A new large class of functions not APN infinitely often

Florian Caullery

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A new large class of functions not APN infinitely often

机译：并非无限频繁地使用APN的一大类新功能

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摘要

We show that there is no vectorial Boolean function of degree 4e, with some conditions on e, which is APN over infinitely many extensions of its field of definition. It is a new step in the proof of the conjecture of Aubry, McGuire and Rodier.

机译：我们证明，在e上有某些条件的情况下，不存在4e级的矢量布尔函数，这是APN在其定义域的无限多个扩展上的结果。这是证明Aubry，McGuire和Rodier猜想的新步骤。

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来源
《Designs, Codes and Crytography》 |2014年第2期|601-614|共14页
作者
Florian Caullery;
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作者单位

Institut of Mathematiques of Marseille, Marseille, France;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类
关键词
Vectorial Boolean functions; Almost perfect non-linear functions; Algebraic surface; CCZ equivalence;

机译：向量布尔函数;几乎完美的非线性函数;代数曲面CCZ等效;

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专利

1. Partially APN Boolean functions and classes of functions that are not APN infinitely often [J] . Budaghyan Lilya, Kaleyski Nikolay S., Kwon Soonhak, Cryptography and Communications . 2020,第3期

机译：部分APN布尔函数和函数类别不确定不确定
2. Functions of degree 4e that are not APN infinitely often [J] . François Rodier Cryptography and Communications . 2011,第4期

机译：4e次函数不是APN无限频繁的函数
3. On the Fourier spectra of the infinite families of quadratic APN functions [J] . Bracken C., Zha Z. Advances in mathematics of communications . 2009,第3期

机译：关于二次APN函数的无限族的傅立叶谱
4. An infinite class of quadratic APN functions which are not equivalent to power mappings [C] . Lilya Budaghyan, Claude Carlet, Patrick Felke, . 2006

机译：无限类的二次APN函数，不等于幂映射
5. Analysis of conduction heat transfer in semi-infinite slabs and infinite quadrants with discrete heat generation sources using Green's function integral methods. [D] . Meza Castillo, Omar Enrique. 2003

机译：使用格林函数积分法分析具有离散生热源的半无限平板和无限象限中的传导传热。
6. CLASSIFICATION OF THE REAL INFINITE SIMPLE AND REAL INFINITE PRIMITIVE LIE ALGEBRAS [O] . Steven Shnider 2016

机译：实无限简单和实无限原始李代数的分类
7. Partially APN Boolean functions and classes of functions that are not APN infinitely often [O] . Lilya Budaghyan, Nikolay S. Kaleyski, Soonhak Kwon, 2019

机译：部分APN布尔函数和函数类别不确定不确定

A new large class of functions not APN infinitely often

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