一类APcN置换及其回旋镖均匀度的研究  

The Study of a Class of APcN Permutations and Its Boomerang Uniformity

作　　者：王艳[1] 朱思敏 李顺波[1] 王焕宇 WANG Yan;ZHU Simin;LI Shunbo;WANG Huanyu(School of Science,Xi'an University of Architecture and Technology,Xi'an,Shaanxi,710055,P.R.China)

机构地区：[1]西安建筑科技大学理学院,陕西西安710055

出　　处：《数学进展》2024年第6期1333-1344,共12页Advances in Mathematics（China）

基　　金：国家自然科学基金(No.61902304);应用数学湖北省重点实验室2022年度开放基金(No.HBAM-202202)。

摘　　要：S盒是设计分组密码的关键部件,也是大多数分组密码中唯一的非线性结构,其密码学指标的好坏直接决定了密码算法的安全强度.为了抵抗各种针对密码系统的攻击,应用于S盒中的密码函数应具有低c-差分均匀度和低回旋镖均匀度.本文利用迹函数构造了一类有限域上的置换函数.通过计算Wile和,研究了该函数的c-差分均匀度与回旋镖均匀度,并得到其是有限域上的几乎完全c-非线性(APcN)函数.S-box is a key component of block cipher design,and it is also the only nonlinear structure in most block ciphers.Its cryptographic index directly determines the security strength of the cipher algorithm.In order to resist various attacks on cryptosystem,the cryptographic functions applied to S-box should have low c-differential uniformity and low boomerang uniformity.This paper constructed a class of permutation functions over finite fields by using trace functions.By calculating Wile sum,the c-differential uniformity and boomerang uniformity of the functions are studied,and it is obtained that they are almost perfect c-nonlinear(APcN)functions over finite fields.

关 键 词：密码函数 c-差分均匀度 回旋镖均匀度 几乎完全c-非线性函数 

分 类 号：O157.4[理学—数学]