{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:ZE2YTWZNLRGJKVK7N5TONXRMLL","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":"dfbc78814f3553d245d0262feaf8b2676be1919c5fce2d8efddbb3fb2e3879d7","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CR","submitted_at":"2012-05-01T13:39:25Z","title_canon_sha256":"94eda0f4ae973caca5bffab3ae36c996e4a29365b2405b3dfae29f4cecdc8804"},"schema_version":"1.0","source":{"id":"1205.0157","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.0157","created_at":"2026-05-18T03:56:35Z"},{"alias_kind":"arxiv_version","alias_value":"1205.0157v1","created_at":"2026-05-18T03:56:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.0157","created_at":"2026-05-18T03:56:35Z"},{"alias_kind":"pith_short_12","alias_value":"ZE2YTWZNLRGJ","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"ZE2YTWZNLRGJKVK7","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"ZE2YTWZN","created_at":"2026-05-18T12:27:30Z"}],"graph_snapshots":[{"event_id":"sha256:41fdaba8005af4f8920d8eaac98f943c5aa21ad448b130f0c68d0f0420a47db2","target":"graph","created_at":"2026-05-18T03:56:35Z","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 (t,n)-threshold secret sharing scheme is a method to distribute a secret among n participants in such a way that any t participants can recover the secret, but no t-1 participants can. In this paper, we propose two secret sharing schemes using non-abelian groups. One scheme is the special case where all the participants must get together to recover the secret. The other one is a (t,n)-threshold scheme that is a combination of Shamir's scheme and the group-theoretic scheme proposed in this paper.","authors_text":"Delaram Kahrobaei, Maggie Habeeb, Vladimir Shpilrain","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CR","submitted_at":"2012-05-01T13:39:25Z","title":"A Secret Sharing Scheme Based on Group Presentations and the Word Problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.0157","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":"sha256:68700f0b6665e1a1ac087959b0b7f2845c67f9676af639e667edaddbf039e9b9","target":"record","created_at":"2026-05-18T03:56:35Z","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":"dfbc78814f3553d245d0262feaf8b2676be1919c5fce2d8efddbb3fb2e3879d7","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CR","submitted_at":"2012-05-01T13:39:25Z","title_canon_sha256":"94eda0f4ae973caca5bffab3ae36c996e4a29365b2405b3dfae29f4cecdc8804"},"schema_version":"1.0","source":{"id":"1205.0157","kind":"arxiv","version":1}},"canonical_sha256":"c93589db2d5c4c95555f6f66e6de2c5af82910903820e9e2dfd5c63877c6a522","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c93589db2d5c4c95555f6f66e6de2c5af82910903820e9e2dfd5c63877c6a522","first_computed_at":"2026-05-18T03:56:35.740811Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:56:35.740811Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"osqfKzl7h88JD/PpcEl0qhfFahFGenb31c9qlUMcy3aPPHEz7r0kwJKt/CwXPn2jqK71Np9u0N0MGhVz48svDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:56:35.741463Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.0157","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:68700f0b6665e1a1ac087959b0b7f2845c67f9676af639e667edaddbf039e9b9","sha256:41fdaba8005af4f8920d8eaac98f943c5aa21ad448b130f0c68d0f0420a47db2"],"state_sha256":"e9611a72285e1464ad311d92b1b506c758ce2ada114c5b48c1ef4c11603a5b01"}