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On APN functions in odd characteristic, the disproof of a conjecture and related problems

Published: May 5, 2025 | arXiv ID: 2505.02585v1

By: Daniele Bartoli, Pantelimon Stanica

Potential Business Impact:

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Business Areas:
NFC Hardware

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 $q$ is larger than~$9587$, 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.

Page Count
19 pages

Category
Mathematics:
Algebraic Geometry