{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:P5LW5T7TKNR6F6266SX2PSLMNZ","short_pith_number":"pith:P5LW5T7T","schema_version":"1.0","canonical_sha256":"7f576ecff35363e2fb5ef4afa7c96c6e66b874e384a3381774354c03ac17438c","source":{"kind":"arxiv","id":"1806.04087","version":1},"attestation_state":"computed","paper":{"title":"Tensor-based Hardness of the Shortest Vector Problem to within Almost Polynomial Factors","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Ishay Haviv, Oded Regev","submitted_at":"2018-06-11T16:17:21Z","abstract_excerpt":"$ \\newcommand{\\SVP}{\\mathsf{SVP}} \\newcommand{\\NP}{\\mathsf{NP}} \\newcommand{\\RTIME}{\\mathsf{RTIME}} \\newcommand{\\RSUBEXP}{\\mathsf{RSUBEXP}} \\newcommand{\\eps}{\\epsilon} \\newcommand{\\poly}{\\mathop{\\mathrm{poly}}} $We show that unless $\\NP \\subseteq \\RTIME (2^{\\poly(\\log{n})})$, there is no polynomial-time algorithm approximating the Shortest Vector Problem ($\\SVP$) on $n$-dimensional lattices in the $\\ell_p$ norm ($1 \\leq p< \\infty$) to within a factor of $2^{(\\log{n})^{1-\\eps}}$ for any $\\eps > 0$. This improves the previous best factor of $2^{(\\log{n})^{1/2-\\eps}}$ under the same complexity as"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1806.04087","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CC","submitted_at":"2018-06-11T16:17:21Z","cross_cats_sorted":[],"title_canon_sha256":"8ec911dd4b5786acf8998a6d18905bc89ac4115af420fd1a87fd8816291456ff","abstract_canon_sha256":"01c5fac770c0346dfb75d1076a6b3422ae0b85687d217dd3aeccbf38d8a7988a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:13:38.577665Z","signature_b64":"NKzfq85PE+0gbpv6M/MYzdm1zdS55sk6Vko6td8lXCR0oYGRd2PmnP1u3TDLYEUhI8NmIHY/8jzb3XMvrU8JCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7f576ecff35363e2fb5ef4afa7c96c6e66b874e384a3381774354c03ac17438c","last_reissued_at":"2026-05-18T00:13:38.576941Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:13:38.576941Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Tensor-based Hardness of the Shortest Vector Problem to within Almost Polynomial Factors","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Ishay Haviv, Oded Regev","submitted_at":"2018-06-11T16:17:21Z","abstract_excerpt":"$ \\newcommand{\\SVP}{\\mathsf{SVP}} \\newcommand{\\NP}{\\mathsf{NP}} \\newcommand{\\RTIME}{\\mathsf{RTIME}} \\newcommand{\\RSUBEXP}{\\mathsf{RSUBEXP}} \\newcommand{\\eps}{\\epsilon} \\newcommand{\\poly}{\\mathop{\\mathrm{poly}}} $We show that unless $\\NP \\subseteq \\RTIME (2^{\\poly(\\log{n})})$, there is no polynomial-time algorithm approximating the Shortest Vector Problem ($\\SVP$) on $n$-dimensional lattices in the $\\ell_p$ norm ($1 \\leq p< \\infty$) to within a factor of $2^{(\\log{n})^{1-\\eps}}$ for any $\\eps > 0$. 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