{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:S5J7VGY6ZKMYIAZNP2SMROEFNJ","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":"57e00435a4cfaee57d55719eedf83004152b77053a68cdfc19fbb979228abb2a","cross_cats_sorted":["cs.CR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-03-01T20:37:04Z","title_canon_sha256":"aa573f299e92559077d5634d072202e3a23ff474ddc4cdb5e1fa6899be477783"},"schema_version":"1.0","source":{"id":"1403.0126","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.0126","created_at":"2026-05-18T02:57:25Z"},{"alias_kind":"arxiv_version","alias_value":"1403.0126v1","created_at":"2026-05-18T02:57:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.0126","created_at":"2026-05-18T02:57:25Z"},{"alias_kind":"pith_short_12","alias_value":"S5J7VGY6ZKMY","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"S5J7VGY6ZKMYIAZN","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"S5J7VGY6","created_at":"2026-05-18T12:28:49Z"}],"graph_snapshots":[{"event_id":"sha256:6a211aa7a3e57b3ac33c1ffaeb56700d0cbcf8640733e4854c42165831b63529","target":"graph","created_at":"2026-05-18T02:57:25Z","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":"Using Semaev's summation polynomials, we derive a new equation for the $\\mathbb{F}_q$-rational points of the trace zero variety of an elliptic curve defined over $\\mathbb{F}_q$. Using this equation, we produce an optimal-size representation for such points. Our representation is compatible with scalar multiplication. We give a point compression algorithm to compute the representation and a decompression algorithm to recover the original point (up to some small ambiguity). The algorithms are efficient for trace zero varieties coming from small degree extension fields. We give explicit equations","authors_text":"Elisa Gorla, Maike Massierer","cross_cats":["cs.CR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-03-01T20:37:04Z","title":"Point compression for the trace zero subgroup over a small degree extension field"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.0126","kind":"arxiv","version":1},"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":"sha256:3ac39088daf3ab5ef162930b773ebd85579b53eb2164f72e3c0e1c87899f50e8","target":"record","created_at":"2026-05-18T02:57:25Z","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":"57e00435a4cfaee57d55719eedf83004152b77053a68cdfc19fbb979228abb2a","cross_cats_sorted":["cs.CR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-03-01T20:37:04Z","title_canon_sha256":"aa573f299e92559077d5634d072202e3a23ff474ddc4cdb5e1fa6899be477783"},"schema_version":"1.0","source":{"id":"1403.0126","kind":"arxiv","version":1}},"canonical_sha256":"9753fa9b1eca9984032d7ea4c8b8856a5d142e61c19ab17372d82262ccecd8a0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9753fa9b1eca9984032d7ea4c8b8856a5d142e61c19ab17372d82262ccecd8a0","first_computed_at":"2026-05-18T02:57:25.696305Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:57:25.696305Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"REIacUkwDVkaZoKRsOOXJeg6JiKoUocoCXw+M/QigFDun9XpXUxpCNRR4JEr62QVxkg3EnyjJAPv+JlqfY5ODw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:57:25.696850Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.0126","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3ac39088daf3ab5ef162930b773ebd85579b53eb2164f72e3c0e1c87899f50e8","sha256:6a211aa7a3e57b3ac33c1ffaeb56700d0cbcf8640733e4854c42165831b63529"],"state_sha256":"23a9e217b7241b99404a400a4076088c0b8bbc72f967b23092a333a6f657b80d"}