网络与信息安全学报 ›› 2017, Vol. 3 ›› Issue (10): 72-76.doi: 10.11959/j.issn.2096-109x.2017.00203

• 学术论文 • 上一篇    

由APN幂函数构造 F 2 2n 上的置换

田诗竹1,2()   

  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)

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 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。

关键词: 有限域, 置换多项式, APN, 幂函数

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.

Key words: finite fields, permutation polynomials, APN, power functions

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