{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:U72HGP7FJG4E5MTKJA7WYMYBTI","short_pith_number":"pith:U72HGP7F","canonical_record":{"source":{"id":"1304.6572","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CR","submitted_at":"2013-04-24T13:15:50Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"9b5afbcf4ab6d31e0026f5068a59f84309407433516f644cab250a0a473dfdfd","abstract_canon_sha256":"236fa72fe259244ce3c91a63f0b0d00ba81de92e4f6e7608b80a40d793d81336"},"schema_version":"1.0"},"canonical_sha256":"a7f4733fe549b84eb26a483f6c33019a1833e10615b157e78dcedf777ad2a0be","source":{"kind":"arxiv","id":"1304.6572","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.6572","created_at":"2026-05-18T03:27:12Z"},{"alias_kind":"arxiv_version","alias_value":"1304.6572v1","created_at":"2026-05-18T03:27:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.6572","created_at":"2026-05-18T03:27:12Z"},{"alias_kind":"pith_short_12","alias_value":"U72HGP7FJG4E","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"U72HGP7FJG4E5MTK","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"U72HGP7F","created_at":"2026-05-18T12:28:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:U72HGP7FJG4E5MTKJA7WYMYBTI","target":"record","payload":{"canonical_record":{"source":{"id":"1304.6572","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CR","submitted_at":"2013-04-24T13:15:50Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"9b5afbcf4ab6d31e0026f5068a59f84309407433516f644cab250a0a473dfdfd","abstract_canon_sha256":"236fa72fe259244ce3c91a63f0b0d00ba81de92e4f6e7608b80a40d793d81336"},"schema_version":"1.0"},"canonical_sha256":"a7f4733fe549b84eb26a483f6c33019a1833e10615b157e78dcedf777ad2a0be","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:27:12.702824Z","signature_b64":"qhsAQ6NIdQTTkUN9vF+gxr3xguTIWDqHjBHollYMEHP/gXsoDPQ6iDb23lOvfrL1y4sGipk/inWd1GKpyz+AAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a7f4733fe549b84eb26a483f6c33019a1833e10615b157e78dcedf777ad2a0be","last_reissued_at":"2026-05-18T03:27:12.702023Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:27:12.702023Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1304.6572","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":"2026-05-18T03:27:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m8m+r9/+WOi7cEjSUbcGtdXLJTasXVjOrjNQL2gxs9stUXOn7yW5L+8uLsvprWN7MvOoSChaFNMzWtFAIRhEDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T17:47:09.763108Z"},"content_sha256":"73b7403f6f7ec6898d6e447481e1c046f8c76a6ea9a6b10d10a2d5281e0e5dea","schema_version":"1.0","event_id":"sha256:73b7403f6f7ec6898d6e447481e1c046f8c76a6ea9a6b10d10a2d5281e0e5dea"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:U72HGP7FJG4E5MTKJA7WYMYBTI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Public key exchange using semidirect product of (semi)groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"cs.CR","authors_text":"Charalambos Koupparis, Delaram Kahrobaei, Maggie Habeeb, Vladimir Shpilrain","submitted_at":"2013-04-24T13:15:50Z","abstract_excerpt":"In this paper, we describe a brand new key exchange protocol based on a semidirect product of (semi)groups (more specifically, on extension of a (semi)group by automorphisms), and then focus on practical instances of this general idea. Our protocol can be based on any group, in particular on any non-commutative group. One of its special cases is the standard Diffie-Hellman protocol, which is based on a cyclic group. However, when our protocol is used with a non-commutative (semi)group, it acquires several useful features that make it compare favorably to the Diffie-Hellman protocol. Here we al"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.6572","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":"2026-05-18T03:27:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HYzvIIJjPVGPqSiqqT1hPATwM5VWaxXboEsPKJnD5VRiOk7uQNqvJRmz+Cryi7az7ul7fRm0RsE2m3iJvHVrBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T17:47:09.763793Z"},"content_sha256":"eab19d4f4041ddd3ad453e367b1d1684d2dfdc8b7632f4e38d6672f5314cad4a","schema_version":"1.0","event_id":"sha256:eab19d4f4041ddd3ad453e367b1d1684d2dfdc8b7632f4e38d6672f5314cad4a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/U72HGP7FJG4E5MTKJA7WYMYBTI/bundle.json","state_url":"https://pith.science/pith/U72HGP7FJG4E5MTKJA7WYMYBTI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/U72HGP7FJG4E5MTKJA7WYMYBTI/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":"2026-06-07T17:47:09Z","links":{"resolver":"https://pith.science/pith/U72HGP7FJG4E5MTKJA7WYMYBTI","bundle":"https://pith.science/pith/U72HGP7FJG4E5MTKJA7WYMYBTI/bundle.json","state":"https://pith.science/pith/U72HGP7FJG4E5MTKJA7WYMYBTI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/U72HGP7FJG4E5MTKJA7WYMYBTI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:U72HGP7FJG4E5MTKJA7WYMYBTI","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":"236fa72fe259244ce3c91a63f0b0d00ba81de92e4f6e7608b80a40d793d81336","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CR","submitted_at":"2013-04-24T13:15:50Z","title_canon_sha256":"9b5afbcf4ab6d31e0026f5068a59f84309407433516f644cab250a0a473dfdfd"},"schema_version":"1.0","source":{"id":"1304.6572","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.6572","created_at":"2026-05-18T03:27:12Z"},{"alias_kind":"arxiv_version","alias_value":"1304.6572v1","created_at":"2026-05-18T03:27:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.6572","created_at":"2026-05-18T03:27:12Z"},{"alias_kind":"pith_short_12","alias_value":"U72HGP7FJG4E","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"U72HGP7FJG4E5MTK","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"U72HGP7F","created_at":"2026-05-18T12:28:02Z"}],"graph_snapshots":[{"event_id":"sha256:eab19d4f4041ddd3ad453e367b1d1684d2dfdc8b7632f4e38d6672f5314cad4a","target":"graph","created_at":"2026-05-18T03:27:12Z","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":"In this paper, we describe a brand new key exchange protocol based on a semidirect product of (semi)groups (more specifically, on extension of a (semi)group by automorphisms), and then focus on practical instances of this general idea. Our protocol can be based on any group, in particular on any non-commutative group. One of its special cases is the standard Diffie-Hellman protocol, which is based on a cyclic group. However, when our protocol is used with a non-commutative (semi)group, it acquires several useful features that make it compare favorably to the Diffie-Hellman protocol. Here we al","authors_text":"Charalambos Koupparis, 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":"2013-04-24T13:15:50Z","title":"Public key exchange using semidirect product of (semi)groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.6572","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":"sha256:73b7403f6f7ec6898d6e447481e1c046f8c76a6ea9a6b10d10a2d5281e0e5dea","target":"record","created_at":"2026-05-18T03:27:12Z","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":"236fa72fe259244ce3c91a63f0b0d00ba81de92e4f6e7608b80a40d793d81336","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CR","submitted_at":"2013-04-24T13:15:50Z","title_canon_sha256":"9b5afbcf4ab6d31e0026f5068a59f84309407433516f644cab250a0a473dfdfd"},"schema_version":"1.0","source":{"id":"1304.6572","kind":"arxiv","version":1}},"canonical_sha256":"a7f4733fe549b84eb26a483f6c33019a1833e10615b157e78dcedf777ad2a0be","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a7f4733fe549b84eb26a483f6c33019a1833e10615b157e78dcedf777ad2a0be","first_computed_at":"2026-05-18T03:27:12.702023Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:27:12.702023Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qhsAQ6NIdQTTkUN9vF+gxr3xguTIWDqHjBHollYMEHP/gXsoDPQ6iDb23lOvfrL1y4sGipk/inWd1GKpyz+AAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:27:12.702824Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.6572","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:73b7403f6f7ec6898d6e447481e1c046f8c76a6ea9a6b10d10a2d5281e0e5dea","sha256:eab19d4f4041ddd3ad453e367b1d1684d2dfdc8b7632f4e38d6672f5314cad4a"],"state_sha256":"a16416367672d069998fff1a3a72b438959d4df6f3aa097f53d9ded5da78c258"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eIkinO7YVq5GLc/K/m4LLQR01Oya+igja0pyUrTcT+n+9WeaNlJ/hm72LXWD3bCpa8+/bY/xPO6DPiUdkFxxAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T17:47:09.767453Z","bundle_sha256":"f37d12826afc7e3ae7111d82b2e692648bf7203ced18cb5e4499db370ffe5d50"}}