Difference between revisions of "APN polynomials over GF(2^n) CCZinequivalent to quadratic functions and monomials"
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Revision as of 20:30, 9 July 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 CCZinequivalent 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. 273288, 2008. https://doi.org/10.1007/s1062300891946
 ↑ M. Brinkmann, G. Leander. On the classification of APN functions up to dimension five. Designs, Codes and Cryptography 49, pp. 273288, 2008. https://doi.org/10.1007/s1062300891946