Crooked functions

Pascale Charpin (1)

1 COSMIQ - Cryptologie symétrique, cryptologie fondée sur les codes et information quantique

Crooked permutations were introduced twenty years ago since they allow to construct interesting objects in graph theory. The field of applications was extended later. Crooked functions, bijective or not, correspond to APN functions and to some optimal codes. We adopt an unified presentation of crooked functions, explaining the connection with partially-bent functions. We then complete some known results and derive new properties. For instance, we observe that crooked functions allow to construct sets of bent functions and define some permutations.

Mots clés: Vectorial function; Boolean function; Derivative; Differential set; Plateaued function; Partially-bent functions; Bent functions; APN function; AB function; Permutation

Domaines: Mathématiques [math]

Pascale Charpin. Crooked functions. Proceedings of the 14th International Conference on Finite Fields and their Applications, Jun 2019, Vancouver, Canada. pp.87-102, ⟨10.1515/9783110621730-007⟩. ⟨hal-02969132⟩