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Journal Articles (Review Article) Journal of Algebra Year : 2023

Polynomials with maximal differential uniformity and the exceptional APN conjecture

Abstract

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.
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Dates and versions

hal-03739111 , version 1 (26-07-2022)

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Yves Aubry, Ali Issa, Fabien Herbaut. Polynomials with maximal differential uniformity and the exceptional APN conjecture. Journal of Algebra, 2023, 635, pp.822-837. ⟨10.1016/j.jalgebra.2023.07.017⟩. ⟨hal-03739111⟩
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