# 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>Edel Y, Pott A. A new almost perfect nonlinear function which is not quadratic. Adv. in Math. of Comm.. 2009 Feb 1;3(1):59-81.</ref> A [[:File:Cubic.txt|Magma implementation of the polynomial]] is available. | + | 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 M, Lender G. On the classification of APN functions up to dimension five. Des. Codes Cryptogr.,49 (2008), 273-288</ref><ref>Edel Y, Pott A. A new almost perfect nonlinear function which is not quadratic. Adv. in Math. of Comm.. 2009 Feb 1;3(1):59-81.</ref> A [[:File:Cubic.txt|Magma implementation of the polynomial]] is available. |

## Revision as of 17:30, 5 November 2019

# 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.