{"paper":{"title":"Polynomial Interpolation and Identity Testing from High Powers over Finite Fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"math.NT","authors_text":"Gabor Ivanyos, Igor Shparlinski, Marek Karpinski, Miklos Santha, Nitin Saxena","submitted_at":"2015-02-23T21:12:46Z","abstract_excerpt":"We consider the problem of recovering (that is, interpolating) and identity testing of a \"hidden\" monic polynomial $f$, given an oracle access to $f(x)^e$ for $x\\in{\\mathbb F_q}$ (extension fields access is not permitted). The naive interpolation algorithm needs $O(e\\, \\mathrm{deg}\\, f)$ queries and thus requires $e\\, \\mathrm{deg}\\, f<q$. We design algorithms that are asymptotically better in certain cases; requiring only $e^{o(1)}$ queries to the oracle. In the randomized (and quantum) setting, we give a substantially better interpolation algorithm, that requires only $O(\\mathrm{deg}\\, f \\log"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.06631","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"}