An infinite class of quadratic APN functions which are not equivalent to power mappings

Abstract

We exhibit an infinite class of almost perfect nonlinear quadratic polynomials from F2n to F2n (n ges 12, n divisible by 3 but not by 9). We prove that these functions are EA-inequivalent to any power function and that they are CCZ-inequivalent to any Gold function. In a forthcoming full paper, we shall also prove that at least some of these functions are CCZ-inequivalent to any Kasami function