{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:NVNDOY2IU3MCSTVTJ6LJNQSVOL","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"92c95f74be06ae1a671861bed944f5034b0bace74500d7285bfcac702111047d","cross_cats_sorted":["cs.CR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2011-12-29T10:05:53Z","title_canon_sha256":"754e570ebfa901bc032c98963c7003907f5d2b5f6281df36f474d5362a124913"},"schema_version":"1.0","source":{"id":"1112.6263","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.6263","created_at":"2026-05-18T02:21:26Z"},{"alias_kind":"arxiv_version","alias_value":"1112.6263v2","created_at":"2026-05-18T02:21:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.6263","created_at":"2026-05-18T02:21:26Z"},{"alias_kind":"pith_short_12","alias_value":"NVNDOY2IU3MC","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"NVNDOY2IU3MCSTVT","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"NVNDOY2I","created_at":"2026-05-18T12:26:37Z"}],"graph_snapshots":[{"event_id":"sha256:32d28b54eb3022a76f810f3fc9e45450b5342e887409171479ea62284db3c700","target":"graph","created_at":"2026-05-18T02:21:26Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"A fundamental problem in computer science is to find all the common zeroes of $m$ quadratic polynomials in $n$ unknowns over $\\mathbb{F}_2$. The cryptanalysis of several modern ciphers reduces to this problem. Up to now, the best complexity bound was reached by an exhaustive search in $4\\log_2 n\\,2^n$ operations. We give an algorithm that reduces the problem to a combination of exhaustive search and sparse linear algebra. This algorithm has several variants depending on the method used for the linear algebra step. Under precise algebraic assumptions on the input system, we show that the determ","authors_text":"Bruno Salvy, Jean-Charles Faug\\`ere, Magali Bardet, Pierre-Jean Spaenlehauer","cross_cats":["cs.CR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2011-12-29T10:05:53Z","title":"On the Complexity of Solving Quadratic Boolean Systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.6263","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:b9f60fc10b3fd76948bd24359e35cc669eaba236da18a192e8f491618855cd9d","target":"record","created_at":"2026-05-18T02:21:26Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"92c95f74be06ae1a671861bed944f5034b0bace74500d7285bfcac702111047d","cross_cats_sorted":["cs.CR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2011-12-29T10:05:53Z","title_canon_sha256":"754e570ebfa901bc032c98963c7003907f5d2b5f6281df36f474d5362a124913"},"schema_version":"1.0","source":{"id":"1112.6263","kind":"arxiv","version":2}},"canonical_sha256":"6d5a376348a6d8294eb34f9696c25572da0ab2a5ecd8d075b73300d84a034760","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6d5a376348a6d8294eb34f9696c25572da0ab2a5ecd8d075b73300d84a034760","first_computed_at":"2026-05-18T02:21:26.896204Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:21:26.896204Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"o9pH2LFN3N/BmwY0W0YeEk6Zk8xVLPX71DP6QrHBI3vopW+0uxtpLZjc6gtOfFiRtdErcoZGCkeBWno3NLncDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:21:26.896932Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.6263","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b9f60fc10b3fd76948bd24359e35cc669eaba236da18a192e8f491618855cd9d","sha256:32d28b54eb3022a76f810f3fc9e45450b5342e887409171479ea62284db3c700"],"state_sha256":"72c6f001cab261ba40ae87ea88d11df30f166399d774bdbd7a2be923ef977456"}