{"paper":{"title":"Differential Spectrum and Boomerang Spectrum of Some Power Mapping","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Jinquan Luo, Yuehui Cui","submitted_at":"2025-06-06T04:41:25Z","abstract_excerpt":"Let $f(x)=x^{s(p^m-1)}$ be a power mapping over $\\mathbb{F}_{p^n}$, where $n=2m$ and $\\gcd(s,p^m+1)=t$. In \\cite{kpm-1}, Hu et al. determined the differential spectrum and boomerang spectrum of the power function $f$, where $t=1$. So what happens if $t\\geq1$? In this paper, we extend the result of \\cite{kpm-1} from $t=1$ to general case. We use a different method than in \\cite{kpm-1} to determine the differential spectrum and boomerang spectrum of $f$ by studying the number of rational points on some curves. This method may be helpful for calculating the differential spectrum and boomerang spe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.05738","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.05738/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}