2 problems

Let $m$ be a positive integer and let $\mathbb{F}_{2^m}$ be the finite field with $2^m$ elements. A function $F:\mathbb{F}_{2^m}\to\mathbb{F}_{2^m}$ is almost perfect nonlinear (AP…

Nonexistence conjecture. For sufficiently large $n$, there are no monomial GAPN functions $f_d$ on $\mathbb{F}_{p^n}$ satisfying