Polynomials with maximal differential uniformity and the exceptional APN conjecture
Résumé
We contribute to the exceptional APN conjecture by showing that no polynomial of degree m = 2 r (2 ℓ + 1) where gcd(r, ℓ) 2, r 2, ℓ 1 with a nonzero second leading coefficient can be APN over infinitely many extensions of the base field. More precisely, we prove that for n sufficiently large, all polynomials of F 2 n [x] of such a degree with a nonzero second leading coefficient have a differential uniformity equal to m − 2.
Domaines
Théorie des nombres [math.NT]| Origine | Fichiers produits par l'(les) auteur(s) |
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