## Cryptology ePrint Archive: Report 2007/098

Classes of Quadratic APN Trinomials and Hexanomials and Related Structures

Lilya Budaghyan and Claude Carlet

Abstract: A method for constructing differentially 4-uniform quadratic hexanomials has been recently introduced by J. Dillon. We give various generalizations of this method and we deduce the constructions of new infinite classes of almost perfect nonlinear quadratic trinomials and hexanomials from $\mathbb{F}_{2^{2m}}$ to $\mathbb{F}_{2^{2m}}$. We check for $m=3$ that some of these functions are CCZ-inequivalent to power functions.

Category / Keywords: secret-key cryptography / Affine equivalence, Almost bent, Almost perfect nonlinear, CCZ-equivalence, Differential uniformity, Nonlinearity, S-box, Vectorial Boolean function