Permutations from APN power functions over <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML">  <msub>  <mi>F</mi>  <mrow>   <msup>    <mn>2</mn>    <mrow>     <mn>2</mn><mi>n</mi></mrow>   </msup>   </mrow> </msub> </math></inline-formula>

Shi-zhu TIAN

doi:10.11959/j.issn.2096-109x.2017.00203

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Permutations from APN power functions over

F_{2^{2 n}}

Papers | 更新时间：2024-06-03

- Permutations from APN power functions over $F_{2^{2 n}}$
- Chinese Journal of Network and Information Security Vol. 3, Issue 10, Pages: 72-76(2017)
- 作者机构：
  
  1. 中国科学院信息工程研究所信息安全国家重点实验室，北京100093
  2. 中国科学院大学，北京 100049
- 作者简介：
- 基金信息：
- DOI：10.11959/j.issn.2096-109x.2017.00203
  CLC： TP393
- Online First：2017-10，
  
  Published：15 October 2017
- 稿件说明：
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Shi-zhu TIAN. Permutations from APN power functions over $F_{2^{2 n}}$ [J]. Chinese Journal of Network and Information Security, 2017, 3(10): 72-76.
DOI：

Shi-zhu TIAN. Permutations from APN power functions over $F_{2^{2 n}}$ [J]. Chinese Journal of Network and Information Security, 2017, 3(10): 72-76. DOI： 10.11959/j.issn.2096-109x.2017.00203.

Permutations from APN power functions over

F_{2^{2 n}}

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摘要

APN 函数是特征为 2 的有限域上达到最低差分均匀度的函数，其中最经典的是 APN 幂函数。在

上的APN幂函数都是3-1函数。推广了前人在奇特征有限域上由2-1函数构造置换的思想，得到偶特征域上由3-1函数构造置换的方法，并由

上的APN幂函数构造置换。根据这种构造，研究了此类置换的差分性质。

Abstract

APN functions have the lowest differential uniform over finite fields with characteristic 2 and the APN power functions are the most classical ones.APN power functions are all 3-1 functions over

.By generalizing the idea of changing 2-1 functions to 1-1 functions over finite fields with odd characteristics

methods to change 3-1 functions over finite fields with even characteristics into permutations were obtained and permutations from APN power functions over

were constructed.According to the construction

the differential properties of permutations obtained by this method were discussed.

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references

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Permutations from APN power functions over F 2 2n

DOI：10.11959/j.issn.2096-109x.2017.00203

摘要

Abstract

关键词

Keywords

references

Permutations from APN power functions over $F_{2^{2 n}}$