{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:HD2C2GVDILWEGE5FW3GXFPMQJP","short_pith_number":"pith:HD2C2GVD","schema_version":"1.0","canonical_sha256":"38f42d1aa342ec4313a5b6cd72bd904bfe35224f4738792f9a7d70ad112eda81","source":{"kind":"arxiv","id":"1210.8114","version":3},"attestation_state":"computed","paper":{"title":"Polynomial-time solutions of computational problems in noncommutative-algebraic cryptography","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.RT"],"primary_cat":"cs.CR","authors_text":"Boaz Tsaban","submitted_at":"2012-10-30T18:34:05Z","abstract_excerpt":"We introduce the \\emph{linear centralizer method}, and use it to devise a provable polynomial time solution of the Commutator Key Exchange Problem, the computational problem on which, in the passive adversary model, the security of the Anshel--Anshel--Goldfeld 1999 \\emph{Commutator} key exchange protocol is based. We also apply this method to the computational problem underlying the \\emph{Centralizer} key exchange protocol, introduced by Shpilrain and Ushakov in 2006.\n  This is the first provable polynomial time cryptanalysis of the Commutator key exchange protocol, hitherto the most important"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1210.8114","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CR","submitted_at":"2012-10-30T18:34:05Z","cross_cats_sorted":["math.GR","math.RT"],"title_canon_sha256":"38fccdd84a3f5da32810cc51c8eece6578384c75270e78a9f7824d71c83b3e07","abstract_canon_sha256":"788d23a988cedd53d02672d384ebcf343802b9f08ebd3467148b2e8b28149bc4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:46:14.443243Z","signature_b64":"BTI3CeJgUUswpkA/etdN0XxkLQ7oW84yhBSincYDPBB7nv67MljXjbt4G3uOyplZ46pdFd6fr7OjVVXkoKUIAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"38f42d1aa342ec4313a5b6cd72bd904bfe35224f4738792f9a7d70ad112eda81","last_reissued_at":"2026-05-18T01:46:14.442540Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:46:14.442540Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Polynomial-time solutions of computational problems in noncommutative-algebraic cryptography","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.RT"],"primary_cat":"cs.CR","authors_text":"Boaz Tsaban","submitted_at":"2012-10-30T18:34:05Z","abstract_excerpt":"We introduce the \\emph{linear centralizer method}, and use it to devise a provable polynomial time solution of the Commutator Key Exchange Problem, the computational problem on which, in the passive adversary model, the security of the Anshel--Anshel--Goldfeld 1999 \\emph{Commutator} key exchange protocol is based. We also apply this method to the computational problem underlying the \\emph{Centralizer} key exchange protocol, introduced by Shpilrain and Ushakov in 2006.\n  This is the first provable polynomial time cryptanalysis of the Commutator key exchange protocol, hitherto the most important"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.8114","kind":"arxiv","version":3},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1210.8114","created_at":"2026-05-18T01:46:14.442624+00:00"},{"alias_kind":"arxiv_version","alias_value":"1210.8114v3","created_at":"2026-05-18T01:46:14.442624+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.8114","created_at":"2026-05-18T01:46:14.442624+00:00"},{"alias_kind":"pith_short_12","alias_value":"HD2C2GVDILWE","created_at":"2026-05-18T12:27:09.501522+00:00"},{"alias_kind":"pith_short_16","alias_value":"HD2C2GVDILWEGE5F","created_at":"2026-05-18T12:27:09.501522+00:00"},{"alias_kind":"pith_short_8","alias_value":"HD2C2GVD","created_at":"2026-05-18T12:27:09.501522+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/HD2C2GVDILWEGE5FW3GXFPMQJP","json":"https://pith.science/pith/HD2C2GVDILWEGE5FW3GXFPMQJP.json","graph_json":"https://pith.science/api/pith-number/HD2C2GVDILWEGE5FW3GXFPMQJP/graph.json","events_json":"https://pith.science/api/pith-number/HD2C2GVDILWEGE5FW3GXFPMQJP/events.json","paper":"https://pith.science/paper/HD2C2GVD"},"agent_actions":{"view_html":"https://pith.science/pith/HD2C2GVDILWEGE5FW3GXFPMQJP","download_json":"https://pith.science/pith/HD2C2GVDILWEGE5FW3GXFPMQJP.json","view_paper":"https://pith.science/paper/HD2C2GVD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1210.8114&json=true","fetch_graph":"https://pith.science/api/pith-number/HD2C2GVDILWEGE5FW3GXFPMQJP/graph.json","fetch_events":"https://pith.science/api/pith-number/HD2C2GVDILWEGE5FW3GXFPMQJP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HD2C2GVDILWEGE5FW3GXFPMQJP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HD2C2GVDILWEGE5FW3GXFPMQJP/action/storage_attestation","attest_author":"https://pith.science/pith/HD2C2GVDILWEGE5FW3GXFPMQJP/action/author_attestation","sign_citation":"https://pith.science/pith/HD2C2GVDILWEGE5FW3GXFPMQJP/action/citation_signature","submit_replication":"https://pith.science/pith/HD2C2GVDILWEGE5FW3GXFPMQJP/action/replication_record"}},"created_at":"2026-05-18T01:46:14.442624+00:00","updated_at":"2026-05-18T01:46:14.442624+00:00"}