Bounds on the degree of APN polynomials The Case of x^(-1)+g(x)

Gregor Leander (1) , François Rodier (2)

1 DTU - Danmarks Tekniske Universitet = Technical University of Denmark
2 IML - Institut de mathématiques de Luminy

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.

Domaines: Géométrie algébrique [math.AG]; Cryptographie et sécurité [cs.CR]

Gregor Leander, François Rodier. Bounds on the degree of APN polynomials The Case of x^(-1)+g(x). 2009. ⟨hal-00356562⟩