一类置换多项式c-差分一致性和回旋镖一致性  

The c-Differential Uniformity and Boomerang Uniformity of a Class of Permutation Polynomials

作　　者：陈范聪 柯品惠[2] 李世唐[2] CHEN Fancong;KE Pinhui;LI Shitang(School of Mathematics and Statistics,Fujian Normal University,350117,Fuzhou,Fujian,China;Key Laboratory of Analytical Mathematics and Applications of Ministry of Education,Fujian Normal University,350117,Fuzhou,Fujian,China)

机构地区：[1]福建师范大学数学与统计学院,福建福州350117 [2]福建师范大学分析数学及应用教育部重点实验室,福建福州350117

出　　处：《淮北师范大学学报(自然科学版)》2025年第1期10-15,共6页Journal of Huaibei Normal University:Natural Sciences

基　　金：国家自然科学基金项目(62272420);福建省自然科学基金项目(2023J01535)。

摘　　要：c-差分一致性和回旋镖一致性是密码函数2个重要的安全指标。利用迹函数以及Weil和,计算F_(2n)上一类新的置换多项式的c-差分一致性和回旋镖一致性,证明在给定条件下,该置换多项式是F_(2n)上的APcN函数。结果表明该类多项式具有较好的c-差分一致性和回旋镖一致性。The c-differential uniformity and the boomerang uniformity are two important secure criteria of cryptographic functions.A new class of permutation polynomial is proposed.By using the trace function and the Weil sum,the c-differential uniformity and the boomerang uniformity of the proposed polynomial are obtained.Furthermore,it is proved that under given conditions the proposed polynomial is an APCN function over F_(2n),which indicates that the proposed polynomials have good c-differential uniformity and boomerang uniformity.

关 键 词：有限域 置换多项式 c-差分一致性 回旋镖一致性 

分 类 号：O157.4[理学—数学]