{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:HAQDA2N4DZ3U6G4MR2PLU2QHD3","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":"8969931c1e2f8ac156bb1fb9a2e1c7a04eb8cfc6f5b7cfef5553dbca8cc6f283","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CR","submitted_at":"2014-03-12T12:04:22Z","title_canon_sha256":"21089758f79bc8c2d6f714b14e15b497e0a7f66cc5ccf482bd23efadb0c56e39"},"schema_version":"1.0","source":{"id":"1404.2226","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.2226","created_at":"2026-05-18T02:44:17Z"},{"alias_kind":"arxiv_version","alias_value":"1404.2226v2","created_at":"2026-05-18T02:44:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.2226","created_at":"2026-05-18T02:44:17Z"},{"alias_kind":"pith_short_12","alias_value":"HAQDA2N4DZ3U","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"HAQDA2N4DZ3U6G4M","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"HAQDA2N4","created_at":"2026-05-18T12:28:30Z"}],"graph_snapshots":[{"event_id":"sha256:565970767450f35f94b4b729b52ff193f909e0d4a621fd85d30b5c4e8c61f32f","target":"graph","created_at":"2026-05-18T02:44:17Z","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":"This paper studies the task of two-sources randomness extractors for elliptic curves defined over finite fields $K$, where $K$ can be a prime or a binary field. In fact, we introduce new constructions of functions over elliptic curves which take in input two random points from two differents subgroups. In other words, for a ginven elliptic curve $E$ defined over a finite field $\\mathbb{F}_q$ and two random points $P \\in \\mathcal{P}$ and $Q\\in \\mathcal{Q}$, where $\\mathcal{P}$ and $\\mathcal{Q}$ are two subgroups of $E(\\mathbb{F}_q)$, our function extracts the least significant bits of the absci","authors_text":"Abdoul Aziz Ciss","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CR","submitted_at":"2014-03-12T12:04:22Z","title":"Two-sources Randomness Extractors for Elliptic Curves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.2226","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":"sha256:856e58abd0b7ef85bce71a437cc5c8517c0efb54e29d248de91355c9ae26bf1a","target":"record","created_at":"2026-05-18T02:44:17Z","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":"8969931c1e2f8ac156bb1fb9a2e1c7a04eb8cfc6f5b7cfef5553dbca8cc6f283","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CR","submitted_at":"2014-03-12T12:04:22Z","title_canon_sha256":"21089758f79bc8c2d6f714b14e15b497e0a7f66cc5ccf482bd23efadb0c56e39"},"schema_version":"1.0","source":{"id":"1404.2226","kind":"arxiv","version":2}},"canonical_sha256":"38203069bc1e774f1b8c8e9eba6a071ed9b1a90d1561cd952d015d73215cfe3f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"38203069bc1e774f1b8c8e9eba6a071ed9b1a90d1561cd952d015d73215cfe3f","first_computed_at":"2026-05-18T02:44:17.713210Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:44:17.713210Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vzmst6pyjfnYpgN9wYhT+pVqU0DaGOsW3LR93t27xpW1Yl6fi2e/E/oK/sqFFJ3/EFSkIgSCoOvo8AEv/TMzBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:44:17.713673Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.2226","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:856e58abd0b7ef85bce71a437cc5c8517c0efb54e29d248de91355c9ae26bf1a","sha256:565970767450f35f94b4b729b52ff193f909e0d4a621fd85d30b5c4e8c61f32f"],"state_sha256":"d924a9ab2c88362916b427710fd580ec79e21ba81ab3914280adb658a96c097e"}