TRINOMIALS WITH HIGH DIFFERENTIAL UNIFORMITY

Yves Aubry (1, 2, 3) , Fabien Herbaut (4, 1) , Ali Issa (2, 5)

1 IMATH - Institut de Mathématiques de Toulon - EA 2134
2 I2M - Institut de Mathématiques de Marseille
3 UTLN - Université de Toulon
4 UCA INSPE - Institut national supérieur du professorat et de l'éducation - Académie de Nice
5 AMU - Aix Marseille Université

The context of this work is the study of the differential uniformity of polynomials defined over finite fields of even characteristic. We provide infinite families of trinomials with high differential uniformity when the base field is large enough. It means in particular that these trinomials are not exceptional almost perfect nonlinear.

Mots clés: Polynomials over finite fields; differential uniformity; Chebotarev theorem; exceptional APN conjecture

Domaines: Théorie des nombres [math.NT]

Yves Aubry, Fabien Herbaut, Ali Issa. TRINOMIALS WITH HIGH DIFFERENTIAL UNIFORMITY. 2024. ⟨hal-04546074⟩