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

Autor:	Leander, Gregor, Rodier, François
Rok vydání:	2009
Předmět:	Mathematics - Algebraic Geometry Computer Science - Cryptography and Security
Druh dokumentu:	Working Paper
Popis:	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 $m \le 3$ where these functions are equivalent to $x^3$.
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/0901.4322 Zobrazit plný text záznamu View this record from Arxiv