On APN functions in odd characteristic, the disproof of a conjecture and related problems
Algebraic Geometry
2025-05-06 v1 Information Theory
math.IT
Number Theory
Abstract
In this paper disprove a conjecture by Pal and Budaghyan (DCC, 2024) on the existence of a family of APN permutations, but showing that if the field's cardinality is larger than~, then those functions will never be APN. Moreover, we discuss other connected families of functions, for potential APN functions, but we show that they are not good candidates for APNess if the underlying field is large, in spite of the fact that they though they are APN for small environments.
Cite
@article{arxiv.2505.02585,
title = {On APN functions in odd characteristic, the disproof of a conjecture and related problems},
author = {Daniele Bartoli and Pantelimon Stanica},
journal= {arXiv preprint arXiv:2505.02585},
year = {2025}
}