C. Beierle

Linearity bounds for APN functions

For $n\ge5$, let $F\colon\mathbb{F}_2^n\to \mathbb{F}_2^n$ be almost perfect nonlinear and write $N=2^n$. It is proven that the linearity $\mathcal{L}(F)$ of $F$, i.e., the largest absolute Walsh coefficient of a nonzero component, is at most $N-10$ in even dimension and at most $N-6$ in odd dimension. This improves th...