• 学术论文 •

### 由APN幂函数构造${F}_{{2}^{2n}}$上的置换

1. 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
• 修回日期:2017-09-10 出版日期:2017-10-01 发布日期:2017-11-13
• 作者简介:田诗竹（1991-），女，湖北黄冈人，中国科学院信息工程研究所博士生，主要研究方向为信息安全、密码学。
• 基金资助:
国家自然科学基金资助项目(61379142)

### Permutations from APN power functions over ${F}_{{2}^{2n}}$

Shi-zhu TIAN1,2()

1. 1 The State Key Lab of Information Security,Institute of Information Engineering,Chinese Academy of Science,Beijing 100093,China
2 University of Chinese Academy of Sciences,Beijing 100049,China
• Revised:2017-09-10 Online:2017-10-01 Published:2017-11-13
• Supported by:
The National Natural Science Foundation of China(61379142)

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${F}_{{2}^{2n}}$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${F}_{{2}^{2n}}$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 ${F}_{{2}^{2n}}$.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 ${F}_{{2}^{2n}}$ were constructed.According to the construction,the differential properties of permutations obtained by this method were discussed.

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