Some APN functions CCZ-equivalent to gold functions and EA-inequivalent to power functions over GF(2^n)
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Some APN functions [math]\displaystyle{ CCZ- }[/math]equivalent to gold functions and EA-enequivalent to power functions over [math]\displaystyle{ \mathbb{F}_{2^n} }[/math]
Some APN functions [math]\displaystyle{ CCZ- }[/math]equivalent to gold functions and EA-enequivalent to power functions over [math]\displaystyle{ \mathbb{F}_{2^n} }[/math] (constructed in [1]
| Functions | Conditions | [math]\displaystyle{ d^\circ }[/math] |
|---|---|---|
| [math]\displaystyle{ x^{2^i+1}+(x^{2^i}+x+tr_n(1)+1)tr(x^{2^i+1}+x\ tr_n(1)) }[/math] | [math]\displaystyle{ n\geq4,\ gcd(i,n)=1 }[/math] | 3 |
| [math]\displaystyle{ [x+tr_{n/3}(x^{2(2^i+1)}+x^{4(2^i+1)})+tr(x)\, tr_{n/3}(x^{2^i+1}+x^{2^{2i}(2^i+1)})]^{2^i+1} }[/math] | [math]\displaystyle{ 6|n,\ gcd(i,n)=1 }[/math] | 4 |
| [math]\displaystyle{ x^{2^i+1}+tr_{n/m}(x^{2^i+1})+x^{2^i}tr_{n/m}(x)+xtr_{n/m}(x)^{2^i}+[tr_{n/m}(x)^{2^i+1}+tr_{n/m}(x^{2^i+1}) +tr_{n/m}(x)]^{\frac{1}{2^i+1}}(x^{2^i}+tr_{n/m}(x)^{2^i}+1)+[tr_{n/m}(x)^{2^i+1}+tr_{n/m}(x^{2^i+1}) +tr_{n/m}(x)]^{\frac{2^i}{2^i+1}}(x+tr_{n/m}(x)) }[/math] | [math]\displaystyle{ m\neq n,\ n\ odd,\ m|n,\ gcd(i,n)=1 }[/math] | [math]\displaystyle{ m+2 }[/math] |
- ↑ Budaghyan, Lilya, Claude Carlet, and Alexander Pott. "New classes of almost bent and almost perfect nonlinear polynomials." IEEE Transactions on Information Theory 52.3 (2006): 1141-1152.