A few more functions that are not APN infinitely often

Details A few more functions that are not APN infinitely often A few more functions that are not APN infinitely often

2009-09-12

arxiv.org/abs/0909.2304v2

Mathematics

Algebraic Geometry

Scientific paper

We consider exceptional APN functions on ${\bf F}_{2^m}$, which by definition are functions that are not APN on infinitely many extensions of ${\bf F}_{2^m}$. Our main result is that polynomial functions of odd degree are not exceptional, provided the degree is not a Gold member ($2^k+1$) or a Kasami-Welch number ($4^k-2^k+1$). We also have partial results on functions of even degree, and functions that have degree $2^k+1$.

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