Some APN functions CCZ-equivalent to Gold functions and EA-inequivalent to power functions over
[1].
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![{\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}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/c9783b892a9af9397f251cce93a833c23b3c2361) |
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![{\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))}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/c681faa145ca3c551c5b95627515398ed9bcbc81) |
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- ↑ L. Budaghyan, C.Carlet, A. Pott. New classes of almost bent and almost perfect nonlinear polynomials. IEEE Trans. Inf. Theoery, vol. 52, no. 3, pp. 1141-1152, 2006. https://doi.org/10.1109/TIT.2005.864481