6eb5e85d72dd7353da9f5ee096ec2411144a41ba4d735600","signer":"crovia.substrate","subject":{"observed_at":"2026-06-30T04:43:04Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2606.26373"},"tsa":{"authority":"crovia.substrate.bootstrap","rfc3161_token":"{\"kind\":\"crovia.bootstrap.tsa\",\"source_jsonl\":\"/opt/crovia/spider/data/news/vendor_press_v1.jsonl\",\"source_seal_merkle_root\":\"spider_vendor_press_v1\",\"upgrade_path\":\"Sessione H \\u2014 OpenTimestamps weekly anchor\"}"},"zk_mode":"clear","zk_proof":null},"ledger":{"leaf_hash":"b27d2215cc8d744b4e17a5e227194bf5f08ea98f91dd50f47725cb03c4df108a","leaf_index":265254,"ledger_path":"/opt/crovia/substrate/axiom_ledger.jsonl"},"merkle_proof":{"hash_alg":"sha256","leaf_prefix":"0x00","node_prefix":"0x01","odd_leaf_rule":"duplicate_last","path":[{"sibling":"d52b04f931cd9ee780b80aa0d8b5c697e6298e91f349fb560e9347a39af77ff7","side":"right"},{"sibling":"3960876416064448ec656a2b3080eb1bd61d29882e03c0f309d17eac0f27dc09","side":"left"},{"sibling":"5081a28547f88f3be1872f7e8c5232fe74b07ff8679a663ad6731ae565277561","side":"left"},{"sibling":"63f284d550fb1493a2cf28a2a28c840d2e692909bd8a09cd1ed1b45705c3c551","side":"right"},{"sibling":"af7c2de27919f42a0e65a43e1a9fafcbeedf56dae0dec0654b19aae478de2b70","side":"right"},{"sibling":"cccd81c33dafd50c7fdc64d63e8563daa68321bb44450ef3ec0b5f8628b5c9d2","side":"left"},{"sibling":"ff273c8201c286328de95b4c3f7ad04c9fb005c67fda3de45c54b72f9f5db5b3","side":"right"},{"sibling":"3cde187de7516743e6cd60012ce336384e260530220514cdd49599ef710e14e5","side":"right"},{"sibling":"2da116eff026ee371a88b8eb1a0aeb87679b487f1fbf1623083121809f754234","side":"right"},{"sibling":"eef13ac8a36eb836ad77846f6ef08d9afa4dcc380a64b88c542b57231522db0a","side":"right"},{"sibling":"a2cf20d97c095bc4fa7c4f5bb4f2266dd953e3d733d7e185aa164763491b312c","side":"left"},{"sibling":"f9b4bed84fa6990c71ad2887c91bda183001f05f6b648f21d1273045a26b11fd","side":"left"},{"sibling":"173d2dc4b29ee04ea41d6d0ebc334c4bc2d46e7ee4230c94765413f24fb4bc42","side":"right"},{"sibling":"112461f7c0ec411116fb5c6c90fe95cea9d8f188b9fe08afe25a837ac02d0071","side":"right"},{"sibling":"ea9488204352c49db8f7daf05eefcd7628ecf9413830346674801a99d0654a94","side":"right"},{"sibling":"6261c13b9922cb657f10d1e5d36ec15d8771cf8766e36c61dcbffb7bed57e396","side":"right"},{"sibling":"fa19aa3faf287618b820bcfceebb366152ad521dd20ef9f51e977816663e448b","side":"right"},{"sibling":"c32f943406b62d1fc59b7f7e243492174c8e1caba8c8a2705f86c773315736e0","side":"right"},{"sibling":"1cecb7f447febd025aac272837c80de218aecc6485d2395a509b2a1f1b9c746e","side":"left"}]},"schema":"crovia.axiom_proof.v1","seal":{"first_collector_run_id":"","first_receipt_hash":"","jsonl_path":"/opt/crovia/substrate/axiom_ledger.jsonl","key_id":"430895f101d38164","last_collector_run_id":"","last_receipt_hash":"","leaf_count":265374,"merkle_root":"9636001ecab173cb6af10dc7c71eb14585daa62f9c0a6f027046f05633156891","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260630T053701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-06-30T05:38:03Z","sig_algorithm":"ed25519","signature":"6d4b8fd9b9da856cbb5fba7540877c6a63fa18a5ec3eaf28dc4d6d1c64921c9c0565f8c95f4b7aec0e7744fd7754844f051baf863db708cad768765b416a7b0c","signer_version":"1.1.0"},"trust_root":{"key_id":"430895f101d38164","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","signature_algorithm":"ed25519","url":"/registry/canon/TRUST_ROOT.md"},"verifier":{"spec":"/registry/canon/AXIOM_RECEIPT_v1.md","url":"/v/axm_a048e661bff000324dd3db3112eda220dcc70c2cd7024b95405deaea9010ec5c"}}