2 problems

Let $n=2m$. For integers $r<m$ with $\gcd(r,m)=1$, define $s$ by … Set $F_1(x)=x^{s(2^m-1)+1}$ over $\mathbb{F}_{2^{2m}}$. A power function is Niho type locally-APN if it is both o…

Let $m$ be even and consider the power function $F(x)=x^{4(2^m-1)+1}$ over $\mathbb{F}_{2^{2m}}$. Its cross-correlation should take at most five distinct values. Niho's conjecture.…