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For all vectorial boolean functions up to dimension 4, we present canonical representatives for all extended affine (EA) and CCZ equivalence classes. We include the size of each class, as well as its ...
Two vectorial Boolean functions are ``CCZ-equivalent'' if there exists an affine permutation mapping the graph of one to the other. It preserves many of the cryptographic properties of a function such...
Recently, many new classes of differentially 44-uniform permutations have been constructed. However, it is difficult to decide whether they are CCZ-inequivalent or not. In this paper, we propose a new...
A function $F$ from \textbf{F}$_{p^n}$ to itself is planar if for any $a\in$\textbf{F}$_{p^n}^*$ the function $F(x+a)-F(x)$ is a permutation. CCZ-equivalence is the most general known equivalence rela...
We study further CCZ-equivalence of (n,m)-functions. We prove that for Boolean functions (that is, for m = 1), CCZ-equivalence coincides with EA-equivalence. On the contrary, we show that for (n,m)...
We prove that, for bent vectorial functions, CCZ-equivalence coincides with EA-equivalence. However, we show that CCZ-equivalence can be used for constructing bent functions which are new up to CCZe...

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