{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:QN7TM6EVDPLNSMHT6LAZ3KAPDJ","short_pith_number":"pith:QN7TM6EV","schema_version":"1.0","canonical_sha256":"837f3678951bd6d930f3f2c19da80f1a46d9e3d42a92c27e4bd5b5737fe864ad","source":{"kind":"arxiv","id":"1201.4725","version":1},"attestation_state":"computed","paper":{"title":"Solving the LPN problem in cube-root time","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CR","authors_text":"Urs Wagner","submitted_at":"2012-01-23T14:33:10Z","abstract_excerpt":"In this paper it is shown that given a sufficient number of (noisy) random binary linear equations, the Learning from Parity with Noise (LPN) problem can be solved in essentially cube root time in the number of unknowns. The techniques used to recover the solution are known from fast correlation attacks on stream ciphers. As in fast correlation attacks, the performance of the algorithm depends on the number of equations given. It is shown that if this number exceeds a certain bound, and the bias of the noisy equations is polynomial in number of unknowns, the running time of the algorithm is re"},"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":"1201.4725","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CR","submitted_at":"2012-01-23T14:33:10Z","cross_cats_sorted":[],"title_canon_sha256":"5715784029a9e66e15c1ddf7bef3d010624d83955e653a411a274243e5ef8b78","abstract_canon_sha256":"68675cd280da061fa61507626a11eb4d9c7a696dec56c930f2e0f87a387d17bd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:04:05.345197Z","signature_b64":"Z3ChuXmCwx2jrSBiYH0r8s4oij5UE9cneQMPvI5zJsqfYgLBW63MM1uLAM7d/mfK9gF/y6IhTbbX71ksAotWDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"837f3678951bd6d930f3f2c19da80f1a46d9e3d42a92c27e4bd5b5737fe864ad","last_reissued_at":"2026-05-18T04:04:05.344782Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:04:05.344782Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Solving the LPN problem in cube-root time","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CR","authors_text":"Urs Wagner","submitted_at":"2012-01-23T14:33:10Z","abstract_excerpt":"In this paper it is shown that given a sufficient number of (noisy) random binary linear equations, the Learning from Parity with Noise (LPN) problem can be solved in essentially cube root time in the number of unknowns. The techniques used to recover the solution are known from fast correlation attacks on stream ciphers. As in fast correlation attacks, the performance of the algorithm depends on the number of equations given. It is shown that if this number exceeds a certain bound, and the bias of the noisy equations is polynomial in number of unknowns, the running time of the algorithm is re"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.4725","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1201.4725","created_at":"2026-05-18T04:04:05.344845+00:00"},{"alias_kind":"arxiv_version","alias_value":"1201.4725v1","created_at":"2026-05-18T04:04:05.344845+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.4725","created_at":"2026-05-18T04:04:05.344845+00:00"},{"alias_kind":"pith_short_12","alias_value":"QN7TM6EVDPLN","created_at":"2026-05-18T12:27:18.751474+00:00"},{"alias_kind":"pith_short_16","alias_value":"QN7TM6EVDPLNSMHT","created_at":"2026-05-18T12:27:18.751474+00:00"},{"alias_kind":"pith_short_8","alias_value":"QN7TM6EV","created_at":"2026-05-18T12:27:18.751474+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/QN7TM6EVDPLNSMHT6LAZ3KAPDJ","json":"https://pith.science/pith/QN7TM6EVDPLNSMHT6LAZ3KAPDJ.json","graph_json":"https://pith.science/api/pith-number/QN7TM6EVDPLNSMHT6LAZ3KAPDJ/graph.json","events_json":"https://pith.science/api/pith-number/QN7TM6EVDPLNSMHT6LAZ3KAPDJ/events.json","paper":"https://pith.science/paper/QN7TM6EV"},"agent_actions":{"view_html":"https://pith.science/pith/QN7TM6EVDPLNSMHT6LAZ3KAPDJ","download_json":"https://pith.science/pith/QN7TM6EVDPLNSMHT6LAZ3KAPDJ.json","view_paper":"https://pith.science/paper/QN7TM6EV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1201.4725&json=true","fetch_graph":"https://pith.science/api/pith-number/QN7TM6EVDPLNSMHT6LAZ3KAPDJ/graph.json","fetch_events":"https://pith.science/api/pith-number/QN7TM6EVDPLNSMHT6LAZ3KAPDJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QN7TM6EVDPLNSMHT6LAZ3KAPDJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QN7TM6EVDPLNSMHT6LAZ3KAPDJ/action/storage_attestation","attest_author":"https://pith.science/pith/QN7TM6EVDPLNSMHT6LAZ3KAPDJ/action/author_attestation","sign_citation":"https://pith.science/pith/QN7TM6EVDPLNSMHT6LAZ3KAPDJ/action/citation_signature","submit_replication":"https://pith.science/pith/QN7TM6EVDPLNSMHT6LAZ3KAPDJ/action/replication_record"}},"created_at":"2026-05-18T04:04:05.344845+00:00","updated_at":"2026-05-18T04:04:05.344845+00:00"}