CCZ-Equivalence
We call two \((m,n,p)\)-functions \(f(x)\) and \(g(x)\) Carlet-Charpin-Zimoviev equivalent (or CCZ-equivalent) provided for any Affine Permutation \(\mathcal{L}\), the image of the graph of \(f(x)\) under \(\mathcal{L}\) is equal to the graph of \(g(x)\). That is:
\[ \mathcal{L}(\mathcal{G}_f)=\mathcal{G}_g \] (sidenote: In general, CCZ-equivalence of two \((m,n,p)\)-functions is hard to prove. However, we do have the following implication: (1). CCZ-equivalence \(\implies\) EA-equivalence )