{"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"}