On the EA-classes of known APN functions in small dimensions

Calderini Marco

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On the EA-classes of known APN functions in small dimensions

机译：在已知APN的EA类上的小尺寸

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Recently Budaghyan et al. (Cryptogr. Commun. 12, 85-100, 2020) introduced a procedure for investigating if CCZ-equivalence can be more general than EA-equivalence together with inverse transformation (when applicable). In this paper, we show that it is possible to use this procedure for classifying, up to EA-equivalence, all known APN functions in dimension 6. We also give some discussion for dimension 7, 8 and 9. In particular, in these cases it is possible to give an upper bound on the EA-classes contained in the CCZ-classes of the known APN functions.

机译：最近Bugaghyan等。（Cryptogr。Communce。12,85-100,2020）介绍了调查的过程，如果CCZ - 当量可以比EA - 等价更为一般，以及逆变换（适用时）。在本文中，我们表明，可以使用此过程来对尺寸6中的所有已知APN函数进行分类。我们还提供了一些讨论尺寸7,8和9。特别是在这些情况下可以在已知APN函数的CCZ类中包含的EA类上提供上限。

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《Cryptography and Communications》 |2020年第5期|821-840|共20页
作者
Calderini Marco;
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作者单位

Univ Bergen Dept Informat PB 7803 N-5020 Bergen Norway;

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原文格式 PDF
正文语种 eng
中图分类
关键词
EA-equivalence; CCZ-equivalence; Boolean functions; APN;

机译：EA - 等价;CCZ - 等价;布尔函数;APN;

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1. Classification of quadratic APN functions with coefficients in F_2 for dimensions up to 9 [J] . Yu Yuyin, Kaleyski Nikolay, Budaghyan Lilya, Finite fields and their applications . 2020,第Deca期

机译：二次APN的分类在F_2中的系数函数，尺寸高达9
2. Isomorphisms and automorphisms of extensions of bilinear dimensional dual hyperovals and quadratic APN functions [J] . Dempwolff Ulrich, Edel Yves Journal of group theory . 2016,第2期

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3. Dimensional dual hyperovals and APN functions with translation groups [J] . Ulrich Dempwolff, Yves Edel Journal of algebraic combinatorics . 2014,第2期

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4. On the Properties of Vectorial Functions with Plateaued Components and Their Consequences on APN Functions [C] . Claude Carlet Iinternational conference on codes, cryptology, and information security . 2015

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On the EA-classes of known APN functions in small dimensions

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