Welcome to the resource topic for 2006/445
Title:
A class of quadratic APN binomials inequivalent to power functions
Authors: Lilya Budaghyan, Claude Carlet, Gregor Leander
Abstract:We exhibit an infinite class of almost perfect nonlinear quadratic binomials from \mathbb{F}_{2^n} to \mathbb{F}_{2^n} (n\geq 12, n divisible by 3 but not by 9). We prove that these functions are EA-inequivalent to any power function and that they are CCZ-inequivalent to any Gold function and to any Kasami function. It means that for n even they are CCZ-inequivalent to any known APN function, and in particular for n=12,24, they are therefore CCZ-inequivalent to any power function. It is also proven that, except in particular cases, the Gold mappings are CCZ-inequivalent to the Kasami and Welch functions.
ePrint: https://eprint.iacr.org/2006/445
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