On a conjecture on APN permutations
Information Theory
2024-10-28 v1 Combinatorics
math.IT
Abstract
The single trivariate representation proposed in [C. Beierle, C. Carlet, G. Leander, L. Perrin, A Further Study of Quadratic APN Permutations in Dimension Nine, arXiv:2104.08008] of the two sporadic quadratic APN permutations in dimension 9 found by Beierle and Leander \cite{Beierle} is further investigated. In particular, using tools from algebraic geometry over finite fields, we prove that such a family does not contain any other APN permutation for larger dimensions.
Cite
@article{arxiv.2105.03702,
title = {On a conjecture on APN permutations},
author = {Daniele Bartoli and Marco Timpanella},
journal= {arXiv preprint arXiv:2105.03702},
year = {2024}
}
Comments
This work has been submitted to the IEEE for possible publication