On APN functions in odd characteristic, the disproof of a conjecture and related problems
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908350541725696 |
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| author | Bartoli, Daniele Stanica, Pantelimon |
| author_facet | Bartoli, Daniele Stanica, Pantelimon |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_02585 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On APN functions in odd characteristic, the disproof of a conjecture and related problems Bartoli, Daniele Stanica, Pantelimon Algebraic Geometry Information Theory Number Theory 11G20, 11T06, 12E20, 14Q10 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. |
| title | On APN functions in odd characteristic, the disproof of a conjecture and related problems |
| topic | Algebraic Geometry Information Theory Number Theory 11G20, 11T06, 12E20, 14Q10 |
| url | https://arxiv.org/abs/2505.02585 |