{"paper":{"title":"Efficient Quantum Fully Homomorphic Encryption","license":"http://creativecommons.org/licenses/by/4.0/","headline":"A novel modular arithmetic program for LWE decryption reduces the quantum resource cost of fully homomorphic encryption to near-linear in the security parameter.","cross_cats":["cs.CR"],"primary_cat":"quant-ph","authors_text":"Fengxia Liu, Kun Tian, Maozhi Xu, Yi Zhang, Zhiming Zheng, Zixian Gong","submitted_at":"2026-04-26T01:48:28Z","abstract_excerpt":"Quantum fully homomorphic encryption (QFHE) enables arbitrary quantum computations on encrypted data, but prior constructions require prohibitive quantum resources--specifically, O(lambda^2) EPR pairs per T-gate evaluation using the Barrington-based approach (DSS16). This paper introduces a unified framework achieving exponential improvement over the generic Barrington-based approach in program length.\n  The central innovation is a novel modular arithmetic program (MA-Program) tailored to learning with errors (LWE) decryption. We show that LWE decryption computes the inner product <sk,ct> mod "},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Our central innovation is a novel MAP tailored to the algebraic structure of Learning-with-Errors (LWE) decryption... This yields branching programs of width O(log λ) and length O(λ log λ), thereby reducing the size of the essential quantum gadget from O(λ^{2.58}) to O(λ log² λ) EPR pairs -- a concrete improvement factor of 2^{15} to 2^{18} for standard security parameters.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The assumption that the novel MAP correctly computes the inner product ⟨sk, c⟩ mod q with the claimed O(log q) state width, and that the mapping via the garden-hose model and MBQC incurs no additional exponential overhead beyond the stated bounds.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A specialized modular arithmetic program for LWE decryption reduces the quantum gadget size in QFHE from O(λ^{2.58}) to O(λ log² λ) EPR pairs.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A novel modular arithmetic program for LWE decryption reduces the quantum resource cost of fully homomorphic encryption to near-linear in the security parameter.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"a6e1444800817dfc08e4208a706bbfe5e6202997027660bb7947c870b049fa84"},"source":{"id":"2604.23490","kind":"arxiv","version":2},"verdict":{"id":"eec1eed2-3fc2-4a66-83ac-d14b1b848d6e","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-08T06:31:50.826809Z","strongest_claim":"Our central innovation is a novel MAP tailored to the algebraic structure of Learning-with-Errors (LWE) decryption... This yields branching programs of width O(log λ) and length O(λ log λ), thereby reducing the size of the essential quantum gadget from O(λ^{2.58}) to O(λ log² λ) EPR pairs -- a concrete improvement factor of 2^{15} to 2^{18} for standard security parameters.","one_line_summary":"A specialized modular arithmetic program for LWE decryption reduces the quantum gadget size in QFHE from O(λ^{2.58}) to O(λ log² λ) EPR pairs.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The assumption that the novel MAP correctly computes the inner product ⟨sk, c⟩ mod q with the claimed O(log q) state width, and that the mapping via the garden-hose model and MBQC incurs no additional exponential overhead beyond the stated bounds.","pith_extraction_headline":"A novel modular arithmetic program for LWE decryption reduces the quantum resource cost of fully homomorphic encryption to near-linear in the security parameter."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.23490/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-21T08:39:47.274274Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T23:04:30.986058Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"d7d1b3ae660635d2b54443273df40fec057e12bd216d8877aef8c825bedc3423"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}