{"paper":{"title":"On the complexity of the Rank Syndrome Decoding problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CR","authors_text":"Julien Schrek, Olivier Ruatta, Philippe Gaborit","submitted_at":"2013-01-06T16:56:53Z","abstract_excerpt":"In this paper we propose two new generic attacks on the Rank Syndrome Decoding (RSD) problem\n  Let $C$ be a random $[n,k]$ rank code over $GF(q^m)$ and let $y=x+e$ be a received word such that $x \\in C$ and the $Rank(e)=r$. The first attack is combinatorial and permits to recover an error $e$ of rank weight $r$ in $min(O((n-k)^3m^3q^{r\\lfloor\\frac{km}{n}\\rfloor}, O((n-k)^3m^3q^{(r-1)\\lfloor\\frac{(k+1)m}{n}\\rfloor}))$ operations on $GF(q)$. This attack dramatically improves on previous attack by introducing the length $n$ of the code in the exponent of the complexity, which was not the case in "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.1026","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"}