A class of quadratic APN binomials inequivalent to power functions.
Lilya Budaghyan, Claude Carlet, Gregor Leander · 2006
We exhibit an infinite class of almost perfect nonlinear quadratic binomials from F2n to F2n (n ≥ 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 and to any Kasami function. It means that for n even they are CCZ-inequivalent to any known APN function, and in particular for n = 12,24, they are therefore CCZ-inequivalent to any power function. It is also proven that, except in particular cases, the Gold mappings are CCZ-inequivalent to the Kasami and Welch functions.