{"paper":{"title":"On the Conjecture on APN Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.CO","math.IT"],"primary_cat":"cs.IT","authors_text":"Heeralal Janwa, Moises Delgado","submitted_at":"2012-07-23T20:24:42Z","abstract_excerpt":"An almost perfect nonlinear (APN) function (necessarily a polynomial function) on a finite field $\\mathbb{F}$ is called exceptional APN, if it is also APN on infinitely many extensions of $\\mathbb{F}$. In this article we consider the most studied case of $\\mathbb{F}=\\mathbb{F}_{2^n}$.\n  A conjecture of Janwa-Wilson and McGuire-Janwa-Wilson (1993/1996), settled in 2011, was that the only exceptional monomial APN functions are the monomials $x^n$, where $n=2^i+1$ or $n={2^{2i}-2^i+1}$ (the Gold or the Kasami exponents respectively). A subsequent conjecture states that any exceptional APN functio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.5528","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"}