On Designs and Multiplier Groups Constructed from Almost Perfect Nonlinear Functions

Let $f:{\mathbb{F}_2^{n}}\to {\mathbb{F}_2^{n}}$ be an almost perfect nonlinear function (APN). The set $D_f:=\{(a,b)\: :\: f(x+a)-f(x)=b\mbox{\ has two solutions}\}$ can be used to distinguish APN functions up to equivalence. We investigate the multiplier groups of theses sets D f . This extends earlier work done by the authors [1].

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