{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:RIWKZZNLYPWX3Q3BGXWS4JHZLI","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":"4bdee157a54d1d28e3994b074283a4f5a607a8c6065dd0e68f4eb0f645f0ee4e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-03-07T22:36:15Z","title_canon_sha256":"cdb7cdc4a55c82e4b18a4c6931803233816a5e4d41486bd3b7f7e728f79b585d"},"schema_version":"1.0","source":{"id":"1603.02328","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.02328","created_at":"2026-05-18T01:19:23Z"},{"alias_kind":"arxiv_version","alias_value":"1603.02328v1","created_at":"2026-05-18T01:19:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.02328","created_at":"2026-05-18T01:19:23Z"},{"alias_kind":"pith_short_12","alias_value":"RIWKZZNLYPWX","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"RIWKZZNLYPWX3Q3B","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"RIWKZZNL","created_at":"2026-05-18T12:30:41Z"}],"graph_snapshots":[{"event_id":"sha256:b4a4af0c78563b75b11278cbaec1b31887ed51a9739419b2a0619f9417ef742e","target":"graph","created_at":"2026-05-18T01:19:23Z","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 introduces a newly developed private key cryptosystem and a public key cryptosystem. In the first one, each letter is encrypted with a different key. Therefore, it is a kind of a one-time pad. The second one is inspired by the ElGamal cryptosystem. Both presented cryptosystems are based on automorphisms of free groups. Given a free group $F$ of finite rank, the automorphism group $Aut(F)$ can be generated by Nielsen transformations, which are the basis of a linear technique to study free groups and general infinite groups. Therefore Nielsen transformations are introduced.","authors_text":"Anja I. S. Moldenhauer, Gerhard Rosenberger","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-03-07T22:36:15Z","title":"Cryptosystems Using Automorphisms of Finitely Generated Free Groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.02328","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":"sha256:8405b1b73c49e49c424174f26eb361f7042b3117ca63f429ec6429a98bd007c0","target":"record","created_at":"2026-05-18T01:19:23Z","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":"4bdee157a54d1d28e3994b074283a4f5a607a8c6065dd0e68f4eb0f645f0ee4e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-03-07T22:36:15Z","title_canon_sha256":"cdb7cdc4a55c82e4b18a4c6931803233816a5e4d41486bd3b7f7e728f79b585d"},"schema_version":"1.0","source":{"id":"1603.02328","kind":"arxiv","version":1}},"canonical_sha256":"8a2cace5abc3ed7dc36135ed2e24f95a05ce3c7528184df5ef047f29fa15c232","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8a2cace5abc3ed7dc36135ed2e24f95a05ce3c7528184df5ef047f29fa15c232","first_computed_at":"2026-05-18T01:19:23.678326Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:19:23.678326Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jJDhbYt5K/SHoGECW5nKTAjjbqXd7GKuhGp/X1U2vVVHulLyGtBjlQJw1FgvBiImQuZ2nI8nq7a1fKBMQxfxBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:19:23.679052Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.02328","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8405b1b73c49e49c424174f26eb361f7042b3117ca63f429ec6429a98bd007c0","sha256:b4a4af0c78563b75b11278cbaec1b31887ed51a9739419b2a0619f9417ef742e"],"state_sha256":"01bf0cd3dc00d3c4130121712c3a63829eb653bd4b8d753c230f67409c965dd6"}