3 problems

APN monomial classification conjecture. No other APN monomials exist over ${\mathbb F}_{2^n}$ up to cyclotomic equivalence.

Let $n$ be even and let $F:\mathbb{F}_{2^n}\to\mathbb{F}_{2^n}$ be a function. Its nonlinearity is … The known maximum nonlinearity is $2^{n-1}-2^{\frac n2}$. Even-dimensional nonl…

Let $k$ be odd, and consider the butterfly structures over $\mathbb{F}_{2^{2k}}$ with exponent $e=3\times 2^t$, whose nonlinearity has been verified experimentally to equal…