{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:QYFBX3Q4UKLQBGOZXHG7ILEQYC","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":"314aec96f06b9fa2c69d488e5b5ea09ff13c53a4bbfc30a6571c78a4d912e06d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-09-23T10:17:22Z","title_canon_sha256":"cb46fbda0b3f5d4e74378d8d33bce88eb0ecc2b72c2062df001ad4fd4a050497"},"schema_version":"1.0","source":{"id":"1509.06909","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.06909","created_at":"2026-05-18T01:30:50Z"},{"alias_kind":"arxiv_version","alias_value":"1509.06909v2","created_at":"2026-05-18T01:30:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.06909","created_at":"2026-05-18T01:30:50Z"},{"alias_kind":"pith_short_12","alias_value":"QYFBX3Q4UKLQ","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"QYFBX3Q4UKLQBGOZ","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"QYFBX3Q4","created_at":"2026-05-18T12:29:39Z"}],"graph_snapshots":[{"event_id":"sha256:8dadc335fa734df36e6834570492d8e1f61711f9378f633defca1382fe848618","target":"graph","created_at":"2026-05-18T01:30:50Z","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":"For a given elliptic curve $\\mathbf{E}$ over a finite field of odd characteristic and a rational function $f$ on $\\mathbf{E}$ we first study the linear complexity profiles of the sequences $f(nG)$, $n=1,2,\\dots$ which complements earlier results of Hess and Shparlinski. We use Edwards coordinates to be able to deal with many $f$ where Hess and Shparlinski's result does not apply. Moreover, we study the linear complexities of the (generalized) elliptic curve power generators $f(e^nG)$, $n=1,2,\\dots$. We present large families of functions $f$ such that the linear complexity profiles of these se","authors_text":"Arne Winterhof, L\\'aszl\\'o M\\'erai","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-09-23T10:17:22Z","title":"On the linear complexity profile of some sequences derived from elliptic curves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.06909","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:b38796a443a84632d6886c69e2d2587531357ef9869bd5b0677a2ac963a2c96a","target":"record","created_at":"2026-05-18T01:30:50Z","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":"314aec96f06b9fa2c69d488e5b5ea09ff13c53a4bbfc30a6571c78a4d912e06d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-09-23T10:17:22Z","title_canon_sha256":"cb46fbda0b3f5d4e74378d8d33bce88eb0ecc2b72c2062df001ad4fd4a050497"},"schema_version":"1.0","source":{"id":"1509.06909","kind":"arxiv","version":2}},"canonical_sha256":"860a1bee1ca2970099d9b9cdf42c90c0a299b8dc82909442fc9c6ee100264ddc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"860a1bee1ca2970099d9b9cdf42c90c0a299b8dc82909442fc9c6ee100264ddc","first_computed_at":"2026-05-18T01:30:50.591919Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:30:50.591919Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"h1Wwgcs1ju5DIRdjrI1Hhwjxn8gH+BiTlKTixdMHk9NdEeFR75t0lHv3H7+Bfh4G+qTYM8AQV/TG+EIujO8vAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:30:50.592448Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.06909","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b38796a443a84632d6886c69e2d2587531357ef9869bd5b0677a2ac963a2c96a","sha256:8dadc335fa734df36e6834570492d8e1f61711f9378f633defca1382fe848618"],"state_sha256":"584bdd6d641612e9fae66788a1410f18708444b829a9a7ba4a23ea04e5892721"}