Maximal Differential Uniformity Polynomials

Yves Aubry (1, 2) , Fabien Herbaut (1, 3, 4) , José Felipe Voloch (5)

1 IMATH - Institut de Mathématiques de Toulon - EA 2134
2 I2M - Institut de Mathématiques de Marseille
3 ESPE Nice - École supérieure du professorat et de l'éducation - Académie de Nice
4 COMUE UCA - COMUE Université Côte d'Azur (2015-2019)
5 University of Canterbury [Christchurch]

We provide explicit infinite families of integers m such that all the polynomials of F2n [x] of degree m have maximal differential uniformity for n large enough. We also prove a conjecture of the third author for these families.

Domaines: Mathématiques [math]; Théorie des nombres [math.NT]

Yves Aubry, Fabien Herbaut, José Felipe Voloch. Maximal Differential Uniformity Polynomials. Acta Arithmetica, 2019, 188 (4), pp.345-366. ⟨10.4064/aa170806-11-7⟩. ⟨hal-01823955⟩