Abstract:
Vectorial Boolean functions whose component functions belong to the same equivalence class are studied. Cases of the affine equivalence and the affine equivalence up to adding a constant are considered. For all elements of $\mathbb{F}_2^m$, the preimage sizes under a vectorial Boolean function $F: \mathbb{F}_2^n \to \mathbb{F}_2^m$ with affine equivalent components have been established. For $F: \mathbb{F}_2^n \to \mathbb{F}_2^m$ whose component functions are all affine equivalent to a function $f: \mathbb{F}_2^n \to \mathbb{F}_2$, estimates for $m$ based on the Hamming weight of $f$ have been obtained. A construction for vectorial Boolean functions meeting the obtained estimates has been proposed. Estimates have been also obtained for vector Boolean functions with components that are affinely equivalent up to the addition of a constant.
Keywords:vectorial Boolean functions, affine equivalence, affine equivalence up to adding a constant, component functions.
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