Trims and extensions of quadratic APN functions

Abstract In this work, we study functions that can be obtained by restricting a vectorial Boolean function $$F :\mathbb {F}_{2}^n \rightarrow \mathbb {F}_{2}^n$$ F:F2n→F2n to an affine hyperplane of dimension $$n-1$$ xmlns:mml="http://www.w3.org/1998/Math/MathML">n-1 and then projecting the output -dimensional space. We show multiset $$2 \cdot (2^n-1)^2$$ xmlns:mml="http://www.w3.org/1998/Math/MathML">2·(2n-1)2 EA-equivalence classes such restrictions defines EA-invariant for on $$\mathbb xmlns:mml="http://www.w3.org/1998/Math/MathML">F2n . Further, all known quadratic APN in $$n < 10$$ xmlns:mml="http://www.w3.org/1998/Math/MathML">n<10 , determine are also APN. Moreover, construct 6368 new eight up extending seven. A special focus work is with maximum linearity. particular, characterize linearity $$2^{n-1}$$ xmlns:mml="http://www.w3.org/1998/Math/MathML">2n-1 property ortho-derivative its restriction linear hyperplane. Using fact seven classified, able obtain classification 8-bit $$2^7$$ xmlns:mml="http://www.w3.org/1998/Math/MathML">27 EA-equivalence.