Generalized Boolean bent functions

Laurent Poinsot (1) , Sami Harari (1)

1 PPF-STIC

The notions of perfect nonlinearity and bent functions are closely dependent on the action of the group of translations over $\mathbb{F}_2^m$. Extending the idea to more generalized groups of involutions without fixed points gives a larger framework to the previous notions. In this paper we largely develop this concept to define $G$-perfect nonlinearity and $G$-bent functions, where $G$ is an Abelian group of involutions, and to show their equivalence as in the classical case.

Domaines: Théorie des groupes [math.GR]; Théorie de l'information et codage [math.IT]; Théorie de l'information [cs.IT]; Cryptographie et sécurité [cs.CR]

Laurent Poinsot, Sami Harari. Generalized Boolean bent functions. INDOCRYPT 2004, Dec 2004, Chennai, India. pp.107-119, ⟨10.1007/b104579⟩. ⟨hal-00460340⟩