Some APN functions
equivalent to gold functions and EA-enequivalent to power functions over 
Some APN functions
equivalent to gold functions and EA-enequivalent to power functions over
(constructed in [1]
| Functions |
Conditions |
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3 |
![{\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}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4cb0f3c8c312d4fd0fee2d45b7c75de68f39ad64) |
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4 |
![{\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))}](https://wikimedia.org/api/rest_v1/media/math/render/svg/41a80717553a296cd61e2fe416a0eeaee0d384ef) |
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- ↑ 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.