# Difference between revisions of "Some APN functions CCZ-equivalent to Gold functions and EA-inequivalent to power functions over GF(2^n)"

Some APN functions CCZ-equivalent to Gold functions and EA-inequivalent to power functions over${\displaystyle \mathbb {F} _{2^{n}}}$[1].
Functions Conditions ${\displaystyle d^{\circ }}$
${\displaystyle x^{2^{i}+1}+(x^{2^{i}}+x+{\mathrm {T} r}_{n}(1)+1){\mathrm {T} r}_{n}(x^{2^{i}+1}+x\ {\mathrm {T} r}_{n}(1))}$ ${\displaystyle n\geqslant 4}$, ${\displaystyle \gcd(i,n)=1}$ ${\displaystyle 3}$
${\displaystyle [x+{\mathrm {T} r}_{n}^{3}(x^{2(2^{i}+1)}+x^{4(2^{i}+1)})+{\mathrm {T} r}_{n}(x){\mathrm {T} r}_{n}^{3}(x^{2^{i}+1}+x^{2^{2i}(2^{i}+1)})]^{2^{i}+1}}$ ${\displaystyle 6|n\ ,\gcd(i,n)=1}$ ${\displaystyle 4}$
${\displaystyle x^{2^{i}+1}+{\mathrm {T} r}_{n}^{m}(x^{2^{i}+1})+x^{2^{i}}{\mathrm {T} r}_{n}^{m}(x)+x\ {\mathrm {T} r}_{n}^{m}(x)^{2^{i}}}$
${\displaystyle +[{\mathrm {T} r}_{n}^{m}(x)^{2^{i}+1}+{\mathrm {T} r}_{n}^{m}(x^{2^{i}+1})+{\mathrm {T} r}_{n}^{m}(x)]^{\frac {1}{2^{i}+1}}(x^{2^{i}}+{\mathrm {T} r}_{n}^{m}(x)^{2^{i}}+1)}$
${\displaystyle +[{\mathrm {T} r}_{n}^{m}(x)^{2^{i}+1}+{\mathrm {T} r}_{n}^{m}(x^{2^{i}+1})+{\mathrm {T} r}_{n}^{m}(x)]^{\frac {2^{i}}{2^{i}+1}}(x+{\mathrm {T} r}_{n}^{m}(x))}$
${\displaystyle \ m\neq n\ ,n\ odd\ ,m|n\ ,\gcd(i,n)=1\ }$ ${\displaystyle \ m+2\ }$