{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2005:HY3KB4ZLU6KRKM4BTQ2NML5J2A","short_pith_number":"pith:HY3KB4ZL","canonical_record":{"source":{"id":"math/0505487","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.GR","submitted_at":"2005-05-24T01:25:27Z","cross_cats_sorted":["cs.CR"],"title_canon_sha256":"4c52777871fc48dcd5307a0dc0ec3ee381f7e503fc3af0f6e62e649e2b8da4a3","abstract_canon_sha256":"75c552e85ff9b5e32f8a805bf5f0d452795f2e78d9888b045588f4cea97c4c22"},"schema_version":"1.0"},"canonical_sha256":"3e36a0f32ba7951533819c34d62fa9d00360019e146a70385b6f4a03a809842f","source":{"kind":"arxiv","id":"math/0505487","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0505487","created_at":"2026-05-18T01:05:23Z"},{"alias_kind":"arxiv_version","alias_value":"math/0505487v1","created_at":"2026-05-18T01:05:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0505487","created_at":"2026-05-18T01:05:23Z"},{"alias_kind":"pith_short_12","alias_value":"HY3KB4ZLU6KR","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"HY3KB4ZLU6KRKM4B","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"HY3KB4ZL","created_at":"2026-05-18T12:25:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2005:HY3KB4ZLU6KRKM4BTQ2NML5J2A","target":"record","payload":{"canonical_record":{"source":{"id":"math/0505487","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.GR","submitted_at":"2005-05-24T01:25:27Z","cross_cats_sorted":["cs.CR"],"title_canon_sha256":"4c52777871fc48dcd5307a0dc0ec3ee381f7e503fc3af0f6e62e649e2b8da4a3","abstract_canon_sha256":"75c552e85ff9b5e32f8a805bf5f0d452795f2e78d9888b045588f4cea97c4c22"},"schema_version":"1.0"},"canonical_sha256":"3e36a0f32ba7951533819c34d62fa9d00360019e146a70385b6f4a03a809842f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:23.438524Z","signature_b64":"mavXKCWsyWn8UYKcd2rTgarnGImVKzOL23IPb6LFISBDD4VtY3ou0g4VDyw17ieEl3L8bQWtAft4DXqax/xpDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3e36a0f32ba7951533819c34d62fa9d00360019e146a70385b6f4a03a809842f","last_reissued_at":"2026-05-18T01:05:23.438033Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:23.438033Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0505487","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:05:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YZsrjXMeo7JXRvRIhhUk+JHDJWwKJkkApbP7sjVwQeLMCrM/gLdFAKZt5Uv0qFnV5WmgTwlT0T2BwGtCKnOtCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T03:58:44.532564Z"},"content_sha256":"6e0a9fdad9c1f5ea9b55e9bda5a22e16124d6f06e74bfbdd8a4535421edadcc5","schema_version":"1.0","event_id":"sha256:6e0a9fdad9c1f5ea9b55e9bda5a22e16124d6f06e74bfbdd8a4535421edadcc5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2005:HY3KB4ZLU6KRKM4BTQ2NML5J2A","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Thompson's group and public key cryptography","license":"","headline":"","cross_cats":["cs.CR"],"primary_cat":"math.GR","authors_text":"Alexander Ushakov, Vladimir Shpilrain","submitted_at":"2005-05-24T01:25:27Z","abstract_excerpt":"Recently, several public key exchange protocols based on symbolic computation in non-commutative (semi)groups were proposed as a more efficient alternative to well established protocols based on numeric computation. Notably, the protocols due to Anshel-Anshel-Goldfeld and Ko-Lee et al. exploited the conjugacy search problem in groups, which is a ramification of the discrete logarithm problem. However, it is a prevalent opinion now that the conjugacy search problem alone is unlikely to provide sufficient level of security no matter what particular group is chosen as a platform.\n In this paper w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0505487","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:05:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+H4SzqbSMB+YYk1mVPtXHFpmgYph57IWAtTlDQDQGUkcl/GSF7aTZVe+Vt1N4Rxyz6+KE/cC/9vWeAEiPzNYDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T03:58:44.532919Z"},"content_sha256":"c81b33eb56746d6a75792d68b36bdc7f61849763f58fd75c9bbe5ab990ef7550","schema_version":"1.0","event_id":"sha256:c81b33eb56746d6a75792d68b36bdc7f61849763f58fd75c9bbe5ab990ef7550"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HY3KB4ZLU6KRKM4BTQ2NML5J2A/bundle.json","state_url":"https://pith.science/pith/HY3KB4ZLU6KRKM4BTQ2NML5J2A/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HY3KB4ZLU6KRKM4BTQ2NML5J2A/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-03T03:58:44Z","links":{"resolver":"https://pith.science/pith/HY3KB4ZLU6KRKM4BTQ2NML5J2A","bundle":"https://pith.science/pith/HY3KB4ZLU6KRKM4BTQ2NML5J2A/bundle.json","state":"https://pith.science/pith/HY3KB4ZLU6KRKM4BTQ2NML5J2A/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HY3KB4ZLU6KRKM4BTQ2NML5J2A/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:HY3KB4ZLU6KRKM4BTQ2NML5J2A","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":"75c552e85ff9b5e32f8a805bf5f0d452795f2e78d9888b045588f4cea97c4c22","cross_cats_sorted":["cs.CR"],"license":"","primary_cat":"math.GR","submitted_at":"2005-05-24T01:25:27Z","title_canon_sha256":"4c52777871fc48dcd5307a0dc0ec3ee381f7e503fc3af0f6e62e649e2b8da4a3"},"schema_version":"1.0","source":{"id":"math/0505487","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0505487","created_at":"2026-05-18T01:05:23Z"},{"alias_kind":"arxiv_version","alias_value":"math/0505487v1","created_at":"2026-05-18T01:05:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0505487","created_at":"2026-05-18T01:05:23Z"},{"alias_kind":"pith_short_12","alias_value":"HY3KB4ZLU6KR","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"HY3KB4ZLU6KRKM4B","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"HY3KB4ZL","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:c81b33eb56746d6a75792d68b36bdc7f61849763f58fd75c9bbe5ab990ef7550","target":"graph","created_at":"2026-05-18T01:05:23Z","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":"Recently, several public key exchange protocols based on symbolic computation in non-commutative (semi)groups were proposed as a more efficient alternative to well established protocols based on numeric computation. Notably, the protocols due to Anshel-Anshel-Goldfeld and Ko-Lee et al. exploited the conjugacy search problem in groups, which is a ramification of the discrete logarithm problem. However, it is a prevalent opinion now that the conjugacy search problem alone is unlikely to provide sufficient level of security no matter what particular group is chosen as a platform.\n In this paper w","authors_text":"Alexander Ushakov, Vladimir Shpilrain","cross_cats":["cs.CR"],"headline":"","license":"","primary_cat":"math.GR","submitted_at":"2005-05-24T01:25:27Z","title":"Thompson's group and public key cryptography"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0505487","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":"sha256:6e0a9fdad9c1f5ea9b55e9bda5a22e16124d6f06e74bfbdd8a4535421edadcc5","target":"record","created_at":"2026-05-18T01:05:23Z","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":"75c552e85ff9b5e32f8a805bf5f0d452795f2e78d9888b045588f4cea97c4c22","cross_cats_sorted":["cs.CR"],"license":"","primary_cat":"math.GR","submitted_at":"2005-05-24T01:25:27Z","title_canon_sha256":"4c52777871fc48dcd5307a0dc0ec3ee381f7e503fc3af0f6e62e649e2b8da4a3"},"schema_version":"1.0","source":{"id":"math/0505487","kind":"arxiv","version":1}},"canonical_sha256":"3e36a0f32ba7951533819c34d62fa9d00360019e146a70385b6f4a03a809842f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3e36a0f32ba7951533819c34d62fa9d00360019e146a70385b6f4a03a809842f","first_computed_at":"2026-05-18T01:05:23.438033Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:23.438033Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mavXKCWsyWn8UYKcd2rTgarnGImVKzOL23IPb6LFISBDD4VtY3ou0g4VDyw17ieEl3L8bQWtAft4DXqax/xpDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:23.438524Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0505487","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6e0a9fdad9c1f5ea9b55e9bda5a22e16124d6f06e74bfbdd8a4535421edadcc5","sha256:c81b33eb56746d6a75792d68b36bdc7f61849763f58fd75c9bbe5ab990ef7550"],"state_sha256":"2b9b322a599785ffc94a90dc54384b6eb459e5ae4df7c057683ac8186bdf1178"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ToYrFTJs6N2c0VKNdMgTfPFeL91+zjQKgNAEQf2P4J4i6BR1NvVicxO2Nd4efgHIpFU2YHKDE8+j612y5gTEBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T03:58:44.534911Z","bundle_sha256":"987492f636274f7cdf564a5c71733c185e9d906072b01142d4056e3f83f84993"}}