# Difference between revisions of "APN polynomials over GF(2^n) CCZ-inequivalent to quadratic functions and monomials"

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− | where is α is primitive in GF(2^6), is the only known example of an APN function CCZ-inequivalent to a monomial or quadratic function <ref>Brinkmann | + | where is α is primitive in GF(2^6), is the only known example of an APN function CCZ-inequivalent to a monomial or quadratic function <ref>M. Brinkmann, G. Leander. On the classification of APN functions up to dimension five. Designs, Codes and Cryptography 49, pp. 273-288, 2008. https://doi.org/10.1007/s10623-008-9194-6</ref><ref>Y. Edel, A. Pott. A new almost perfect nonlinear function which is not quadratic. Advances in Mathematics of Communications 3 (1), pp. 59-81, 2009. https://doi.org/10.3934/amc.2009.3.59</ref>. A [[:File:Cubic.txt|Magma implementation of the polynomial]] is available. |

## Latest revision as of 10:32, 27 August 2020

# n = 6

The polynomial

x^{3} + α^{17}(x^{17} + x^{18} + x^{20} + x^{24}) + α^{14}( Tr( α^{52}x^{3} + α^{6}x^{5} + α^{19}x^{7} + α^{28}x^{11} + α^{2}x^{13}) + (α^{2}x)^{9} + (α^{2}x)^{18} + (α^{2}x)^{36} + x^{21} + x^{42})

where is α is primitive in GF(2^6), is the only known example of an APN function CCZ-inequivalent to a monomial or quadratic function ^{[1]}^{[2]}. A Magma implementation of the polynomial is available.

- ↑ M. Brinkmann, G. Leander. On the classification of APN functions up to dimension five. Designs, Codes and Cryptography 49, pp. 273-288, 2008. https://doi.org/10.1007/s10623-008-9194-6
- ↑ Y. Edel, A. Pott. A new almost perfect nonlinear function which is not quadratic. Advances in Mathematics of Communications 3 (1), pp. 59-81, 2009. https://doi.org/10.3934/amc.2009.3.59