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Extended Affine and CCZ Equivalence up to Dimension 4
boolean functions extended affine equivalence CCZ equivalence
2019/4/1
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 ...
On CCZ-Equivalence, Extended-Affine Equivalence, and Function Twisting
Boolean functions CCZ-Equivalence EA-equivalence
2018/8/2
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...
A New Method to Investigate the CCZ-Equivalence between Functions with Low Differential Uniformity
Differentially 44-uniform function Projected differential spectrum Substitution boxes
2016/12/12
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...
On isotopisms of commutative presemifields and CCZ-equivalence of functions
Commutative semifield CCZ-equivalence EA-equivalence isotopism of presemifields Perfect nonlinear Planar function
2010/10/11
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...
CCZ-equivalence and Boolean functions
Affine equivalence Almost perfect nonlinear Bent function
2009/6/11
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)...
On CCZ-equivalence and its use in secondary constructions of bent functions
Affine equivalence Almost perfect nonlinear Bent function
2009/6/11
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...