{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:PZV4WQMVFKGMM7BCCFSQGX5JO2","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":"04978ad43b5c769bbc89e5272d2b8a53c23f6aa447d9df4e3226dcf34bfdaf1d","cross_cats_sorted":["cs.CR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-04-19T21:15:28Z","title_canon_sha256":"b2bc24060a10f89747a475609a2f1e0fb9ad5020ae72bab0c107255c6a16695d"},"schema_version":"1.0","source":{"id":"1104.3882","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.3882","created_at":"2026-05-18T03:57:25Z"},{"alias_kind":"arxiv_version","alias_value":"1104.3882v2","created_at":"2026-05-18T03:57:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.3882","created_at":"2026-05-18T03:57:25Z"},{"alias_kind":"pith_short_12","alias_value":"PZV4WQMVFKGM","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"PZV4WQMVFKGMM7BC","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"PZV4WQMV","created_at":"2026-05-18T12:26:39Z"}],"graph_snapshots":[{"event_id":"sha256:3ebea1b4721664bda134443e0fa126afed660d3ae76343c874ac319c7aac6506","target":"graph","created_at":"2026-05-18T03:57:25Z","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":"We propose a simple deterministic test for deciding whether or not an element $a \\in \\F_{2^n}^{\\times}$ or $\\F_{3^n}^{\\times}$ is a zero of the corresponding Kloosterman sum over these fields, and rigorously analyse its runtime. The test seems to have been overlooked in the literature. The expected cost of the test for binary fields is a single point-halving on an associated elliptic curve, while for ternary fields the expected cost is one half of a point-thirding on an associated elliptic curve. For binary fields of practical interest, this represents an O(n) speedup over the previous fastest","authors_text":"Omran Ahmadi, Robert Granger","cross_cats":["cs.CR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-04-19T21:15:28Z","title":"An efficient deterministic test for Kloosterman sum zeros"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.3882","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":"sha256:0219286175b4e2d0c3c0340519ccd220bc34e1b33f159da4f540038b63615d33","target":"record","created_at":"2026-05-18T03:57:25Z","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":"04978ad43b5c769bbc89e5272d2b8a53c23f6aa447d9df4e3226dcf34bfdaf1d","cross_cats_sorted":["cs.CR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-04-19T21:15:28Z","title_canon_sha256":"b2bc24060a10f89747a475609a2f1e0fb9ad5020ae72bab0c107255c6a16695d"},"schema_version":"1.0","source":{"id":"1104.3882","kind":"arxiv","version":2}},"canonical_sha256":"7e6bcb41952a8cc67c221165035fa97681d959f3e4a216091a1fcb40ca91f162","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7e6bcb41952a8cc67c221165035fa97681d959f3e4a216091a1fcb40ca91f162","first_computed_at":"2026-05-18T03:57:25.259801Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:57:25.259801Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Gg3WEDF1cuEpn7vZ8+w66v2+fXRYUmUwWmhNnNsGQ6gXY8WxD42WmDsbfy/lAeeLxlyOXBaHFdwC1LghtOZFCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:57:25.260693Z","signed_message":"canonical_sha256_bytes"},"source_id":"1104.3882","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0219286175b4e2d0c3c0340519ccd220bc34e1b33f159da4f540038b63615d33","sha256:3ebea1b4721664bda134443e0fa126afed660d3ae76343c874ac319c7aac6506"],"state_sha256":"ad394f231355e7d11f6dcc2e30b8b4bc42ff68713348f7143102270fe80ed8d3"}