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Some APN functions <math>CCZ-</math>equivalent to gold functions and EA-enequivalent to power functions over <math>\mathbb{F}_{2^n}</math>
Some APN functions <math>CCZ-</math>equivalent to gold functions and EA-enequivalent to power functions over <math>\mathbb{F}_{2^n}</math> (constructed in [1]
| Functions | Conditions | <math>d^\circ</math> |
|---|---|---|
| <math>x^{2^i+1}+(x^{2^i}+tr_n(1)+1)tr(x^{2^i+1}+xtr_n(1))</math> | <math>n\geq4,\ gcd(i,n)=1</math> | 3 |
| <math>x+tr_{n/3}(x^{2(2^i+1)}+x^{4(2^i+1)})+tr_n(x)\, tr_{n/3}(x^{2^i+1}+x^{2^{2i}(2^i+1)})^{2^i+1}</math> | <math>6|n,\ gcd(i,n)=1</math> | 4 |
| <math>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>m\neq n,\ n\ odd,\ m|n,\ gcd(i,n)=1</math> | <math>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.