Bounds on the degree of APN polynomials The Case of x^(-1)+g(x)
Résumé
We prove that functions f:F_{2^m} to F_{2^m} of the form f(x)=x^(-1)+g(x) where g is any non-affine polynomial are APN on at most a finite number of fields F_{2^m}. Furthermore we prove that when the degree of g is less then 7 such functions are APN only if m <4 where these functions are equivalent to x^3.
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