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| HAL: hal-00415755, version 1 |
| arXiv: 0909.2304 |
| Detailed view |  Export this paper |
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| Available versions: | v1 (2009-09-12) | v2 (2009-11-13) |
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| A few more functions that are not APN infinitely often |
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| Yves Aubry 1Gary Mcguire 2 |
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| (2009-09-04) |
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| We consider exceptional APN functions on ${\bf F}_{2^m}$, which by definition are functions that are not APN on infinitely many extensions of ${\bf F}_{2^m}$. Our main result is that polynomial functions of odd degree are not exceptional, provided the degree is not a Gold member ($2^k+1$) or a Kasami-Welch number ($4^k-2^k+1$). We also have partial results on functions of even degree, and functions that have degree $2^k+1$. |
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| 1: | Institut de Mathématiques de Luminy (IML) |
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CNRS : UPR9016 |
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| 2: | Développement de l'enfant |
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University College Dublin (UCB) |
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| Subject | : | Mathematics/Algebraic Geometry |
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| Boolean functions – APN functions – exceptional polynomials |
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| Attached file list to this document: | ||||||||||
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| hal-00415755, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00415755 | |
| oai:hal.archives-ouvertes.fr:hal-00415755 | |
| From: Yves Aubry | |
| Submitted on: Friday, 11 September 2009 23:06:31 | |
| Updated on: Saturday, 12 September 2009 06:49:31 | |
