摘要
设N={α_(0),α_(1),…,α_(n-1)}是E在F上的一组基,构造了一类给定乘法表及复杂度为3n-2的低复杂度正规基,根据迹函数和乘法表的相关概念,证明其对偶基M的生成元的形式,并证明了对偶基的复杂度为3n-2或3n-3.计算了E在F上的伪自对偶多项式基和弱自对偶多项式基的复杂度.为密码学领域寻找优化的算法,选择合适的基提供了理论依据.
Suppose that N={α_(0),α_(1),…,α_(n-1)}is a basis of E over F,some low complexity normal bases with complexity 3 n-2 was constructed and multiplication table was given.According to the related concepts of the trace function and multiplication table,it proved that the form of the generator of their dual basis and their dual bases has complexity 3 n-2 or 3 n-3.Furthermore,it calculated the complexity of the pseudo-self-dual polynomial bases and the weak self-dual polynomial bases of E over F.This provides a theoretical basis for finding optimized algorithms and selecting appropriate bases in the field of cryptography.
作者
张妍
苏丹丹
ZHANG Yan;SU Dandan(School of Mathematics,Liaoning Normal University,Dalian 116081,China;School of Cultural Tourism and Creativity,Foshan Polytechnic,Foshan 528000,China)
出处
《辽宁师范大学学报（自然科学版）》
CAS
2024年第1期21-28,共8页
Journal of Liaoning Normal University:Natural Science Edition
基金
国家自然科学基金资助重大项目(10990011)
校级重点项目(KY2020Z02)
校级高层次人才项目(KY2022G03)。
关键词
正规基
多项式基
对偶基
复杂度
normal basis
polynomial basis
dual basis
complexity
