On the Equivalence of Quadratic APN Functions
Abstract
Establishing the CCZ-equivalence of a pair of APN functions is generally quite difficult. In some cases, when seeking to show that a putative new infinite family of APN functions is CCZ inequivalent to an already known family, we rely on computer calculation for small values of n. In this paper we present a method to prove the inequivalence of quadratic APN functions with the Gold functions. Our main result is that a quadratic function is CCZ-equivalent to an APN Gold function if and only if it is EA-equivalent to that Gold function. As an application of this result, we prove that a trinomial family of APN functions that exist on finite fields of order 2^n where n = 2 mod 4 are CCZ inequivalent to the Gold functions. The proof relies on some knowledge of the automorphism group of a code associated with such a function.
Keywords
Cite
@article{arxiv.1101.1508,
title = {On the Equivalence of Quadratic APN Functions},
author = {Eimear Byrne and Carl Bracken and Gary McGuire and Gabriele Nebe},
journal= {arXiv preprint arXiv:1101.1508},
year = {2011}
}
Comments
13 pg